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Sample records for quadratic nonlinear photonic

  1. Solitons in quadratic nonlinear photonic crystals

    DEFF Research Database (Denmark)

    Corney, Joel Frederick; Bang, Ole

    2001-01-01

    We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....

  2. Engineering quadratic nonlinear photonic crystals for frequency conversion of lasers

    Science.gov (United States)

    Chen, Baoqin; Hong, Lihong; Hu, Chenyang; Zhang, Chao; Liu, Rongjuan; Li, Zhiyuan

    2018-03-01

    Nonlinear frequency conversion offers an effective way to extend the laser wavelength range. Quadratic nonlinear photonic crystals (NPCs) are artificial materials composed of domain-inversion structures whose sign of nonlinear coefficients are modulated with desire to implement quasi-phase matching (QPM) required for nonlinear frequency conversion. These structures can offer various reciprocal lattice vectors (RLVs) to compensate the phase-mismatching during the quadratic nonlinear optical processes, including second-harmonic generation (SHG), sum-frequency generation and the cascaded third-harmonic generation (THG). The modulation pattern of the nonlinear coefficients is flexible, which can be one-dimensional or two-dimensional (2D), be periodic, quasi-periodic, aperiodic, chirped, or super-periodic. As a result, these NPCs offer very flexible QPM scheme to satisfy various nonlinear optics and laser frequency conversion problems via design of the modulation patterns and RLV spectra. In particular, we introduce the electric poling technique for fabricating QPM structures, a simple effective nonlinear coefficient model for efficiently and precisely evaluating the performance of QPM structures, the concept of super-QPM and super-periodically poled lithium niobate for finely tuning nonlinear optical interactions, the design of 2D ellipse QPM NPC structures enabling continuous tunability of SHG in a broad bandwidth by simply changing the transport direction of pump light, and chirped QPM structures that exhibit broadband RLVs and allow for simultaneous radiation of broadband SHG, THG, HHG and thus coherent white laser from a single crystal. All these technical, theoretical, and physical studies on QPM NPCs can help to gain a deeper insight on the mechanisms, approaches, and routes for flexibly controlling the interaction of lasers with various QPM NPCs for high-efficiency frequency conversion and creation of novel lasers.

  3. Parametric localized modes in quadratic nonlinear photonic structures

    DEFF Research Database (Denmark)

    Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole

    2001-01-01

    interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi2 equations) and find, numerically and analytically, the spatially localized solutions-discrete gap solitons. For a single nonlinear interface...

  4. Spatial solitons in nonlinear photonic crystals

    DEFF Research Database (Denmark)

    Corney, Joel Frederick; Bang, Ole

    2000-01-01

    We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero.......We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero....

  5. Designing quadratic nonlinear photonic crystal fibers for soliton compression to few-cycle pulses

    DEFF Research Database (Denmark)

    Bache, Morten; Moses, Jeffrey; Lægsgaard, Jesper

    2007-01-01

    phase shifts accessible. This self-defocusing nonlinearity can be used to compress a pulse when combined with normal dispersion, and problems normally encountered due to self-focusing in cubic media are avoided. Thus, having no power limit, in bulk media a self-defocusing soliton compressor can create...... high-energy near single-cycle fs pulses (Liu et al., 2006). However, the group-velocity mismatch (GVM) between the FW and second harmonic (SH), given by the inverse group velocity difference d12=1/Vg,1 - 1/Vg,2, limits the pulse quality and compression ratio. Especially very short input pulses (...

  6. Impurity solitons with quadratic nonlinearities

    DEFF Research Database (Denmark)

    Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis

    1998-01-01

    We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton...

  7. Quadratic soliton self-reflection at a quadratically nonlinear interface

    Science.gov (United States)

    Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai

    2003-11-01

    The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.

  8. Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers

    International Nuclear Information System (INIS)

    Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.

    2005-01-01

    The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized πelectrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules

  9. Nonlinear dynamics of quadratically cubic systems

    International Nuclear Information System (INIS)

    Rudenko, O V

    2013-01-01

    We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)

  10. Walking solitons in quadratic nonlinear media

    OpenAIRE

    Torner Sabata, Lluís; Mazilu, D; Mihalache, Dumitru

    1996-01-01

    We study self-action of light in parametric wave interactions in nonlinear quadratic media. We show the existence of stationary solitons in the presence of Poynting vector beam walk-off or different group velocities between the waves. We discover that the new solitons constitute a two-parameter family, and they exist for different wave intensities and transverse velocities. We discuss the properties of the walking solitons and their experimental implications. Peer Reviewed

  11. Two-photon Anderson localization in a disordered quadratic waveguide array

    International Nuclear Information System (INIS)

    Bai, Y F; Xu, P; Lu, L L; Zhong, M L; Zhu, S N

    2016-01-01

    We theoretically investigate two-photon Anderson localization in a χ (2) waveguide array with off-diagonal disorder. The nonlinear parametric down-conversion process would enhance both the single-photon and the two-photon Anderson localization. In the strong disorder regime, the two-photon position correlation exhibits a bunching distribution around the pumped waveguides, which is independent of pumping conditions and geometrical structures of waveguide arrays. Quadratic nonlinearity can be supplied as a new ingredient for Anderson localization. Also, our results pave the way for engineering quantum states through nonlinear quantum walks. (paper)

  12. Nonlinear silicon photonics

    Science.gov (United States)

    Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.

    2017-09-01

    Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.

  13. Nonlinear Photonics 2014: introduction.

    Science.gov (United States)

    Akhmediev, N; Kartashov, Yaroslav

    2015-01-12

    International Conference "Nonlinear Photonics-2014" took place in Barcelona, Spain on July 27-31, 2014. It was a part of the "Advanced Photonics Congress" which is becoming a traditional notable event in the world of photonics. The current focus issue of Optics Express contains contributions from the participants of the Conference and the Congress. The articles in this focus issue by no means represent the total number of the congress contributions (around 400). However, it demonstrates wide range of topics covered at the event. The next conference of this series is to be held in 2016 in Australia, which is the home of many researchers working in the field of photonics in general and nonlinear photonics in particular.

  14. Nonlinear photonic metasurfaces

    Science.gov (United States)

    Li, Guixin; Zhang, Shuang; Zentgraf, Thomas

    2017-03-01

    Compared with conventional optical elements, 2D photonic metasurfaces, consisting of arrays of antennas with subwavelength thickness (the 'meta-atoms'), enable the manipulation of light-matter interactions on more compact platforms. The use of metasurfaces with spatially varying arrangements of meta-atoms that have subwavelength lateral resolution allows control of the polarization, phase and amplitude of light. Many exotic phenomena have been successfully demonstrated in linear optics; however, to meet the growing demand for the integration of more functionalities into a single optoelectronic circuit, the tailorable nonlinear optical properties of metasurfaces will also need to be exploited. In this Review, we discuss the design of nonlinear photonic metasurfaces — in particular, the criteria for choosing the materials and symmetries of the meta-atoms — for the realization of nonlinear optical chirality, nonlinear geometric Berry phase and nonlinear wavefront engineering. Finally, we survey the application of nonlinear photonic metasurfaces in optical switching and modulation, and we conclude with an outlook on their use for terahertz nonlinear optics and quantum information processing.

  15. Nonlinear silicon photonics

    Science.gov (United States)

    Tsia, Kevin K.; Jalali, Bahram

    2010-05-01

    An intriguing optical property of silicon is that it exhibits a large third-order optical nonlinearity, with orders-ofmagnitude larger than that of silica glass in the telecommunication band. This allows efficient nonlinear optical interaction at relatively low power levels in a small footprint. Indeed, we have witnessed a stunning progress in harnessing the Raman and Kerr effects in silicon as the mechanisms for enabling chip-scale optical amplification, lasing, and wavelength conversion - functions that until recently were perceived to be beyond the reach of silicon. With all the continuous efforts developing novel techniques, nonlinear silicon photonics is expected to be able to reach even beyond the prior achievements. Instead of providing a comprehensive overview of this field, this manuscript highlights a number of new branches of nonlinear silicon photonics, which have not been fully recognized in the past. In particular, they are two-photon photovoltaic effect, mid-wave infrared (MWIR) silicon photonics, broadband Raman effects, inverse Raman scattering, and periodically-poled silicon (PePSi). These novel effects and techniques could create a new paradigm for silicon photonics and extend its utility beyond the traditionally anticipated applications.

  16. Nonlocal description of X waves in quadratic nonlinear materials

    DEFF Research Database (Denmark)

    Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole

    2006-01-01

    We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...

  17. Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

    Science.gov (United States)

    Acikmese, Ahmet Behcet; Corless, Martin

    2004-01-01

    We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

  18. Nonlinear Photonic Crystal Fibers

    DEFF Research Database (Denmark)

    Hansen, Kim Per

    2004-01-01

    Despite the general recession in the global economy and the collapse of the optical telecommunication market, research within specialty fibers is thriving. This is, more than anything else, due to the technology transition from standard all-glass fibers to photonic crystal fibers, which, instead....... The freedom to design the dispersion profile of the fibers is much larger and it is possible to create fibers, which support only a single spatial mode, regardless of wavelength. In comparison, the standard dispersion-shifted fibers are limited by a much lower index-contrast between the core and the cladding...... in 1996, and are today on their way to become the dominating technology within the specialty fiber field. Whether they will replace the standard fiber in the more traditional areas like telecommunication transmission, is not yet clear, but the nonlinear photonic crystal fibers are here to stay....

  19. Spatiotemporal solitons in quadratic nonlinear media

    Indian Academy of Sciences (India)

    Optical solitons are localized electromagnetic waves that propagate stably in .... conversion generates a nonlinear phase shift ∆ΦNL at the FH frequency. ... to incidence on the SHG crystal (lithium iodate or barium borate, cut for type-I interac-.

  20. Wave propagation in elastic medium with heterogeneous quadratic nonlinearity

    International Nuclear Information System (INIS)

    Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin

    2011-01-01

    This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.

  1. Quadratic grating apodized photon sieves for simultaneous multiplane microscopy

    Science.gov (United States)

    Cheng, Yiguang; Zhu, Jiangping; He, Yu; Tang, Yan; Hu, Song; Zhao, Lixin

    2017-10-01

    We present a new type of imaging device, named quadratic grating apodized photon sieve (QGPS), used as the objective for simultaneous multiplane imaging in X-rays. The proposed QGPS is structured based on the combination of two concepts: photon sieves and quadratic gratings. Its design principles are also expounded in detail. Analysis of imaging properties of QGPS in terms of point-spread function shows that QGPS can image multiple layers within an object field onto a single image plane. Simulated and experimental results in visible light both demonstrate the feasibility of QGPS for simultaneous multiplane imaging, which is extremely promising to detect dynamic specimens by X-ray microscopy in the physical and life sciences.

  2. Stationary walking solitons in bulk quadratic nonlinear media

    OpenAIRE

    Mihalache, Dumitru; Mazilu, D; Crasonavn, L C; Torner Sabata, Lluís

    1997-01-01

    We study the mutual trapping of fundamental and second-harmonic light beams propagating in bulk quadratic nonlinear media in the presence of Poynting vector beam walk-off. We show numerically the existence of a two-parameter family of (2 + 1)-dimensional stationary, spatial walking solitons. We have found that the solitons exist at various values of material parameters with different wave intensities and soliton velocities. We discuss the differences between (2 + 1) and (1 + 1)-dimensional wa...

  3. Integrable systems with quadratic nonlinearity in Fourier space

    International Nuclear Information System (INIS)

    Marikhin, V.G.

    2003-01-01

    The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The known systems of this type such as KdV, intermediate long-wave equation (ILW), Camassa-Holm and Degasperis-Procesi systems are represented in this list. Some new systems are obtained as well. Two-dimensional and discrete generalizations are discussed

  4. Low photon count based digital holography for quadratic phase cryptography.

    Science.gov (United States)

    Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Ryle, James P; Healy, John J; Lee, Byung-Geun; Sheridan, John T

    2017-07-15

    Recently, the vulnerability of the linear canonical transform-based double random phase encryption system to attack has been demonstrated. To alleviate this, we present for the first time, to the best of our knowledge, a method for securing a two-dimensional scene using a quadratic phase encoding system operating in the photon-counted imaging (PCI) regime. Position-phase-shifting digital holography is applied to record the photon-limited encrypted complex samples. The reconstruction of the complex wavefront involves four sparse (undersampled) dataset intensity measurements (interferograms) at two different positions. Computer simulations validate that the photon-limited sparse-encrypted data has adequate information to authenticate the original data set. Finally, security analysis, employing iterative phase retrieval attacks, has been performed.

  5. BRST operator for superconformal algebras with quadratic nonlinearity

    International Nuclear Information System (INIS)

    Khviengia, Z.; Sezgin, E.

    1993-07-01

    We construct the quantum BRST operators for a large class of superconformal and quasi-superconformal algebras with quadratic nonlinearity. The only free parameter in these algebras is the level of the (super) Kac-Moody sector. The nilpotency of the quantum BRST operator imposes a condition on the level. We find this condition for (quasi) superconformal algebras with a Kac-Moody sector based on a simple Lie algebra and for the Z 2 x Z 2 -graded superconformal algebras with a Kac-Moody sector based on the superalgebra osp(N modul 2M) or sl (N + 2 modul N). (author). 22 refs, 3 tabs

  6. Nonlinear photonic quasicrystals

    International Nuclear Information System (INIS)

    Freedman, B.; Bartal, G.; Segev, M.; Lifshitz, R.; Christodoulides, D.; Fleischer, J.

    2005-01-01

    Full Text:Quasicrystals are structures with long-range order and no periodicity, whose unique structural and physical properties have intrigued scientists ever since their discovery and initial theoretical analysis more than two decades ago. The lack of periodicity excludes the use of well-established theoretical and experimental tools for the analysis of quasicrystals, including such notions as the Brillouin zone and Bloch theorem. Instead, the quasiperiodic atomic arrangement gives rise to unique properties such as a hierarchy of effective Brillouin (or Jones) zones, yielding a fractal-like band structure, and the existence of unique phason degrees of freedom. Generally, in atomic quasicrystals it is very difficult to directly observe the evolution of electronic wave-packets propagating through the structure, or the dynamics of the structure itself. Photonic quasicrystals, on the other hand, are macroscopic objects and hence their internal wave dynamics can be locally excited and directly imaged. Here, we employ optical induction to create 2D photonic quasicrystals, and explore wave transport phenomena in quasicrystals in ways that were impossible until now. We demonstrate linear tunneling-transport of light initiated at different crystal sites, and observe the formation of lattice solitons when the light is made sufficiently intense. We experiment with dynamical photonic quasicrystals, in which crystal sites interact with one another, and directly observe dislocation dynamics: creation, healing, and local structural rearrangement due to phason flips. Our experiments show that photonic quasicrystals are an excellent model system through which one can study the universal features of wave dynamics in quasiperiodic structures, that should apply not only to photonics, but also to other systems such as matter waves in quasiperiodic traps, generic pattern-forming systems as in parametrically-excited surface waves, liquid quasicrystals, as well as the more familiar

  7. Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier

    DEFF Research Database (Denmark)

    Neumeyer, Stefan; Sorokin, Vladislav; Thomsen, Jon Juel

    2016-01-01

    We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing–Mathieu equation with appended quadratic nonlinearity is considered as the model system......, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic...... nonlinearities may generate additional amplitude–frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi...

  8. SOLVING NONLINEAR KLEIN-GORDON EQUATION WITH A QUADRATIC NONLINEAR TERM USING HOMOTOPY ANALYSIS METHOD

    Directory of Open Access Journals (Sweden)

    H. Jafari

    2010-07-01

    Full Text Available In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM.Comparisons are made between the Adomian decomposition method (ADM, the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.

  9. Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality

    Science.gov (United States)

    Acikmese, Ahmet Behcet; Martin, Corless

    2004-01-01

    We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.

  10. Asymptotic behavior for a quadratic nonlinear Schrodinger equation

    Directory of Open Access Journals (Sweden)

    Pavel I. Naumkin

    2008-02-01

    Full Text Available We study the initial-value problem for the quadratic nonlinear Schrodinger equation $$displaylines{ iu_{t}+frac{1}{2}u_{xx}=partial _{x}overline{u}^{2},quad xin mathbb{R},; t>1, cr u(1,x=u_{1}(x,quad xin mathbb{R}. }$$ For small initial data $u_{1}in mathbf{H}^{2,2}$ we prove that there exists a unique global solution $uin mathbf{C}([1,infty ;mathbf{H}^{2,2}$ of this Cauchy problem. Moreover we show that the large time asymptotic behavior of the solution is defined in the region $|x|leq Csqrt{t}$ by the self-similar solution $frac{1}{sqrt{t}}MS(frac{x}{sqrt{t}}$ such that the total mass $$ frac{1}{sqrt{t}}int_{mathbb{R}}MS(frac{x}{sqrt{t}} dx=int_{mathbb{R}}u_{1}(xdx, $$ and in the far region $|x|>sqrt{t}$ the asymptotic behavior of solutions has rapidly oscillating structure similar to that of the cubic nonlinear Schrodinger equations.

  11. Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities (vol 24, pg 2752, 2007)

    DEFF Research Database (Denmark)

    Bache, Morten; Moses, J.; Wise, F.W.

    2010-01-01

    Erratum for [M. Bache, J. Moses, and F. W. Wise, "Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities," J. Opt. Soc. Am. B 24, 2752-2762 (2007)].......Erratum for [M. Bache, J. Moses, and F. W. Wise, "Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities," J. Opt. Soc. Am. B 24, 2752-2762 (2007)]....

  12. Noise-induced chaos in a quadratically nonlinear oscillator

    International Nuclear Information System (INIS)

    Gan Chunbiao

    2006-01-01

    The present paper focuses on the noise-induced chaos in a quadratically nonlinear oscillator. Simple zero points of the stochastic Melnikov integral theoretically mean the necessary rising of noise-induced chaotic response in the system based on the stochastic Melnikov method. To quantify the noise-induced chaos, the boundary of the system's safe basin is firstly studied and it is shown to be incursively fractal when chaos arises. Three cases are considered in simulating the safe basin of the system, i.e., the system is excited only by the harmonic excitation, by both the harmonic and the Gaussian white noise excitations, and only by the Gaussian white noise excitation. Secondly, the leading Lyapunov exponent by Rosenstein's algorithm is shown to quantify the chaotic nature of the sample time series of the system. The results show that the boundary of the safe basin can also be fractal even if the system is excited only by the external Gaussian white noise. Most importantly, the almost-harmonic, the noise-induced chaotic and the thoroughly random responses can be found in the system

  13. Focus issue introduction: nonlinear photonics.

    Science.gov (United States)

    Akhmediev, Nail; Rottwitt, Karsten

    2012-11-19

    It is now 23 years since the first Topical Meeting "Nonlinear Guided Wave Phenomena" (Houston, TX, February 2-4, 1989) has been organised by George Stegeman and Allan Boardman with support of the Optical Society of America. These series of the OSA conferences known as NLGW, continued under the name "Nonlinear Photonics" starting from 2007. The latest one, in Colorado Springs in June 17-21, 2012 has been a great success despite the fierce fires advancing around the city at the time of the conference. This Focus issue is a collection of several papers presented at the conference with extended content submitted to Optics Express. Although this collection is small in comparison to the total number of papers presented at the conference, it gives a flavor of the topics considered at the meeting. It is also worthy to mention here that the next meeting "Nonlinear Photonics" is planned to be held in Barcelona - one of the main European centers on this subject.

  14. Nonlinear Photonics and Novel Optical Phenomena

    CERN Document Server

    Morandotti, Roberto

    2012-01-01

    Nonlinear Photonics and Novel Optical Phenomena contains contributed chapters from leading experts in nonlinear optics and photonics, and provides a comprehensive survey of fundamental concepts as well as hot topics in current research on nonlinear optical waves and related novel phenomena. The book covers self-accelerating airy beams, integrated photonics based on high index doped-silica glass, linear and nonlinear spatial beam dynamics in photonic lattices and waveguide arrays, polariton solitons and localized structures in semiconductor microcavities, terahertz waves, and other novel phenomena in different nanophotonic and optical systems.

  15. A Modified Lindstedt–Poincaré Method for a Strongly Nonlinear System with Quadratic and Cubic Nonlinearities

    Directory of Open Access Journals (Sweden)

    S.H. Chen

    1996-01-01

    Full Text Available A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.

  16. On solutions of stochastic oscillatory quadratic nonlinear equations using different techniques, a comparison study

    International Nuclear Information System (INIS)

    El-Tawil, M A; Al-Jihany, A S

    2008-01-01

    In this paper, nonlinear oscillators under quadratic nonlinearity with stochastic inputs are considered. Different methods are used to obtain first order approximations, namely, the WHEP technique, the perturbation method, the Pickard approximations, the Adomian decompositions and the homotopy perturbation method (HPM). Some statistical moments are computed for the different methods using mathematica 5. Comparisons are illustrated through figures for different case-studies

  17. A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring

    Directory of Open Access Journals (Sweden)

    Yong Li

    2014-01-01

    Full Text Available The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features.

  18. All-optical signal processing in quadratic nonlinear materials

    DEFF Research Database (Denmark)

    Johansen, Steffen Kjær

    2002-01-01

    of materials with a second order nonlinearity, the so-called X(2) materials, is faster and stronger than that of more conventional materials with a cubic nonlinearity. The X(2) materials support spatial solitons consisting of two coupled components, the fundamental wave (FW) and its second harmonic (SH......). During this project the interaction between such spatial solitons has been investigated theoretically through perturbation theory and experimentally via numerical simulations. The outcome of this research isnew theoretical tools for quantitatively predicting the escape angle, i.e. the angle of incidence...... are dedicated to this part of the research. In chapter 4 the generality of the theoretical approach is emphasised with the derivation and verification of equivalent tools for media with a saturable nonlinearity. The strength of the X(2) nonlinearity strongly depends on the phase mismatch between the FW...

  19. Exact solutions for oscillators with quadratic damping and mixed-parity nonlinearity

    International Nuclear Information System (INIS)

    Lai, S K; Chow, K W

    2012-01-01

    Exact vibration modes of a nonlinear oscillator, which contains both quadratic friction and a mixed-parity restoring force, are derived analytically. Two families of exact solutions are obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behaviour of the system in response to changes in physical parameters that concern nonlinearity. The physical significance of the signs (i.e. attractive or repulsive nature) of the linear, quadratic and cubic restoring forces is discussed. A qualitative analysis is also conducted to provide valuable physical insight into the nature of the system. (paper)

  20. A New Chaotic Attractor with Quadratic Exponential Nonlinear Term from Chen’s Attractor

    Directory of Open Access Journals (Sweden)

    Iftikhar Ahmed

    2014-02-01

    Full Text Available In this paper a new three-dimensional chaotic system is proposed, which relies on a nonlinear exponential term and a nonlinear quadratic cross term necessary for folding trajectories. Basic dynamical characteristics of the new system are analyzed. Compared with the Chen system, the equilibrium points of the new system does not contain the origin, and has a greater positive Lyapunov index, can produce more complex shaped chaotic attractor.

  1. An Analysis and Design for Nonlinear Quadratic Systems Subject to Nested Saturation

    Directory of Open Access Journals (Sweden)

    Minsong Zhang

    2013-01-01

    Full Text Available This paper considers the stability problem for nonlinear quadratic systems with nested saturation input. The interesting treatment method proposed to nested saturation here is put into use a well-established linear differential control tool. And the new conclusions include the existing conclusion on this issue and have less conservatism than before. Simulation example illustrates the effectiveness of the established methodologies.

  2. Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

    Directory of Open Access Journals (Sweden)

    Minsong Zhang

    2014-01-01

    Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.

  3. An application of nonlinear programming to the design of regulators of a linear-quadratic formulation

    Science.gov (United States)

    Fleming, P.

    1983-01-01

    A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.

  4. On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity

    Directory of Open Access Journals (Sweden)

    Koh Kim Jie

    2017-01-01

    Full Text Available Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity related to kinematics update arises when implementing the time integration-iterative algorithm. In present work, an Euler-Bernoulli beam vibration problem with quadratic damping nonlinearity is addressed as the main source of quadratic damping nonlinearity arises from drag force estimation, which is generally valid only for slender structures. Employing Newton-Raphson formulation, tangent stiffness components associated with quadratic damping nonlinearity requires velocity input for evaluation purpose. For this reason, two mathematically equivalent algorithm structures with different kinematics arrangement are tested. Both algorithm structures result in the same accuracy and convergence characteristic of solution.

  5. Unidirectional transmission in 1D nonlinear photonic crystal based on topological phase reversal by optical nonlinearity

    OpenAIRE

    Chong Li; Xiaoyong Hu; Hong Yang; Qihuang Gong

    2017-01-01

    We propose a scheme of unidirectional transmission in a 1D nonlinear topological photonic crystal based on the topological edge state and three order optical nonlinearity. The 1D photonic crystals consists of a nonlinear photonic crystal L and a linear photonic crystal R. In the backward direction, light is totally reflected for the photons transmission prohibited by the bandgap. While in the forward direction, light interacts with the nonlinear photonic crystal L by optical Kerr effect, brin...

  6. Photonic surfaces for designable nonlinear power shaping

    Energy Technology Data Exchange (ETDEWEB)

    Biswas, Roshni, E-mail: rbiswas@usc.edu; Povinelli, Michelle L. [Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089 (United States)

    2015-02-09

    We propose a method for designing nonlinear input-output power response based on absorptive resonances of nanostructured surfaces. We show that various power transmission trends can be obtained by placing a photonic resonance mode at the appropriate detuning from the laser wavelength. We demonstrate our results in a silicon photonic crystal slab at a laser wavelength of 808 nm. We quantify the overall spectral red shift as a function of laser power. The shift results from absorptive heating and the thermo-optic effect. We then demonstrate devices with increasing, decreasing, and non-monotonic transmission as a function of laser power. The transmission changes are up to 7.5 times larger than in unpatterned silicon. The strong nonlinear transmission is due to a combination of resonantly enhanced absorption, reduced thermal conductivity, and the resonant transmission lineshape. Our results illustrate the possibility of designing different nonlinear power trends within a single materials platform at a given wavelength of interest.

  7. Photonic surfaces for designable nonlinear power shaping

    International Nuclear Information System (INIS)

    Biswas, Roshni; Povinelli, Michelle L.

    2015-01-01

    We propose a method for designing nonlinear input-output power response based on absorptive resonances of nanostructured surfaces. We show that various power transmission trends can be obtained by placing a photonic resonance mode at the appropriate detuning from the laser wavelength. We demonstrate our results in a silicon photonic crystal slab at a laser wavelength of 808 nm. We quantify the overall spectral red shift as a function of laser power. The shift results from absorptive heating and the thermo-optic effect. We then demonstrate devices with increasing, decreasing, and non-monotonic transmission as a function of laser power. The transmission changes are up to 7.5 times larger than in unpatterned silicon. The strong nonlinear transmission is due to a combination of resonantly enhanced absorption, reduced thermal conductivity, and the resonant transmission lineshape. Our results illustrate the possibility of designing different nonlinear power trends within a single materials platform at a given wavelength of interest

  8. Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media

    International Nuclear Information System (INIS)

    Kartashov, Yaroslav V; Egorov, Alexey A; Vysloukh, Victor A; Torner, Lluis

    2004-01-01

    We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We show how saturation of the nonlinear response results in the appearance of stability (instability) bands in a focusing (defocusing) medium, which is in sharp contrast with the properties of periodic waves in Kerr media. One of the key results discovered is the stabilization of multicolour periodic waves in quadratic media. In particular, dark-type waves are shown to be metastable, while bright-type waves are completely stable in a broad range of energy flows and material parameters. This yields the first known example of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons. Such results open the way to the experimental observation of the corresponding self-sustained periodic wave patterns

  9. Solutions to the equations describing materials with competing quadratic and cubic nonlinearities

    International Nuclear Information System (INIS)

    Li-Na, Zhao; Ji, Lin; Zi-Shuang, Tong

    2009-01-01

    The Lie group theoretical method is used to study the equations describing materials with competing quadratic and cubic nonlinearities. The equations share some of the nice properties of soliton equations. From the elliptic functions expansion method, we obtain large families of analytical solutions, in special cases, we have the periodic, kink and solitary solutions of the equations. Furthermore, we investigate the stability of these solutions under the perturbation of amplitude noises by numerical simulation

  10. On the Cauchy problem for a Sobolev-type equation with quadratic non-linearity

    International Nuclear Information System (INIS)

    Aristov, Anatoly I

    2011-01-01

    We investigate the asymptotic behaviour as t→∞ of the solution of the Cauchy problem for a Sobolev-type equation with quadratic non-linearity and develop ideas used by I. A. Shishmarev and other authors in the study of classical and Sobolev-type equations. Conditions are found under which it is possible to consider the case of an arbitrary dimension of the spatial variable.

  11. Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

    Science.gov (United States)

    Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

    2018-04-01

    Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

  12. A new chaotic attractor with two quadratic nonlinearities, its synchronization and circuit implementation

    Science.gov (United States)

    Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Gundara, G.; Mada Sanjaya, W. S.; Subiyanto

    2018-03-01

    A 3-D new chaotic attractor with two quadratic nonlinearities is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new chaotic system has three unstable equilibrium points. The new chaotic attractor is dissipative in nature. As an engineering application, adaptive synchronization of identical new chaotic attractors is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic attractor model.

  13. Stationary solutions and self-trapping in discrete quadratic nonlinear systems

    DEFF Research Database (Denmark)

    Bang, Ole; Christiansen, Peter Leth; Clausen, Carl A. Balslev

    1998-01-01

    We consider the simplest equations describing coupled quadratic nonlinear (chi((2))) systems, which each consists of a fundamental mode resonantly interacting with its second harmonic. Such discrete equations apply, e.g., to optics, where they can describe arrays of chi((2)) waveguides...... the nonintegrable dimer reduce to the discrete nonlinear Schrodinger (DNLS) equation with two degrees of freedom, which is integrable. We show how the stationary solutions to the two systems correspond to each other and how the self-trapped DNLS solutions gradually develop chaotic dynamics in the chi((2)) system...

  14. Accuracy Improvement of the Method of Multiple Scales for Nonlinear Vibration Analyses of Continuous Systems with Quadratic and Cubic Nonlinearities

    Directory of Open Access Journals (Sweden)

    Akira Abe

    2010-01-01

    and are the driving and natural frequencies, respectively. The application of Galerkin's procedure to the equation of motion yields nonlinear ordinary differential equations with quadratic and cubic nonlinear terms. The steady-state responses are obtained by using the discretization approach of the MMS in which the definition of the detuning parameter, expressing the relationship between the natural frequency and the driving frequency, is changed in an attempt to improve the accuracy of the solutions. The validity of the solutions is discussed by comparing them with solutions of the direct approach of the MMS and the finite difference method.

  15. Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques

    International Nuclear Information System (INIS)

    Glowinski, R.; Le Tallec, P.

    1984-01-01

    The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity

  16. Photon attenuation correction technique in SPECT based on nonlinear optimization

    International Nuclear Information System (INIS)

    Suzuki, Shigehito; Wakabayashi, Misato; Okuyama, Keiichi; Kuwamura, Susumu

    1998-01-01

    Photon attenuation correction in SPECT was made using a nonlinear optimization theory, in which an optimum image is searched so that the sum of square errors between observed and reprojected projection data is minimized. This correction technique consists of optimization and step-width algorithms, which determine at each iteration a pixel-by-pixel directional value of search and its step-width, respectively. We used the conjugate gradient and quasi-Newton methods as the optimization algorithm, and Curry rule and the quadratic function method as the step-width algorithm. Statistical fluctuations in the corrected image due to statistical noise in the emission projection data grew as the iteration increased, depending on the combination of optimization and step-width algorithms. To suppress them, smoothing for directional values was introduced. Computer experiments and clinical applications showed a pronounced reduction in statistical fluctuations of the corrected image for all combinations. Combinations using the conjugate gradient method were superior in noise characteristic and computation time. The use of that method with the quadratic function method was optimum if noise property was regarded as important. (author)

  17. Few-cycle nonlinear mid-IR pulse generated with cascaded quadratic nonlinearities

    DEFF Research Database (Denmark)

    Bache, Morten; Liu, Xing; Zhou, Binbin

    Generating few-cycle energetic and broadband mid-IR pulses is an urgent current challenge in nonlinear optics. Cascaded second-harmonic generation (SHG) gives access to an ultrafast and octave-spanning self-defocusing nonlinearity: when ΔkL >> 2π the pump experiences a Kerr-like nonlinear index...

  18. Saturation and stability of nonlinear photonic crystals

    International Nuclear Information System (INIS)

    Franco-Ortiz, M; Corella-Madueño, A; Rosas-Burgos, R A; Adrian Reyes, J; Avendaño, Carlos G

    2017-01-01

    We consider a one-dimensional photonic crystal made by an infinite set of nonlinear nematic films immersed in a linear dielectric medium. The thickness of each equidistant film is negligible and its refraction index depends continuously on the electric field intensity, giving rise to all the involved nonlinear terms, which joints from a starting linear index for negligible amplitudes to a final saturation index for extremely large field intensities. We show that the nonlinear exact solutions of this system form an intensity-dependent band structure which we calculate and analyze. Next, we ponder a finite version of this system; that is, we take a finite array of linear dielectric stacks of the same size separated by the same nonlinear extremely thin nematic slabs and find the reflection coefficients for this arrangement and obtain the dependence on the wave number and intensity of the incident wave. As a final step we analyze the stability of the analytical solutions of the nonlinear crystal by following the evolution of an additive amplitude to the analytical nonlinear solution we have found here. We discuss our results and state our conclusions. (paper)

  19. Soliton compression to few-cycle pulses with a high quality factor by engineering cascaded quadratic nonlinearities

    DEFF Research Database (Denmark)

    Zeng, Xianglong; Guo, Hairun; Zhou, Binbin

    2012-01-01

    We propose an efficient approach to improve few-cycle soliton compression with cascaded quadratic nonlinearities by using an engineered multi-section structure of the nonlinear crystal. By exploiting engineering of the cascaded quadratic nonlinearities, in each section soliton compression...... with a low effective order is realized, and high-quality few-cycle pulses with large compression factors are feasible. Each subsequent section is designed so that the compressed pulse exiting the previous section experiences an overall effective self-defocusing cubic nonlinearity corresponding to a modest...... soliton order, which is kept larger than unity to ensure further compression. This is done by increasing the cascaded quadratic nonlinearity in the new section with an engineered reduced residual phase mismatch. The low soliton orders in each section ensure excellent pulse quality and high efficiency...

  20. Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

    International Nuclear Information System (INIS)

    Kolesov, Andrei Yu; Rozov, Nikolai Kh

    2002-01-01

    For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied

  1. Three-wave interaction in two-component quadratic nonlinear lattices

    DEFF Research Database (Denmark)

    Konotop, V. V.; Cunha, M. D.; Christiansen, Peter Leth

    1999-01-01

    We investigate a two-component lattice with a quadratic nonlinearity and find with the multiple scale technique that integrable three-wave interaction takes place between plane wave solutions when these fulfill resonance conditions. We demonstrate that. energy conversion and pulse propagation known...... from three-wave interaction is reproduced in the lattice and that exact phase matching of parametric processes can be obtained in non-phase-matched lattices by tilting the interacting plane waves with respect to each other. [S1063-651X(99)15110-9]....

  2. One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

    Science.gov (United States)

    Shapovalov, A. V.

    2018-04-01

    The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

  3. Multiple-octave spanning high-energy mid-IR supercontinuum generation in bulk quadratic nonlinear crystals

    DEFF Research Database (Denmark)

    Zhou, Binbin; Bache, Morten

    2016-01-01

    Bright and broadband coherent mid-IR radiation is important for exciting and probing molecular vibrations. Using cascaded nonlinearities in conventional quadratic nonlinear crystals like lithium niobate, self-defocusing near-IR solitons have been demonstrated that led to very broadband...

  4. Effect of P T symmetry on nonlinear waves for three-wave interaction models in the quadratic nonlinear media

    Science.gov (United States)

    Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao

    2018-04-01

    We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.

  5. New hybrid non-linear transformations of divergent perturbation series for quadratic Zeeman effects

    International Nuclear Information System (INIS)

    Belkic, D.

    1989-01-01

    The problem of hydrogen atoms in an external uniform magnetic field (quadratic Zeeman effect) is studied by means of perturbation theory. The power series for the ground-state energy in terms of magnetic-field strength B is divergent. Nevertheless, it is possible to induce convergence of this divergent series by applying various non-linear transformations. These transformations of originally divergent perturbation series yield new sequences, which then converge. The induced convergence is, however, quite slow. A new hybrid Shanks-Levin non-linear transform is devised here for accelerating these slowly converging series and sequences. Significant improvement in the convergence rate is obtained. Agreement with the exact results is excellent. (author)

  6. Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

    Science.gov (United States)

    Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

    2018-01-01

    In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

  7. Unidirectional transmission in 1D nonlinear photonic crystal based on topological phase reversal by optical nonlinearity

    Directory of Open Access Journals (Sweden)

    Chong Li

    2017-02-01

    Full Text Available We propose a scheme of unidirectional transmission in a 1D nonlinear topological photonic crystal based on the topological edge state and three order optical nonlinearity. The 1D photonic crystals consists of a nonlinear photonic crystal L and a linear photonic crystal R. In the backward direction, light is totally reflected for the photons transmission prohibited by the bandgap. While in the forward direction, light interacts with the nonlinear photonic crystal L by optical Kerr effect, bringing a topological phase reversal and results the topological edge mode arising at the interface which could transmit photons through the bandgaps both of the photonic crystal L and R. When the signal power intensity larger than a moderate low threshold value of 10.0 MW/cm2, the transmission contrast ratio could remain at 30 steadily.

  8. Propagation of a femtosecond laser pulse with duration of several optical oscillation periods in a medium with a quadratic nonlinearity

    International Nuclear Information System (INIS)

    Akopyan, A A; Oganesyan, D L

    1998-01-01

    It is shown that the wave equation can be solved by the method of unidirectional waves for a pulse with a duration of several oscillation periods in a medium with a quadratic nonlinearity, such as a group-3m crystal. The wave equation reduces to a system of two equations for waves with different polarisations. (laser applications and other topics in quantum electronics)

  9. Group-velocity matched nonlinear photonic crystal fibers

    DEFF Research Database (Denmark)

    Bache, Morten; Lægsgaard, Jesper; Bang, Ole

    2006-01-01

    A quadratic nonlinear index-guiding silica PCF is optimized for efficient second-harmonic generation through dispersion calculations. Zero group-velocity mismatch is possible for any pump wavelength above 780 nm. Very high conversion efficiencies and bandwidths are found....

  10. A nonlinear model for fluid flow in a multiple-zone composite reservoir including the quadratic gradient term

    International Nuclear Information System (INIS)

    Wang, Xiao-Lu; Fan, Xiang-Yu; Nie, Ren-Shi; Huang, Quan-Hua; He, Yong-Ming

    2013-01-01

    Based on material balance and Darcy's law, the governing equation with the quadratic pressure gradient term was deduced. Then the nonlinear model for fluid flow in a multiple-zone composite reservoir including the quadratic gradient term was established and solved using a Laplace transform. A series of standard log–log type curves of 1-zone (homogeneous), 2-zone and 3-zone reservoirs were plotted and nonlinear flow characteristics were analysed. The type curves governed by the coefficient of the quadratic gradient term (β) gradually deviate from those of a linear model with time elapsing. Qualitative and quantitative analyses were implemented to compare the solutions of the linear and nonlinear models. The results showed that differences of pressure transients between the linear and nonlinear models increase with elapsed time and β. At the end, a successful application of the theoretical model data against the field data shows that the nonlinear model will be a good tool to evaluate formation parameters more accurately. (paper)

  11. A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

    Science.gov (United States)

    Fleming, P.

    1985-01-01

    A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

  12. Optical switching in nonlinear photonic crystals lightly doped with nanostructures

    Energy Technology Data Exchange (ETDEWEB)

    Singh, Mahi R [Department of Physics and Astronomy, University of Western Ontario, London, ON N6A 3K7 (Canada); Lipson, R H [Department of Chemistry, University of Western Ontario, London, ON N6A 5B7 (Canada)

    2008-01-14

    A possible switching mechanism has been investigated for nonlinear photonic crystals doped with an ensemble of non-interacting three-level nanoparticles. In this scheme, an intense pump laser field is used to change the refractive index of the nonlinear photonic crystal while a weaker probe field monitors an absorption transition in the nanoparticles. In the absence of the strong laser field the system transmits the probe field when the resonance energy of the nanoparticles lies near the edge of the photonic band gap due to strong coupling between the photonic crystal and the nanoparticles. However, upon application of an intense pump laser field the system becomes absorbing due to a band edge frequency shift that arises due to a nonlinear Kerr effect which changes the refractive index of the crystal. It is anticipated that the optical switching mechanism described in this work can be used to make new types of photonic devices.

  13. Geometry and quadratic nonlinearity of charge transfer complexes in solution: A theoretical study

    International Nuclear Information System (INIS)

    Mukhopadhyay, S.; Ramasesha, S.; Pandey, Ravindra; Das, Puspendu K.

    2011-01-01

    In this paper, we have computed the quadratic nonlinear optical (NLO) properties of a class of weak charge transfer (CT) complexes. These weak complexes are formed when the methyl substituted benzenes (donors) are added to strong acceptors like chloranil (CHL) or di-chloro-di-cyano benzoquinone (DDQ) in chloroform or in dichloromethane. The formation of such complexes is manifested by the presence of a broad absorption maximum in the visible range of the spectrum where neither the donor nor the acceptor absorbs. The appearance of this visible band is due to CT interactions, which result in strong NLO responses. We have employed the semiempirical intermediate neglect of differential overlap (INDO/S) Hamiltonian to calculate the energy levels of these CT complexes using single and double configuration interaction (SDCI). The solvent effects are taken into account by using the self-consistent reaction field (SCRF) scheme. The geometry of the complex is obtained by exploring different relative molecular geometries by rotating the acceptor with respect to the fixed donor about three different axes. The theoretical geometry that best fits the experimental energy gaps, β HRS and macroscopic depolarization ratios is taken to be the most probable geometry of the complex. Our studies show that the most probable geometry of these complexes in solution is the parallel displaced structure with a significant twist in some cases.

  14. Neural network-based nonlinear model predictive control vs. linear quadratic gaussian control

    Science.gov (United States)

    Cho, C.; Vance, R.; Mardi, N.; Qian, Z.; Prisbrey, K.

    1997-01-01

    One problem with the application of neural networks to the multivariable control of mineral and extractive processes is determining whether and how to use them. The objective of this investigation was to compare neural network control to more conventional strategies and to determine if there are any advantages in using neural network control in terms of set-point tracking, rise time, settling time, disturbance rejection and other criteria. The procedure involved developing neural network controllers using both historical plant data and simulation models. Various control patterns were tried, including both inverse and direct neural network plant models. These were compared to state space controllers that are, by nature, linear. For grinding and leaching circuits, a nonlinear neural network-based model predictive control strategy was superior to a state space-based linear quadratic gaussian controller. The investigation pointed out the importance of incorporating state space into neural networks by making them recurrent, i.e., feeding certain output state variables into input nodes in the neural network. It was concluded that neural network controllers can have better disturbance rejection, set-point tracking, rise time, settling time and lower set-point overshoot, and it was also concluded that neural network controllers can be more reliable and easy to implement in complex, multivariable plants.

  15. AlGaAs-On-Insulator nonlinear photonics

    DEFF Research Database (Denmark)

    Pu, Minhao; Ottaviano, Luisa; Semenova, Elizaveta

    We present an AlGaAs-on-insulator platform for integrated nonlinear photonics. We demonstrate the highest reported conversion efficiency and ultra-broadband four-wave mixing for an integrated platform around 1550nm......We present an AlGaAs-on-insulator platform for integrated nonlinear photonics. We demonstrate the highest reported conversion efficiency and ultra-broadband four-wave mixing for an integrated platform around 1550nm...

  16. Nonlinear Gain Saturation in Active Slow Light Photonic Crystal Waveguides

    DEFF Research Database (Denmark)

    Chen, Yaohui; Mørk, Jesper

    2013-01-01

    We present a quantitative three-dimensional analysis of slow-light enhanced traveling wave amplification in an active semiconductor photonic crystal waveguides. The impact of slow-light propagation on the nonlinear gain saturation of the device is investigated.......We present a quantitative three-dimensional analysis of slow-light enhanced traveling wave amplification in an active semiconductor photonic crystal waveguides. The impact of slow-light propagation on the nonlinear gain saturation of the device is investigated....

  17. Azimuthal asymmetry in processes of nonlinear QED for linearly polarized photon

    International Nuclear Information System (INIS)

    Bajer, V.N.; Mil'shtejn, A.I.

    1994-01-01

    Cross sections of nonlinear QED processes (photon-photon scattering, photon splitting in a Coulomb field, and Delbrueck scattering) are considered for linearly polarized initial photon. The cross sections have sizeable azimuthal asymmetry. 15 refs.; 3 figs

  18. The study of nonlinear two-photon phenomenon in photonic crystals doped with nanoparticles

    Energy Technology Data Exchange (ETDEWEB)

    Singh, Mahi R [Department of Physics and Astronomy, University of Western Ontario, London, N6A 3K7 (Canada)

    2007-02-28

    A theory of the nonlinear two-photon absorption has been developed in a photonic crystal doped with an ensemble of four-level nanoparticles. We have considered that the nanoparticles are interacting with the photonic crystal. An expression of two-photon absorption has been obtained by using the density matrix method. The effect of the dipole-dipole interaction has also been included in the formulation. Interesting new phenomena have been predicted. For example, it is found that the inhibition of two-photon absorption can be turned on and off when the decay resonance energies of the four-level nanoparticles are moved within the energy band.

  19. Transverse effects in nonlinear optics: Toward the photon superfluid

    Science.gov (United States)

    McCormick, Colin Fraser

    Nonlinear optics displays a wealth of transverse effects. These effects are particularly rich in the presence of an optical cavity. Many considerations suggest that in a Kerr nonlinear cavity a new state of light known as a "photon superfluid" can form, with strong analogies to atomic superfluids. The conditions for the formation of the photon superfluid include requirements on the cavity, input light fields and the nonlinear medium as well as various timescales. The most favorable candidate nonlinear medium for observing the photon super-fluid is an atomic vapor. With a strong and fast Kerr effect, atomic vapors also have the advantage of a Kerr coefficient that is tunable in both magnitude and sign. A series of z-scan experiments in far-detuned atomic rubidium vapor is reported, measuring the Kerr coefficient and determining its functional dependence on detuning to be that of a Doppler-broadened two-level model with adiabatic following of the electric field by the atom pseudomoment. Saturation effects are found to be important. Z-scan measurements for detunings within the Doppler profile are shown to agree well with numerical simulations based on the Doppler-broadened model. Agreement between absorptive and refractive non-linear coefficients is evidence of the Kramers-Kronig relations at work, even in this nonlinear system. The formation of the photon superfluid is discussed and the calculation of a new process, nearly collinear four-wave mixing, is presented. This process is essentially an inverse beam filamentation that is likely to be the underlying physical mechanism for transverse cooling and condensation of photons in a nonlinear optical cavity. Nearly collinear four-wave mixing may also be related to phenomena in general nonlinear physics, including modulation instability and Fermi-Pasta-Ulam recurrence.

  20. Photon-pair generation in nonlinear metal-dielectric one-dimensional photonic structures

    Czech Academy of Sciences Publication Activity Database

    Javůrek, D.; Svozilík, J.; Peřina ml., Jan

    2014-01-01

    Roč. 90, č. 5 (2014), "053813-1"-"053813-14" ISSN 1050-2947 R&D Projects: GA ČR GAP205/12/0382 Institutional support: RVO:68378271 Keywords : photon pairs * nonlinear metal-dielectric * one-dimensional photonic structures Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.808, year: 2014

  1. Applications of Random Nonlinear Photonic Crystals Based on Strontium Tetraborate

    Directory of Open Access Journals (Sweden)

    Alexandre I. Zaitsev

    2012-10-01

    Full Text Available Properties of strontium tetraborate (SBO and features of as-grown anti-parallel domains are summarized. From the point of view of nonlinear optics, these domains form nonlinear photonic crystals (NPC. Applications of NPC to the deep ultraviolet generation and fs pulse diagnostics are described. NPC and SBO are prospective media for the creation of a widely tunable source of fs pulses in the vacuum ultraviolet and for autocorrelation diagnostics of broadly tunable sources.

  2. Estimating nonlinear selection gradients using quadratic regression coefficients: double or nothing?

    Science.gov (United States)

    Stinchcombe, John R; Agrawal, Aneil F; Hohenlohe, Paul A; Arnold, Stevan J; Blows, Mark W

    2008-09-01

    The use of regression analysis has been instrumental in allowing evolutionary biologists to estimate the strength and mode of natural selection. Although directional and correlational selection gradients are equal to their corresponding regression coefficients, quadratic regression coefficients must be doubled to estimate stabilizing/disruptive selection gradients. Based on a sample of 33 papers published in Evolution between 2002 and 2007, at least 78% of papers have not doubled quadratic regression coefficients, leading to an appreciable underestimate of the strength of stabilizing and disruptive selection. Proper treatment of quadratic regression coefficients is necessary for estimation of fitness surfaces and contour plots, canonical analysis of the gamma matrix, and modeling the evolution of populations on an adaptive landscape.

  3. A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems

    KAUST Repository

    Domínguez, Luis F.

    2012-06-25

    An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear programming subproblem and a mixed-integer nonlinear programming subproblem to provide a series of parametric upper and lower bounds. The primal subproblem is formulated by fixing the integer variables and solved through a series of multiparametric quadratic programming (mp-QP) problems based on quadratic approximations of the objective function, while the deterministic master subproblem is formulated so as to provide feasible integer solutions for the next primal subproblem. To reduce the computational effort when infeasibilities are encountered at the vertices of the critical regions (CRs) generated by the primal subproblem, a simplicial approximation approach is used to obtain CRs that are feasible at each of their vertices. The algorithm terminates when there does not exist an integer solution that is better than the one previously used by the primal problem. Through a series of examples, the proposed algorithm is compared with a multiparametric mixed-integer outer approximation (mp-MIOA) algorithm to demonstrate its computational advantages. © 2012 American Institute of Chemical Engineers (AIChE).

  4. Nonlinear Equalization of Microwave Photonic Links

    Science.gov (United States)

    2016-10-31

    1][2] [3] (2) 123 is a combinatorial factor describing the number of unique permutations of frequency indicies...nonlinear equalizer works on the entire Nyquist band and is synthesized directly from mathematical requirements instead of using best- fit methods

  5. A Quasi-Dynamic Optimal Control Strategy for Non-Linear Multivariable Processes Based upon Non-Quadratic Objective Functions

    Directory of Open Access Journals (Sweden)

    Jens G. Balchen

    1984-10-01

    Full Text Available The problem of systematic derivation of a quasi-dynamic optimal control strategy for a non-linear dynamic process based upon a non-quadratic objective function is investigated. The wellknown LQG-control algorithm does not lead to an optimal solution when the process disturbances have non-zero mean. The relationships between the proposed control algorithm and LQG-control are presented. The problem of how to constrain process variables by means of 'penalty' - terms in the objective function is dealt with separately.

  6. Mid-IR femtosecond frequency conversion by soliton-probe collision in phase-mismatched quadratic nonlinear crystals

    DEFF Research Database (Denmark)

    Liu, Xing; Zhou, Binbin; Guo, Hairun

    2015-01-01

    in a quadratic nonlinear crystal (beta-barium borate) in the normal dispersion regime due to cascaded (phase-mismatched) second-harmonic generation, and the mid-IR converted wave is formed in the anomalous dispersion regime between. lambda = 2.2-2.4 mu m as a resonant dispersive wave. This process relies...... on nondegenerate four-wave mixing mediated by an effective negative cross-phase modulation term caused by cascaded soliton-probe sum-frequency generation. (C) 2015 Optical Society of America...

  7. A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models

    Science.gov (United States)

    Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen

    2012-01-01

    Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent…

  8. Photon nonlinear mixing in subcarrier multiplexed quantum key distribution systems.

    Science.gov (United States)

    Capmany, José

    2009-04-13

    We provide, for the first time to our knowledge, an analysis of the influence of nonlinear photon mixing on the end to end quantum bit error rate (QBER) performance of subcarrier multiplexed quantum key distribution systems. The results show that negligible impact is to be expected for modulation indexes in the range of 2%.

  9. On-chip steering of entangled photons in nonlinear photonic crystals.

    Science.gov (United States)

    Leng, H Y; Yu, X Q; Gong, Y X; Xu, P; Xie, Z D; Jin, H; Zhang, C; Zhu, S N

    2011-08-16

    One promising technique for working toward practical photonic quantum technologies is to implement multiple operations on a monolithic chip, thereby improving stability, scalability and miniaturization. The on-chip spatial control of entangled photons will certainly benefit numerous applications, including quantum imaging, quantum lithography, quantum metrology and quantum computation. However, external optical elements are usually required to spatially control the entangled photons. Here we present the first experimental demonstration of on-chip spatial control of entangled photons, based on a domain-engineered nonlinear photonic crystal. We manipulate the entangled photons using the inherent properties of the crystal during the parametric downconversion, demonstrating two-photon focusing and beam-splitting from a periodically poled lithium tantalate crystal with a parabolic phase profile. These experimental results indicate that versatile and precise spatial control of entangled photons is achievable. Because they may be operated independent of any bulk optical elements, domain-engineered nonlinear photonic crystals may prove to be a valuable ingredient in on-chip integrated quantum optics.

  10. Nonlinear switching dynamics in a photonic-crystal nanocavity

    International Nuclear Information System (INIS)

    Yu, Yi; Palushani, Evarist; Heuck, Mikkel; Vukovic, Dragana; Peucheret, Christophe; Yvind, Kresten; Mork, Jesper

    2014-01-01

    We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching contrast.

  11. Nonlinear switching dynamics in a photonic-crystal nanocavity

    DEFF Research Database (Denmark)

    Yu, Yi; Palushani, Evarist; Heuck, Mikkel

    2014-01-01

    We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When...... of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching...... the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms...

  12. Photonic Crystal Nanocavity Devices for Nonlinear Signal Processing

    DEFF Research Database (Denmark)

    Yu, Yi

    , membranization of InP/InGaAs structure and wet etching. Experimental investigation of the switching dynamics of InP photonic crystal nanocavity structures are carried out using short-pulse homodyne pump-probe techniques, both in the linear and nonlinear region where the cavity is perturbed by a relatively small......This thesis deals with the investigation of InP material based photonic crystal cavity membrane structures, both experimentally and theoretically. The work emphasizes on the understanding of the physics underlying the structures’ nonlinear properties and their applications for all-optical signal...... processing. Based on the previous fabrication recipe developed in our III-V platform, several processing techniques are developed and optimized for the fabrication of InP photonic crystal membrane structures. Several key issues are identified to ensure a good device quality such as air hole size control...

  13. Temporal nonlinear beam dynamics in infiltrated photonic crystal fibers

    DEFF Research Database (Denmark)

    Bennet, Francis; Rosberg, Christian Romer; Neshev, Dragomir N.

    Liquid-infiltrated photonic crystal fibers (PCFs) offer a new way of studying light propagation in periodic and discrete systems. A wide range of available fiber structures combined with the ease of infiltration opens up a range of novel experimental opportunities for optical detection and bio...... the evolution of the fiber output beam in the few micro or milliseconds after the beam is turned on. The characterization of the temporal behavior of the thermal nonlinear response provides important information about the nonlocality associated with heat diffusion inside the fiber, thus enabling studies of long...... and technological potential of liquid-infiltrated PCFs it is important to understand the temporal dynamics of nonlinear beam propagation in such structures. In this work we consider thermally induced spatial nonlinear effects in infiltrated photonic crystal fibers. We experimentally study the temporal dynamics...

  14. Study of nonlinear effects in photonic crystals doped with nanoparticles

    Energy Technology Data Exchange (ETDEWEB)

    Singh, Mahi R [Department of Physics and Astronomy, University of Western Ontario, London, N6A 3K7 Ontario (Canada)

    2008-07-14

    A theory of nonlinear phenomena has been developed for a photonic crystal in the presence of a pump and a coupling laser field. The crystal is doped with an ensemble of four-level nanoparticle impurities. It is considered that the impurity particles are not only interacting with the photonic crystal but also with each other via dipole-dipole interaction. An expression for the susceptibility has been obtained using the density matrix method. The nonlinear effects due to the coupling and the pump fields have been included in the formulation. The absorption spectrum has been calculated in the presence of the strong coupling and pump fields for an isotropic photonic crystal made from dielectric spheres. The photonic crystal has a gap to midgap ratio of about 21%. It is predicted that the absorption spectrum in the photonic crystal can have zero, one, two or three absorptionless states by tuning one of the transition energies within the bands. This is an interesting phenomenon which can be used to make photonic switching devices. We have also calculated the absorption spectrum in the presence of the dipole-dipole interaction. It is found that a symmetric absorption spectrum changes to an asymmetric one due to this interaction. It is also found that there is a large enhancement in the absorption and the dispersion simultaneously for certain values of the detuning and concentration.

  15. Study of nonlinear effects in photonic crystals doped with nanoparticles

    International Nuclear Information System (INIS)

    Singh, Mahi R

    2008-01-01

    A theory of nonlinear phenomena has been developed for a photonic crystal in the presence of a pump and a coupling laser field. The crystal is doped with an ensemble of four-level nanoparticle impurities. It is considered that the impurity particles are not only interacting with the photonic crystal but also with each other via dipole-dipole interaction. An expression for the susceptibility has been obtained using the density matrix method. The nonlinear effects due to the coupling and the pump fields have been included in the formulation. The absorption spectrum has been calculated in the presence of the strong coupling and pump fields for an isotropic photonic crystal made from dielectric spheres. The photonic crystal has a gap to midgap ratio of about 21%. It is predicted that the absorption spectrum in the photonic crystal can have zero, one, two or three absorptionless states by tuning one of the transition energies within the bands. This is an interesting phenomenon which can be used to make photonic switching devices. We have also calculated the absorption spectrum in the presence of the dipole-dipole interaction. It is found that a symmetric absorption spectrum changes to an asymmetric one due to this interaction. It is also found that there is a large enhancement in the absorption and the dispersion simultaneously for certain values of the detuning and concentration

  16. Fabrication of three-dimensional polymer quadratic nonlinear grating structures by layer-by-layer direct laser writing technique

    Science.gov (United States)

    Bich Do, Danh; Lin, Jian Hung; Diep Lai, Ngoc; Kan, Hung-Chih; Hsu, Chia Chen

    2011-08-01

    We demonstrate the fabrication of a three-dimensional (3D) polymer quadratic nonlinear (χ(2)) grating structure. By performing layer-by-layer direct laser writing (DLW) and spin-coating approaches, desired photobleached grating patterns were embedded in the guest--host dispersed-red-1/poly(methylmethacrylate) (DR1/PMMA) active layers of an active-passive alternative multilayer structure through photobleaching of DR1 molecules. Polyvinyl-alcohol and SU8 thin films were deposited between DR1/PMMA layers serving as a passive layer to separate DR1/PMMA active layers. After applying the corona electric field poling to the multilayer structure, nonbleached DR1 molecules in the active layers formed polar distribution, and a 3D χ(2) grating structure was obtained. The χ(2) grating structures at different DR1/PMMA nonlinear layers were mapped by laser scanning second harmonic (SH) microscopy, and no cross talk was observed between SH images obtained from neighboring nonlinear layers. The layer-by-layer DLW technique is favorable to fabricating hierarchical 3D polymer nonlinear structures for optoelectronic applications with flexible structural design.

  17. Properties of entangled photon pairs generated in one-dimensional nonlinear photonic-band-gap structures

    International Nuclear Information System (INIS)

    Perina, Jan Jr.; Centini, Marco; Sibilia, Concita; Bertolotti, Mario; Scalora, Michael

    2006-01-01

    We have developed a rigorous quantum model of spontaneous parametric down-conversion in a nonlinear 1D photonic-band-gap structure based upon expansion of the field into monochromatic plane waves. The model provides a two-photon amplitude of a created photon pair. The spectra of the signal and idler fields, their intensity profiles in the time domain, as well as the coincidence-count interference pattern in a Hong-Ou-Mandel interferometer are determined both for cw and pulsed pumping regimes in terms of the two-photon amplitude. A broad range of parameters characterizing the emitted down-converted fields can be used. As an example, a structure composed of 49 layers of GaN/AlN is analyzed as a suitable source of photon pairs having high efficiency

  18. Nonlinear spatial mode imaging of hybrid photonic crystal fibers

    DEFF Research Database (Denmark)

    Petersen, Sidsel Rübner; Alkeskjold, Thomas Tanggaard; Laurila, Marko

    2013-01-01

    Degenerate spontaneous four wave mixing is studied for the rst time in a large mode area hybrid photonic crystal ber, where light con nement is achieved by combined index- and bandgap guiding. Four wave mixing products are generated on the edges of the bandgaps, which is veri ed by numerical and ...... and experimental results. Since the core mode is in resonance with cladding modes near the bandedges an unconventional measurement technique is used, in this work named nonlinear spatial mode imaging....

  19. A new two-scroll chaotic attractor with three quadratic nonlinearities, its adaptive control and circuit design

    Science.gov (United States)

    Lien, C.-H.; Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Sanjaya, W. S. M.; Subiyanto

    2018-03-01

    A 3-D new two-scroll chaotic attractor with three quadratic nonlinearities is investigated in this paper. First, the qualitative and dynamical properties of the new two-scroll chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new two-scroll dissipative chaotic system has three unstable equilibrium points. As an engineering application, global chaos control of the new two-scroll chaotic system with unknown system parameters is designed via adaptive feedback control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic two-scroll attractor model.

  20. How universal is the period doubling phenomenon in equations with quadratic nonlinearity

    International Nuclear Information System (INIS)

    Malta, C.P.; Oliveira, C.R. de.

    1983-09-01

    Varying one parameter, the solution of nonlinear 1 sup(st) order differential equation with time delay tau is Fourier analysed. After the Hopf bifurcation, period-doubling phenomenon always occurs when tau is one of the fixed parameters (both for small and large tau). Varying tau, there are values of the fixed parameters for which no period-doubling occurs. 'Chaos' follows the period-doubling sequence and the rate at which 'chaos' is approached is very close to the universal delta = 4.6692016... characterising the period-doubling sequence to chaos in nonlinear difference equations. (Author) [pt

  1. Geometry and transport in a model of two coupled quadratic nonlinear waveguides

    DEFF Research Database (Denmark)

    Stirling, James R.; Bang, Ole; Christiansen, Peter Leth

    2008-01-01

    This paper applies geometric methods developed to understand chaos and transport in Hamiltonian systems to the study of power distribution in nonlinear waveguide arrays. The specific case of two linearly coupled X(2) waveguides is modeled and analyzed in terms of transport and geometry in the pha...

  2. Nonlinear Bloch waves in metallic photonic band-gap filaments

    International Nuclear Information System (INIS)

    Kaso, Artan; John, Sajeev

    2007-01-01

    We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10-50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell's equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament

  3. Nonlinear Bloch waves in metallic photonic band-gap filaments

    Science.gov (United States)

    Kaso, Artan; John, Sajeev

    2007-11-01

    We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10 50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell’s equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament.

  4. Constrained quadratic stabilization of discrete-time uncertain nonlinear multi-model systems using piecewise affine state-feedback

    Directory of Open Access Journals (Sweden)

    Olav Slupphaug

    1999-07-01

    Full Text Available In this paper a method for nonlinear robust stabilization based on solving a bilinear matrix inequality (BMI feasibility problem is developed. Robustness against model uncertainty is handled. In different non-overlapping regions of the state-space called clusters the plant is assumed to be an element in a polytope which vertices (local models are affine systems. In the clusters containing the origin in their closure, the local models are restricted to be linear systems. The clusters cover the region of interest in the state-space. An affine state-feedback is associated with each cluster. By utilizing the affinity of the local models and the state-feedback, a set of linear matrix inequalities (LMIs combined with a single nonconvex BMI are obtained which, if feasible, guarantee quadratic stability of the origin of the closed-loop. The feasibility problem is attacked by a branch-and-bound based global approach. If the feasibility check is successful, the Liapunov matrix and the piecewise affine state-feedback are given directly by the feasible solution. Control constraints are shown to be representable by LMIs or BMIs, and an application of the control design method to robustify constrained nonlinear model predictive control is presented. Also, the control design method is applied to a simple example.

  5. Invited Article: Multiple-octave spanning high-energy mid-IR supercontinuum generation in bulk quadratic nonlinear crystals

    Directory of Open Access Journals (Sweden)

    Binbin Zhou

    2016-08-01

    Full Text Available Bright and broadband coherent mid-IR radiation is important for exciting and probing molecular vibrations. Using cascaded nonlinearities in conventional quadratic nonlinear crystals like lithium niobate, self-defocusing near-IR solitons have been demonstrated that led to very broadband supercontinuum generation in the visible, near-IR, and short-wavelength mid-IR. Here we conduct an experiment where a mid-IR crystal is pumped in the mid-IR. The crystal is cut for noncritical interaction, so the three-wave mixing of a single mid-IR femtosecond pump source leads to highly phase-mismatched second-harmonic generation. This self-acting cascaded process leads to the formation of a self-defocusing soliton at the mid-IR pump wavelength and after the self-compression point multiple octave-spanning supercontinua are observed. The results were recorded in a commercially available crystal LiInS2 pumped in the 3-4 μm range with 85 fs 50 μJ pulse energy, with the broadest supercontinuum covering 1.6-7.0 μm. We measured up 30 μJ energy in the supercontinuum, and the energy promises to scale favorably with an increased pump energy. Other mid-IR crystals can readily be used as well to cover other pump wavelengths and target other supercontinuum wavelength ranges.

  6. Asymmetric induced cubic nonlinearities in homogeneous and quasi-phase-matched quadratic materials: signature and importance

    DEFF Research Database (Denmark)

    Bang, Ole; Corney, Joel Frederick

    2001-01-01

    In continuous-wave operation asymmetric induced nonlinearities induce an intensity-dependent phase mismatch that implies a nonzero so-called separatrix intensity, the crossing of which changes the one-period phase shift of the fundamental by Pi , with obvious use in switching applications.......We derived a formula for this QPM-induced separatrix intensity that corrects earlier estimates by a factor of 5.3, and we found the optimum crystal lengths for a flat phase-versus-intensity response on each side of the separatrix...

  7. Formalism of photons in a nonlinear microring resonator

    Science.gov (United States)

    Tran, Quang Loc; Yupapin, Preecha

    2018-03-01

    In this paper, using short Gaussian pulses input from a monochromatic light source, we simulate the photon distribution and analyse the output gate's signals of PANDA nonlinear ring resonator. The present analysis is restricted to directional couplers characterized by two parameters, the power coupling coefficient κ and power coupling loss γ. Add/drop filters are also employed and investigated for the suitable to implement in the practical communication system. The experiment was conducted by using the combination of Lumerical FDTD Solutions and Lumerical MODE Solutions software.

  8. Highly Nonlinear and Birefringent Spiral Photonic Crystal Fiber

    Directory of Open Access Journals (Sweden)

    S. Revathi

    2014-01-01

    Full Text Available We propose and design a spiral photonic crystal fiber with elliptical air holes for achieving high birefringence, large nonlinearity, and negative dispersion. The structure is designed using chalcogenide glass (As2S3 for different ellipticity ratios of air holes in the cladding and the effect on various properties is observed. The proposed structure has birefringence of the order 10−2, nonlinearity of 26739.42 W−1 m−1, and dispersion of −1136.69 at 0.85 μm. An accurate numerical approach based on finite element method is used for the design and simulation of the structure. Due to high birefringence and negative dispersion, the proposed structure can be used for polarization control and dispersion compensation, respectively.

  9. Nonlinear Photonic Systems for V- and W-Band Antenna Remoting Applications

    Science.gov (United States)

    2016-10-22

    AFRL-AFOSR-JP-TR-2016-0088 Nonlinear Photonic Systems for V- and W-Band Antenna Remoting Applications Sheng-Kwang Hwang NATIONAL CHENG KUNG...2016 2. REPORT TYPE Final 3. DATES COVERED (From - To) 26 May 2015 to 25 May 2016 4. TITLE AND SUBTITLE Nonlinear Photonic Systems for V- and W-Band...TERMS nonlinear, photonic , antenna, remote, microwave, amplification, bandwith, modulation 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT SAR

  10. Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

    Science.gov (United States)

    Cummings, Patrick

    We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

  11. Wave Propagation in Linear and Nonlinear Photonic Band-Gap Materials

    National Research Council Canada - National Science Library

    Venakides, Stephanos

    2003-01-01

    .... Development of 3D boundary element code for EM scattering off photonic crystal slabs. Development of 2D FDTD code that includes nonlinearities and use in studying resonant phenomena. Nonlinear Effects...

  12. Photonic band structure calculations using nonlinear eigenvalue techniques

    International Nuclear Information System (INIS)

    Spence, Alastair; Poulton, Chris

    2005-01-01

    This paper considers the numerical computation of the photonic band structure of periodic materials such as photonic crystals. This calculation involves the solution of a Hermitian nonlinear eigenvalue problem. Numerical methods for nonlinear eigenvalue problems are usually based on Newton's method or are extensions of techniques for the standard eigenvalue problem. We present a new variation on existing methods which has its derivation in methods for bifurcation problems, where bordered matrices are used to compute critical points in singular systems. This new approach has several advantages over the current methods. First, in our numerical calculations the new variation is more robust than existing techniques, having a larger domain of convergence. Second, the linear systems remain Hermitian and are nonsingular as the method converges. Third, the approach provides an elegant and efficient way of both thinking about the problem and organising the computer solution so that only one linear system needs to be factorised at each stage in the solution process. Finally, first- and higher-order derivatives are calculated as a natural extension of the basic method, and this has advantages in the electromagnetic problem discussed here, where the band structure is plotted as a set of paths in the (ω,k) plane

  13. Photonics

    CERN Document Server

    Andrews, David L

    2015-01-01

    Discusses the basic physical principles underlying Biomedical Photonics, spectroscopy and microscopy This volume discusses biomedical photonics, spectroscopy and microscopy, the basic physical principles underlying the technology and its applications. The topics discussed in this volume are: Biophotonics; Fluorescence and Phosphorescence; Medical Photonics; Microscopy; Nonlinear Optics; Ophthalmic Technology; Optical Tomography; Optofluidics; Photodynamic Therapy; Image Processing; Imaging Systems; Sensors; Single Molecule Detection; Futurology in Photonics. Comprehensive and accessible cov

  14. Nonlinear optics at the single-photon level inside a hollow core fiber

    DEFF Research Database (Denmark)

    Hofferberth, Sebastian; Peyronel, Thibault; Liang, Qiyu

    2011-01-01

    Cold atoms inside a hollow core fiber provide an unique system for studying optical nonlinearities at the few-photon level. Confinement of both atoms and photons inside the fiber core to a diameter of just a few wavelengths results in high electric field intensity per photon and large optical...

  15. Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

    Science.gov (United States)

    Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

    2018-05-01

    We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

  16. On-demand single-photon state generation via nonlinear absorption

    International Nuclear Information System (INIS)

    Hong Tao; Jack, Michael W.; Yamashita, Makoto

    2004-01-01

    We propose a method for producing on-demand single-photon states based on collision-induced exchanges of photons and unbalanced linear absorption between two single-mode light fields. These two effects result in an effective nonlinear absorption of photons in one of the modes, which can lead to single-photon states. A quantum nonlinear attenuator based on such a mechanism can absorb photons in a normal input light pulse and terminate the absorption at a single-photon state. Because the output light pulses containing single photons preserve the properties of the input pulses, we expect this method to be a means for building a highly controllable single-photon source

  17. Dye molecules as single-photon sources and large optical nonlinearities on a chip

    International Nuclear Information System (INIS)

    Hwang, J; Hinds, E A

    2011-01-01

    We point out that individual organic dye molecules, deposited close to optical waveguides on a photonic chip, can act as single-photon sources. A thin silicon nitride strip waveguide is expected to collect 28% of the photons from a single dibenzoterrylene molecule. These molecules can also provide large, localized optical nonlinearities, which are enough to discriminate between one photon or two through a differential phase shift of 2 0 per photon. This new atom-photon interface may be used as a resource for processing quantum information.

  18. Incorporation of amphiphilic ruthenium(II) ammine complexes into Langmuir-Blodgett thin films with switchable quadratic nonlinear optical behavior.

    Science.gov (United States)

    Boubekeur-Lecaque, Leïla; Coe, Benjamin J; Harris, James A; Helliwell, Madeleine; Asselberghs, Inge; Clays, Koen; Foerier, Stijn; Verbiest, Thierry

    2011-12-19

    Nine nonlinear optical (NLO) chromophores with pyridinium electron acceptors have been synthesized by complexing new proligands with {Ru(II)(NH(3))(5)}(2+) electron-donor centers. The presence of long alkyl/fluoroalkyl chain substituents imparts amphiphilic properties, and these cationic complexes have been characterized as their PF(6)(-) salts by using various techniques including electronic absorption spectroscopy and cyclic voltammetry. Each complex shows three reversible/quasireversible redox processes; a Ru(III/II) oxidation and two ligand-based reductions. The energies of the intense visible d → π* metal-to-ligand charge-transfer (MLCT) absorptions correlate to some extent with the ligand reduction potentials. (1)H NMR spectroscopy also provides insights into the relative electron-withdrawing strengths of the new ligands. Single crystal X-ray structures have been determined for two of the proligand salts and one complex salt, [Ru(II)(NH(3))(5)(4-C(16)H(33)PhQ(+))]Cl(3)·3.25H(2)O (PhQ(+) = N-phenyl-4,4'-bipyridinium), showing centrosymmetric packing structures in each case. The PF(6)(-) analogue of the latter complex has been used to deposit reproducibly high-quality, multilayered Langmuir-Blodgett (LB) thin films. These films show a strong second harmonic generation (SHG) response from a 1064 nm laser; their MLCT absorbance increases linearly with the number of layers (N) and I(2ω)/I(ω)(2) (I(2ω) = intensity at 532 nm; I(ω) = intensity at 1064 nm) scales quadratically with N, consistent with homogeneous deposition. LB films on indium tin oxide (ITO)-coated glass show electrochemically induced switching of the SHG response, with a decrease in activity of about 50% on Ru(II) → Ru(III) oxidation. This effect is reversible, but reproducible over only a few cycles before the signal from the Ru(II) species diminishes. This work extrapolates our original solution studies (Coe, B. J. et al. Angew. Chem., Int. Ed.1999, 38, 366) to the first demonstration of

  19. Strong nonlinearity-induced correlations for counterpropagating photons scattering on a two-level emitter

    DEFF Research Database (Denmark)

    Nysteen, Anders; McCutcheon, Dara; Mørk, Jesper

    2015-01-01

    We analytically treat the scattering of two counterpropagating photons on a two-level emitter embedded in an optical waveguide. We find that the nonlinearity of the emitter can give rise to significant pulse-dependent directional correlations in the scattered photonic state, which could be quanti......We analytically treat the scattering of two counterpropagating photons on a two-level emitter embedded in an optical waveguide. We find that the nonlinearity of the emitter can give rise to significant pulse-dependent directional correlations in the scattered photonic state, which could...

  20. Self-Assembly of Nanocomposite Nonlinear Optical Materials for Photonic Devices, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — This program targets the development of new highly anisotropic nonlinear optical nanocomposite materials for NASA and non-NASA applications in advanced photonic and...

  1. Few-photon Non-linearities in Nanophotonic Devices for Quantum Information Technology

    DEFF Research Database (Denmark)

    Nysteen, Anders

    In this thesis we investigate few-photon non-linearities in all-optical, on-chip circuits, and we discuss their possible applications in devices of interest for quantum information technology, such as conditional two-photon gates and single-photon sources. In order to propose efficient devices...... the scattered photons. Even though the non-linearity also alters the pulse spectrum due to a four-wave mixing process, we demonstrate that input pulses with a Gaussian spectrum can be mapped to the output with up to 80 % fidelity. Using two identical two-level emitters, we propose a setup for a deterministic...... by the capturing process. Semiconductor quantum dots (QDs) are promising for realizing few-photon non-linearities in solid-state implementations, although coupling to phonon modes in the surrounding lattice have significant influence on the dynamics. By accounting for the commonly neglected asymmetry between...

  2. Photon blockade in optomechanical systems with a position-modulated Kerr-type nonlinear coupling

    Science.gov (United States)

    Zhang, X. Y.; Zhou, Y. H.; Guo, Y. Q.; Yi, X. X.

    2018-03-01

    We explore the photon blockade in optomechanical systems with a position-modulated Kerr-type nonlinear coupling, i.e. H_int˜\\hat{a}\\dagger2\\hat{a}^2(\\hat{b}_1^\\dagger+\\hat{b}_1) . We find that the Kerr-type nonlinear coupling can enhance the photon blockade greatly. We evaluate the equal-time second-order correlation function of the cavity photons and find that the optimal photon blockade does not happen at the single photon resonance. By working within the few-photon subspace, we get an approximate analytical expression for the correlation function and the condition for the optimal photon blockade. We also find that the photon blockade effect is not always enhanced as the Kerr-type nonlinear coupling strength g 2 increases. At some values of g 2, the photon blockade is even weakened. For the system we considered here, the second-order correlation function can be smaller than 1 even in the unresolved sideband regime. By numerically simulating the master equation of the system, we also find that the thermal noise of the mechanical environment can enhance the photon blockade. We give out an explanation for this counter-intuitive phenomenon qualitatively.

  3. Tailoring nonlinearity and dispersion of photonic crystal fibers using hybrid cladding

    International Nuclear Information System (INIS)

    Zhao-lun, Liu; Lan-tian, Hou; Wei, Wang

    2009-01-01

    We present a hybrid cladding photonic crystal fiber for shaping high nonlinear and flattened dispersion in a wide range of wavelengths. The new structure adopts hybrid cladding with different pitches, air-holes diameters and air-holes arrayed fashions. The full-vector finite element method with perfectly matched layer is used to investigate the characteristics of the hybrid cladding photonic crystal fiber such as nonlinearity and dispersion properties. The influence of the cladding structure parameters on the nonlinear coefficient and geometric dispersion is analyzed. High nonlinear coefficient and the dispersion properties of fibers are tailored by adjusting the cladding structure parameters. A novel hybrid cladding photonic crystal fiber with high nonlinear coefficient and dispersion flattened which is suited for super continuum generation is designed. (author)

  4. A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems

    KAUST Repository

    Domí nguez, Luis F.; Pistikopoulos, Efstratios N.

    2012-01-01

    An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear

  5. Giant nonlinear interaction between two optical beams via a quantum dot embedded in a photonic wire

    DEFF Research Database (Denmark)

    Nguyen, H.A.; Grange, T.; Reznychenko, B.

    2018-01-01

    a tailored photonic environment. Here, we demonstrate a two-mode giant nonlinearity with a single semiconductor quantum dot (QD) embedded in a photonic wire antenna. We exploit two detuned optical transitions associated with the exciton-biexciton QD level scheme. Owing to the broadband waveguide antenna...

  6. Study on TVD parameters sensitivity of a crankshaft using multiple scale and state space method considering quadratic and cubic non-linearities

    Directory of Open Access Journals (Sweden)

    R. Talebitooti

    Full Text Available In this paper the effect of quadratic and cubic non-linearities of the system consisting of the crankshaft and torsional vibration damper (TVD is taken into account. TVD consists of non-linear elastomer material used for controlling the torsional vibration of crankshaft. The method of multiple scales is used to solve the governing equations of the system. Meanwhile, the frequency response of the system for both harmonic and sub-harmonic resonances is extracted. In addition, the effects of detuning parameters and other dimensionless parameters for a case of harmonic resonance are investigated. Moreover, the external forces including both inertia and gas forces are simultaneously applied into the model. Finally, in order to study the effectiveness of the parameters, the dimensionless governing equations of the system are solved, considering the state space method. Then, the effects of the torsional damper as well as all corresponding parameters of the system are discussed.

  7. Multi-piecewise quadratic nonlinearity memristor and its 2N-scroll and 2N + 1-scroll chaotic attractors system.

    Science.gov (United States)

    Wang, Chunhua; Liu, Xiaoming; Xia, Hu

    2017-03-01

    In this paper, two kinds of novel ideal active flux-controlled smooth multi-piecewise quadratic nonlinearity memristors with multi-piecewise continuous memductance function are presented. The pinched hysteresis loop characteristics of the two memristor models are verified by building a memristor emulator circuit. Using the two memristor models establish a new memristive multi-scroll Chua's circuit, which can generate 2N-scroll and 2N+1-scroll chaotic attractors without any other ordinary nonlinear function. Furthermore, coexisting multi-scroll chaotic attractors are found in the proposed memristive multi-scroll Chua's circuit. Phase portraits, Lyapunov exponents, bifurcation diagrams, and equilibrium point analysis have been used to research the basic dynamics of the memristive multi-scroll Chua's circuit. The consistency of circuit implementation and numerical simulation verifies the effectiveness of the system design.

  8. Universal continuous-variable quantum computation: Requirement of optical nonlinearity for photon counting

    International Nuclear Information System (INIS)

    Bartlett, Stephen D.; Sanders, Barry C.

    2002-01-01

    Although universal continuous-variable quantum computation cannot be achieved via linear optics (including squeezing), homodyne detection, and feed-forward, inclusion of ideal photon-counting measurements overcomes this obstacle. These measurements are sometimes described by arrays of beam splitters to distribute the photons across several modes. We show that such a scheme cannot be used to implement ideal photon counting and that such measurements necessarily involve nonlinear evolution. However, this requirement of nonlinearity can be moved ''off-line,'' thereby permitting universal continuous-variable quantum computation with linear optics

  9. Separable quadratic stochastic operators

    International Nuclear Information System (INIS)

    Rozikov, U.A.; Nazir, S.

    2009-04-01

    We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)

  10. Quadratic Damping

    Science.gov (United States)

    Fay, Temple H.

    2012-01-01

    Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

  11. Nonlinear properties of a graded-index photonic heterostructure

    Indian Academy of Sciences (India)

    Photonic crystals (PCs), which exhibit photonic band structures due to ... because of their small lattice constant, which must be comparable to the wavelength [6]. ... This type of structure can create a defect mode with frequency ω0 = 2πc/λ0.

  12. Limitations of two-level emitters as nonlinearities in two-photon controlled-PHASE gates

    DEFF Research Database (Denmark)

    Nysteen, Anders; McCutcheon, Dara P. S.; Heuck, Mikkel

    2017-01-01

    We investigate the origin of imperfections in the fidelity of a two-photon controlled-PHASE gate based on two-level-emitter nonlinearities. We focus on a passive system that operates without external modulations to enhance its performance. We demonstrate that the fidelity of the gate is limited...... by opposing requirements on the input pulse width for one-and two-photon-scattering events. For one-photon scattering, the spectral pulse width must be narrow compared with the emitter linewidth, while two-photon-scattering processes require the pulse width and emitter linewidth to be comparable. We find...

  13. Time Reversal of Arbitrary Photonic Temporal Modes via Nonlinear Optical Frequency Conversion

    OpenAIRE

    Raymer, Michael G; Reddy, Dileep V; van Enk, Steven J; McKinstrie, Colin J

    2017-01-01

    Single-photon wave packets can carry quantum information between nodes of a quantum network. An important general operation in photon-based quantum information systems is blind reversal of a photon's temporal wave-packet envelope, that is, the ability to reverse an envelope without knowing the temporal state of the photon. We present an all-optical means for doing so, using nonlinear-optical frequency conversion driven by a short pump pulse. This scheme allows for quantum operations such as a...

  14. A Photonic Basis for Deriving Nonlinear Optical Response

    Science.gov (United States)

    Andrews, David L.; Bradshaw, David S.

    2009-01-01

    Nonlinear optics is generally first presented as an extension of conventional optics. Typically the subject is introduced with reference to a classical oscillatory electric polarization, accommodating correction terms that become significant at high intensities. The material parameters that quantify the extent of the nonlinear response are cast as…

  15. Nonlinear optical sub-bandgap excitation of ZnO-based photonic resonators

    Energy Technology Data Exchange (ETDEWEB)

    Bader, Christina A.; Zeuner, Franziska; Bader, Manuel H. W.; Zentgraf, Thomas; Meier, Cedrik [Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, Warburger Str. 100, 33098 Paderborn (Germany)

    2015-12-07

    Zinc oxide (ZnO) is a versatile candidate for photonic devices due to its highly efficient optical emission. However, for pumping of ZnO photonic devices UV-sources are required. Here, we investigate the alternative usage of widely available pulsed near-infrared (NIR)-sources and compare the efficiency of linear and nonlinear excitation processes. We found that bulk ZnO, ZnO thin films grown by molecular beam epitaxy, and ZnO/SiO{sub 2} microdisk devices exhibit strong nonlinear response when excited with NIR pulses (λ ≈ 1060 nm). In addition, we show that the ZnO/SiO{sub 2} microdisks exhibit sharp whispering gallery modes over the blue-yellow part of the visible spectrum for both excitation conditions and high Q-factors up to Q = 4700. The results demonstrate that nonlinear excitation is an efficient way to pump ZnO photonic devices.

  16. Efficient non-linear two-photon effects from the Cesium 6D manifold

    Science.gov (United States)

    Haluska, Nathan D.; Perram, Glen P.; Rice, Christopher A.

    2018-02-01

    We report several non-linear process that occur when two-photon pumping the cesium 6D states. Cesium vapor possess some of the largest two-photon pump cross sections in nature. Pumping these cross sections leads to strong amplified spontaneous emission that we observe on over 17 lasing lines. These new fields are strong enough to couple with the pump to create additional tunable lines. We use a heat pipe with cesium densities of 1014 to 1016 cm-3 and 0 to 5 Torr of helium buffer gas. The cesium 6D States are interrogated by both high energy pulses and low power CW sources. We observe four-wave mixing, six-wave mixing, potential two-photon lasing, other unknown nonlinear processes, and the persistence of some processes at low thresholds. This system is also uniquely qualified to support two-photon lasing under the proper conditions.

  17. Analysis, Adaptive Control and Adaptive Synchronization of a Nine-Term Novel 3-D Chaotic System with Four Quadratic Nonlinearities and its Circuit Simulation

    Directory of Open Access Journals (Sweden)

    S. Vaidyanathan

    2014-11-01

    Full Text Available This research work describes a nine-term novel 3-D chaotic system with four quadratic nonlinearities and details its qualitative properties. The phase portraits of the 3-D novel chaotic system simulated using MATLAB, depict the strange chaotic attractor of the system. For the parameter values chosen in this work, the Lyapunov exponents of the novel chaotic system are obtained as L1 = 6.8548, L2 = 0 and L3 = −32.8779. Also, the Kaplan-Yorke dimension of the novel chaotic system is obtained as DKY = 2.2085. Next, an adaptive controller is design to achieve global stabilization of the 3-D novel chaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global chaos synchronization of two identical novel chaotic systems with unknown system parameters. Finally, an electronic circuit realization of the novel chaotic system is presented using SPICE to confirm the feasibility of the theoretical model.

  18. Suppression of two-photon resonantly enhanced nonlinear processes in extended media

    International Nuclear Information System (INIS)

    Garrett, W.R.; Moore, M.A.; Payne, M.G.; Wunderlich, R.K.

    1988-11-01

    On the basis of combined experimental and theoretical studies of nonlinear processes associated with two-photon excitations near 3d and 4d states in Na, we show how resonantly enhanced stimulated hyper-Raman emission, parametric four-wave mixing processes and total resonant two-photon absorption can become severely suppressed through the actions of internally generated fields on the total atomic response in extended media. 7 refs., 3 figs

  19. Self-Similar Nanocavity Design with Ultrasmall Mode Volume for Single-Photon Nonlinearities

    DEFF Research Database (Denmark)

    Choi, Hyeongrak; Heuck, Mikkel; Englund, Dirk R.

    2017-01-01

    We propose a photonic crystal nanocavity design with self-similar electromagnetic boundary conditions, achieving ultrasmall mode volume (V-eff). The electric energy density of a cavity mode can be maximized in the air or dielectric region, depending on the choice of boundary conditions. We illust...... at the single-photon level. These features open new directions in cavity quantum electrodynamics, spectroscopy, and quantum nonlinear optics....

  20. Spectral transformations in the regime of pulse self-trapping in a nonlinear photonic crystal

    International Nuclear Information System (INIS)

    Novitsky, Denis V.

    2011-01-01

    We consider the interaction of a femtosecond light pulse with a one-dimensional photonic crystal with relaxing cubic nonlinearity in the regime of self-trapping. By use of numerical simulations, it is shown that, under certain conditions, the spectra of reflected and transmitted light possess the properties of narrowband (quasimonochromatic) or wideband (continuumlike) radiation. It is remarkable that these spectral features appear due to a significant frequency shift and occur inside a photonic band gap of the structure under investigation.

  1. Giant nonlinear interaction between two optical beams via a quantum dot embedded in a photonic wire

    Science.gov (United States)

    Nguyen, H. A.; Grange, T.; Reznychenko, B.; Yeo, I.; de Assis, P.-L.; Tumanov, D.; Fratini, F.; Malik, N. S.; Dupuy, E.; Gregersen, N.; Auffèves, A.; Gérard, J.-M.; Claudon, J.; Poizat, J.-Ph.

    2018-05-01

    Optical nonlinearities usually appear for large intensities, but discrete transitions allow for giant nonlinearities operating at the single-photon level. This has been demonstrated in the last decade for a single optical mode with cold atomic gases, or single two-level systems coupled to light via a tailored photonic environment. Here, we demonstrate a two-mode giant nonlinearity with a single semiconductor quantum dot (QD) embedded in a photonic wire antenna. We exploit two detuned optical transitions associated with the exciton-biexciton QD level scheme. Owing to the broadband waveguide antenna, the two transitions are efficiently interfaced with two free-space laser beams. The reflection of one laser beam is then controlled by the other beam, with a threshold power as low as 10 photons per exciton lifetime (1.6 nW ). Such a two-color nonlinearity opens appealing perspectives for the realization of ultralow-power logical gates and optical quantum gates, and could also be implemented in an integrated photonic circuit based on planar waveguides.

  2. Frequency comb generation by a continuous-wave-pumped optical parametric oscillator based on cascading quadratic nonlinearities.

    Science.gov (United States)

    Ulvila, Ville; Phillips, C R; Halonen, Lauri; Vainio, Markku

    2013-11-01

    We report optical frequency comb generation by a continuous-wave pumped optical parametric oscillator (OPO) without any active modulation. The OPO is configured as singly resonant with an additional nonlinear crystal (periodically poled MgO:LiNbO3) placed inside the OPO for phase mismatched second harmonic generation (SHG) of the resonating signal beam. The phase mismatched SHG causes cascading χ(2) nonlinearities, which can substantially increase the effective χ(3) nonlinearity in MgO:LiNbO3, leading to spectral broadening of the OPO signal beam via self-phase modulation. The OPO generates a stable 4 THz wide (-30 dB) frequency comb centered at 1.56 μm.

  3. Time evolution of absorption process in nonlinear metallic photonic crystals

    Energy Technology Data Exchange (ETDEWEB)

    Singh, Mahi R.; Hatef, Ali [Department of Physics and Astronomy, University of Western Ontario, London (Canada)

    2009-05-15

    The time evolution of the absorption coefficient in metallic photonic crystals has been studied numerically. These crystals are made from metallic spheres which are arranged periodically in air. The refractive index of the metallic spheres depends on the plasma frequency. Probe and pump fields are applied to monitor the absorption process. Ensembles of three-level particles are embedded in the crystal. Nanoparticles are interacting with the metallic crystals via the electron-photon interaction. It is found that when the resonance states lie away from the band edges system goes to transparent state. (copyright 2009 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  4. Randomly poled nonlinear crystals as a source of photon pairs

    Czech Academy of Sciences Publication Activity Database

    Peřina ml., Jan; Svozilík, J.

    2011-01-01

    Roč. 83, č. 3 (2011), 033808/1-033808/14 ISSN 1050-2947 R&D Projects: GA MŠk(CZ) OC09026; GA AV ČR IAA100100713; GA MŠk(CZ) 1M06002 Institutional research plan: CEZ:AV0Z10100522 Keywords : parametric down conversion * production of entangled photons * nonclassical states of the electromagnetic field * entangled photon states Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.878, year: 2011 http://arxiv.org/PS_cache/arxiv/pdf/1101/1101.0757v1.pdf

  5. Characterization of the bistable wideband optical filter on the basis of nonlinear 2D photonic crystal

    Energy Technology Data Exchange (ETDEWEB)

    Guryev, I. V., E-mail: guryev@ieee.org; Sukhoivanov, I. A., E-mail: guryev@ieee.org; Andrade Lucio, J. A., E-mail: guryev@ieee.org; Manzano, O. Ibarra, E-mail: guryev@ieee.org; Rodriguez, E. Vargaz, E-mail: guryev@ieee.org; Gonzales, D. Claudio, E-mail: guryev@ieee.org; Chavez, R. I. Mata, E-mail: guryev@ieee.org; Gurieva, N. S., E-mail: guryev@ieee.org [University of Guanajuato, Engineering division (Mexico)

    2014-05-15

    In our work, we investigated the wideband optical filter on the basis of nonlinear photonic crystal. The all-optical flip-flop using ultra-short pulses with duration lower than 200 fs is obtained in such filters. Here we pay special attention to the stability problem of the nonlinear element. To investigate this problem, the temporal response demonstrating the flip-flop have been computed within the certain range of the wavelengths as well as at different input power.

  6. Slow light enhanced optical nonlinearity in a silicon photonic crystal coupled-resonator optical waveguide.

    Science.gov (United States)

    Matsuda, Nobuyuki; Kato, Takumi; Harada, Ken-Ichi; Takesue, Hiroki; Kuramochi, Eiichi; Taniyama, Hideaki; Notomi, Masaya

    2011-10-10

    We demonstrate highly enhanced optical nonlinearity in a coupled-resonator optical waveguide (CROW) in a four-wave mixing experiment. Using a CROW consisting of 200 coupled resonators based on width-modulated photonic crystal nanocavities in a line defect, we obtained an effective nonlinear constant exceeding 10,000 /W/m, thanks to slow light propagation combined with a strong spatial confinement of light achieved by the wavelength-sized cavities.

  7. The band structures of three-dimensional nonlinear plasma photonic crystals

    Directory of Open Access Journals (Sweden)

    Hai-Feng Zhang

    2018-01-01

    Full Text Available In this paper, the properties of the photonic band gaps (PBGs for three-dimensional (3D nonlinear plasma photonic crystals (PPCs are theoretically investigated by the plane wave expansion method, whose equations for calculations also are deduced. The configuration of 3D nonlinear PPCs is the Kerr nonlinear dielectric spheres (Kerr effect is considered inserted in the plasma background with simple-cubic lattices. The inserted dielectric spheres are Kerr nonlinear dielectrics whose relative permittivities are the functions of the external light intensity. Three different Kerr nonlinear dielectrics are considered, which can be expressed as the functions of space coordinates. The influences of the parameters for the Kerr nonlinear dielectrics on the PBGs also are discussed. The calculated results demonstrate that the locations, bandwidths and number of PBGs can be manipulated with the different Kerr nonlinear dielectrics. Compared with the conventional 3D dielectric PCs and PPCs with simple-cubic lattices, the more PBGs or larger PBG can be achieved in the 3D nonlinear PPCs. Those results provide a new way to design the novel devices based on the PPCs.

  8. Photonic single nonlinear-delay dynamical node for information processing

    Science.gov (United States)

    Ortín, Silvia; San-Martín, Daniel; Pesquera, Luis; Gutiérrez, José Manuel

    2012-06-01

    An electro-optical system with a delay loop based on semiconductor lasers is investigated for information processing by performing numerical simulations. This system can replace a complex network of many nonlinear elements for the implementation of Reservoir Computing. We show that a single nonlinear-delay dynamical system has the basic properties to perform as reservoir: short-term memory and separation property. The computing performance of this system is evaluated for two prediction tasks: Lorenz chaotic time series and nonlinear auto-regressive moving average (NARMA) model. We sweep the parameters of the system to find the best performance. The results achieved for the Lorenz and the NARMA-10 tasks are comparable to those obtained by other machine learning methods.

  9. Orthogonality preserving infinite dimensional quadratic stochastic operators

    International Nuclear Information System (INIS)

    Akın, Hasan; Mukhamedov, Farrukh

    2015-01-01

    In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators

  10. Quadratic algebras

    CERN Document Server

    Polishchuk, Alexander

    2005-01-01

    Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.

  11. Linear and nonlinear modeling of light propagation in hollow-core photonic crystal fiber

    DEFF Research Database (Denmark)

    Roberts, John; Lægsgaard, Jesper

    2009-01-01

    Hollow core photonic crystal fibers (HC-PCFs) find applications which include quantum and non-linear optics, gas detection and short high-intensity laser pulse delivery. Central to most applications is an understanding of the linear and nonlinear optical properties. These require careful modeling....... The intricacies of modeling various forms of HC-PCF are reviewed. An example of linear dispersion engineering, aimed at reducing and flattening the group velocity dispersion, is then presented. Finally, a study of short high intensity pulse delivery using HC-PCF in both dispersive and nonlinear (solitonic...

  12. Cascaded two-photon nonlinearity in a one-dimensional waveguide with multiple two-level emitters

    Science.gov (United States)

    Roy, Dibyendu

    2013-01-01

    We propose and theoretically investigate a model to realize cascaded optical nonlinearity with few atoms and photons in one-dimension (1D). The optical nonlinearity in our system is mediated by resonant interactions of photons with two-level emitters, such as atoms or quantum dots in a 1D photonic waveguide. Multi-photon transmission in the waveguide is nonreciprocal when the emitters have different transition energies. Our theory provides a clear physical understanding of the origin of nonreciprocity in the presence of cascaded nonlinearity. We show how various two-photon nonlinear effects including spatial attraction and repulsion between photons, background fluorescence can be tuned by changing the number of emitters and the coupling between emitters (controlled by the separation). PMID:23948782

  13. Energetic mid-IR femtosecond pulse generation by self-defocusing soliton-induced dispersive waves in a bulk quadratic nonlinear crystal

    DEFF Research Database (Denmark)

    Zhou, Binbin; Guo, Hairun; Bache, Morten

    2015-01-01

    Generating energetic femtosecond mid-IR pulses is crucial for ultrafast spectroscopy, and currently relies on parametric processes that, while efficient, are also complex. Here we experimentally show a simple alternative that uses a single pump wavelength without any pump synchronization and with...... by using large-aperture crystals. The technique can readily be implemented with other crystals and laser wavelengths, and can therefore potentially replace current ultrafast frequency-conversion processes to the mid-IR....... and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO3 cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband (∼ 1,000 cm−1) mid-IR pulses around 3.0 μm are generated with excellent spatio-temporal pulse...... quality, having up to 10.5 μJ energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily...

  14. Experimental demonstration of non-reciprocal transmission in a nonlinear photonic-crystal Fano structure

    DEFF Research Database (Denmark)

    Yu, Yi; Chen, Yaohui; Hu, Hao

    2015-01-01

    We suggest and experimentally demonstrate a photonic-crystal structure with more than 30 dB difference between forward and backward transmission levels. The non-reciprocity relies on the combination of ultrafast carrier nonlinearities and spatial symmetry breaking in a Fano structure employing...

  15. Nonlinear Silicon Photonic Signal Processing Devices for Future Optical Networks

    Directory of Open Access Journals (Sweden)

    Cosimo Lacava

    2017-01-01

    Full Text Available In this paper, we present a review on silicon-based nonlinear devices for all optical nonlinear processing of complex telecommunication signals. We discuss some recent developments achieved by our research group, through extensive collaborations with academic partners across Europe, on optical signal processing using silicon-germanium and amorphous silicon based waveguides as well as novel materials such as silicon rich silicon nitride and tantalum pentoxide. We review the performance of four wave mixing wavelength conversion applied on complex signals such as Differential Phase Shift Keying (DPSK, Quadrature Phase Shift Keying (QPSK, 16-Quadrature Amplitude Modulation (QAM and 64-QAM that dramatically enhance the telecom signal spectral efficiency, paving the way to next generation terabit all-optical networks.

  16. Strong nonlinear photonic responses from microbiologically synthesized tellurium nanocomposites

    Science.gov (United States)

    Liao, K.-S.; Wang, Jingyuan; Dias, S.; Dewald, J.; Alley, N.J.; Baesman, S.M.; Oremland, R.S.; Blau, W.J.; Curran, S.A.

    2010-01-01

    A new class of nanomaterials, namely microbiologically-formed nanorods composed of elemental tellurium [Te(0)] that forms unusual nanocomposites when combined with poly(m-phenylenevinylene-co-2,5-dioctoxy-phenylenevinylene) (PmPV) is described. These bio-nanocomposites exhibit excellent broadband optical limiting at 532 and 1064 nm. Nonlinear scattering, originating from the laser induced solvent bubbles and microplasmas, is responsible for this nonlinear behavior. The use of bacterially-formed Te(0) when combined with an organic chemical host (e.g., PmPV) is a new green method of nanoparticle syntheses. This opens the possibilities of using unique, biologically synthesized materials to advance future nanoelectronic and nanophotonic applications. ?? 2009 Elsevier B.V. All rights reserved.

  17. Micro-/nanoscale multi-field coupling in nonlinear photonic devices

    Science.gov (United States)

    Yang, Qing; Wang, Yubo; Tang, Mingwei; Xu, Pengfei; Xu, Yingke; Liu, Xu

    2017-08-01

    The coupling of mechanics/electronics/photonics may improve the performance of nanophotonic devices not only in the linear region but also in the nonlinear region. This review letter mainly presents the recent advances on multi-field coupling in nonlinear photonic devices. The nonlinear piezoelectric effect and piezo-phototronic effects in quantum wells and fibers show that large second-order nonlinear susceptibilities can be achieved, and second harmonic generation and electro-optic modulation can be enhanced and modulated. Strain engineering can tune the lattice structures and induce second order susceptibilities in central symmetry semiconductors. By combining the absorption-based photoacoustic effect and intensity-dependent photobleaching effect, subdiffraction imaging can be achieved. This review will also discuss possible future applications of these novel effects and the perspective of their research. The review can help us develop a deeper knowledge of the substance of photon-electron-phonon interaction in a micro-/nano- system. Moreover, it can benefit the design of nonlinear optical sensors and imaging devices with a faster response rate, higher efficiency, more sensitivity and higher spatial resolution which could be applied in environmental detection, bio-sensors, medical imaging and so on.

  18. Single-photon blockade in a hybrid cavity-optomechanical system via third-order nonlinearity

    Science.gov (United States)

    Sarma, Bijita; Sarma, Amarendra K.

    2018-04-01

    Photon statistics in a weakly driven optomechanical cavity, with Kerr-type nonlinearity, are analyzed both analytically and numerically. The single-photon blockade effect is demonstrated via calculations of the zero-time-delay second-order correlation function g (2)(0). The analytical results obtained by solving the Schrödinger equation are in complete conformity with the results obtained through numerical solution of the quantum master equation. A systematic study on the parameter regime for observing photon blockade in the weak coupling regime is reported. The parameter regime where the photon blockade is not realizable due to the combined effect of nonlinearities owing to the optomechanical coupling and the Kerr-effect is demonstrated. The experimental feasibility with state-of-the-art device parameters is discussed and it is observed that photon blockade could be generated at the telecommunication wavelength. An elaborate analysis of the thermal effects on photon antibunching is presented. The system is found to be robust against pure dephasing-induced decoherences and thermal phonon number fluctuations.

  19. Numeric treatment of nonlinear second order multi-point boundary value problems using ANN, GAs and sequential quadratic programming technique

    Directory of Open Access Journals (Sweden)

    Zulqurnain Sabir

    2014-06-01

    Full Text Available In this paper, computational intelligence technique are presented for solving multi-point nonlinear boundary value problems based on artificial neural networks, evolutionary computing approach, and active-set technique. The neural network is to provide convenient methods for obtaining useful model based on unsupervised error for the differential equations. The motivation for presenting this work comes actually from the aim of introducing a reliable framework that combines the powerful features of ANN optimized with soft computing frameworks to cope with such challenging system. The applicability and reliability of such methods have been monitored thoroughly for various boundary value problems arises in science, engineering and biotechnology as well. Comprehensive numerical experimentations have been performed to validate the accuracy, convergence, and robustness of the designed scheme. Comparative studies have also been made with available standard solution to analyze the correctness of the proposed scheme.

  20. Nonlinear neutrino-photon interactions inside strong laser pulses

    Energy Technology Data Exchange (ETDEWEB)

    Meuren, Sebastian; Keitel, Christoph H.; Di Piazza, Antonino [Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg (Germany)

    2016-07-01

    As different neutrino mass eigenstates exist, only the lightest neutrino is absolutely stable. However, due to the small phase space and the GIM suppression mechanism the radiative neutrino lifetime is much larger than the age of the universe. Interestingly, the photon-emission probability by a neutrino is drastically increased in the presence of an external background field. Therefore, it is natural to ask the question whether this so-called ''electromagnetic catalysis'' could be studied in an laboratory experiment using existing and upcoming laser facilities. To shed light on this question, we derive the vector-axialvector coupling tensor in the presence of an arbitrary plane-wave background field, which is needed for the calculation of the radiative neutrino decay. Furthermore, we study the Adler-Bell-Jackiw anomaly associated with this object in detail.

  1. Nonlinear photons in the type-I Bianchi universe

    International Nuclear Information System (INIS)

    Svaiter, N.F.

    1984-01-01

    It is shown that there exist several anisotropic solutions for the non-minimal coupled electromagnetic and gravitational field equations. A solution to vacuum is firstly presented, and afterwards a solution with matter and electric field, where the photon acquires a 'mass' proportional to the square root of the curvature scalar. This solution presents a true singularity in τ=0. A Kasner-like solution is also presented, with matter to the Einstein equations, where appears an ultra-relativistic perfect fluid (p=p). These two models give a good description of the universe dynamics in the neighborhood of the singularity. In this model, near to the singularity, does not occur the phenomenon described by lifshitz of the 'vacuum stage' because the influence of the matter can not be disregarded in regions near to the singularity. (L.C.) [pt

  2. Photon correlations in a two-site nonlinear cavity system under coherent drive and dissipation

    International Nuclear Information System (INIS)

    Ferretti, Sara; Andreani, Lucio Claudio; Tuereci, Hakan E.; Gerace, Dario

    2010-01-01

    We calculate the normalized second-order correlation function for a system of two tunnel-coupled photonic resonators, each one exhibiting a single-photon nonlinearity of the Kerr type. We employ a full quantum formulation: The master equation for the model, which takes into account both a coherent continuous drive and radiative as well as nonradiative dissipation channels, is solved analytically in steady state through a perturbative approach, and the results are compared to exact numerical simulations. The degree of second-order coherence displays values between 0 and 1, and divides the diagram identified by the two energy scales of the system - the tunneling and the nonlinear Kerr interaction - into two distinct regions separated by a crossover. When the tunneling term dominates over the nonlinear one, the system state is delocalized over both cavities, and the emitted light is coherent. In the opposite limit, photon blockade sets in, and the system shows an insulatorlike state with photons locked on each cavity, identified by antibunching of emitted light.

  3. Self-similar photonic crystal cavity with ultrasmall mode volume for single-photon nonlinearities

    DEFF Research Database (Denmark)

    Choi, Hyeongrak; Heuck, Mikkel; Englund, Dirk

    2017-01-01

    We propose a photonic crystal cavity design with self-similar structure to achieve ultrasmall mode volume. We describe the concept with a silicon-air nanobeam cavity at λ ∼ 1550nm, reaching a mode volume of ∼ 7.01 × 10∼5λ3.......We propose a photonic crystal cavity design with self-similar structure to achieve ultrasmall mode volume. We describe the concept with a silicon-air nanobeam cavity at λ ∼ 1550nm, reaching a mode volume of ∼ 7.01 × 10∼5λ3....

  4. Probabilistically cloning two single-photon states using weak cross-Kerr nonlinearities

    International Nuclear Information System (INIS)

    Zhang, Wen; Rui, Pinshu; Zhang, Ziyun; Yang, Qun

    2014-01-01

    By using quantum nondemolition detectors (QNDs) based on weak cross-Kerr nonlinearities, we propose an experimental scheme for achieving 1→2 probabilistic quantum cloning (PQC) of a single-photon state, secretly choosing from a two-state set. In our scheme, after a QND is performed on the to-be-cloned photon and the assistant photon, a single-photon projection measurement is performed by a polarization beam splitter (PBS) and two single-photon trigger detectors (SPTDs). The measurement is to judge whether the PQC should be continued. If the cloning fails, a cutoff is carried out and some operations are omitted. This makes our scheme economical. If the PQC is continued according to the measurement result, two more QNDs and some unitary operations are performed on the to-be-cloned photon and the cloning photon to achieve the PQC in a nearly deterministic way. Our experimental scheme for PQC is feasible for future technology. Furthermore, the quantum logic network of our PQC scheme is presented. In comparison with similar networks, our PQC network is simpler and more economical. (paper)

  5. Determination and evaluation of gas holdup time with the quadratic equation model and comparison with nonlinear equation models for isothermal gas chromatography

    Science.gov (United States)

    Wu, Liejun; Chen, Maoxue; Chen, Yongli; Li, Qing X.

    2013-01-01

    Gas holdup time (tM) is a basic parameter in isothermal gas chromatography (GC). Determination and evaluation of tM and retention behaviors of n-alkanes under isothermal GC conditions have been extensively studied since the 1950s, but still remains unresolved. The difference equation (DE) model [J. Chromatogr. A 1260:215–223] reveals retention behaviors of n-alkanes excluding tM, while the quadratic equation (QE) model [J. Chromatogr. A 1260:224–231] including tM is suitable for applications. In the present study, tM values were calculated with the QE model, which is referred to as tMT, evaluated and compared with other three typical nonlinear models. The QE model gives an accurate estimation of tM in isothermal GC. The tMT values are highly accurate, stable, and easy to calculate and use. There is only one tMT value at each GC condition. The proper classification of tM values can clarify their disagreement and facilitate GC retention data standardization for which tMT values are promising reference tM values. PMID:23726077

  6. Simulation of nonlinear benchmarks and sheet metal forming processes using linear and quadratic solid–shell elements combined with advanced anisotropic behavior models

    Directory of Open Access Journals (Sweden)

    Wang Peng

    2016-01-01

    Full Text Available A family of prismatic and hexahedral solid‒shell (SHB elements with their linear and quadratic versions is presented in this paper to model thin 3D structures. Based on reduced integration and special treatments to eliminate locking effects and to control spurious zero-energy modes, the SHB solid‒shell elements are capable of modeling most thin 3D structural problems with only a single element layer, while describing accurately the various through-thickness phenomena. In this paper, the SHB elements are combined with fully 3D behavior models, including orthotropic elastic behavior for composite materials and anisotropic plastic behavior for metallic materials, which allows describing the strain/stress state in the thickness direction, in contrast to traditional shell elements. All SHB elements are implemented into ABAQUS using both standard/quasi-static and explicit/dynamic solvers. Several benchmark tests have been conducted, in order to first assess the performance of the SHB elements in quasi-static and dynamic analyses. Then, deep drawing of a hemispherical cup is performed to demonstrate the capabilities of the SHB elements in handling various types of nonlinearities (large displacements and rotations, anisotropic plasticity, and contact. Compared to classical ABAQUS solid and shell elements, the results given by the SHB elements show good agreement with the reference solutions.

  7. Progress Toward Single-Photon-Level Nonlinear Optics in Crystalline Microcavities

    Science.gov (United States)

    Kowligy, Abijith S.

    Over the last two decades, the emergence of quantum information science has uncovered many practical applications in areas such as communications, imaging, and sensing where harnessing quantum features of Nature provides tremendous benefits over existing methods exploiting classical physical phenomena. In this effort, one of the frontiers of research has been to identify and utilize quantum phenomena that are not susceptible to environmental and parasitic noise processes. Quantum photonics has been at the forefront of these studies because it allows room-temperature access to its inherently quantum-mechanical features, and allows leveraging the mature telecommunication industry. Accompanying the weak environmental influence, however, are also weak optical nonlinearities. Efficient nonlinear optical interactions are indispensible for many of the existing protocols for quantum optical computation and communication, e.g. high-fidelity entangling quantum logic gates rely on large nonlinear responses at the one- or few-photon-level. While this has been addressed to a great extent by interfacing photons with single quantum emitters and cold atomic gases, scalability has remained elusive. In this work, we identify the macroscopic second-order nonlinear polarization as a robust platform to address this challenge, and utilize the recent advances in the burgeoning field of optical microcavities to enhance this nonlinear response. In particular, we show theoretically that by using the quantum Zeno effect, low-noise, single-photon-level optical nonlinearities can be realized in lithium niobate whispering-gallery-mode microcavities, and present experimental progress toward this goal. Using the measured strength of the second-order nonlinear response in lithium niobate, we modeled the nonlinear system in the strong coupling regime using the Schrodinger picture framework and theoretically demonstrated that the single-photon-level operation can be observed for cavity lifetimes in

  8. Pulse carving using nanocavity-enhanced nonlinear effects in photonic crystal Fano structures

    DEFF Research Database (Denmark)

    Bekele, Dagmawi Alemayehu; Yu, Yi; Hu, Hao

    2018-01-01

    We experimentally demonstrate the use of a photonic crystal Fano resonance for carving-out short pulses from long-duration input pulses. This is achieved by exploiting an asymmetric Fano resonance combined with carrier-induced nonlinear effects in a photonic crystal membrane structure. The use...... of a nanocavity concentrates the input field to a very small volume leading to an efficient nonlinear resonance shift that carves a short pulse out of the input pulse. Here, we demonstrate shortening of ∼500  ps and ∼100  ps long pulses to ∼30  ps and ∼20  ps pulses, respectively. Furthermore, we demonstrate...

  9. Wave propagation in photonic crystals and metamaterials: Surface waves, nonlinearity and chirality

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Bingnan [Iowa State Univ., Ames, IA (United States)

    2009-01-01

    Photonic crystals and metamaterials, both composed of artificial structures, are two interesting areas in electromagnetism and optics. New phenomena in photonic crystals and metamaterials are being discovered, including some not found in natural materials. This thesis presents my research work in the two areas. Photonic crystals are periodically arranged artificial structures, mostly made from dielectric materials, with period on the same order of the wavelength of the working electromagnetic wave. The wave propagation in photonic crystals is determined by the Bragg scattering of the periodic structure. Photonic band-gaps can be present for a properly designed photonic crystal. Electromagnetic waves with frequency within the range of the band-gap are suppressed from propagating in the photonic crystal. With surface defects, a photonic crystal could support surface modes that are localized on the surface of the crystal, with mode frequencies within the band-gap. With line defects, a photonic crystal could allow the propagation of electromagnetic waves along the channels. The study of surface modes and waveguiding properties of a 2D photonic crystal will be presented in Chapter 1. Metamaterials are generally composed of artificial structures with sizes one order smaller than the wavelength and can be approximated as effective media. Effective macroscopic parameters such as electric permittivity ϵ, magnetic permeability μ are used to characterize the wave propagation in metamaterials. The fundamental structures of the metamaterials affect strongly their macroscopic properties. By designing the fundamental structures of the metamaterials, the effective parameters can be tuned and different electromagnetic properties can be achieved. One important aspect of metamaterial research is to get artificial magnetism. Metallic split-ring resonators (SRRs) and variants are widely used to build magnetic metamaterials with effective μ < 1 or even μ < 0. Varactor based

  10. Tunable, Room Temperature THZ Emitters Based on Nonlinear Photonics

    Science.gov (United States)

    Sinha, Raju

    The Terahertz (1012 Hz) region of the electromagnetic spectrum covers the frequency range from roughly 300 GHz to 10 THz, which is in between the microwave and infrared regimes. The increasing interest in the development of ultra-compact, tunable room temperature Terahertz (THz) emitters with wide-range tunability has stimulated in-depth studies of different mechanisms of THz generation in the past decade due to its various potential applications such as biomedical diagnosis, security screening, chemical identification, life sciences and very high speed wireless communication. Despite the tremendous research and development efforts, all the available state-of-the-art THz emitters suffer from either being large, complex and costly, or operating at low temperatures, lacking tunability, having a very short spectral range and a low output power. Hence, the major objective of this research was to develop simple, inexpensive, compact, room temperature THz sources with wide-range tunability. We investigated THz radiation in a hybrid optical and THz micro-ring resonators system. For the first time, we were able to satisfy the DFG phase matching condition for the above-mentioned THz range in one single device geometry by employing a modal phase matching technique and using two separately designed resonators capable of oscillating at input optical waves and generated THz waves. In chapter 6, we proposed a novel plasmonic antenna geometry – the dimer rod-tapered antenna (DRTA), where we created a hot-spot in the nanogap between the dimer arms with a very large intensity enhancement of 4.1x105 at optical resonant wavelength. Then, we investigated DFG operation in the antenna geometry by incorporating a nonlinear nanodot in the hot-spot of the antenna and achieved continuously tunable enhanced THz radiation across 0.5-10 THz range. In chapter 8, we designed a multi-metallic resonators providing an ultrasharp toroidal response at THz frequency, then fabricated and

  11. A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions

    International Nuclear Information System (INIS)

    Jian Jinbao; Hu Qingjie; Tang Chunming; Zheng Haiyan

    2007-01-01

    In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported

  12. Silicon Photonics: All-Optical Devices for Linear and Nonlinear Applications

    Science.gov (United States)

    Driscoll, Jeffrey B.

    Silicon photonics has grown rapidly since the first Si electro-optic switch was demonstrated in 1987, and the field has never grown more quickly than it has over the past decade, fueled by milestone achievements in semiconductor processing technologies for low loss waveguides, high-speed Si modulators, Si lasers, Si detectors, and an enormous toolbox of passive and active integrated devices. Silicon photonics is now on the verge of major commercialization breakthroughs, and optical communication links remain the force driving integrated and Si photonics towards the first commercial telecom and datacom transceivers; however other potential and future applications are becoming uncovered and refined as researchers reveal the benefits of manipulating photons on the nanoscale. This thesis documents an exploration into the unique guided-wave and nonlinear properties of deeply-scaled high-index-contrast sub-wavelength Si waveguides. It is found that the tight confinement inherent to single-mode channel waveguides on the silicon-on-insulator platform lead to a rich physics, which can be leveraged for new devices extending well beyond simple passive interconnects and electro-optic devices. The following chapters will concentrate, in detail, on a number of unique physical features of Si waveguides and extend these attributes towards new and interesting devices. Linear optical properties and nonlinear optical properties are investigated, both of which are strongly affected by tight optical confinement of the guided waveguide modes. As will be shown, tight optical confinement directly results in strongly vectoral modal components, where the electric and magnetic fields of the guided modes extend into all spatial dimensions, even along the axis of propagation. In fact, the longitudinal electric and magnetic field components can be just as strong as the transverse fields, directly affecting the modal group velocity and energy transport properties since the longitudinal fields

  13. Dynamical invariants for variable quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Suslov, Sergei K

    2010-01-01

    We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.

  14. Nonlinear adaptive optics: aberration correction in three photon fluorescence microscopy for mouse brain imaging

    Science.gov (United States)

    Sinefeld, David; Paudel, Hari P.; Wang, Tianyu; Wang, Mengran; Ouzounov, Dimitre G.; Bifano, Thomas G.; Xu, Chris

    2017-02-01

    Multiphoton fluorescence microscopy is a well-established technique for deep-tissue imaging with subcellular resolution. Three-photon microscopy (3PM) when combined with long wavelength excitation was shown to allow deeper imaging than two-photon microscopy (2PM) in biological tissues, such as mouse brain, because out-of-focus background light can be further reduced due to the higher order nonlinear excitation. As was demonstrated in 2PM systems, imaging depth and resolution can be improved by aberration correction using adaptive optics (AO) techniques which are based on shaping the scanning beam using a spatial light modulator (SLM). In this way, it is possible to compensate for tissue low order aberration and to some extent, to compensate for tissue scattering. Here, we present a 3PM AO microscopy system for brain imaging. Soliton self-frequency shift is used to create a femtosecond source at 1675 nm and a microelectromechanical (MEMS) SLM serves as the wavefront shaping device. We perturb the 1020 segment SLM using a modified nonlinear version of three-point phase shifting interferometry. The nonlinearity of the fluorescence signal used for feedback ensures that the signal is increasing when the spot size decreases, allowing compensation of phase errors in an iterative optimization process without direct phase measurement. We compare the performance for different orders of nonlinear feedback, showing an exponential growth in signal improvement as the nonlinear order increases. We demonstrate the impact of the method by applying the 3PM AO system for in-vivo mouse brain imaging, showing improvement in signal at 1-mm depth inside the brain.

  15. Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics.

    Science.gov (United States)

    Liu, Xiaofeng; Guo, Qiangbing; Qiu, Jianrong

    2017-04-01

    Low-dimensional (LD) materials demonstrate intriguing optical properties, which lead to applications in diverse fields, such as photonics, biomedicine and energy. Due to modulation of electronic structure by the reduced structural dimensionality, LD versions of metal, semiconductor and topological insulators (TIs) at the same time bear distinct nonlinear optical (NLO) properties as compared with their bulk counterparts. Their interaction with short pulse laser excitation exhibits a strong nonlinear character manifested by NLO absorption, giving rise to optical limiting or saturated absorption associated with excited state absorption and Pauli blocking in different materials. In particular, the saturable absorption of these emerging LD materials including two-dimensional semiconductors as well as colloidal TI nanoparticles has recently been utilized for Q-switching and mode-locking ultra-short pulse generation across the visible, near infrared and middle infrared wavelength regions. Beside the large operation bandwidth, these ultrafast photonics applications are especially benefit from the high recovery rate as well as the facile processibility of these LD materials. The prominent NLO response of these LD materials have also provided new avenues for the development of novel NLO and photonics devices for all-optical control as well as optical circuits beyond ultrafast lasers. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  16. Two and four photon absorption and nonlinear refraction in undoped, chromium doped and copper doped ZnS quantum dots

    Science.gov (United States)

    Sharma, Dimple; Malik, B. P.; Gaur, Arun

    2015-12-01

    The ZnS quantum dots (QDs) with Cr and Cu doping were synthesized by chemical co-precipitation method. The nanostructures of the prepared undoped and doped ZnS QDs were characterized by UV-vis spectroscopy, Transmission electron microscopy (TEM) and X-ray diffraction (XRD). The sizes of QDs were found to be within 3-5 nm range. The nonlinear parameters viz. Two photon absorption coefficient (β2), nonlinear refractive index (n2), third order nonlinear susceptibility (χ3) at wavelength 532 nm and Four photon absorption coefficient (β4) at wavelength 1064 nm have been calculated by Z-scan technique using nanosecond Nd:YAG laser in undoped, Cr doped and Cu doped ZnS QDs. Higher values of nonlinear parameters for doped ZnS infer that they are potential material for the development of photonics devices and sensor protection applications.

  17. Thermal optical nonlinearity in photonic crystal fibers filled with nematic liquid crystals doped with gold nanoparticles

    Science.gov (United States)

    Lesiak, Piotr; Budaszewski, Daniel; Bednarska, Karolina; Wójcik, Michał; Sobotka, Piotr; Chychłowski, Miłosz; Woliński, Tomasz R.

    2017-05-01

    In this work we studied a newly reported class of nonlinear effects observed in 5CB liquid crystals doped with gold nanoparticles (GNPs). The size of the GNP was determined by direct TEM imaging and by X-ray scattering of the diluted NP solution. GNPs was coated by thiols with the ratio of mesogenic to n-alkyl thiols varying from 1:2 to 1:1. The research involved comparing properties of both undoped and doped 5CB (nematic LC) by infiltrating LC cell and microholes of the photonic crystal fiber (PCF) separately. In our experiment the PCF fiber type LMA-10 made by NKT Photonics as host material has been used.

  18. Effects of noninstantaneous nonlinear processes on photon-pair generation by spontaneous four-wave mixing

    DEFF Research Database (Denmark)

    Koefoed, Jacob Gade; Christensen, Jesper Bjerge; Rottwitt, Karsten

    2017-01-01

    We present a general model, based on a Hamiltonian approach, for the joint quantum state of photon pairs generated through pulsed spontaneous four-wave mixing, including nonlinear phase modulation and a finite material response time. For the case of a silica fiber, it is found that the pair......-production rate depends weakly on the waveguide temperature, due to higher-order Raman scattering events, and more strongly on pump-pair frequency detuning. From the analytical model, a numerical scheme is derived, based on the well-known split-step method. This scheme allows computation of joint states where......-dependent change in quantum-mechanical purity may be observed in silica. This shows that Raman scattering not only introduces noise, but can also drastically change the spectral correlations in photon pairs when pumped with short pulses....

  19. Phase Properties of Photon-Added Coherent States for Nonharmonic Oscillators in a Nonlinear Kerr Medium

    Science.gov (United States)

    Jahanbakhsh, F.; Honarasa, G.

    2018-04-01

    The potential of nonharmonic systems has several applications in the field of quantum physics. The photon-added coherent states for annharmonic oscillators in a nonlinear Kerr medium can be used to describe some quantum systems. In this paper, the phase properties of these states including number-phase Wigner distribution function, Pegg-Barnett phase distribution function, number-phase squeezing and number-phase entropic uncertainty relations are investigated. It is found that these states can be considered as the nonclassical states.

  20. Nonlinear behavior of photoluminescence from silicon particles under two-photon excitation

    International Nuclear Information System (INIS)

    Xu Xingsheng; Yokoyama, Shiyoshi

    2011-01-01

    Two-photon excited fluorescence (TPEF) under continuous-wave excitation from silicon particles produced by a pulsed laser is investigated. Spectra and images of TPEF from silicon particles are studied under different excitation intensities and operation modes (continuous wave or pulse). It is found that the photoluminescence depends superlinearly on the excitation intensity and that the spectral shape and peaks vary with different silicon particles. The above phenomena show the nonlinear behavior of TPEF from silicon particles, and stimulated emission is a possible process.

  1. Nonclassical-light generation in a photonic-band-gap nonlinear planar waveguide

    International Nuclear Information System (INIS)

    Perina, Jan Jr.; Sibilia, Concita; Tricca, Daniela; Bertolotti, Mario

    2004-01-01

    The optical parametric process occurring in a photonic-band-gap planar waveguide is studied from the point of view of nonclassical-light generation. The nonlinearly interacting optical fields are described by the generalized superposition of coherent signals and noise using the method of operator linear corrections to a classical strong solution. Scattered backward-propagating fields are taken into account. Squeezed light as well as light with sub-Poissonian statistics can be obtained in two-mode fields under the specified conditions

  2. Soliton-based ultrafast multi-wavelength nonlinear switching in dual-core photonic crystal fibre

    International Nuclear Information System (INIS)

    Stajanca, P; Pysz, D; Michalka, M; Bugar, I; Andriukaitis, G; Balciunas, T; Fan, G; Baltuska, A

    2014-01-01

    Systematic experimental study of ultrafast multi-wavelength all-optical switching performance in a dual-core photonic crystal fibre is presented. The focus is on nonlinearly induced switching between the two output ports at non-excitation wavelengths, which are generated during nonlinear propagation of femtosecond pulses in the anomalous dispersion region of a dual-core photonic crystal fibre made of multicomponent glass. Spatial and spectral characteristics of the fibre output radiation were measured separately for both fibre cores under various polarization and intensity conditions upon selective, individual excitation of each fibre core. Polarization-controlled nonlinear switching performance at multiple non-excitation wavelengths was demonstrated in the long-wavelength optical communication bands and beyond. Depending on the input pulse polarization, narrowband switching operation at 1560 nm and 1730 nm takes place with double core extinction ratio contrasts of 9 dB and 14.5 dB, respectively. Moreover, our approach allows switching with simultaneous wavelength shift from 1650 to 1775 nm with extinction ratio contrast larger than 18 dB. In addition, non-reciprocal behaviour of the soliton fission process under different fibre core excitations was observed and its effect on the multi-wavelength nonlinear switching performance was explained, taking into account the slight dual-core structure asymmetry. The obtained results represent ultrafast all-optical switching with an extended dimension of wavelength shift, controllable with both the input radiation intensity and the polarization by simple propagation along a 14 mm long fibre. (paper)

  3. Wave propagation in ordered, disordered, and nonlinear photonic band gap materials

    Energy Technology Data Exchange (ETDEWEB)

    Lidorikis, Elefterios [Iowa State Univ., Ames, IA (United States)

    1999-12-10

    Photonic band gap materials are artificial dielectric structures that give the promise of molding and controlling the flow of optical light the same way semiconductors mold and control the electric current flow. In this dissertation the author studied two areas of photonic band gap materials. The first area is focused on the properties of one-dimensional PBG materials doped with Kerr-type nonlinear material, while, the second area is focused on the mechanisms responsible for the gap formation as well as other properties of two-dimensional PBG materials. He first studied, in Chapter 2, the general adequacy of an approximate structure model in which the nonlinearity is assumed to be concentrated in equally-spaced very thin layers, or 6-functions, while the rest of the space is linear. This model had been used before, but its range of validity and the physical reasons for its limitations were not quite clear yet. He performed an extensive examination of many aspects of the model's nonlinear response and comparison against more realistic models with finite-width nonlinear layers, and found that the d-function model is quite adequate, capturing the essential features in the transmission characteristics. The author found one exception, coming from the deficiency of processing a rigid bottom band edge, i.e. the upper edge of the gaps is always independent of the refraction index contrast. This causes the model to miss-predict that there are no soliton solutions for a positive Kerr-coefficient, something known to be untrue.

  4. Propagation of optical vortex beams and nucleation of vortex-antivortex pairs in disordered nonlinear photonic lattices

    International Nuclear Information System (INIS)

    Cho, Yeong-Kwon; Kim, Ki-Hong

    2014-01-01

    The propagation of optical vortex beams through disordered nonlinear photonic lattices is numerically studied. The vortex beams are generated by using a superposition of several Gaussian laser beams arranged in a radially-symmetric manner. The paraxial nonlinear Schroedinger equation describing the longitudinal propagation of the beam array through nonlinear triangular photonic lattices with two-dimensional disorder is solved numerically by using the split-step Fourier method. We find that due to the spatial disorder, the vortex beam is destabilized after propagating a finite distance and new vortex-antivortex pairs are nucleated at the positions of perfect destructive interference. We also find that in the presence of a self-focusing nonlinearity, the vortex-antivortex pair nucleation is suppressed and the vortex beam becomes more stable, while a self-defocusing nonlinearity enhances the vortex-antivortex pair nucleation.

  5. Quantum state detection and state preparation based on cavity-enhanced nonlinear interaction of atoms with single photon

    Science.gov (United States)

    Hosseini, Mahdi

    Our ability to engineer quantum states of light and matter has significantly advanced over the past two decades, resulting in the production of both Gaussian and non-Gaussian optical states. The resulting tailored quantum states enable quantum technologies such as quantum optical communication, quantum sensing as well as quantum photonic computation. The strong nonlinear light-atom interaction is the key to deterministic quantum state preparation and quantum photonic processing. One route to enhancing the usually weak nonlinear light-atom interactions is to approach the regime of cavity quantum electrodynamics (cQED) interaction by means of high finesse optical resonators. I present results from the MIT experiment of large conditional cross-phase modulation between a signal photon, stored inside an atomic quantum memory, and a control photon that traverses a high-finesse optical cavity containing the atomic memory. I also present a scheme to probabilistically change the amplitude and phase of a signal photon qubit to, in principle, arbitrary values by postselection on a control photon that has interacted with that state. Notably, small changes of the control photon polarization measurement basis by few degrees can substantially change the amplitude and phase of the signal state. Finally, I present our ongoing effort at Purdue to realize similar peculiar quantum phenomena at the single photon level on chip scale photonic systems.

  6. Fabrication and Characterization of Linear and Nonlinear Photonic Devices in Fused Silica by Femtosecond Laser Writing

    Science.gov (United States)

    Ng, Jason Clement

    Femtosecond laser processing is a flexible, three-dimensional (3D) fabrication technique used to make integrated low-loss photonic devices in fused silica. My work expanded the suite of available optical devices through the design and optimization of linear optical components such as low-loss (70-nm spectral window. My work further complemented femtosecond laser processing with the development of nonlinear device capabilities. While thermal poling is a well known process, significant challenges had restricted the development of nonlinear devices in fused silica. The laser writing process would erase the induced nonlinearity (erasing) while a written waveguide core acted as a barrier to the thermal poling process (blocking). Using second harmonic (SH) microscopy, the effectiveness of thermal poling on laser-written waveguides was systematically analyzed leading to the technique of "double poling", which effectively overcomes the two challenges of erasing and blocking. In this new process the substrate is poled before and after waveguide writing to restore the induced nonlinearity within the vicinity of the waveguide to enable effective poling for inducing a second-order nonlinearity (SON) in fused silica. A new flexible, femtosecond laser based erasure process was also developed to enable quasi-phase matching and to form arbitrarily chirped gratings. Following this result, second harmonic generation (SHG) in a quasiphase-matched (QPM) femtosecond laser written waveguide device was demonstrated. SHG in a chirped QPM structure was also demonstrated to illustrate the flexibility of the femtosecond laser writing technique. These are the first demonstration of frequency doubling in an all-femtosecond-laser-written structure. A maximum SHG conversion efficiency of 1.3 +/- 0.1x10 -11/W-cm-2 was achieved for the fundamental wavelength of 1552.8 nm with a phase-matching bandwidth of 4.4 nm for a 10.0-mm-long waveguide. For a shorter sample, an effective SON of chi(2) = 0

  7. Integrated liquid-core optical fibers for ultra-efficient nonlinear liquid photonics.

    Science.gov (United States)

    Kieu, K; Schneebeli, L; Norwood, R A; Peyghambarian, N

    2012-03-26

    We have developed a novel integrated platform for liquid photonics based on liquid core optical fiber (LCOF). The platform is created by fusion splicing liquid core optical fiber to standard single-mode optical fiber making it fully integrated and practical - a major challenge that has greatly hindered progress in liquid-photonic applications. As an example, we report here the realization of ultralow threshold Raman generation using an integrated CS₂ filled LCOF pumped with sub-nanosecond pulses at 532 nm and 1064 nm. The measured energy threshold for the Stokes generation is 1nJ, about three orders of magnitude lower than previously reported values in the literature for hydrogen gas, a popular Raman medium. The integrated LCOF platform opens up new possibilities for ultralow power nonlinear optics such as efficient white light generation for displays, mid-IR generation, slow light generation, parametric amplification, all-optical switching and wavelength conversion using liquids that have orders of magnitude larger optical nonlinearities compared with silica glass.

  8. An integrated nonlinear optical loop mirror in silicon photonics for all-optical signal processing

    Directory of Open Access Journals (Sweden)

    Zifei Wang

    2018-02-01

    Full Text Available The nonlinear optical loop mirror (NOLM has been studied for several decades and has attracted considerable attention for applications in high data rate optical communications and all-optical signal processing. The majority of NOLM research has focused on silica fiber-based implementations. While various fiber designs have been considered to increase the nonlinearity and manage dispersion, several meters to hundreds of meters of fiber are still required. On the other hand, there is increasing interest in developing photonic integrated circuits for realizing signal processing functions. In this paper, we realize the first-ever passive integrated NOLM in silicon photonics and demonstrate its application for all-optical signal processing. In particular, we show wavelength conversion of 10 Gb/s return-to-zero on-off keying (RZ-OOK signals over a wavelength range of 30 nm with error-free operation and a power penalty of less than 2.5 dB, we achieve error-free nonreturn to zero (NRZ-to-RZ modulation format conversion at 10 Gb/s also with a power penalty of less than 2.8 dB, and we obtain error-free all-optical time-division demultiplexing of a 40 Gb/s RZ-OOK data signal into its 10 Gb/s tributary channels with a maximum power penalty of 3.5 dB.

  9. Influence of pump-field scattering on nonclassical-light generation in a photonic-band-gap nonlinear planar waveguide

    International Nuclear Information System (INIS)

    Perina, Jan Jr.; Sibilia, Concita; Tricca, Daniela; Bertolotti, Mario

    2005-01-01

    Optical parametric process occurring in a nonlinear planar waveguide can serve as a source of light with nonclassical properties. The properties of the generated fields are substantially modified by scattering of the nonlinearly interacting fields in a photonic-band-gap structure inside the waveguide. A general quantum model of linear operator amplitude corrections to the amplitude mean values and its numerical analysis provide conditions for efficient squeezed-light generation as well as generation of light with sub-Poissonian photon-number statistics. The destructive influence of phase mismatch of the nonlinear interaction can fully be compensated using a suitable photonic-band-gap structure inside the waveguide. Also an increase of the signal-to-noise ratio of the incident optical field can be reached in the waveguide

  10. Quadratic spatial soliton interactions

    Science.gov (United States)

    Jankovic, Ladislav

    Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30

  11. Multiple nonlinear Bragg diffraction of femtosecond laser pulses in a {\\chi^{(2)}} photonic lattice with hexagonal domains

    Science.gov (United States)

    Vyunishev, A. M.; Arkhipkin, V. G.; Baturin, I. S.; Akhmatkhanov, A. R.; Shur, V. Ya; Chirkin, A. S.

    2018-04-01

    The frequency doubling of femtosecond laser pulses in a two-dimensional (2D) rectangular nonlinear photonic lattice with hexagonal domains is studied experimentally and theoretically. The broad fundamental spectrum enables frequency conversion under nonlinear Bragg diffraction for a series of transverse orders at a fixed longitudinal quasi-phase-matching order. The consistent nonstationary theory of the frequency doubling of femtosecond laser pulses is developed using the representation based on the reciprocal lattice of the structure. The calculated spatial distribution of the second-harmonic spectral intensity agrees well with the experimental data. The condition for multiple nonlinear Bragg diffraction in a 2D nonlinear photonic lattice is offered. The hexagonal shape of the domains contributes to multibeam second harmonic excitation. The maximum conversion efficiency for a series of transverse orders in the range 0.01%-0.03% is obtained.

  12. Nonlinear ionization of many-electron systems over a broad photon-energy range

    International Nuclear Information System (INIS)

    Karamatskou, Antonia

    2015-11-01

    Rapid developments in laser technology and, in particular, the advances in the realm of free-electron lasers have initiated tremendous progress in both theoretical and experimental atomic, molecular and optical physics. Owing to high intensities in combination with short pulse durations we can enter the utterly nonlinear regime of light-matter interaction and study the dynamics and features of matter under extreme conditions. The capabilities of X-ray free-electron laser sources have promoted the importance of nonlinear optics also in the X-ray regime. I show in my thesis how we can exploit the nonlinear response regime to reveal hidden information about resonance structures that are not resolved in the weak-field regime. This prospect points to many applications for future investigations of various complex systems with free-electron lasers. In the present thesis the interaction of atomic closed-shell systems with ultrashort and strong laser pulses is investigated. Over a broad photon-energy range the characteristics of the atomic shell are studied with a particular focus on the nonlinear response regime and on electron correlation effects. Several computational extensions of the XCID package for multi-electron dynamics are presented and their applications in various studies are demonstrated; a completely new capability of the numerical method is realized by implementing the calculation of photoelectron spectra and by calculating eigenstates of the many-electron Hamiltonian. The field of study within the present work encompasses (1) the strong-field regime, where the question of the adiabatic character in tunneling ionization is discussed and analyzed, especially for the case of few-cycle pulses; (2) the XUV regime, in which we show for the first time that the collectivity in resonant excitation reveals new information; and (3) the (hard) x-ray regime, which is highly relevant for x-ray free-electron laser experiments, and where we show how important two-photon

  13. Interaction between a dark spot and a two-dimensional nonlinear photonic lattice with fully incoherent white light

    International Nuclear Information System (INIS)

    Liu, Zhaohong; Liu, Simin; Guo, Ru; Song, Tao; Zhu, Nan

    2007-01-01

    We study experimentally the interaction of a dark spot with a nonlinear photonic lattice with fully incoherent white light emitted from an incandescent bulb in the self-defocussing photovoltaic media when the dark spot is aimed at different positions of lattices with different lattice spacing. In this case a host of novel phenomena is demonstrated, including dark spot induced lattice dislocation-deformation, the annihilation of the dark spot and so on. Results demonstrate that the interaction between incoherent dark spot and photonic lattice is always attraction and the large-spacing photonic lattice is analogous to the continuous medium

  14. Nonlinear interaction of photons and phonons in electron-positron plasmas

    International Nuclear Information System (INIS)

    Tajima, T.; Taniuti, T.

    1990-03-01

    Nonlinear interaction of electromagnetic waves and acoustic modes in an electron-positron plasma is investigated. The plasma of electrons and positrons is quite plastic so that the imposition of electromagnetic (EM) waves causes depression of the plasma and other structural imprints on it through either the nonresonant or resonant interaction. Our theory shows that the nonresonant interaction can lead to the coalescence of photons and collapse of plasma cavity in higher (≥ 2) dimensions. The resonant interaction, in which the group velocity of EM waves is equal to the phase velocity of acoustic waves, is analyzed and a set of basic equations of the system is derived via the reductive perturbation theory. We find new solutions of solitary types: bright solitons, kink solitons, and dark solitons as the solutions to these equations. Our computation hints their stability. An impact of the present theory on astrophysical plasma settings is expected, including the cosmological relativistically hot electron-positron plasma. 20 refs., 9 figs

  15. 16-channel DWDM based on 1D defect mode nonlinear photonic crystal

    Science.gov (United States)

    Kalhan, Abhishek; Sharma, Sanjeev; Kumar, Arun

    2018-05-01

    We propose a sixteen-channel Dense Wavelength Division Multiplexer (DWDM), using the 1-D defect mode nonlinear photonic crystal which is a function of intensity as well as wavelength. Here, we consider an alternate layer of two semiconductor materials in which we found the bandgap of materials when defect layer is introduced then 16-channel dense wavelength division multiplexer is obtained within bandgap. From the theoretical analysis, we can achieve average quality factor of 7800.4, the uniform spectral line-width of 0.2 nm, crosstalk of -31.4 dB, central wavelength changes 0.07 nm/(1GW/cm2) and 100% transmission efficiency. Thus, Sixteen-channel DWDM has very high quality factor, low crosstalk, near 100% power transmission efficiency and small channel spacing (1.44 nm).

  16. Mode-selective mapping and control of vectorial nonlinear-optical processes in multimode photonic-crystal fibers.

    Science.gov (United States)

    Hu, Ming-Lie; Wang, Ching-Yue; Song, You-Jian; Li, Yan-Feng; Chai, Lu; Serebryannikov, Evgenii; Zheltikov, Aleksei

    2006-02-06

    We demonstrate an experimental technique that allows a mapping of vectorial nonlinear-optical processes in multimode photonic-crystal fibers (PCFs). Spatial and polarization modes of PCFs are selectively excited in this technique by varying the tilt angle of the input beam and rotating the polarization of the input field. Intensity spectra of the PCF output plotted as a function of the input field power and polarization then yield mode-resolved maps of nonlinear-optical interactions in multimode PCFs, facilitating the analysis and control of nonlinear-optical transformations of ultrashort laser pulses in such fibers.

  17. Cascaded Quadratic Soliton Compression in Waveguide Structures

    DEFF Research Database (Denmark)

    Guo, Hairun

    between the Kerr nonlinear effects and the dispersive effects in the medium. A Kerr-like nonlinearity is produced through the cascaded phase mismatched quadratic process, e.g. the second harmonic generation process, which can be flexibly tuned in both the sign and the amplitude, making possible a strong......-phase-matching technology is not necessarily needed. In large-RI-changed waveguides, CQSC is extended to the mid-infrared range to generate single-cycle pulses with purely nonlinear interactions, since an all-normal dispersion profile could be achieved within the guidance band. We believe that CQSC in quadratic waveguides...

  18. Extreme nonlinearities in InAs/InP nanowire gain media: the two-photon induced laser

    DEFF Research Database (Denmark)

    Capua, Amir; Kami, Ouri; Eisenstein, Gadi

    2012-01-01

    We demonstrate a novel laser oscillation scheme in an InAs / InP wire-like quantum dash gain medium. A short optical pulse excites carriers by two photon absorption which relax to the energy levels providing gain thereby enabling laser oscillations. The nonlinear dynamic interaction is analyzed a...

  19. Emission of orbital-angular-momentum-entangled photon pairs in a nonlinear ring fiber utilizing spontaneous parametric down-conversion

    Czech Academy of Sciences Publication Activity Database

    Javůrek, D.; Svozilík, J.; Peřina ml., Jan

    2014-01-01

    Roč. 90, č. 4 (2014), "043844-1"-"043844-12" ISSN 1050-2947 R&D Projects: GA ČR GAP205/12/0382 Institutional support: RVO:68378271 Keywords : photon pairs * orbital-angular-momentum-entangled * nonlinear ring fiber * spontaneous parametric down-conversion Subject RIV: BH - Optics , Masers, Lasers Impact factor: 2.808, year: 2014

  20. A Trust-region-based Sequential Quadratic Programming Algorithm

    DEFF Research Database (Denmark)

    Henriksen, Lars Christian; Poulsen, Niels Kjølstad

    This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints.......This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....

  1. Optimal Quadratic Programming Algorithms

    CERN Document Server

    Dostal, Zdenek

    2009-01-01

    Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This title presents various algorithms for solving large QP problems. It is suitable as an introductory text on quadratic programming for graduate students and researchers

  2. Self-Replicating Quadratics

    Science.gov (United States)

    Withers, Christopher S.; Nadarajah, Saralees

    2012-01-01

    We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

  3. Analytical results for a conditional phase shift between single-photon pulses in a nonlocal nonlinear medium

    Science.gov (United States)

    Viswanathan, Balakrishnan; Gea-Banacloche, Julio

    2018-03-01

    It has been suggested that second-order nonlinearities could be used for quantum logic at the single-photon level. Specifically, successive two-photon processes in principle could accomplish the phase shift (conditioned on the presence of two photons in the low-frequency modes) |011 〉→i |100 〉→-|011 〉 . We have analyzed a recent scheme proposed by Xia et al. [Phys. Rev. Lett. 116, 023601 (2016)], 10.1103/PhysRevLett.116.023601 to induce such a conditional phase shift between two single-photon pulses propagating at different speeds through a nonlinear medium with a nonlocal response. We present here an analytical solution for the most general case, i.e., for an arbitrary response function, initial state, and pulse velocity, which supports their numerical observation that a π phase shift with unit fidelity is possible, in principle, in an appropriate limit. We also discuss why this is possible in this system, despite the theoretical objections to the possibility of conditional phase shifts on single photons that were raised some time ago by Shapiro [Phys. Rev. A 73, 062305 (2006)], 10.1103/PhysRevA.73.062305 and by Gea-Banacloche [Phys. Rev. A 81, 043823 (2010)], 10.1103/PhysRevA.81.043823 one of us.

  4. The effect of magnetic field on bistability in 1D photonic crystal doped by magnetized plasma and coupled nonlinear defects

    International Nuclear Information System (INIS)

    Mehdian, H.; Mohammadzahery, Z.; Hasanbeigi, A.

    2014-01-01

    In this work, we study the defect mode and bistability behavior of 1-D photonic band gap structure with magnetized plasma and coupled nonlinear defects. The transfer matrix method has been employed to investigate the magnetic field effect on defect mode frequency and bistability threshold. The obtained results show that the frequency of defect mode and bistability threshold can be altered, without changing the structure of the photonic multilayer. Therefore, the bistability behavior of the subjected structure in the presence of magnetized plasma can be utilized in manufacturing wide frequency range devices

  5. Photonics

    CERN Document Server

    Andrews, David L

    2015-01-01

    Discusses the basic physical principles underlying the technology instrumentation of photonics This volume discusses photonics technology and instrumentation. The topics discussed in this volume are: Communication Networks; Data Buffers; Defense and Security Applications; Detectors; Fiber Optics and Amplifiers; Green Photonics; Instrumentation and Metrology; Interferometers; Light-Harvesting Materials; Logic Devices; Optical Communications; Remote Sensing; Solar Energy; Solid-State Lighting; Wavelength Conversion Comprehensive and accessible coverage of the whole of modern photonics Emphas

  6. Photonics

    CERN Document Server

    Andrews, David L

    2015-01-01

    Discusses the basic physical principles underlying thescience and technology of nanophotonics, its materials andstructures This volume presents nanophotonic structures and Materials.Nanophotonics is photonic science and technology that utilizeslight/matter interactions on the nanoscale where researchers arediscovering new phenomena and developing techniques that go wellbeyond what is possible with conventional photonics andelectronics.The topics discussed in this volume are: CavityPhotonics; Cold Atoms and Bose-Einstein Condensates; Displays;E-paper; Graphene; Integrated Photonics; Liquid Cry

  7. Photonics

    CERN Document Server

    Andrews, David L

    2015-01-01

    This book covers modern photonics accessibly and discusses the basic physical principles underlying all the applications and technology of photonicsThis volume covers the basic physical principles underlying the technology and all applications of photonics from statistical optics to quantum optics. The topics discussed in this volume are: Photons in perspective; Coherence and Statistical Optics; Complex Light and Singular Optics; Electrodynamics of Dielectric Media; Fast and slow Light; Holography; Multiphoton Processes; Optical Angular Momentum; Optical Forces, Trapping and Manipulation; Pol

  8. Quadratic Lagrangians and Legendre transformation

    International Nuclear Information System (INIS)

    Magnano, G.

    1988-01-01

    In recent years interest is grown about the so-called non-linear Lagrangians for gravitation. In particular, the quadratic lagrangians are currently believed to play a fundamental role both for quantum gravity and for the super-gravity approach. The higher order and high degree of non-linearity of these theories make very difficult to extract physical information out of them. The author discusses how the Legendre transformation can be applied to a wide class of non-linear theories: it corresponds to a conformal transformation whenever the Lagrangian depends only on the scalar curvature, while it has a more general form if the Lagrangian depends on the full Ricci tensor

  9. All-optical switching based on a tunable Fano-like resonance in nonlinear ferroelectric photonic crystals

    International Nuclear Information System (INIS)

    Chai, Zhen; Hu, Xiaoyong; Gong, Qihuang

    2013-01-01

    A low-power all-optical switching is presented based on the all-optical tunable Fano-like resonance in a two-dimensional nonlinear ferroelectric photonic crystal made of polycrystalline lithium niobate. An asymmetric Fano-like line shape is achieved in the transmission spectrum by using two cascaded and uncoupled photonic crystal microcavities. The physical mechanism underlying the all-optical switching is attributed to the dynamic shift of the Fano-like resonance peak caused by variations in the dispersion relations of the photonic crystal structure induced by pump light. A large switching efficiency of 61% is reached under excitation of a weak pump light with an intensity as low as 1 MW cm −2 . (paper)

  10. Gravitation and quadratic forms

    International Nuclear Information System (INIS)

    Ananth, Sudarshan; Brink, Lars; Majumdar, Sucheta; Mali, Mahendra; Shah, Nabha

    2017-01-01

    The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

  11. Gravitation and quadratic forms

    Energy Technology Data Exchange (ETDEWEB)

    Ananth, Sudarshan [Indian Institute of Science Education and Research,Pune 411008 (India); Brink, Lars [Department of Physics, Chalmers University of Technology,S-41296 Göteborg (Sweden); Institute of Advanced Studies and Department of Physics & Applied Physics,Nanyang Technological University,Singapore 637371 (Singapore); Majumdar, Sucheta [Indian Institute of Science Education and Research,Pune 411008 (India); Mali, Mahendra [School of Physics, Indian Institute of Science Education and Research,Thiruvananthapuram, Trivandrum 695016 (India); Shah, Nabha [Indian Institute of Science Education and Research,Pune 411008 (India)

    2017-03-31

    The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

  12. Generation of green frequency comb from chirped χ{sup (2)} nonlinear photonic crystals

    Energy Technology Data Exchange (ETDEWEB)

    Lai, C.-M. [Department of Electronic Engineering, Ming Chuan University, Taoyuan, Taiwan (China); Chang, K.-H.; Yang, Z.-Y.; Fu, S.-H.; Tsai, S.-T.; Hsu, C.-W.; Peng, L.-H. [Department of Electrical Engineering and Graduate Institute of Photonics and Optoelectronics, National Taiwan University, Taipei, Taiwan (China); Yu, N. E. [Advanced Photonics Research Institute, Gwangju Institute of Science and Technology, Gwangju (Korea, Republic of); Boudrioua, A. [LPL, CNRS - UMR 7538, Université Paris 13, Sorbone Paris Cité (France); Kung, A. H. [Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan (China); Institute of Photonics Technologies, National Tsing Hua University, Hsinchu, Taiwan (China)

    2014-12-01

    Spectrally broad frequency comb generation over 510–555 nm range was reported on chirped quasi-phase-matching (QPM) χ{sup (2)} nonlinear photonic crystals of 12 mm length with periodicity stepwise increased from 5.9 μm to 7.1 μm. When pumped with nanosecond infrared (IR) frequency comb derived from a QPM optical parametric oscillator (OPO) and spanned over 1040 nm to 1090 nm wavelength range, the 520 nm to 545 nm up-converted green spectra were shown to consist of contributions from (a) second-harmonic generation among the signal or the idler modes, and (b) sum-frequency generation (SFG) from the neighboring pairs of the signal or the idler modes. These mechanisms led the up-converted green frequency comb to have the same mode spacing of 450 GHz as that in the IR-OPO pump comb. As the pump was further detuned from the aforementioned near-degeneracy point and moved toward the signal (1020–1040 nm) and the idler (1090–1110 nm) spectral range, the above QPM parametric processes were preserved in the chirped QPM devices to support up-converted green generation in the 510–520 nm and the 545–555 nm spectral regime. Additional 530–535 nm green spectral generation was also observed due to concurrence of multi-wavelength SFG processes between the (signal, idler) mode pairs. These mechanisms facilitate the chirped QPM device to support a single-pass up-conversion efficiency ∼10% when subject to an IR-OPO pump comb with 200 mW average power operated near- or off- the degeneracy point.

  13. Pulse reshaping in photonic crystal waveguides and microcavities with Kerr nonlinearity: Critical issues for all-optical switching

    International Nuclear Information System (INIS)

    Vujic, Dragan; John, Sajeev

    2005-01-01

    We delineate critical issues for 'controlling light with light' in photonic crystal (PC) waveguides coupled to Kerr-nonlinear microresonators. These arise from (a) fundamental trade-off between switching speed and switching intensity threshold inherent in high-quality Q-factor cavities and (b) the dynamical nonlinear oscillation of such cavities in response to incident light pulses. Using finite-difference time-domain simulations of electromagnetic pulse propagation, we consider both (i) a nonlinear Fabry-Perot microresonator (embedded within a PC waveguide) exhibiting a narrow transmission resonance and (ii) a nonlinear point defect (side-coupled to a PC waveguide) exhibiting a narrow reflection spectrum. We describe self-induced switching from transmission to reflection induced by pulse intensity tuning as well as control of pulse transmission induced by the secondary, continuous (cw) laser field propagating through the same PC waveguide. For the Fabry-Perot microresonator, a well-defined self-switching threshold is obtained. However, this is accompanied by considerable temporal and spectral distortion of the pulse caused by the oscillatory nonlinear response of the microresonator. When the quality factor of the microresonator is increased, the switching intensity threshold can be lowered but the pulse transit (switching) time and the pulse distortion are increased. For the side-coupled microresonator, a gradual (not sharp) self-switching behavior as a function of incident intensity is obtained. For both the Fabry-Perot and side-coupled nonlinear microresonators, control of pulse transmission can be achieved by means of a secondary cw laser field. The cw power required for switching with realistic Kerr nonlinearities is in excess of 1 W/μm 2 and may cause optical damage to the semiconducting PC backbone. Both instantaneous and noninstantaneous Kerr-response models are considered. Our results underscore the limitations and trade-offs inherent in the possible

  14. orthogonal and scaling transformations of quadratic functions

    African Journals Online (AJOL)

    Preferred Customer

    functions of sub-problems of various nonlinear programming problems that employ methods such as sequential quadratic programming and trust-region methods (Sorensen, 1982; Eldersveld,. 1991; Nocedal and Wright, 1999). Various problems in Algebra, Functional Analysis,. Analytic Geometry and Computational Mathe-.

  15. Nonlinear optical and multiphoton processes for in situ manipulation and conversion of photons: applications to energy and healthcare (Conference Presentation)

    Science.gov (United States)

    Prasad, Paras N.

    2017-02-01

    Chiral control of nonlinear optical functions holds a great promise for a wide range of applications including optical signal processing, bio-sensing and chiral bio-imaging. In chiral polyfluorene thin films, we demonstrated extremely large chiral nonlinearity. The physics of manipulating excitation dynamics for photon transformation will be discussed, along with nanochemistry control of upconversion in hierarchically built organic chromophore coupled-core-multiple shell nanostructures which enable introduce new, organic-inorganic energy transfer routes for broadband light harvesting and increased upconversion efficiency via multistep cascaded energy transfer. We are pursuing the applications of photon conversion technology in IR harvesting for photovoltaics, high contrast bioimaging, photoacoustic imaging, photodynamic therapy, and optogenetics. An important application is in Brain research and Neurophotonics for functional mapping and modulation of brain activities. Another new direction pursued is magnetic field control of light in in a chiral polymer nanocomposite to achieve large magneto-optic coefficient which can enable sensing of extremely weak magnetic field due to brain waves. Finally, we will consider the thought provoking concept of utilizing photons to quantify, through magneto-optics, and augment - through nanoptogenetics, the cognitive states, thus paving the path way to a quantified human paradigm.

  16. Generating mid-IR octave-spanning supercontinua and few-cycle pulses with solitons in phase-mismatched quadratic nonlinear crystals

    DEFF Research Database (Denmark)

    Bache, Morten; Guo, Hairun; Zhou, Binbin

    2013-01-01

    We discuss a novel method for generating octave-spanning supercontinua and few-cycle pulses in the important mid-IR wavelength range. The technique relies on strongly phase-mismatched cascaded second-harmonic generation (SHG) in mid-IR nonlinear frequency conversion crystals. Importantly we here...... of the promising crystals: in one case soliton pulse compression from 50 fs to 15 fs (1.5 cycles) at 3.0 μm is achieved, and at the same time a 3-cycle dispersive wave at 5.0 μm is formed that can be isolated using a long-pass filter. In another example we show that extremely broadband supercontinua can form...

  17. Theoretical and computational studies of disorder-induced scattering and nonlinear optical interactions in slow-light photonic crystal waveguides

    Science.gov (United States)

    Mann, Nishan Singh

    Photonic crystal waveguides (PCWs) are nano-scale devices offering an exciting platform for exploring and exploiting enhanced linear and nonlinear light-matter interactions, aided in-part by slowing down the group velocity (vg) of on-chip photons. However, with potential applications in telecommunications, bio-sensing and quantum computing, the road to commercialization and practical devices is hindered by our limited understanding of the influence of structural disorder on linear and nonlinear light propagation. This thesis refines and develops state-of-the-art mathematical and numerical models for understanding the important role of disorder-related optical phenomena for PCWs in the linear and optical nonlinear regime. The importance of Bloch modes is demonstrated by computing the power loss caused by disorder-induced scattering for various dispersion engineered PCWs. The theoretical results are found to be in very good agreement with related experiments and it is shown how dispersion engineered designs can minimize the Bloch fields around spatial imperfections resulting in a radical departure from the usual assumed scaling vg. -2 of backscatteringlosses. We also conduct a systematic investigation of the influence of intra-hole correlation length, a parameter characterizing disorder on backscattering losses and find the loss behaviour to be qualitatively dependent on waveguide design and frequency. We then model disorder-induced resonance shifts to compute the ensemble averaged disordered density of states, accounting for important local field effects which are crucial in achieving good qualitative agreement with experiments. Lastly, motivated by emerging experiments examining enhanced nonlinear interactions, we develop an intuitive time dependent coupled mode formalism to derive propagation equations describing nonlinear pulse propagation in the presence of disorder-induced multiple scattering. The framework establishes a natural length scale for each physical

  18. Accurate nonlocal theory for cascaded quadratic soliton compression

    DEFF Research Database (Denmark)

    Bache, Morten; Bang, Ole; Moses, Jeffrey

    2007-01-01

    We study soliton compression in bulk quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....

  19. Guises and disguises of quadratic divergences

    Energy Technology Data Exchange (ETDEWEB)

    Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)

    2014-12-15

    In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

  20. Faithfully quadratic rings

    CERN Document Server

    Dickmann, M

    2015-01-01

    In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of T-isometry, where T is a preorder of the given ring, A, or T = A^2. (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in

  1. Engineering spectrally unentangled photon pairs from nonlinear microring resonators by pump manipulation

    DEFF Research Database (Denmark)

    Christensen, Jesper Bjerge; Koefoed, Jacob Gade; Rottwitt, Karsten

    2018-01-01

    The future of integrated quantum photonics relies heavily on the ability to engineer refined methods for preparing the quantum states needed to implement various quantum protocols. An important example of such states is quantum-correlated photon pairs, which can be efficiently generated using spo...

  2. Quadratic measurement and conditional state preparation in an optomechanical system

    DEFF Research Database (Denmark)

    A. Brawley, George; Vanner, Michael A.; Bowen, Warwick P.

    2014-01-01

    We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator.......We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator....

  3. Ultra-flattened nearly-zero dispersion and ultrahigh nonlinear slot silicon photonic crystal fibers with ultrahigh birefringence

    Science.gov (United States)

    Liao, Jianfei; Xie, Yingmao; Wang, Xinghua; Li, Dongbo; Huang, Tianye

    2017-07-01

    A slot silicon photonic crystal fiber (PCF) is proposed to simultaneously achieve ultrahigh birefringence, large nonlinearity and ultra-flattened nearly-zero dispersion over a wide wavelength range. By taking advantage on the slot effect, ultrahigh birefringence up to 0.0736 and ultrahigh nonlinear coefficient up to 211.48 W-1 m-1 for quasi-TE mode can be obtained at the wavelength of 1.55 μm. Moreover, ultra-flattened dispersion of 0.49 ps/(nm km) for quasi-TE mode can be achieved over a 180 nm wavelength range with low dispersion slope of 1.85 × 10-3 ps/(nm2 km) at 1.55 μm. Leveraging on these advantages, the proposed slot PCF has great potential for efficient all-optical signal processing applications.

  4. Efficient continuous-wave nonlinear frequency conversion in high-Q gallium nitride photonic crystal cavities on silicon

    Directory of Open Access Journals (Sweden)

    Mohamed Sabry Mohamed

    2017-03-01

    Full Text Available We report on nonlinear frequency conversion from the telecom range via second harmonic generation (SHG and third harmonic generation (THG in suspended gallium nitride slab photonic crystal (PhC cavities on silicon, under continuous-wave resonant excitation. Optimized two-dimensional PhC cavities with augmented far-field coupling have been characterized with quality factors as high as 4.4 × 104, approaching the computed theoretical values. The strong enhancement in light confinement has enabled efficient SHG, achieving a normalized conversion efficiency of 2.4 × 10−3 W−1, as well as simultaneous THG. SHG emission power of up to 0.74 nW has been detected without saturation. The results herein validate the suitability of gallium nitride for integrated nonlinear optical processing.

  5. Rescuing Quadratic Inflation

    CERN Document Server

    Ellis, John; Sueiro, Maria

    2014-01-01

    Inflationary models based on a single scalar field $\\phi$ with a quadratic potential $V = \\frac{1}{2} m^2 \\phi^2$ are disfavoured by the recent Planck constraints on the scalar index, $n_s$, and the tensor-to-scalar ratio for cosmological density perturbations, $r_T$. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on $n_s$ and $r_T$. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.

  6. Investigation on nonlinear optical and dielectric properties of L-arginine doped ZTC crystal to explore photonic device applications

    Directory of Open Access Journals (Sweden)

    Anis Mohd

    2016-09-01

    Full Text Available The present study is focused to explore the photonic device applications of L-arginine doped ZTC (LA-ZTC crystals using nonlinear optical (NLO and dielectric studies. The LA-ZTC crystals have been grown by slow evaporation solution technique. The chemical composition and surface of LA-ZTC crystal have been analyzed by means of energy dispersive spectroscopy (EDS and surface scanning electron microscopy (SEM techniques. The Vicker’s microhardness study has been carried out to determine the hardness, work hardening index, yield strength and elastic stiffness of LA-ZTC crystal. The enhanced SHG efficiency of LA-ZTC crystal has been ascertained using the Kurtz-Perry powder SHG test. The closed-and-open aperture Z-scan technique has been employed to confirm the third order nonlinear optical nature of LA-ZTC crystal. The Z-scan transmittance data has been utilized to calculate the superior cubic susceptibility, nonlinear refractive index, nonlinear absorption coefficient and figure of merit of LA-ZTC crystal. The behavior of dielectric constant and dielectric loss of LA-ZTC crystal at different temperatures has been investigated using the dielectric analysis.

  7. Improved Microwave Photonic Links via Receive-Side Nonlinear Signal Processing, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — We propose to significantly enhance the state-of-the-art of photonically-assisted microwave measurement and distribution systems by incorporating a highly efficient...

  8. Engineering non-linear resonator mode interactions in circuit QED by continuous driving: Manipulation of a photonic quantum memory

    Science.gov (United States)

    Reagor, Matthew; Pfaff, Wolfgang; Heeres, Reinier; Ofek, Nissim; Chou, Kevin; Blumoff, Jacob; Leghtas, Zaki; Touzard, Steven; Sliwa, Katrina; Holland, Eric; Albert, Victor V.; Frunzio, Luigi; Devoret, Michel H.; Jiang, Liang; Schoelkopf, Robert J.

    2015-03-01

    Recent advances in circuit QED have shown great potential for using microwave resonators as quantum memories. In particular, it is possible to encode the state of a quantum bit in non-classical photonic states inside a high-Q linear resonator. An outstanding challenge is to perform controlled operations on such a photonic state. We demonstrate experimentally how a continuous drive on a transmon qubit coupled to a high-Q storage resonator can be used to induce non-linear dynamics of the resonator. Tailoring the drive properties allows us to cancel or enhance non-linearities in the system such that we can manipulate the state stored in the cavity. This approach can be used to either counteract undesirable evolution due to the bare Hamiltonian of the system or, ultimately, to perform logical operations on the state encoded in the cavity field. Our method provides a promising pathway towards performing universal control for quantum states stored in high-coherence resonators in the circuit QED platform.

  9. Quadratic reactivity fuel cycle model

    International Nuclear Information System (INIS)

    Lewins, J.D.

    1985-01-01

    For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau 2 as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau 2 in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper

  10. In-chip microstructures and photonic devices fabricated by nonlinear laser lithography deep inside silicon

    Science.gov (United States)

    Tokel, Onur; Turnalı, Ahmet; Makey, Ghaith; Elahi, Parviz; ćolakoǧlu, Tahir; Ergeçen, Emre; Yavuz, Ã.-zgün; Hübner, René; Zolfaghari Borra, Mona; Pavlov, Ihor; Bek, Alpan; Turan, Raşit; Kesim, Denizhan Koray; Tozburun, Serhat; Ilday, Serim; Ilday, F. Ã.-mer

    2017-10-01

    Silicon is an excellent material for microelectronics and integrated photonics1-3, with untapped potential for mid-infrared optics4. Despite broad recognition of the importance of the third dimension5,6, current lithography methods do not allow the fabrication of photonic devices and functional microelements directly inside silicon chips. Even relatively simple curved geometries cannot be realized with techniques like reactive ion etching. Embedded optical elements7, electronic devices and better electronic-photonic integration are lacking8. Here, we demonstrate laser-based fabrication of complex 3D structures deep inside silicon using 1-µm-sized dots and rod-like structures of adjustable length as basic building blocks. The laser-modified Si has an optical index different to that in unmodified parts, enabling the creation of numerous photonic devices. Optionally, these parts can be chemically etched to produce desired 3D shapes. We exemplify a plethora of subsurface—that is, `in-chip'—microstructures for microfluidic cooling of chips, vias, micro-electro-mechanical systems, photovoltaic applications and photonic devices that match or surpass corresponding state-of-the-art device performances.

  11. In-chip microstructures and photonic devices fabricated by nonlinear laser lithography deep inside silicon.

    Science.gov (United States)

    Tokel, Onur; Turnali, Ahmet; Makey, Ghaith; Elahi, Parviz; Çolakoğlu, Tahir; Ergeçen, Emre; Yavuz, Özgün; Hübner, René; Borra, Mona Zolfaghari; Pavlov, Ihor; Bek, Alpan; Turan, Raşit; Kesim, Denizhan Koray; Tozburun, Serhat; Ilday, Serim; Ilday, F Ömer

    2017-10-01

    Silicon is an excellent material for microelectronics and integrated photonics1-3 with untapped potential for mid-IR optics4. Despite broad recognition of the importance of the third dimension5,6, current lithography methods do not allow fabrication of photonic devices and functional microelements directly inside silicon chips. Even relatively simple curved geometries cannot be realised with techniques like reactive ion etching. Embedded optical elements, like in glass7, electronic devices, and better electronic-photonic integration are lacking8. Here, we demonstrate laser-based fabrication of complex 3D structures deep inside silicon using 1 µm-sized dots and rod-like structures of adjustable length as basic building blocks. The laser-modified Si has a different optical index than unmodified parts, which enables numerous photonic devices. Optionally, these parts are chemically etched to produce desired 3D shapes. We exemplify a plethora of subsurface, i.e. , " in-chip" microstructures for microfluidic cooling of chips, vias, MEMS, photovoltaic applications and photonic devices that match or surpass the corresponding state-of-the-art device performances.

  12. Photonics

    Science.gov (United States)

    1991-01-01

    Optoelectronic materials and devices are examined. Optoelectronic devices, which generate, detect, modulate, or switch electromagnetic radiation are being developed for a variety of space applications. The program includes spatial light modulators, solid state lasers, optoelectronic integrated circuits, nonlinear optical materials and devices, fiber optics, and optical networking photovoltaic technology and optical processing.

  13. Direct measurements of multi-photon induced nonlinear lattice dynamics in semiconductors via time-resolved x-ray scattering.

    Science.gov (United States)

    Williams, G Jackson; Lee, Sooheyong; Walko, Donald A; Watson, Michael A; Jo, Wonhuyk; Lee, Dong Ryeol; Landahl, Eric C

    2016-12-22

    Nonlinear optical phenomena in semiconductors present several fundamental problems in modern optics that are of great importance for the development of optoelectronic devices. In particular, the details of photo-induced lattice dynamics at early time-scales prior to carrier recombination remain poorly understood. We demonstrate the first integrated measurements of both optical and structural, material-dependent quantities while also inferring the bulk impulsive strain profile by using high spatial-resolution time-resolved x-ray scattering (TRXS) on bulk crystalline gallium arsenide. Our findings reveal distinctive laser-fluence dependent crystal lattice responses, which are not described by previous TRXS experiments or models. The initial linear expansion of the crystal upon laser excitation stagnates at a laser fluence corresponding to the saturation of the free carrier density before resuming expansion in a third regime at higher fluences where two-photon absorption becomes dominant. Our interpretations of the lattice dynamics as nonlinear optical effects are confirmed by numerical simulations and by additional measurements in an n-type semiconductor that allows higher-order nonlinear optical processes to be directly observed as modulations of x-ray diffraction lineshapes.

  14. Highly-nonlinear polarization-maintaining As2Se3-based photonic quasi-crystal fiber for supercontinuum generation

    Science.gov (United States)

    Zhao, Tongtong; Lian, Zhenggang; Benson, Trevor; Wang, Xin; Zhang, Wan; Lou, Shuqin

    2017-11-01

    We propose an As2Se3-based photonic quasi-crystal fiber (PQF) with high nonlinearity and birefringence. By optimizing the structure parameters, a nonlinear coefficient up to 2079 W-1km-1 can be achieved at the wavelength of 2 μm; the birefringence reaches up to the order of 10-2 due to the introduction of large circular air holes in the cladding. Using an optical pulse with a peak power of 6 kW, a pulse width of 150 fs, and a central wavelength of 2.94 μm as the pump pulse, a mid-infrared polarized supercontinuum is obtained by using a 15 mm long PQF. The spectral width for x- and y-polarizations covers 1 μm-10.2 μm and 1 μm-12.5 μm, respectively. The polarization state can be well maintained when the incident angle of the input pulse changes within ±2°. The proposed PQF, with high nonlinear coefficient and birefringence, has potential applications in mid-infrared polarization-maintaining supercontinuum generation.

  15. Non-linear QCD dynamics in two-photon interactions at high energies

    Energy Technology Data Exchange (ETDEWEB)

    Carvalho, F. [Depto de Ciencias Exatas e da Terra, Universidade Federal de Sao Paulo Rua Arthur Riedel 275, Jd. Eldorado, Cep 09972-270, Diadema, SP (Brazil); Navarra, F. S.; Cazaroto, E. [Instituto de Fisica, Universidade de Sao Paulo, Rua do Matao, Travessa R, 187, 05508-090 Sao Paulo, SP (Brazil); Goncalves, V. P. [Instituto de Fisica e Matematica, Universidade Federal de Pelotas Caixa Postal 354, 96010-900, Pelotas, RS (Brazil)

    2013-03-25

    Assuming that the dipole - dipole cross section can be related with the dipole - proton cross section, we calculate the total {gamma}{gamma}, {gamma}*{gamma}* cross-sections and the real photon structure function F{sup {gamma}}{sub 2}(x,Q{sup 2}) using the recent solution of the BK equation with running coupling constant.

  16. On Convex Quadratic Approximation

    NARCIS (Netherlands)

    den Hertog, D.; de Klerk, E.; Roos, J.

    2000-01-01

    In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

  17. Aspects of Quadratic Gravity

    CERN Document Server

    Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio

    2016-01-01

    We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...

  18. A Quadratic Spring Equation

    Science.gov (United States)

    Fay, Temple H.

    2010-01-01

    Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

  19. Flat super-continuum generation based on normal dispersion nonlinear photonic crystal fibre

    DEFF Research Database (Denmark)

    Chow, K.K.; Takushima, Y.; Lin, C.

    2006-01-01

    Flat super-continuum generation spanning over the whole telecommunication band using a passively modelocked fibre laser source at 1550 nm together with a dispersion-flattened nonlinear photoinc crystal fibre is demonstrated. Since the pulses propagate in the normal dispersion regime of the fibre...

  20. Antimony orthophosphate glasses with large nonlinear refractive indices, low two-photon absorption coefficients, and ultrafast response

    International Nuclear Information System (INIS)

    Falcao-Filho, E.L.; Araujo, Cid B. de; Bosco, C.A.C.; Maciel, G.S.; Acioli, L.H.; Nalin, M.; Messaddeq, Y.

    2005-01-01

    Antimony glasses based on the composition Sb 2 O 3 -SbPO 4 were prepared and characterized. The samples present high refractive index, good transmission from 380 to 2000 nm, and high thermal stability. The nonlinear refractive index, n 2 , of the samples was studied using the optical Kerr shutter technique at 800 nm. The third-order correlation signals between pump and probe pulses indicate ultrafast response ( 2 was observed by adding lead oxide to the Sb 2 O 3 -SbPO 4 composition. Large values of n 2 ≅10 -14 cm 2 /W and negligible two-photon absorption coefficients (smaller than 0.01 cm/GW) were determined for all samples. The glass compositions studied present appropriate figure-of-merit for all-optical switching applications

  1. High-contrast controllable switching based on polystyrene nonlinear cavities in 2D hole-type photonic crystals

    Science.gov (United States)

    Paghousi, Roohollah; Fasihi, Kiazand

    2018-05-01

    We present a new high-contrast controllable switch, which is based on a polystyrene nonlinear cavity, and is implemented in a two dimensional (2D) hole-type photonic crystal (PC). We show that by applying a control signal, the input power can be transmitted to the output waveguide with a high contrast ratio. The operation of the proposed device is investigated through the use of coupled-mode theory (CMT) and finite-difference time-domain (FDTD) method. The contrast ratio of the proposed device varies between 18 and 23, which is higher than the corresponding value in the previous investigations. Based on the simulation results, with increasing the control power the range of operating power will be increased, while the contrast ratio will be decreased. It has been shown that in a modified structure, at the expense of the range of operating power and the contrast ratio, the control power can be decreased, considerably.

  2. Non-linear mixing in coupled photonic crystal nanobeam cavities due to cross-coupling opto-mechanical mechanisms

    Energy Technology Data Exchange (ETDEWEB)

    Ramos, Daniel, E-mail: daniel.ramos@csic.es; Frank, Ian W.; Deotare, Parag B.; Bulu, Irfan; Lončar, Marko [School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 (United States)

    2014-11-03

    We investigate the coupling between mechanical and optical modes supported by coupled, freestanding, photonic crystal nanobeam cavities. We show that localized cavity modes for a given gap between the nanobeams provide weak optomechanical coupling with out-of-plane mechanical modes. However, we show that the coupling can be significantly increased, more than an order of magnitude for the symmetric mechanical mode, due to optical resonances that arise from the interaction of the localized cavity modes with standing waves formed by the reflection from thesubstrate. Finally, amplification of motion for the symmetric mode has been observed and attributed to the strong optomechanical interaction of our hybrid system. The amplitude of these self-sustained oscillations is large enough to put the system into a non-linear oscillation regime where a mixing between the mechanical modes is experimentally observed and theoretically explained.

  3. Heterodyne pump probe measurements of nonlinear dynamics in an indium phosphide photonic crystal cavity

    DEFF Research Database (Denmark)

    Heuck, Mikkel; Combrié, S.; Lehoucq, G.

    2013-01-01

    Using a sensitive two-color heterodyne pump-probe technique, we investigate the carrier dynamics of an InP photonic crystal nanocavity. The heterodyne technique provides unambiguous results for all wavelength configurations, including the degenerate case, which cannot be investigated with the wid......Using a sensitive two-color heterodyne pump-probe technique, we investigate the carrier dynamics of an InP photonic crystal nanocavity. The heterodyne technique provides unambiguous results for all wavelength configurations, including the degenerate case, which cannot be investigated...... with the widely used homodyne technique. A model based on coupled mode theory including two carrier distributions is introduced to account for the relaxation dynamics, which is assumed to be governed by both diffusion and recombination....

  4. Correction method of nonlinearity due to logarithm operation for X-ray CT projection data with noise in photon-starved state

    International Nuclear Information System (INIS)

    Iwamoto, Shin-ichiro; Shiozaki, Akira

    2007-01-01

    In the acquisition of projection data of X-ray CT, logarithm operation is indispensable. But noise distribution is nonlinearly projected by the logarithm operation, and this deteriorates the precision of CT number. This influence becomes particularly remarkable when only a few photons are caught with a detector. It generates a strong streak artifact (SA) in a reconstructed image. Previously we have clarified the influence of the nonlinearity by statistical analysis and proposed a correction method for such nonlinearity. However, there is a problem that the compensation for clamp processing cannot be performed and that the suppression of SA is not enough in photon shortage state. In this paper, we propose a new technique for correcting the nonlinearity due to logarithm operation for noisy data by combining the previously presented method and an adaptive filtering method. The technique performs an adaptive filtering only when the number of captured photons is very few. Moreover we quantitatively evaluate the influence of noise on the reconstructed image in the proposed method by the experiment using numerical phantoms. The experimental results show that there is less influence on spatial resolution despite suppressing SA effectively and that CT number are hardly dependent on the number of the incident photons. (author)

  5. Wavelength conversion of a 40 Gb/s RZ-DPSK signal using four-wave mixing in a dispersion-flattened highly nonlinear photonic crystal fiber

    DEFF Research Database (Denmark)

    Andersen, Peter Andreas; Tokle, Torger; Geng, Yan

    2005-01-01

    Wavelength conversion of a 40-Gb/s return-to-zero differential phase-shift keying signal is demonstrated in a highly nonlinear photonic crystal fiber (HNL-PCF) for the first time. A conversion efficiency of -20 dB for a pump power of 23 dBm and a conversion bandwidth of 31 nm, essentially limited...

  6. Hidden conic quadratic representation of some nonconvex quadratic optimization problems

    NARCIS (Netherlands)

    Ben-Tal, A.; den Hertog, D.

    The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated

  7. Binary classification posed as a quadratically constrained quadratic ...

    Indian Academy of Sciences (India)

    Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or ...

  8. Natural Silk as a Photonics Component: a Study on Its Light Guiding and Nonlinear Optical Properties

    OpenAIRE

    Kujala, Sami; Mannila, Anna; Karvonen, Lasse; Kieu, Khanh; Sun, Zhipei

    2016-01-01

    Silk fibers are expected to become a pathway to biocompatible and bioresorbable waveguides, which could be used to deliver localized optical power for various applications, e.g., optical therapy or imaging inside living tissue. Here, for the first time, the linear and nonlinear optical properties of natural silk fibers have been studied. The waveguiding properties of silk fibroin of largely unprocessed Bombyx mori silkworm silk are assessed using two complementary methods, and found to be on ...

  9. Experimental photonic generation of chirped pulses using nonlinear dispersion-based incoherent processing.

    Science.gov (United States)

    Rius, Manuel; Bolea, Mario; Mora, José; Ortega, Beatriz; Capmany, José

    2015-05-18

    We experimentally demonstrate, for the first time, a chirped microwave pulses generator based on the processing of an incoherent optical signal by means of a nonlinear dispersive element. Different capabilities have been demonstrated such as the control of the time-bandwidth product and the frequency tuning increasing the flexibility of the generated waveform compared to coherent techniques. Moreover, the use of differential detection improves considerably the limitation over the signal-to-noise ratio related to incoherent processing.

  10. Photon induced non-linear quantized double layer charging in quaternary semiconducting quantum dots.

    Science.gov (United States)

    Nair, Vishnu; Ananthoju, Balakrishna; Mohapatra, Jeotikanta; Aslam, M

    2018-03-15

    Room temperature quantized double layer charging was observed in 2 nm Cu 2 ZnSnS 4 (CZTS) quantum dots. In addition to this we observed a distinct non-linearity in the quantized double layer charging arising from UV light modulation of double layer. UV light irradiation resulted in a 26% increase in the integral capacitance at the semiconductor-dielectric (CZTS-oleylamine) interface of the quantum dot without any change in its core size suggesting that the cause be photocapacitive. The increasing charge separation at the semiconductor-dielectric interface due to highly stable and mobile photogenerated carriers cause larger electrostatic forces between the quantum dot and electrolyte leading to an enhanced double layer. This idea was supported by a decrease in the differential capacitance possible due to an enhanced double layer. Furthermore the UV illumination enhanced double layer gives us an AC excitation dependent differential double layer capacitance which confirms that the charging process is non-linear. This ultimately illustrates the utility of a colloidal quantum dot-electrolyte interface as a non-linear photocapacitor. Copyright © 2017 Elsevier Inc. All rights reserved.

  11. Quadratic Diophantine equations

    CERN Document Server

    Andreescu, Titu

    2015-01-01

    This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

  12. Isotropy of quadratic forms

    Indian Academy of Sciences (India)

    V. Suresh University Of Hyderabad Hyderabad

    2008-10-31

    Oct 31, 2008 ... We say that (a1,··· ,an) is a zero of the polynomial f if f (a1,··· ,an) = 0. One of the main problems in Mathematics is to determine whether the given polynomial has a (non-trivial) zero or not. For example, let us recall the Fermat's last theorem: V. Suresh University Of Hyderabad Hyderabad. Isotropy of quadratic ...

  13. Polarization dependence of two-photon absorption coefficient and nonlinear susceptibility tensor in InP

    International Nuclear Information System (INIS)

    Matsusue, Toshio; Bando, Hiroyuki; Fujita, Shoichi; Takayama, Yusuke

    2011-01-01

    Two-photon absorption (TPA) effect in (001) InP is investigated using fs laser. Its dependences on wavelength and polarization are clarified by single and double beam methods with linearly polarized lights. Characteristic features are revealed and discussed with scaling law, crystal bonding and mutual relation of polarizations for double beams. The results are successfully analyzed on the basis of the third-order susceptibility tensor for comprehensive understanding of TPA effect at any polarization geometry. (copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  14. Velocity-changing collisional effects in nonlinear atomic spectroscopy and photon echo decay in gases

    Science.gov (United States)

    Herman, R. M.

    1983-01-01

    A general theory of atomic dipole coherence under the influence of collisional phase changes, inelastic effects and optically active atom velocity changes, including those due to anisotropic interactions is presented. Velocity change effects are obtained in closed form. Line shapes appear as convolutions of standard pressure broadening contours with velocity-change contours. Width and shift parameters for the He-broadened Na D lines at 2 m bar pressure, 380 K are calculated, as are He-induced photon echo decay rates for these lines. Overall agreement with xperiment is reasonably good.

  15. Soliton interaction in quadratic and cubic bulk media

    DEFF Research Database (Denmark)

    Johansen, Steffen Kjær; Bang, Ole

    2000-01-01

    Summary form only given. The understanding of how and to what extend the cubic nonlinearity affects beam propagation and spatial soliton formation in quadratic media is of vital importance in fundamental and applied nonlinear physics. We consider beam propagation under type-I SHG conditions...... in lossless bulk second order nonlinear optical materials with a nonvanishing third order nonlinearity. It is known that in pure second order systems a single soliton can never collapse whereas in systems with both nonlinearities and that stable single soliton propagation can only in some circumstances...

  16. Optical nonlinearities of colloidal InP@ZnS core-shell quantum dots probed by Z-scan and two-photon excited emission

    International Nuclear Information System (INIS)

    Wawrzynczyk, Dominika; Szeremeta, Janusz; Samoc, Marek; Nyk, Marcin

    2015-01-01

    Spectrally resolved nonlinear optical properties of colloidal InP@ZnS core-shell quantum dots of various sizes were investigated with the Z-scan technique and two-photon fluorescence excitation method using a femtosecond laser system tunable in the range from 750 nm to 1600 nm. In principle, both techniques should provide comparable results and can be interchangeably used for determination of the nonlinear optical absorption parameters, finding maximal values of the cross sections and optimizing them. We have observed slight differences between the two-photon absorption cross sections measured by the two techniques and attributed them to the presence of non-radiative paths of absorption or relaxation. The most significant value of two-photon absorption cross section σ 2 for 4.3 nm size InP@ZnS quantum dot was equal to 2200 GM, while the two-photon excitation action cross section σ 2 Φ was found to be 682 GM at 880 nm. The properties of these cadmium-free colloidal quantum dots can be potentially useful for nonlinear bioimaging

  17. Ultrafast Mid-IR Nonlinear Optics in Gas-filled Hollow-core Photonic Crystal Fibers

    DEFF Research Database (Denmark)

    Habib, Selim

    Invention of hollow-core fiber has been proven an ideal medium to study light-gas interaction. Tight confinement of light inside hollowcore fiber allows unremitting and tailored interaction between light and gas over long distances. In this work, we used a special kind of hollowcore fiber − hollow......-core anti-resonant (HC-AR) fiber to study the various nonlinear effects filled with Raman free noble gas. One of the main striking features of HC-AR fiber is that ∼99.99% light can be guided inside the central hollow-core region, which significantly enhances damage threshold level. HC-AR fiber can sustain...... be tuned by simply changing the pressure of the gas while at the same time providing extremely wide transparency ranges. In this thesis, we propose several low-loss broadband guidance HC-AR fibers and investigate soliton-plasma dynamics using HC-AR fiber filled with noble gas in the mid-IR. The combined...

  18. Nonlinear performance of asymmetric coupler based on dual-core photonic crystal fiber: Towards sub-nanojoule solitonic ultrafast all-optical switching

    Science.gov (United States)

    Curilla, L.; Astrauskas, I.; Pugzlys, A.; Stajanca, P.; Pysz, D.; Uherek, F.; Baltuska, A.; Bugar, I.

    2018-05-01

    We demonstrate ultrafast soliton-based nonlinear balancing of dual-core asymmetry in highly nonlinear photonic crystal fiber at sub-nanojoule pulse energy level. The effect of fiber asymmetry was studied experimentally by selective excitation and monitoring of individual fiber cores at different wavelengths between 1500 nm and 1800 nm. Higher energy transfer rate to non-excited core was observed in the case of fast core excitation due to nonlinear asymmetry balancing of temporal solitons, which was confirmed by the dedicated numerical simulations based on the coupled generalized nonlinear Schrödinger equations. Moreover, the simulation results correspond qualitatively with the experimentally acquired dependences of the output dual-core extinction ratio on excitation energy and wavelength. In the case of 1800 nm fast core excitation, narrow band spectral intensity switching between the output channels was registered with contrast of 23 dB. The switching was achieved by the change of the excitation pulse energy in sub-nanojoule region. The performed detailed analysis of the nonlinear balancing of dual-core asymmetry in solitonic propagation regime opens new perspectives for the development of ultrafast nonlinear all-optical switching devices.

  19. Ultra-fast analog-to-digital converter based on a nonlinear triplexer and an optical coder with a photonic crystal structure.

    Science.gov (United States)

    Mehdizadeh, Farhad; Soroosh, Mohammad; Alipour-Banaei, Hamed; Farshidi, Ebrahim

    2017-03-01

    In this paper, we propose what we believe is a novel all-optical analog-to-digital converter (ADC) based on photonic crystals. The proposed structure is composed of a nonlinear triplexer and an optical coder. The nonlinear triplexer is for creating discrete levels in the continuous optical input signal, and the optical coder is for generating a 2-bit standard binary code out of the discrete levels coming from the nonlinear triplexer. Controlling the resonant mode of the resonant rings through optical intensity is the main objective and working mechanism of the proposed structure. The maximum delay time obtained for the proposed structure was about 5 ps and the total footprint is about 1520  μm2.

  20. Quadratic brackets from symplectic forms

    International Nuclear Information System (INIS)

    Alekseev, Anton Yu.; Todorov, Ivan T.

    1994-01-01

    We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite-dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is the appearance of quadratic Poisson brackets for group-like variables. It is believed that upon quantization they lead to quadratic exchange algebras. ((orig.))

  1. Students' Understanding of Quadratic Equations

    Science.gov (United States)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-01-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

  2. Initial post dynamic buckling of a quadratic-cubic column ...

    African Journals Online (AJOL)

    In this investigation, we determine the dynamic buckling load of an imperfect finite column resting on a mixed quadratic-cubic nonlinear elastic foundation trapped by an explicitly time dependent sinusoidally slowly varying dynamic load .The resultant coefficients are dynamically slowly varying and the formulation contains ...

  3. Gain scheduled linear quadratic control for quadcopter

    Science.gov (United States)

    Okasha, M.; Shah, J.; Fauzi, W.; Hanouf, Z.

    2017-12-01

    This study exploits the dynamics and control of quadcopters using Linear Quadratic Regulator (LQR) control approach. The quadcopter’s mathematical model is derived using the Newton-Euler method. It is a highly manoeuvrable, nonlinear, coupled with six degrees of freedom (DOF) model, which includes aerodynamics and detailed gyroscopic moments that are often ignored in many literatures. The linearized model is obtained and characterized by the heading angle (i.e. yaw angle) of the quadcopter. The adopted control approach utilizes LQR method to track several reference trajectories including circle and helix curves with significant variation in the yaw angle. The controller is modified to overcome difficulties related to the continuous changes in the operating points and eliminate chattering and discontinuity that is observed in the control input signal. Numerical non-linear simulations are performed using MATLAB and Simulink to illustrate to accuracy and effectiveness of the proposed controller.

  4. Large-scale sequential quadratic programming algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Eldersveld, S.K.

    1992-09-01

    The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.

  5. Elliptical As2Se3 filled core ultra-high-nonlinearity and polarization-maintaining photonic crystal fiber with double hexagonal lattice cladding

    Science.gov (United States)

    Li, Feng; He, Menghui; Zhang, Xuedian; Chang, Min; Wu, Zhizheng; Liu, Zheng; Chen, Hua

    2018-05-01

    A high birefringence and ultra-high nonlinearity photonic crystal fiber (PCF) is proposed, which is composed of an elliptical As2Se3-doped core and an inner cladding with hexagonal lattice. Optical properties of the PCF are simulated by the full-vector finite element method. The simulation results show that the high birefringence of ∼0.33, ultra-high-nonlinearity coefficient of 300757 W-1km-1 and the low confinement loss can be achieved in the proposed PCF simultaneously at the wavelength of 1.55 μm. Furthermore, by comparison with the other two materials (80PbO•20Ga2O3, As2S3) filled in the core, the As2Se3-doped PCF is found to have the highest birefringence and nonlinearity due to its higher refractive index and nonlinear refractive index. The flattened dispersion feature, as well as the low confinement loss of the proposed PCF structure make it suitable as a wide range of applications, such as the coherent optical communications, polarization-maintaining and nonlinear optics, etc.

  6. Nonlinear coupled mode approach for modeling counterpropagating solitons in the presence of disorder-induced multiple scattering in photonic crystal waveguides

    Science.gov (United States)

    Mann, Nishan; Hughes, Stephen

    2018-02-01

    We present the analytical and numerical details behind our recently published article [Phys. Rev. Lett. 118, 253901 (2017), 10.1103/PhysRevLett.118.253901], describing the impact of disorder-induced multiple scattering on counterpropagating solitons in photonic crystal waveguides. Unlike current nonlinear approaches using the coupled mode formalism, we account for the effects of intraunit cell multiple scattering. To solve the resulting system of coupled semilinear partial differential equations, we introduce a modified Crank-Nicolson-type norm-preserving implicit finite difference scheme inspired by the transfer matrix method. We provide estimates of the numerical dispersion characteristics of our scheme so that optimal step sizes can be chosen to either minimize numerical dispersion or to mimic the exact dispersion. We then show numerical results of a fundamental soliton propagating in the presence of multiple scattering to demonstrate that choosing a subunit cell spatial step size is critical in accurately capturing the effects of multiple scattering, and illustrate the stochastic nature of disorder by simulating soliton propagation in various instances of disordered photonic crystal waveguides. Our approach is easily extended to include a wide range of optical nonlinearities and is applicable to various photonic nanostructures where power propagation is bidirectional, either by choice, or as a result of multiple scattering.

  7. On Characterization of Quadratic Splines

    DEFF Research Database (Denmark)

    Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong

    2005-01-01

    that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general....

  8. A series of fluorene-based two-photon absorbing molecules: synthesis, linear and nonlinear characterization, and bioimaging

    Science.gov (United States)

    Andrade, Carolina D.; Yanez, Ciceron O.; Rodriguez, Luis; Belfield, Kevin D.

    2010-01-01

    The synthesis, structural, and photophysical characterization of a series of new fluorescent donor–acceptor and acceptor-acceptor molecules, based on the fluorenyl ring system, with two-photon absorbing properties is described. These new compounds exhibited large Stokes shifts, high fluorescent quantum yields, and, significantly, high two-photon absorption cross sections, making them well suited for two-photon fluorescence microscopy (2PFM) imaging. Confocal and two-photon fluorescence microscopy imaging of COS-7 and HCT 116 cells incubated with probe I showed endosomal selectivity, demonstrating the potential of this class of fluorescent probes in multiphoton fluorescence microscopy. PMID:20481596

  9. A bistriphenylamine-substituted spirobifluorene derivative exhibiting excellent nonlinearity/transparency/thermal stability trade-off and strong two-photon induced blue fluorescence

    Energy Technology Data Exchange (ETDEWEB)

    Yin, Hongyao [Department of Chemistry, Shanghai Normal University, Shanghai 200234 (China); Xiao, Haibo, E-mail: xiaohb@shnu.edu.cn [Department of Chemistry, Shanghai Normal University, Shanghai 200234 (China); Ding, Lei [Department of Chemistry, Shanghai Normal University, Shanghai 200234 (China); Zhang, Chun; Ren, Aiming [State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023 (China); Li, Bo [Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai 200241 (China)

    2015-02-01

    A spirobifluorene-bridged donor/donor chromophore, 2,7-bis-(4-(N,N-diphenylamino)phen-1-yl)-9,9′-spirobifluorene (SPF-TP), was found to combine excellent transparency in the near UV–visible region (λ{sub cut-off} ≤ 420 nm), large two-photon absorption cross-section (4.5 × 10{sup 3}GM) and high thermal stability (T{sub d} = 501 °C). In comparison to the reported two-photon absorption molecules, SPF-TP represents the best thermal stability so far described in the literature. The main electronic factors explaining the high two-photon absorption activities of SPF-TP were analyzed by theoretical calculations. Cyclic voltammograms were employed to explore the causes of the excellent transparency of SPF-TP. It was found that the spiroconjugation effect is responsible for the excellent nonlinearity/transparency/thermal stability trade-off in SPF-TP. In addition, SPF-TP is also a good two-photon induced blue fluorescent material with high fluorescence quantum yield (Φ = 0.90, in THF). - Highlights: • We report a molecule exhibiting excellent transparency. • The two-photon absorption cross-section is as large as 4.5 × 10{sup 3}GM. • The molecule exhibits excellent thermal stability. • The molecule is a good two-photon induced blue fluorescent material. • The spiroconjugation effect explains the excellent properties.

  10. A bistriphenylamine-substituted spirobifluorene derivative exhibiting excellent nonlinearity/transparency/thermal stability trade-off and strong two-photon induced blue fluorescence

    International Nuclear Information System (INIS)

    Yin, Hongyao; Xiao, Haibo; Ding, Lei; Zhang, Chun; Ren, Aiming; Li, Bo

    2015-01-01

    A spirobifluorene-bridged donor/donor chromophore, 2,7-bis-(4-(N,N-diphenylamino)phen-1-yl)-9,9′-spirobifluorene (SPF-TP), was found to combine excellent transparency in the near UV–visible region (λ cut-off  ≤ 420 nm), large two-photon absorption cross-section (4.5 × 10 3 GM) and high thermal stability (T d  = 501 °C). In comparison to the reported two-photon absorption molecules, SPF-TP represents the best thermal stability so far described in the literature. The main electronic factors explaining the high two-photon absorption activities of SPF-TP were analyzed by theoretical calculations. Cyclic voltammograms were employed to explore the causes of the excellent transparency of SPF-TP. It was found that the spiroconjugation effect is responsible for the excellent nonlinearity/transparency/thermal stability trade-off in SPF-TP. In addition, SPF-TP is also a good two-photon induced blue fluorescent material with high fluorescence quantum yield (Φ = 0.90, in THF). - Highlights: • We report a molecule exhibiting excellent transparency. • The two-photon absorption cross-section is as large as 4.5 × 10 3 GM. • The molecule exhibits excellent thermal stability. • The molecule is a good two-photon induced blue fluorescent material. • The spiroconjugation effect explains the excellent properties

  11. Bidirectional quantum teleportation of unknown photons using path-polarization intra-particle hybrid entanglement and controlled-unitary gates via cross-Kerr nonlinearity

    Science.gov (United States)

    Heo, Jino; Hong, Chang-Ho; Lim, Jong-In; Yang, Hyung-Jin

    2015-05-01

    We propose an arbitrary controlled-unitary (CU) gate and a bidirectional quantum teleportation (BQTP) scheme. The proposed CU gate utilizes photonic qubits (photons) with cross-Kerr nonlinearities (XKNLs), X-homodyne detectors, and linear optical elements, and consists of the consecutive operation of a controlled-path (C-path) gate and a gathering-path (G-path) gate. It is almost deterministic and feasible with current technology when a strong coherent state and weak XKNLs are employed. Based on the CU gate, we present a BQTP scheme that simultaneously teleports two unknown photons between distant users by transmitting only one photon in a path-polarization intra-particle hybrid entangled state. Consequently, it is possible to experimentally implement BQTP with a certain success probability using the proposed CU gate. Project supported by the Ministry of Science, ICT&Future Planning, Korea, under the C-ITRC (Convergence Information Technology Research Center) Support program (NIPA-2013-H0301-13-3007) supervised by the National IT Industry Promotion Agency.

  12. Nonlinear polarization dynamics in a weakly birefringent all-normal dispersion photonic crystal fiber : toward a practical coherent fiber supercontinuum laser

    DEFF Research Database (Denmark)

    Tu, Haohua; Liu, Yuan; Liu, Xiaomin

    2012-01-01

    Dispersion-flattened dispersion-decreased all-normal dispersion (DFDD-ANDi) photonic crystal fibers have been identified as promising candidates for high-spectral-power coherent supercontinuum (SC) generation. However, the effects of the unintentional birefringence of the fibers on the SC generat...... of polarization-maintaining DFDD-ANDi fibers to avoid these adverse effects in pursuing a practical coherent fiber SC laser.......Dispersion-flattened dispersion-decreased all-normal dispersion (DFDD-ANDi) photonic crystal fibers have been identified as promising candidates for high-spectral-power coherent supercontinuum (SC) generation. However, the effects of the unintentional birefringence of the fibers on the SC...... generation have been ignored. This birefringence is widely present in nonlinear non-polarization maintaining fibers with a typical core size of 2 µm, presumably due to the structural symmetry breaks introduced in the fiber drawing process. We find that an intrinsic form-birefringence on the order of 10...

  13. Dhage Iteration Method for Generalized Quadratic Functional Integral Equations

    Directory of Open Access Journals (Sweden)

    Bapurao C. Dhage

    2015-01-01

    Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.

  14. Nonlinear Dynamics of Photonics for Optical Signal Processing - Optical Frequency Conversion and Optical DSB-to-SSB Conversion

    Science.gov (United States)

    2015-09-17

    photonic system. ML: master laser; SL: slave laser; L; lens; PBS: polarizing beam splitter ; M: mirror; HW: half-wave plate; FR: Faraday rotator; V...microwave generation and stabilization, and photonic microwave amplification. 15. SUBJECT TERMS Non -linear Dynamics, Add-drop

  15. Distributed nonlinear optical response

    DEFF Research Database (Denmark)

    Nikolov, Nikola Ivanov

    2005-01-01

    of bound states of out of phase bright solitons and dark solitons. Also, the newly introduced analogy between the nonlocal cubic nonlinear and the quadratic nonlinear media, presented in paper B and Chapter 3 is discussed. In particular it supplies intuitive physical meaning of the formation of solitons...... in quadratic nonlinear media. In the second part of the report (Chapter 4), the possibility to obtain light with ultrabroad spectrum due to the interplay of many nonlinear effects based on cubic nonlinearity is investigated thoroughly. The contribution of stimulated Raman scattering, a delayed nonlinear...... a modified nonlinear Schroedinger model equation. Chapter 4 and papers D and E are dedicated to this part of the research....

  16. Qubit-qubit entanglement dynamics control via external classical pumping and Kerr nonlinearity mediated by a single detuned cavity field powered by two-photon processes

    Science.gov (United States)

    Ateto, M. S.

    2017-11-01

    The nonlinear time-dependent two-photon Hamiltonian of a couple of classically pumped independent qubits is analytically solved, and the corresponding time evolution unitary operator, in an exact form, is derived. Using the concurrence, entanglement dynamics between the qubits under the influence of a wide range of effective parameters are examined and, in detail, analyzed. Observations analysis is documented with aid of the field phase-space distribution Wigner function. A couple of initial qubit states is considered, namely similar excited states and a Bell-like pure state. It is demonstrated that an initial Bell-like pure state is as well typical initial qubits setting for robust, regular and a high degree of entanglement. Moreover, it is established that high-constant Kerr media represent an effective tool for generating periodical entanglement at fixed time cycles of maxima reach unity forever when qubits are initially in a Bell-like pure state. Further, it is showed that the medium strength of the classical pumping stimulates efficiently qubits entanglement, specially, when the interaction occurs off resonantly. However, the high-intensity pumping thermalizes the coherent distribution of photons, thus, the least photons number is used and, hence, the least minimum degree of qubits entanglement could be created. Furthermore, when the cavity field and external pumping are detuned, the external pumping acts like an auxiliary effective frequency for the cavity, as a result, the field Gaussian distribution acquires linear chirps, and consequently, more entanglement revivals appear in the same cycle during timescale.

  17. Stability in quadratic torsion theories

    Energy Technology Data Exchange (ETDEWEB)

    Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)

    2017-11-15

    We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

  18. Stability in quadratic torsion theories

    International Nuclear Information System (INIS)

    Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado

    2017-01-01

    We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

  19. Wavelength conversion, time demultiplexing and multicasting based on cross-phase modulation and four-wave mixing in dispersion-flattened highly nonlinear photonic crystal fiber

    International Nuclear Information System (INIS)

    Hui, Zhan-Qiang; Zhang, Jian-Guo

    2012-01-01

    We propose the use of cross-phase modulation (XPM) and four-wave mixing (FWM) in dispersion-flattened highly nonlinear photonic crystal fibers (HNL-PCFs) to implement the functionalities of wavelength conversion, simultaneous time demultiplexing and wavelength multicasting in optical time-division multiplexing (OTDM) systems. The experiments on wavelength conversion at 80 Gbit s −1 and OTDM demultiplexing from 80 to 10 Gbit s −1 with wavelength multicasting of two channels are successfully demonstrated to validate the proposed scheme, which are carried out by using two segments of dispersion-flattened HNL-PCFs with lengths of 100 and 50 m, respectively. Moreover, the bit error rate (BER) performance is also measured. The results show that our designed system can achieve a power penalty of less than 4.6 dB for two multicasting channels with a 24 nm wavelength span at the BER of 10 −9 when compared with the 10 Gbit/s back-to-back measurement. The proposed system is transparent to bit rate since only an ultrafast third-order nonlinear effect is used. The resulting configuration is compact, robust and reliable, benefiting from the use of dispersion-flattened HNL-PCFs with short lengths. This also makes the proposed system more flexible in the operational wavelengths than those based on dispersion-shifted fibers and traditional highly nonlinear fibers. (paper)

  20. VO{sub 2}-like thermo-optical switching effect in one-dimensional nonlinear defective photonic crystals

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Juan, E-mail: juanzhang@staff.shu.edu.cn, E-mail: ywang@siom.ac.cn; Zhang, Rongjun [Key Laboratory of Specialty Fiber Optics and Optical Access Networks, School of Communication and Information Engineering, Shanghai University, Shanghai 200072 (China); Wang, Yang, E-mail: juanzhang@staff.shu.edu.cn, E-mail: ywang@siom.ac.cn [Key Laboratory of High Power Laser Materials, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800 (China)

    2015-06-07

    A new approach to achieve VO{sub 2}-like thermo-optical switching in a one-dimensional photonic crystal by the combination of thermo-optical and optical Kerr effects was proposed and numerically demonstrated in this study. The switching temperature and the hysteresis width can be tuned in a wide temperature range. Steep transition, high optical contrast, and low pumping power can be achieved at the same time. This kind of one-dimensional photonic crystal-based bistable switch will be low-cost, easy-to-fabricate, and versatile in practical applications compared with traditional VO{sub 2}-type one.

  1. Enhanced Cerenkov second-harmonic generation in a planar nonlinear waveguide that reproduces a one-dimensional photonic bandgap structure

    International Nuclear Information System (INIS)

    Pezzetta, D.; Sibilia, C.; Bertolotti, M.; Ramponi, R.; Osellame, R.; Marangoni, M.; Haus, J. W.; Scalora, M.; Bloemer, M. J.; Bowden, C. M.

    2002-01-01

    Second-harmonic generation in the Cerenkov configuration is investigated under conditions for which the use of a linear grating fabricated on top of the waveguide reproduces a photonic bandgap structure. The fundamental mode of the guide at the fundamental frequency is tuned at the photonic band-edge resonance, thus producing great confinement and enhancement of the electromagnetic field inside the structure. The conversion efficiency achieved in both the forward and the backward directions is at least 1 order of magnitude greater than that of a conventional Cerenkov emission in a waveguide of the same length. An analysis of the tolerances of the grating period on the conversion efficiency is presented

  2. Design of Linear-Quadratic-Regulator for a CSTR process

    Science.gov (United States)

    Meghna, P. R.; Saranya, V.; Jaganatha Pandian, B.

    2017-11-01

    This paper aims at creating a Linear Quadratic Regulator (LQR) for a Continuous Stirred Tank Reactor (CSTR). A CSTR is a common process used in chemical industries. It is a highly non-linear system. Therefore, in order to create the gain feedback controller, the model is linearized. The controller is designed for the linearized model and the concentration and volume of the liquid in the reactor are kept at a constant value as required.

  3. Quadratic prediction of factor scores

    NARCIS (Netherlands)

    Wansbeek, T

    1999-01-01

    Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic

  4. On quadratic variation of martingales

    Indian Academy of Sciences (India)

    On quadratic variation of martingales. 459. The proof relied on the theory of stochastic integration. Subsequently, in Karandikar. [4], the formula was derived using only Doob's maximal inequality. Thus this could be the starting point for the development of stochastic calculus for continuous semimartingales without bringing in ...

  5. Quadratic divergences and dimensional regularisation

    International Nuclear Information System (INIS)

    Jack, I.; Jones, D.R.T.

    1990-01-01

    We present a detailed analysis of quadratic and quartic divergences in dimensionally regulated renormalisable theories. We perform explicit three-loop calculations for a general theory of scalars and fermions. We find that the higher-order quartic divergences are related to the lower-order ones by the renormalisation group β-functions. (orig.)

  6. Quadratic third-order tensor optimization problem with quadratic constraints

    Directory of Open Access Journals (Sweden)

    Lixing Yang

    2014-05-01

    Full Text Available Quadratically constrained quadratic programs (QQPs problems play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Semidenite programming (SDP relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation provides the exact optimal value, i.e., there is a zero duality gap. However, this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective.In this paper, we consider a certain QQP where the variable is neither vector nor matrix but a third-order tensor. This problem can be viewed as a generalization of the ordinary QQP with vector or matrix as it's variant. Under some mild conditions, we rst show that SDP relaxation provides exact optimal solutions for the original problem. Then we focus on two classes of homogeneous quadratic tensor programming problems which have no requirements on the constraints number. For one, we provide an easily implemental polynomial time algorithm to approximately solve the problem and discuss the approximation ratio. For the other, we show there is no gap between the SDP relaxation and itself.

  7. Diffusion Based Photon Mapping

    DEFF Research Database (Denmark)

    Schjøth, Lars; Fogh Olsen, Ole; Sporring, Jon

    2007-01-01

    . To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features......, while eliminating noise. We call our method diffusion based photon mapping....

  8. Diffusion Based Photon Mapping

    DEFF Research Database (Denmark)

    Schjøth, Lars; Olsen, Ole Fogh; Sporring, Jon

    2006-01-01

    . To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features......, while eliminating noise. We call our method diffusion based photon mapping....

  9. Nonlinear spectral imaging of human normal skin, basal cell carcinoma and squamous cell carcinoma based on two-photon excited fluorescence and second-harmonic generation

    Science.gov (United States)

    Xiong, S. Y.; Yang, J. G.; Zhuang, J.

    2011-10-01

    In this work, we use nonlinear spectral imaging based on two-photon excited fluorescence (TPEF) and second harmonic generation (SHG) for analyzing the morphology of collagen and elastin and their biochemical variations in basal cell carcinoma (BCC), squamous cell carcinoma (SCC) and normal skin tissue. It was found in this work that there existed apparent differences among BCC, SCC and normal skin in terms of their thickness of the keratin and epithelial layers, their size of elastic fibers, as well as their distribution and spectral characteristics of collagen. These differences can potentially be used to distinguish BCC and SCC from normal skin, and to discriminate between BCC and SCC, as well as to evaluate treatment responses.

  10. Air-guided photonic-crystal-fiber pulse-compression delivery of multimegawatt femtosecond laser output for nonlinear-optical imaging and neurosurgery

    Science.gov (United States)

    Lanin, Aleksandr A.; Fedotov, Il'ya V.; Sidorov-Biryukov, Dmitrii A.; Doronina-Amitonova, Lyubov V.; Ivashkina, Olga I.; Zots, Marina A.; Sun, Chi-Kuang; Ömer Ilday, F.; Fedotov, Andrei B.; Anokhin, Konstantin V.; Zheltikov, Aleksei M.

    2012-03-01

    Large-core hollow photonic-crystal fibers (PCFs) are shown to enable a fiber-format air-guided delivery of ultrashort infrared laser pulses for neurosurgery and nonlinear-optical imaging. With an appropriate dispersion precompensation, an anomalously dispersive 15-μm-core hollow PCF compresses 510-fs, 1070-nm light pulses to a pulse width of about 110 fs, providing a peak power in excess of 5 MW. The compressed PCF output is employed to induce a local photodisruption of corpus callosum tissues in mouse brain and is used to generate the third harmonic in brain tissues, which is captured by the PCF and delivered to a detector through the PCF cladding.

  11. Controllable nonlinearity in a dual-coupling optomechanical system under a weak-coupling regime

    Science.gov (United States)

    Zhu, Gui-Lei; Lü, Xin-You; Wan, Liang-Liang; Yin, Tai-Shuang; Bin, Qian; Wu, Ying

    2018-03-01

    Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Here we investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and quadratic coupling. Interestingly, a controllable optomechanical nonlinearity is obtained by applying a driving laser into the cavity. This controllable optomechanical nonlinearity can be enhanced into a strong coupling regime, even if the system is initially in the weak-coupling regime. Moreover, the system dissipation can be suppressed effectively, which allows the appearance of phonon sideband and photon blockade effects in the weak-coupling regime. This work may inspire the exploration of a dual-coupling optomechanical system as well as its applications in modern quantum science.

  12. Exact solutions to quadratic gravity

    Czech Academy of Sciences Publication Activity Database

    Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

    2017-01-01

    Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025

  13. On Quadratic Variation of Martingales

    Indian Academy of Sciences (India)

    where D ( [ 0 , ∞ ) , R ) denotes the class of real valued r.c.l.l. functions on [ 0 , ∞ ) such that for a locally square integrable martingale ( M t ) with r.c.l.l. paths,. Ψ ( M . ( ) ) = A . ( ). gives the quadratic variation process (written usually as [ M , M ] t ) of ( M t ) . We also show that this process ( A t ) is the unique increasing ...

  14. Exact solutions to quadratic gravity

    Czech Academy of Sciences Publication Activity Database

    Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

    2017-01-01

    Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025

  15. Extending the Scope of Robust Quadratic Optimization

    NARCIS (Netherlands)

    Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand

    In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in

  16. Entanglement analysis of a two-atom nonlinear Jaynes-Cummings model with nondegenerate two-photon transition, Kerr nonlinearity, and two-mode Stark shift

    Science.gov (United States)

    Baghshahi, H. R.; Tavassoly, M. K.; Faghihi, M. J.

    2014-12-01

    An entangled state, as an essential tool in quantum information processing, may be generated through the interaction between light and matter in cavity quantum electrodynamics. In this paper, we study the interaction between two two-level atoms and a two-mode field in an optical cavity enclosed by a medium with Kerr nonlinearity in the presence of a detuning parameter and Stark effect. It is assumed that the atom-field coupling and third-order susceptibility of the Kerr medium depend on the intensity of the light. In order to investigate the dynamics of the introduced system, we obtain the exact analytical form of the state vector of the considered atom-field system under initial conditions which may be prepared for the atoms (in a coherent superposition of their ground and upper states) and the fields (in a standard coherent state). Then, in order to evaluate the degree of entanglement between the subsystems, we investigate the dynamics of the entanglement by employing the entanglement of formation. Finally, we analyze in detail the influences of the Stark shift, the deformed Kerr medium, the intensity-dependent coupling, and also the detuning parameter on the behavior of this measure for different subsystems. The numerical results show that the amount of entanglement between the different subsystems can be controlled by choosing the evolved parameters appropriately.

  17. Entanglement analysis of a two-atom nonlinear Jaynes–Cummings model with nondegenerate two-photon transition, Kerr nonlinearity, and two-mode Stark shift

    International Nuclear Information System (INIS)

    Baghshahi, H R; Tavassoly, M K; Faghihi, M J

    2014-01-01

    An entangled state, as an essential tool in quantum information processing, may be generated through the interaction between light and matter in cavity quantum electrodynamics. In this paper, we study the interaction between two two-level atoms and a two-mode field in an optical cavity enclosed by a medium with Kerr nonlinearity in the presence of a detuning parameter and Stark effect. It is assumed that the atom–field coupling and third-order susceptibility of the Kerr medium depend on the intensity of the light. In order to investigate the dynamics of the introduced system, we obtain the exact analytical form of the state vector of the considered atom–field system under initial conditions which may be prepared for the atoms (in a coherent superposition of their ground and upper states) and the fields (in a standard coherent state). Then, in order to evaluate the degree of entanglement between the subsystems, we investigate the dynamics of the entanglement by employing the entanglement of formation. Finally, we analyze in detail the influences of the Stark shift, the deformed Kerr medium, the intensity-dependent coupling, and also the detuning parameter on the behavior of this measure for different subsystems. The numerical results show that the amount of entanglement between the different subsystems can be controlled by choosing the evolved parameters appropriately. (paper)

  18. Influence of dispersion of nonlinearity on coherent supercontinuum generation bandwidth in photonic crystal fibers pumped at 2 μm

    DEFF Research Database (Denmark)

    Klimczak, Mariusz; Siwicki, Bartlomiej; Zhou, Binbin

    2017-01-01

    Sources of spectrally broadband and coherent light are necessary for frequency metrology and ultrashort pulse generation. Near-infrared (NIR) wavelengths are practical for such devices because of the emergence of robust and reasonably priced femtosecond lasers operating in this part of spectrum...... lasers as pump sources, exceeding the 2400 nm barrier has proved a challenge. ANDi SC requires strong nonlinear response of the optical material, since self-phase modulation (SPM) and optical wave breaking (OWB) mediated four-wave mixing (FWM) are almost exclusively shaping the ANDi SC pulses. Flatness...

  19. Multi-photon absorption limits to heralded single photon sources

    Science.gov (United States)

    Husko, Chad A.; Clark, Alex S.; Collins, Matthew J.; De Rossi, Alfredo; Combrié, Sylvain; Lehoucq, Gaëlle; Rey, Isabella H.; Krauss, Thomas F.; Xiong, Chunle; Eggleton, Benjamin J.

    2013-01-01

    Single photons are of paramount importance to future quantum technologies, including quantum communication and computation. Nonlinear photonic devices using parametric processes offer a straightforward route to generating photons, however additional nonlinear processes may come into play and interfere with these sources. Here we analyse spontaneous four-wave mixing (SFWM) sources in the presence of multi-photon processes. We conduct experiments in silicon and gallium indium phosphide photonic crystal waveguides which display inherently different nonlinear absorption processes, namely two-photon (TPA) and three-photon absorption (ThPA), respectively. We develop a novel model capturing these diverse effects which is in excellent quantitative agreement with measurements of brightness, coincidence-to-accidental ratio (CAR) and second-order correlation function g(2)(0), showing that TPA imposes an intrinsic limit on heralded single photon sources. We build on these observations to devise a new metric, the quantum utility (QMU), enabling further optimisation of single photon sources. PMID:24186400

  20. Coherent states for quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes

    2011-01-01

    The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.

  1. Quadratic Variation by Markov Chains

    DEFF Research Database (Denmark)

    Hansen, Peter Reinhard; Horel, Guillaume

    We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...

  2. Factorization method of quadratic template

    Science.gov (United States)

    Kotyrba, Martin

    2017-07-01

    Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.

  3. Optimal control linear quadratic methods

    CERN Document Server

    Anderson, Brian D O

    2007-01-01

    This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the

  4. Limits to compression with cascaded quadratic soliton compressors

    DEFF Research Database (Denmark)

    Bache, Morten; Bang, Ole; Krolikowski, Wieslaw

    2008-01-01

    We study cascaded quadratic soliton compressors and address the physical mechanisms that limit the compression. A nonlocal model is derived, and the nonlocal response is shown to have an additional oscillatory component in the nonstationary regime when the group-velocity mismatch (GVM) is strong....... This inhibits efficient compression. Raman-like perturbations from the cascaded nonlinearity, competing cubic nonlinearities, higher-order dispersion, and soliton energy may also limit compression, and through realistic numerical simulations we point out when each factor becomes important. We find......, the simulations show that reaching single-cycle duration is ultimately inhibited by competing cubic nonlinearities as well as dispersive waves, that only show up when taking higher-order dispersion into account....

  5. Strained Silicon Photonics

    Directory of Open Access Journals (Sweden)

    Ralf B. Wehrspohn

    2012-05-01

    Full Text Available A review of recent progress in the field of strained silicon photonics is presented. The application of strain to waveguide and photonic crystal structures can be used to alter the linear and nonlinear optical properties of these devices. Here, methods for the fabrication of strained devices are summarized and recent examples of linear and nonlinear optical devices are discussed. Furthermore, the relation between strain and the enhancement of the second order nonlinear susceptibility is investigated, which may enable the construction of optically active photonic devices made of silicon.

  6. Photonic microwave carrier recovery using period-one nonlinear dynamics of semiconductor lasers for OFDM-RoF coherent detection.

    Science.gov (United States)

    Hung, Yu-Han; Yan, Jhih-Heng; Feng, Kai-Ming; Hwang, Sheng-Kwang

    2017-06-15

    This study investigates an all-optical scheme based on period-one (P1) nonlinear dynamics of semiconductor lasers, which regenerates the microwave carrier of an orthogonal frequency division multiplexing radio-over-fiber (OFDM-RoF) signal and uses it as a microwave local oscillator for coherent detection. Through the injection locking established between the OFDM-RoF signal and the P1 dynamics, frequency synchronization with highly preserved phase quality is inherently achieved between the recovered microwave carrier and the microwave carrier of the OFDM-RoF signal. A bit-error ratio down to 1.9×10-9 is achieved accordingly using the proposed scheme for coherent detection of a 32-GHz OFDM-RoF signal carrying 4  Gb/s 16-quadrature amplitude modulation data. No electronic microwave generators or electronic phase-locked loops are thus required. The proposed system can be operated up to at least 100 GHz and can be self-adapted to certain changes in the operating microwave frequency.

  7. Quadratically convergent MCSCF scheme using Fock operators

    International Nuclear Information System (INIS)

    Das, G.

    1981-01-01

    A quadratically convergent formulation of the MCSCF method using Fock operators is presented. Among its advantages the present formulation is quadratically convergent unlike the earlier ones based on Fock operators. In contrast to other quadratically convergent schemes as well as the one based on generalized Brillouin's theorem, this method leads easily to a hybrid scheme where the weakly coupled orbitals (such as the core) are handled purely by Fock equations, while the rest of the orbitals are treated by a quadratically convergent approach with a truncated virtual space obtained by the use of the corresponding Fock equations

  8. Geometrical and Graphical Solutions of Quadratic Equations.

    Science.gov (United States)

    Hornsby, E. John, Jr.

    1990-01-01

    Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

  9. Nonclassicality and entanglement criteria for bipartite optical fields characterized by quadratic detectors

    Czech Academy of Sciences Publication Activity Database

    Peřina Jr., J.; Arkhipov, I.I.; Michálek, Václav; Haderka, Ondřej

    2017-01-01

    Roč. 96, č. 4 (2017), s. 1-15, č. článku 043845. ISSN 2469-9926 Institutional support: RVO:68378271 Keywords : parametric down-conversion * photon statistic * bipartite optical fields * quadratic detectors Subject RIV: BH - Optics, Masers, Lasers OBOR OECD: Optics (including laser optics and quantum optics) Impact factor: 2.925, year: 2016

  10. Multiobjective Optimization Involving Quadratic Functions

    Directory of Open Access Journals (Sweden)

    Oscar Brito Augusto

    2014-01-01

    Full Text Available Multiobjective optimization is nowadays a word of order in engineering projects. Although the idea involved is simple, the implementation of any procedure to solve a general problem is not an easy task. Evolutionary algorithms are widespread as a satisfactory technique to find a candidate set for the solution. Usually they supply a discrete picture of the Pareto front even if this front is continuous. In this paper we propose three methods for solving unconstrained multiobjective optimization problems involving quadratic functions. In the first, for biobjective optimization defined in the bidimensional space, a continuous Pareto set is found analytically. In the second, applicable to multiobjective optimization, a condition test is proposed to check if a point in the decision space is Pareto optimum or not and, in the third, with functions defined in n-dimensional space, a direct noniterative algorithm is proposed to find the Pareto set. Simple problems highlight the suitability of the proposed methods.

  11. Two-Photon Fluorescence Microscopy Developed for Microgravity Fluid Physics

    Science.gov (United States)

    Fischer, David G.; Zimmerli, Gregory A.; Asipauskas, Marius

    2004-01-01

    Recent research efforts within the Microgravity Fluid Physics Branch of the NASA Glenn Research Center have necessitated the development of a microscope capable of high-resolution, three-dimensional imaging of intracellular structure and tissue morphology. Standard optical microscopy works well for thin samples, but it does not allow the imaging of thick samples because of severe degradation caused by out-of-focus object structure. Confocal microscopy, which is a laser-based scanning microscopy, provides improved three-dimensional imaging and true optical sectioning by excluding the out-of-focus light. However, in confocal microscopy, out-of-focus object structure is still illuminated by the incoming beam, which can lead to substantial photo-bleaching. In addition, confocal microscopy is plagued by limited penetration depth, signal loss due to the presence of a confocal pinhole, and the possibility of live-cell damage. Two-photon microscopy is a novel form of laser-based scanning microscopy that allows three-dimensional imaging without many of the problems inherent in confocal microscopy. Unlike one-photon microscopy, it utilizes the nonlinear absorption of two near-infrared photons. However, the efficiency of two-photon absorption is much lower than that of one-photon absorption because of the nonlinear (i.e., quadratic) electric field dependence, so an ultrafast pulsed laser source must typically be employed. On the other hand, this stringent energy density requirement effectively localizes fluorophore excitation to the focal volume. Consequently, two-photon microscopy provides optical sectioning and confocal performance without the need for a signal-limiting pinhole. In addition, there is a reduction in photo-damage because of the longer excitation wavelength, a reduction in background fluorescence, and a 4 increase in penetration depth over confocal methods because of the reduction in Rayleigh scattering.

  12. Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

    DEFF Research Database (Denmark)

    Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog

    2012-01-01

    In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....

  13. Quadratic independence of coordinate functions of certain ...

    Indian Academy of Sciences (India)

    ... are `quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on C ( M ) such that the action leaves invariant the linear span of the above coordinate functions.

  14. Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...

    African Journals Online (AJOL)

    Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...

  15. An example in linear quadratic optimal control

    NARCIS (Netherlands)

    Weiss, George; Zwart, Heiko J.

    1998-01-01

    We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme

  16. Quadratic Boost A-Source Impedance Network

    DEFF Research Database (Denmark)

    Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii

    2016-01-01

    A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance...

  17. Diffusion Based Photon Mapping

    DEFF Research Database (Denmark)

    Schjøth, Lars; Sporring, Jon; Fogh Olsen, Ole

    2008-01-01

    . To address this problem, we introduce a photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way, we preserve important illumination features, while...

  18. Designing microstructured polymer optical fibers for cascaded quadratic soliton compression of femtosecond pulses

    DEFF Research Database (Denmark)

    Bache, Morten

    2009-01-01

    The dispersion of index-guiding microstructured polymer optical fibers is calculated for second-harmonic generation. The quadratic nonlinearity is assumed to come from poling of the polymer, which in this study is chosen to be the cyclic olefin copolymer Topas. We found a very large phase mismatc...

  19. Molecular design for nonpolar chiral-axial quadratic nonlinear optics

    Science.gov (United States)

    Wiggers, Gregory A.

    In this thesis the hyperpolarizability of various multi-dimensional molecules is studied theoretically/computationally, with particular focus on the second-rank Kleinman-disallowed (KD) component of the hyperpolarizability. This component, which transforms as a second-rank traceless symmetric tensor, could be utilized in certain chiral-axial molecular alignment schemes to produce a bulk response. Nonpolar chiral-axial systems have been proposed in contrast to polar media, which utilize the vector component of the molecular hyperpolarizability and require parallel alignment of the molecular dipoles. Such parallel alignment of dipoles must be "frozen in" in order to overcome the natural tendency for dipoles to align anti-parallel. This limits the density of chromophores that can be loaded into a polar material. Nonpolar materials do not have such limits in theory. The two geometric classes of molecules that can most easily be incorporated into nonpolar chiral-uniaxial materials are propeller-shaped (C3 or D3 symmetry) and Λ-shaped (C2v symmetry). This work describes efforts to design molecules within these classes that would be suitable for bulk NLO materials. The sum-over-states (SOS) expression is used to model the molecular hyperpolarizability, and quantum chemical calculations, along with linear absorption data (when available) provide the necessary parameters to evaluate truncated forms of the SOS expression. A host of chemical and geometric modifications will be considered in order to elucidate important structure/function relationships. Also, the SOS model will be tested in some cases when experimental measurements (via Kleinman-disallowed hyper-Rayleigh scattering) are available. While a majority of this work focuses on multi-dimensional molecules, a small section deals with the question of optimizing the hyperpolarizability of a one-dimensional system. It is suggested that the recently-proposed idea of "modulated conjugation" as a means for improving intrinsic molecular hyperpolarizability is based on subtle misinterpretations of computational results. Even so, the concept of modulated conjugation may lead to improved hyperpolarizabilities and possible reasons are discussed.

  20. Diagonalizing quadratic bosonic operators by non-autonomous flow equations

    CERN Document Server

    Bach, Volker

    2016-01-01

    The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocketâe"Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.

  1. Quadratic Hedging of Basis Risk

    Directory of Open Access Journals (Sweden)

    Hardy Hulley

    2015-02-01

    Full Text Available This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.

  2. linear-quadratic-linear model

    Directory of Open Access Journals (Sweden)

    Tanwiwat Jaikuna

    2017-02-01

    Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.

  3. Generation and dynamics of quadratic birefringent spatial gap solitons

    International Nuclear Information System (INIS)

    Anghel-Vasilescu, P.; Dorignac, J.; Geniet, F.; Leon, J.; Taki, A.

    2011-01-01

    A method is proposed to generate and study the dynamics of spatial light solitons in a birefringent medium with quadratic nonlinearity. Although no analytical expression for propagating solitons has been obtained, our numerical simulations show the existence of stable localized spatial solitons in the frequency forbidden band gap of the medium. The dynamics of these objects is quite rich and manifests for instance elastic reflections, or inelastic collisions where two solitons merge and propagate as a single solitary wave. We derive the dynamics of the slowly varying envelopes of the three fields (second harmonic pump and two-component signal) and study this new system theoretically. We show that it does present a threshold for nonlinear supratransmission that can be calculated from a series expansion approach with a very high accuracy. Specific physical implications of our theoretical predictions are illustrated on LiGaTe 2 (LGT) crystals. Once irradiated by a cw laser beam of 10 μm wavelength, at an incidence beyond the extinction angle, such crystals will transmit light, in the form of spatial solitons generated in the nonlinear regime above the nonlinear supratransmission threshold.

  4. Designing Camera Networks by Convex Quadratic Programming

    KAUST Repository

    Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao

    2015-01-01

    be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution

  5. Schur Stability Regions for Complex Quadratic Polynomials

    Science.gov (United States)

    Cheng, Sui Sun; Huang, Shao Yuan

    2010-01-01

    Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

  6. Quadratic Functionals with General Boundary Conditions

    International Nuclear Information System (INIS)

    Dosla, Z.; Dosly, O.

    1997-01-01

    The purpose of this paper is to give the Reid 'Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in terms of Riccati equation solutions

  7. Linear quadratic optimization for positive LTI system

    Science.gov (United States)

    Muhafzan, Yenti, Syafrida Wirma; Zulakmal

    2017-05-01

    Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.

  8. Radiotherapy treatment planning linear-quadratic radiobiology

    CERN Document Server

    Chapman, J Donald

    2015-01-01

    Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil

  9. Classification of ξ(s)-Quadratic Stochastic Operators on 2D simplex

    International Nuclear Information System (INIS)

    Mukhamedov, Farrukh; Saburov, Mansoor; Qaralleh, Izzat

    2013-01-01

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some QSO has been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for the quadratic stochastic operators. To study this problem it was investigated several classes of such QSO. In this paper we study ξ (s) -QSO class of operators. We study such kind of operators on 2D simplex. We first classify these ξ (s) -QSO into 20 classes. Further, we investigate the dynamics of one class of such operators.

  10. Nonlinear diffraction from a virtual beam

    DEFF Research Database (Denmark)

    Saltiel, Solomon M.; Neshev, Dragomir N.; Krolikowski, Wieslaw

    2010-01-01

    We observe experimentally a novel type of nonlinear diffraction in the process of two-wave mixing on a nonlinear quadratic grating.We demonstrate that when the nonlinear grating is illuminated simultaneously by two noncollinear beams, a second-harmonic diffraction pattern is generated by a virtual...... beam propagating along the bisector of the two pump beams. The observed iffraction phenomena is a purely nonlinear effect that has no analogue in linear diffraction...

  11. Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension

    International Nuclear Information System (INIS)

    Qu Gai-Zhu; Zhang Shun-Li; Li Yao-Long

    2014-01-01

    In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators. (general)

  12. Micro and nano lasers for digital photonics

    NARCIS (Netherlands)

    Hill, M.T.; Oei, Y.S.; Zhu, Y.C.; Smit, M.K.

    2007-01-01

    The small size, low-power and high-speed of nano-lasers make them an attractive nonlinear element for digital photonics. Further miniaturization of lasers below the diffraction limit is required before digital photonics can compete with electronics.

  13. Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

    DEFF Research Database (Denmark)

    Guo, Hairun; Zeng, Xianglong; Zhou, Binbin

    2013-01-01

    We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...

  14. Photon-photon interactions

    International Nuclear Information System (INIS)

    Gilman, F.J.

    1980-01-01

    A brief summary of the present status of photon-photon interactions is presented. Stress is placed on the use of two-photon collisions to test present ideas on the quark constituents of hadrons and on the theory of strong interactions

  15. Vacuum solutions of Bianchi cosmologies in quadratic gravity

    International Nuclear Information System (INIS)

    Deus, Juliano Alves de; Muller, Daniel

    2011-01-01

    Full text: In this work we solve numerically the vacuum solutions of field equations of Bianchi homogeneous universes in the context of Semiclassical theory. Our interest is to study the quadratic theory of gravity with regard in the cosmological description of our universe in periods of intense fields. Bianchi cosmologies are anisotropic homogeneous cosmological models, but can include the isotropic models as particular cases (Bianchi I, VII and IX include homogeneous and isotropic Friedmann models plane, hyperbolic and spherical, respectively). Homogeneous models are good cosmological representations of our universe. With focus in solutions for intense fields, like the early universe, where isotropy is not necessarily required, the adopted scenario is the vacuum solutions, where the geometry is dominant in determining the gravitation. Still following in this way, the Semiclassical theory, which considers quantum matter fields propagating in classical geometrical background, is addressed to give the field equations. This formalism leads to fourth-order ordinary differential equations, in contrast to second-order equations from General Relativity. The Lagrangian of the theory is quadratic in the Ricci scalar and in the Ricci tensor. The equations system is highly non-linear and can be only numerically solved, except perhaps for few particular cases. We obtained numerical solutions for Bianchi V II A evolving to Minkowski and to de Sitter solutions, and also to singularities. The both first and second solutions were obtained choosing initial conditions near from respective exact vacuum solutions from Einstein theory, which are also exact solutions of the quadratic theory. Other Bianchi types are still under study. (author)

  16. Linear-quadratic control and quadratic differential forms for multidimensional behaviors

    NARCIS (Netherlands)

    Napp, D.; Trentelman, H.L.

    2011-01-01

    This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look

  17. Polyhedral combinatorics of the cardinality constrained quadratic knapsack problem and the quadratic selective travelling salesman problem

    DEFF Research Database (Denmark)

    Mak, Vicky; Thomadsen, Tommy

    2006-01-01

    This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...

  18. STRUCTURE OPTIMIZATION OF RESERVATION BY PRECISE QUADRATIC REGULARIZATION

    Directory of Open Access Journals (Sweden)

    KOSOLAP A. I.

    2015-11-01

    Full Text Available The problem of optimization of the structure of systems redundancy elements. Such problems arise in the design of complex systems. To improve the reliability of operation of such systems of its elements are duplicated. This increases system cost and improves its reliability. When optimizing these systems is maximized probability of failure of the entire system while limiting its cost or the cost is minimized for a given probability of failure-free operation. A mathematical model of the problem is a discrete backup multiextremal. To search for the global extremum of currently used methods of Lagrange multipliers, coordinate descent, dynamic programming, random search. These methods guarantee a just and local solutions are used in the backup tasks of small dimension. In the work for solving redundancy uses a new method for accurate quadratic regularization. This method allows you to convert the original discrete problem to the maximization of multi vector norm on a convex set. This means that the diversity of the tasks given to the problem of redundancy maximize vector norm on a convex set. To solve the problem, a reformed straightdual interior point methods. Currently, it is the best method for local optimization of nonlinear problems. Transformed the task includes a new auxiliary variable, which is determined by dichotomy. There have been numerous comparative numerical experiments in problems with the number of redundant subsystems to one hundred. These experiments confirm the effectiveness of the method of precise quadratic regularization for solving problems of redundancy.

  19. On bent and semi-bent quadratic Boolean functions

    DEFF Research Database (Denmark)

    Charpin, P.; Pasalic, Enes; Tavernier, C.

    2005-01-01

    correlation and high nonlinearity. We say that such a sequence is generated by a semi-bent function. Some new families of such function, represented by f(x) = Sigma(i=1)(n-1/2) c(i)Tr(x(2t+1)), n odd and c(i) is an element of F-2, have recently (2002) been introduced by Khoo et al. We first generalize......The maximum-length sequences, also called m-sequences, have received a lot of attention since the late 1960s. In terms of linear-feedback shift register (LFSR) synthesis they are usually generated by certain power polynomials over a finite field and in addition are characterized by a low cross...... their results to even n. We further investigate the conditions on the choice of ci for explicit definitions of new infinite families having three and four trace terms. Also, a class of nonpermutation polynomials whose composition with a quadratic function yields again a quadratic semi-bent function is specified...

  20. Engineered nonlinear lattices

    DEFF Research Database (Denmark)

    Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.

    1999-01-01

    We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...... discrete equation. The proposed structure therefore provides an experimental setting for exploring discrete effects in a controlled manner. In particular, we show propagation of breathers that are eventually trapped by discreteness. When the stripes are wide the beams evolve in a structure we term...

  1. Complete modulational-instability gain spectrum of nonlinear quasi-phase-matching gratings

    DEFF Research Database (Denmark)

    Corney, Joel F.; Bang, Ole

    2004-01-01

    We consider plane waves propagating in quadratic nonlinear slab waveguides with nonlinear quasi-phasematching gratings. We predict analytically and verify numerically the complete gain spectrum for transverse modulational instability, including hitherto undescribed higher-order gain bands....

  2. Optimal Piecewise-Linear Approximation of the Quadratic Chaotic Dynamics

    Directory of Open Access Journals (Sweden)

    J. Petrzela

    2012-04-01

    Full Text Available This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provided

  3. Wind turbine power tracking using an improved multimodel quadratic approach.

    Science.gov (United States)

    Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier

    2010-07-01

    In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables. 2010 ISA. Published by Elsevier Ltd. All rights reserved.

  4. Photon–phonon parametric oscillation induced by quadratic coupling in an optomechanical resonator

    International Nuclear Information System (INIS)

    Zhang, Lin; Ji, Fengzhou; Zhang, Xu; Zhang, Weiping

    2017-01-01

    A direct photon–phonon parametric effect of quadratic coupling on the mean-field dynamics of an optomechanical resonator in the large-scale-movement regime is found and investigated. Under a weak pumping power, the mechanical resonator damps to a steady state with a nonlinear static response sensitively modified by the quadratic coupling. When the driving power increases beyond the static energy balance, the steady states lose their stabilities via Hopf bifurcations, and the resonator produces stable self-sustained oscillation (limit-circle behavior) of discrete energies with step-like amplitudes due to the parametric effect of quadratic coupling, which can be understood roughly by the power balance between gain and loss on the resonator. A further increase in the pumping power can induce a chaotic dynamic of the resonator via a typical routine of period-doubling bifurcation, but which can be stabilized by the parametric effect through an inversion-bifurcation process back to the limit-circle states. The bifurcation-to-inverse-bifurcation transitions are numerically verified by the maximal Lyapunov exponents of the dynamics, which indicate an efficient way of suppressing the chaotic behavior of the optomechanical resonator by quadratic coupling. Furthermore, the parametric effect of quadratic coupling on the dynamic transitions of an optomechanical resonator can be conveniently detected or traced by the output power spectrum of the cavity field. (paper)

  5. Indirect quantum tomography of quadratic Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)

    2011-01-15

    A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

  6. PSQP: Puzzle Solving by Quadratic Programming.

    Science.gov (United States)

    Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

    2017-02-01

    In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

  7. On orthogonality preserving quadratic stochastic operators

    Energy Technology Data Exchange (ETDEWEB)

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)

    2015-05-15

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

  8. Bound constrained quadratic programming via piecewise

    DEFF Research Database (Denmark)

    Madsen, Kaj; Nielsen, Hans Bruun; Pinar, M. C.

    1999-01-01

    of a symmetric, positive definite matrix, and is solved by Newton iteration with line search. The paper describes the algorithm and its implementation including estimation of lambda/sub 1/ , how to get a good starting point for the iteration, and up- and downdating of Cholesky factorization. Results of extensive......We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. It involves a lower bound of lambda/sub 1/ , the smallest eigenvalue...

  9. On orthogonality preserving quadratic stochastic operators

    International Nuclear Information System (INIS)

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

    2015-01-01

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too

  10. Eigenfunctions of quadratic hamiltonians in Wigner representation

    International Nuclear Information System (INIS)

    Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.

    1984-01-01

    Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail

  11. Nonlinear optics at interfaces

    International Nuclear Information System (INIS)

    Chen, C.K.

    1980-12-01

    Two aspects of surface nonlinear optics are explored in this thesis. The first part is a theoretical and experimental study of nonlinear intraction of surface plasmons and bulk photons at metal-dielectric interfaces. The second part is a demonstration and study of surface enhanced second harmonic generation at rough metal surfaces. A general formulation for nonlinear interaction of surface plasmons at metal-dielectric interfaces is presented and applied to both second and third order nonlinear processes. Experimental results for coherent second and third harmonic generation by surface plasmons and surface coherent antiStokes Raman spectroscopy (CARS) are shown to be in good agreement with the theory

  12. Photon-photon collisions

    International Nuclear Information System (INIS)

    Burke, D.L.

    1982-10-01

    Studies of photon-photon collisions are reviewed with particular emphasis on new results reported to this conference. These include results on light meson spectroscopy and deep inelastic e#betta# scattering. Considerable work has now been accumulated on resonance production by #betta##betta# collisions. Preliminary high statistics studies of the photon structure function F 2 /sup #betta#/(x,Q 2 ) are given and comments are made on the problems that remain to be solved

  13. Photon-photon collisions

    International Nuclear Information System (INIS)

    Haissinski, J.

    1986-06-01

    The discussions presented in this paper deal with the following points: distinctive features of gamma-gamma collisions; related processes; photon-photon elastic scattering in the continuum and γγ →gg; total cross section; γγ → V 1 V 2 (V=vector meson); radiative width measurements and light meson spectroscopy; exclusive channels at large /t/; jets and inclusive particle distribution in γγ collisions; and, the photon structure function F γ 2

  14. A nonlinear plate control without linearization

    Directory of Open Access Journals (Sweden)

    Yildirim Kenan

    2017-03-01

    Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

  15. Photon-photon colliders

    International Nuclear Information System (INIS)

    Sessler, A.M.

    1995-04-01

    Since the seminal work by Ginsburg, et at., the subject of giving the Next Linear Collider photon-photon capability, as well as electron-positron capability, has drawn much attention. A 1990 article by V.I. Teinov describes the situation at that time. In March 1994, the first workshop on this subject was held. This report briefly reviews the physics that can be achieved through the photon-photon channel and then focuses on the means of achieving such a collider. Also reviewed is the spectrum of backscattered Compton photons -- the best way of obtaining photons. We emphasize the spectrum actually obtained in a collider with both polarized electrons and photons (peaked at high energy and very different from a Compton spectrum). Luminosity is estimated for the presently considered colliders, and interaction and conversion-point geometries are described. Also specified are laser requirements (such as wavelength, peak power, and average power) and the lasers that might be employed. These include conventional and free-electron lasers. Finally, we describe the R ampersand D necessary to make either of these approaches viable and explore the use of the SLC as a test bed for a photon-photon collider of very high energy

  16. Quadratic mass relations in topological bootstrap theory

    International Nuclear Information System (INIS)

    Jones, C.E.; Uschersohn, J.

    1980-01-01

    From the requirement of reality of discontinuities of scattering amplitudes at the spherical level of the topological bootstrap theory, a large number of mass relations for hadrons is derived. Quadratic mass formulas for the symmetry-breaking pattern of both mesons and baryon is obtained and their relation to conventional models of symmetry breaking is briefly discussed

  17. STABILIZED SEQUENTIAL QUADRATIC PROGRAMMING: A SURVEY

    Directory of Open Access Journals (Sweden)

    Damián Fernández

    2014-12-01

    Full Text Available We review the motivation for, the current state-of-the-art in convergence results, and some open questions concerning the stabilized version of the sequential quadratic programming algorithm for constrained optimization. We also discuss the tools required for its local convergence analysis, globalization challenges, and extentions of the method to the more general variational problems.

  18. The Quadratic Selective Travelling Salesman Problem

    DEFF Research Database (Denmark)

    Thomadsen, Tommy; Stidsen, Thomas K.

    2003-01-01

    A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional...

  19. Fundamental quadratic variational principle underlying general relativity

    International Nuclear Information System (INIS)

    Atkins, W.K.

    1983-01-01

    The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed

  20. Investigating Students' Mathematical Difficulties with Quadratic Equations

    Science.gov (United States)

    O'Connor, Bronwyn Reid; Norton, Stephen

    2016-01-01

    This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…

  1. Commuting quantum traces for quadratic algebras

    International Nuclear Information System (INIS)

    Nagy, Zoltan; Avan, Jean; Doikou, Anastasia; Rollet, Genevieve

    2005-01-01

    Consistent tensor products on auxiliary spaces, hereafter denoted 'fusion procedures', and commuting transfer matrices are defined for general quadratic algebras, nondynamical and dynamical, inspired by results on reflection algebras. Applications of these procedures then yield integer-indexed families of commuting Hamiltonians

  2. Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients

    Directory of Open Access Journals (Sweden)

    Xue-Gang Zhou

    2014-01-01

    Full Text Available The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.

  3. Quadratic Plus Linear Operators which Preserve Pure States of Quantum Systems: Small Dimensions

    International Nuclear Information System (INIS)

    Saburov, Mansoor

    2014-01-01

    A mathematical formalism of quantum mechanics says that a pure state of a quantum system corresponds to a vector of norm 1 and an observable is a self-adjoint operator on the space of states. It is of interest to describe all linear or nonlinear operators which preserve the pure states of the system. In the linear case, it is nothing more than isometries of Hilbert spaces. In the nonlinear case, this problem was open. In this paper, in the small dimensional spaces, we shall describe all quadratic plus linear operators which preserve pure states of the quantum system

  4. Dressing method and quadratic bundles related to symmetric spaces. Vanishing boundary conditions

    Science.gov (United States)

    Valchev, T. I.

    2016-02-01

    We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m + n)/S(U(m) × U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear Schrödinger equation which serves as a motivational example for our general considerations. We extensively discuss how one can apply Zakharov-Shabat's dressing procedure to derive reflectionless potentials obeying zero boundary conditions. Those could be used for one to construct fast decaying solutions to any nonlinear equation belonging to the same hierarchy. One can distinguish between generic soliton type solutions and rational solutions.

  5. Gain-scheduled Linear Quadratic Control of Wind Turbines Operating at High Wind Speed

    DEFF Research Database (Denmark)

    Østergaard, Kasper Zinck; Stoustrup, Jakob; Brath, Per

    2007-01-01

    This paper addresses state estimation and linear quadratic (LQ) control of variable speed variable pitch wind turbines. On the basis of a nonlinear model of a wind turbine, a set of operating conditions is identified and a LQ controller is designed for each operating point. The controller gains...... are then interpolated linearly to get a control law for the entire operating envelope. A nonlinear state estimator is designed as a combination of two unscented Kalman filters and a linear disturbance estimator. The gain-scheduling variable (wind speed) is then calculated from the output of these state estimators...

  6. Linear quadratic Gaussian controller design for plasma current, position and shape control system in ITER

    International Nuclear Information System (INIS)

    Belyakov, V.; Kavin, A.; Rumyantsev, E.; Kharitonov, V.; Misenov, B.; Ovsyannikov, A.; Ovsyannikov, D.; Veremei, E.; Zhabko, A.; Mitrishkin, Y.

    1999-01-01

    This paper is focused on the linear quadratic Gaussian (LQG) controller synthesis methodology for the ITER plasma current, position and shape control system as well as power derivative management system. It has been shown that some poloidal field (PF) coils have less influence on reference plasma-wall gaps control during plasma disturbances and hence they have been used to reduce total control power derivative by means of the additional non-linear feedback. The design has been done on the basis of linear models. Simulation was provided for non-linear model and results are presented and discussed. (orig.)

  7. Progress in neuromorphic photonics

    Science.gov (United States)

    Ferreira de Lima, Thomas; Shastri, Bhavin J.; Tait, Alexander N.; Nahmias, Mitchell A.; Prucnal, Paul R.

    2017-03-01

    As society's appetite for information continues to grow, so does our need to process this information with increasing speed and versatility. Many believe that the one-size-fits-all solution of digital electronics is becoming a limiting factor in certain areas such as data links, cognitive radio, and ultrafast control. Analog photonic devices have found relatively simple signal processing niches where electronics can no longer provide sufficient speed and reconfigurability. Recently, the landscape for commercially manufacturable photonic chips has been changing rapidly and now promises to achieve economies of scale previously enjoyed solely by microelectronics. By bridging the mathematical prowess of artificial neural networks to the underlying physics of optoelectronic devices, neuromorphic photonics could breach new domains of information processing demanding significant complexity, low cost, and unmatched speed. In this article, we review the progress in neuromorphic photonics, focusing on photonic integrated devices. The challenges and design rules for optoelectronic instantiation of artificial neurons are presented. The proposed photonic architecture revolves around the processing network node composed of two parts: a nonlinear element and a network interface. We then survey excitable lasers in the recent literature as candidates for the nonlinear node and microring-resonator weight banks as the network interface. Finally, we compare metrics between neuromorphic electronics and neuromorphic photonics and discuss potential applications.

  8. Geometric Approaches to Quadratic Equations from Other Times and Places.

    Science.gov (United States)

    Allaire, Patricia R.; Bradley, Robert E.

    2001-01-01

    Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

  9. Coherent states of systems with quadratic Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica

    2015-06-15

    Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)

  10. Coherent states of systems with quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.

    2015-01-01

    Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)

  11. On quadratic residue codes and hyperelliptic curves

    Directory of Open Access Journals (Sweden)

    David Joyner

    2008-01-01

    Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''

  12. Quaternion orders, quadratic forms, and Shimura curves

    CERN Document Server

    Alsina, Montserrat

    2004-01-01

    Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...

  13. Quadratic hamiltonians and relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.

    1981-01-01

    For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru

  14. Lambda-lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, O.; Schultz, U.P.

    2004-01-01

    -lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters......Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...

  15. Quadratic Interpolation and Linear Lifting Design

    Directory of Open Access Journals (Sweden)

    Joel Solé

    2007-03-01

    Full Text Available A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing the l2-norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.

  16. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2002-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

  17. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2003-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

  18. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2004-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

  19. Temporal quadratic expansion nodal Green's function method

    International Nuclear Information System (INIS)

    Liu Cong; Jing Xingqing; Xu Xiaolin

    2000-01-01

    A new approach is presented to efficiently solve the three-dimensional space-time reactor dynamics equation which overcomes the disadvantages of current methods. In the Temporal Quadratic Expansion Nodal Green's Function Method (TQE/NGFM), the Quadratic Expansion Method (QEM) is used for the temporal solution with the Nodal Green's Function Method (NGFM) employed for the spatial solution. Test calculational results using TQE/NGFM show that its time step size can be 5-20 times larger than that of the Fully Implicit Method (FIM) for similar precision. Additionally, the spatial mesh size with NGFM can be nearly 20 times larger than that using the finite difference method. So, TQE/NGFM is proved to be an efficient reactor dynamics analysis method

  20. Quadratic Term Structure Models in Discrete Time

    OpenAIRE

    Marco Realdon

    2006-01-01

    This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a r...

  1. Least Squares Problems with Absolute Quadratic Constraints

    Directory of Open Access Journals (Sweden)

    R. Schöne

    2012-01-01

    Full Text Available This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.

  2. Stochastic Linear Quadratic Optimal Control Problems

    International Nuclear Information System (INIS)

    Chen, S.; Yong, J.

    2001-01-01

    This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well

  3. Advances and challenges in label-free nonlinear optical imaging using two-photon excitation fluorescence and second harmonic generation for cancer research

    NARCIS (Netherlands)

    Thomas, Giju; van Voskuilen, Johan; Gerritsen, Hans C.; Sterenborg, H. J. C. M.

    2014-01-01

    Nonlinear optical imaging (NLOI) has emerged to be a promising tool for bio-medical imaging in recent times. Among the various applications of NLOI, its utility is the most significant in the field of pre-clinical and clinical cancer research. This review begins by briefly covering the core

  4. Quadratic tracer dynamical models tobacco growth

    International Nuclear Information System (INIS)

    Qiang Jiyi; Hua Cuncai; Wang Shaohua

    2011-01-01

    In order to study the non-uniformly transferring process of some tracer dosages, we assume that the absorption of some tracer by tobacco is a quadratic function of the tracer quantity of the tracer in the case of fast absorption, whereas the exclusion of the tracer from tobacco is a linear function of the tracer quantity in the case of slow exclusion, after the tracer is introduced into tobacco once at zero time. A single-compartment quadratic dynamical model of Logistic type is established for the leaves of tobacco. Then, a two-compartment quadratic dynamical model is established for leaves and calms of the tobacco. Qualitative analysis of the models shows that the tracer applied to the leaves of the tobacco is excluded finally; however, the tracer stays at the tobacco for finite time. Two methods are also given for computing the parameters in the models. Finally, the results of the models are verified by the 32 P experiment for the absorption of tobacco. (authors)

  5. A Finite Continuation Algorithm for Bound Constrained Quadratic Programming

    DEFF Research Database (Denmark)

    Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.

    1999-01-01

    The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...

  6. Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

    Science.gov (United States)

    Laine, A. D.

    2015-01-01

    There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

  7. Estimation of bone Calcium-to-Phosphorous mass ratio using dual-energy nonlinear polynomial functions

    International Nuclear Information System (INIS)

    Sotiropoulou, P; Koukou, V; Martini, N; Nikiforidis, G; Michail, C; Kandarakis, I; Fountos, G; Kounadi, E

    2015-01-01

    In this study an analytical approximation of dual-energy inverse functions is presented for the estimation of the calcium-to-phosphorous (Ca/P) mass ratio, which is a crucial parameter in bone health. Bone quality could be examined by the X-ray dual-energy method (XDEM), in terms of bone tissue material properties. Low- and high-energy, log- intensity measurements were combined by using a nonlinear function, to cancel out the soft tissue structures and generate the dual energy bone Ca/P mass ratio. The dual-energy simulated data were obtained using variable Ca and PO 4 thicknesses on a fixed total tissue thickness. The XDEM simulations were based on a bone phantom. Inverse fitting functions with least-squares estimation were used to obtain the fitting coefficients and to calculate the thickness of each material. The examined inverse mapping functions were linear, quadratic, and cubic. For every thickness, the nonlinear quadratic function provided the optimal fitting accuracy while requiring relative few terms. The dual-energy method, simulated in this work could be used to quantify bone Ca/P mass ratio with photon-counting detectors. (paper)

  8. Photon-photon collisions

    Energy Technology Data Exchange (ETDEWEB)

    Brodsky, S.J.

    1985-01-01

    The study of photon-photon collisions has progressed enormously, stimulated by new data and new calculational tools for QCD. In the future we can expect precise determinations of ..cap alpha../sub s/ and ..lambda../sup ms/ from the ..gamma..*..gamma.. ..-->.. ..pi../sup 0/ form factor and the photon structure function, as well as detailed checks of QCD, determination of the shape of the hadron distribution amplitudes from ..gamma gamma.. ..-->.. H anti H, reconstruction of sigma/sub ..gamma gamma../ from exclusive channels at low W/sub ..gamma gamma../, definitive studies of high p/sub T/ hadron and jet production, and studies of threshold production of charmed systems. Photon-photon collisions, along with radiative decays of the psi and UPSILON, are ideal for the study of multiquark and gluonic resonances. We have emphasized the potential for resonance formation near threshold in virtually every hadronic exclusive channel, including heavy quark states c anti c c anti c, c anti c u anti u, etc. At higher energies SLC, LEP, ...) parity-violating electroweak effects and Higgs production due to equivalent Z/sup 0/ and W/sup + -/ beams from e ..-->.. eZ/sup 0/ and e ..-->.. nu W will become important. 44 references.

  9. Photon-photon collisions

    International Nuclear Information System (INIS)

    Brodsky, S.J.

    1985-01-01

    The study of photon-photon collisions has progressed enormously, stimulated by new data and new calculational tools for QCD. In the future we can expect precise determinations of α/sub s/ and Λ/sup ms/ from the γ*γ → π 0 form factor and the photon structure function, as well as detailed checks of QCD, determination of the shape of the hadron distribution amplitudes from γγ → H anti H, reconstruction of sigma/sub γγ/ from exclusive channels at low W/sub γγ/, definitive studies of high p/sub T/ hadron and jet production, and studies of threshold production of charmed systems. Photon-photon collisions, along with radiative decays of the psi and UPSILON, are ideal for the study of multiquark and gluonic resonances. We have emphasized the potential for resonance formation near threshold in virtually every hadronic exclusive channel, including heavy quark states c anti c c anti c, c anti c u anti u, etc. At higher energies SLC, LEP, ...) parity-violating electroweak effects and Higgs production due to equivalent Z 0 and W +- beams from e → eZ 0 and e → nu W will become important. 44 references

  10. Photon-photon collisions

    International Nuclear Information System (INIS)

    Field, J.H.

    1984-01-01

    The current status, both theoretical and experimental, of two photon collision physics is reviewed with special emphasis on recent experimental results from e + e - storage rings. After a complete presentation of the helicity amplitude formalism for the general process e + e - → Xe + e - , various approximations (transverse photon, Weisaecker Williams) are discussed. Beam polarisation effects and radiative corrections are also briefly considered. A number of specific processes, for which experimental results are now available, are then described. In each case existing theoretical prediction are confronted with experimental results. The processes described include single resonance production, lepton and hadron pair production, the structure functions of the photon, the production of high Psub(T) jets and the total photon photon cross section. In the last part of the review the current status of the subject is summarised and some comments are made on future prospects. These include both extrapolations of current research to higher energy machines (LEP, HERA) as well as a brief mention of both the technical realisation and the physics interest of the real γγ and eγ collisions which may be possible using linear electron colliders in the 1 TeV energy range

  11. Nonlinear optical systems

    CERN Document Server

    Lugiato, Luigi; Brambilla, Massimo

    2015-01-01

    Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.

  12. Quadratic stochastic operators: Results and open problems

    International Nuclear Information System (INIS)

    Ganikhodzhaev, R.N.; Rozikov, U.A.

    2009-03-01

    The history of the quadratic stochastic operators can be traced back to the work of S. Bernshtein (1924). For more than 80 years this theory has been developed and many papers were published. In recent years it has again become of interest in connection with numerous applications in many branches of mathematics, biology and physics. But most results of the theory were published in non English journals, full text of which are not accessible. In this paper we give a brief description of the results and discuss several open problems. (author)

  13. Sequential Quadratic Programming Algorithms for Optimization

    Science.gov (United States)

    1989-08-01

    quadratic program- ma ng (SQ(2l ) aIiatain.seenis to be relgarded aIs tie( buest choice for the solution of smiall. dlense problema (see S tour L)toS...For the step along d, note that a < nOing + 3 szH + i3.ninA A a K f~Iz,;nd and from Id1 _< ,,, we must have that for some /3 , np , 11P11 < dn"p. 5.2...Nevertheless, many of these problems are considered hard to solve. Moreover, for some of these problems the assumptions made in Chapter 2 to establish the

  14. Applications of nonlinear fiber optics

    CERN Document Server

    Agrawal, Govind

    2008-01-01

    * The only book describing applications of nonlinear fiber optics * Two new chapters on the latest developments: highly nonlinear fibers and quantum applications* Coverage of biomedical applications* Problems provided at the end of each chapterThe development of new highly nonlinear fibers - referred to as microstructured fibers, holey fibers and photonic crystal fibers - is the next generation technology for all-optical signal processing and biomedical applications. This new edition has been thoroughly updated to incorporate these key technology developments.The bo

  15. TUNING PARAMETER LINEAR QUADRATIC TRACKING MENGGUNAKAN ALGORITMA GENETIKA UNTUK PENGENDALIAN GERAK LATERAL QUADCOPTER

    Directory of Open Access Journals (Sweden)

    Farid Choirul Akbar

    2016-04-01

    Full Text Available Gerakan lateral quadcopter dapat dilakukan apabila quadcopter dapat menjaga kestabilan pada saat hover, sehingga quadcopter dapat melakukan gerak rotasi. Perubahan sudut roll akan mengakibatkan gerak translasi pada sumbu Y, sedangkan perubahan sudut pitch akan mengakibatkan gerak translasi pada sumbu X. Disisi lain, quadcopter merupakan suatu sistem non-linear dan memiliki kestabilan yang rendah sehingga rentan terhadap gangguan. Pada penelitian Tugas Akhir ini dirancang pengendalian gerak rotasi quadcopter menggunakan Linear Quadratic Regulator (LQR dan Linear Quadratic Tracking (LQT untuk pengendalian gerak translasi. Untuk mendapatkan parameter dari LQT digunakan Algoritma Genetika (GA. Hasil tuning GA yang digunakan pada LQT memiliki nilai Qx 700,1884, nilai Qy 700,6315, nilai Rx 0,1568, dan  nilai Ry 0,1579. Respon LQT tersebut memiliki RMSE pada sumbu X dan sumbu Y sebesar 1,99 % serta memiliki time lagging 0,35 detik. Dengan hasil tersebut quadcopter mampu men-tracking trajectory berbentuk segitigaTekni

  16. New generalized conjugate gradient methods for the non-quadratic model in unconstrained optimization

    International Nuclear Information System (INIS)

    Al-Bayati, A.

    2001-01-01

    This paper present two new conjugate gradient algorithms which use the non-quadratic model in unconstrained optimization. The first is a new generalized self-scaling variable metric algorithm based on the sloboda generalized conjugate gradient method which is invariant to a nonlinear scaling of a stricity convex quadratic function; the second is an interleaving between the generalized sloboda method and the first algorithm; all these algorithm use exact line searches. Numerical comparisons over twenty test functions show that the interleaving algorithm is best overall and requires only about half the function evaluations of the Sloboda method: interleaving algorithms are likely to be preferred when the dimensionality of the problem is increased. (author). 29 refs., 1 tab

  17. Modified Emden-type equation with dissipative term quadratic in velocity

    International Nuclear Information System (INIS)

    Ghosh, Subrata; Talukdar, B; Das, Umapada; Saha, Aparna

    2012-01-01

    Based on some physical observation we introduce a generalized modified Emden-type equation (MEE) with a position-dependent dissipative term which is quadratic in velocity. Unlike the usual MEE, the first integral of the proposed generalized MEE is such that one can express the velocity of the system as a function of coordinate for all values of the parameters of the system. This permits us to study the dynamical properties of the system using straightforward analytical methods. The results presented in the phase diagram and plots of vector fields clearly delineate how does the presence of quadratic damping affect the motion of our nonlinear oscillator. From the differential equation provided by the first integral of the generalized MEE, we have found an approximate analytical solution of the equation which reproduces the time variation of the corresponding numerical solution to a fair degree of accuracy. (paper)

  18. Non-chaotic behaviour for a class of quadratic jerk equations

    International Nuclear Information System (INIS)

    Malasoma, J.-M.

    2009-01-01

    It is shown that a class constituted by 27 different types of non-linear third-order differential equations of the form x - =j(x,x . ,x), where j is a quadratic polynomial with only one or two terms, and for which ∂j(x,y,z)/∂z is not a constant function of time, does not exhibit chaos. The three-dimensional dynamical systems associated to these equations are not necessarily dissipative everywhere nor conservative everywhere in the corresponding phase spaces. Our results include and improve some recent results obtained by Yang and Chen who only considered the case where j was a homogeneous quadratic polynomial with two terms.

  19. On the reflection point where light reflects to a known destination on quadratic surfaces.

    Science.gov (United States)

    Gonçalves, Nuno

    2010-01-15

    We address the problem of determining the reflection point on a specular surface where a light ray that travels from a source to a target is reflected. The specular surfaces considered are those expressed by a quadratic equation. So far, there is no closed form explicit equation for the general solution of this determination of the reflection point, and the usual approach is to use the Snell law or the Fermat principle whose equations are derived in multidimensional nonlinear minimizations. We prove in this Letter that one can impose a set of three restrictions to the reflection point that can impose a set of three restrictions that culminates in a very elegant formalism of searching the reflection point in a unidimensional curve in space. This curve is the intersection of two quadratic equations. Some applications of this framework are also discussed.

  20. Nonlinear absorption dynamics using field-induced surface hopping: zinc porphyrin in water.

    Science.gov (United States)

    Röhr, Merle I S; Petersen, Jens; Wohlgemuth, Matthias; Bonačić-Koutecký, Vlasta; Mitrić, Roland

    2013-05-10

    We wish to present the application of our field-induced surface-hopping (FISH) method to simulate nonlinear absorption dynamics induced by strong nonresonant laser fields. We provide a systematic comparison of the FISH approach with exact quantum dynamics simulations on a multistate model system and demonstrate that FISH allows for accurate simulations of nonlinear excitation processes including multiphoton electronic transitions. In particular, two different approaches for simulating two-photon transitions are compared. The first approach is essentially exact and involves the solution of the time-dependent Schrödinger equation in an extended manifold of excited states, while in the second one only transiently populated nonessential states are replaced by an effective quadratic coupling term, and dynamics is performed in a considerably smaller manifold of states. We illustrate the applicability of our method to complex molecular systems by simulating the linear and nonlinear laser-driven dynamics in zinc (Zn) porphyrin in the gas phase and in water. For this purpose, the FISH approach is connected with the quantum mechanical-molecular mechanical approach (QM/MM) which is generally applicable to large classes of complex systems. Our findings that multiphoton absorption and dynamics increase the population of higher excited states of Zn porphyrin in the nonlinear regime, in particular in solution, provides a means for manipulating excited-state properties, such as transient absorption dynamics and electronic relaxation. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  1. On a quadratic inverse eigenvalue problem

    International Nuclear Information System (INIS)

    Cai, Yunfeng; Xu, Shufang

    2009-01-01

    This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable

  2. Phase space eigenfunctions of multidimensional quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Dodonov, V.V.; Man'ko, V.I.

    1986-01-01

    We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)

  3. Quadratic forms for Feynman-Kac semigroups

    International Nuclear Information System (INIS)

    Hibey, Joseph L.; Charalambous, Charalambos D.

    2006-01-01

    Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions

  4. Facets for the Cardinality Constrained Quadratic Knapsack Problem and the Quadratic Selective Travelling Salesman Problem

    DEFF Research Database (Denmark)

    Mak, Vicky; Thomadsen, Tommy

    2004-01-01

    A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...

  5. Quadratic residues and non-residues selected topics

    CERN Document Server

    Wright, Steve

    2016-01-01

    This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.

  6. CONFERENCE: Photon-photon collisions

    International Nuclear Information System (INIS)

    Anon.

    1983-01-01

    Despite being difficult to observe, photon-photon collisions have opened up a range of physics difficult, or even impossible, to access by other methods. The progress which has been made in this field was evident at the fifth international workshop on photon-photon collisions, held in Aachen from 13-16 April and attended by some 120 physicists

  7. Exact cancellation of quadratic divergences in top condensation models

    International Nuclear Information System (INIS)

    Blumhofer, A.

    1995-01-01

    We discuss the hierarchy problem and the corresponding quadratic divergences in the top mode Standard Model. Quadratic divergences appear at each order 1/N c since fermionic and bosonic contributions are of different order 1/N c . It is shown that the full dynamical system to all orders in 1/N c admits a solution, where the sum of all quadratic divergent contributions disappears. ((orig.))

  8. Determination of photon detector coefficient in neutron flux study

    International Nuclear Information System (INIS)

    Jedol Dayou; Azali Muhammad; Abd Aziz Mohamed; Abdul Razak Daud; Elias Saniman

    1995-01-01

    The efficiency of photon detector which is normally used in neutron flux measurement has been studied. The data obtain have been plotted using mathematical models in the form of reciprocal, exponential and semilog equation and subsequently efficiency coefficient of the detector has been determined. Beside that, energy quadratic equation model has also been used. It has been found that equation model selection is very important in the detector efficiency coefficient determination. In the case of energy quadratic equation, it has been found that the selection of energy set influenced the result. It can be concluded that energy quadratic equation is the best model in the neutron flux determination

  9. Magnitude and nature of the quadratic electro-optic effect in potassium dihydrogen phosphate and ammonium dihydrogen phosphate crystals

    International Nuclear Information System (INIS)

    Gunning, Mark J.; Raab, Roger E.; Kucharczyk, Wlodimierz

    2001-01-01

    Measurements of the magnitude and the sign of certain quadratic electro-optic coefficients of potassium dihydrogen phosphate (KDP) and ammonium dihydrogen phosphate (ADP) were made with an actively stabilized Michelson interferometer. The results obtained for these coefficients are, in units of 10 -20 m 2 V -2 (as opposed to literature values of order 10 -18 m 2 V -2 ), as follows: (KDP)g xxxx =-3.4±0.5, g yyxx =-0.2±0.4, and g zzxx =-0.7±0.4; (ADP)g xxxx =-7.4±1.0, g yyxx =-1.7±0.9, and g zzxx =-1.4±0.9. The quadratic Faust--Henry coefficient describing the lattice and the electronic contributions to the quadratic electro-optic effect in KDP and ADP is estimated from our results. These show that the nonlinear susceptibility responsible for the quadratic electro-optic effect in these crystals is due mainly to nonlinear interactions of the low-frequency electric field with the crystal lattice. Copyright 2001 Optical Society of America

  10. Distance matrices and quadratic embedding of graphs

    Directory of Open Access Journals (Sweden)

    Nobuaki Obata

    2018-04-01

    Full Text Available A connected graph is said to be of QE class if it admits  a quadratic embedding in a Hilbert space, or equivalently, if the distance matrix is conditionally negative definite. Several criteria for a graph to be of QE class are derived from the point of view of graph operations. For a quantitative criterion the QE constant is introduced and concrete examples are shown with explicit calculation. If the distance matrix admits a constant row sum, the QE constant coincides with the second largest eigenvalue of the distance matrix. The QE constants are determined for all graphs on $n$ vertices with $n\\le5$, among which two are not of QE class.

  11. Low-rank quadratic semidefinite programming

    KAUST Repository

    Yuan, Ganzhao

    2013-04-01

    Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.

  12. Charged black holes in quadratic gravity

    International Nuclear Information System (INIS)

    Matyjasek, Jerzy; Tryniecki, Dariusz

    2004-01-01

    Iterative solutions to fourth-order gravity describing static and electrically charged black holes are constructed. The obtained solutions are parametrized by two integration constants which are related to the electric charge and the exact location of the event horizon. Special emphasis is put on the extremal black holes. It is explicitly demonstrated that in the extremal limit the exact location of the (degenerate) event horizon is given by r + =|e|. Similarly to the classical Reissner-Nordstroem solution, the near-horizon geometry of the charged black holes in quadratic gravity, when expanded into the whole manifold, is simply that of Bertotti and Robinson. Similar considerations have been carried out for boundary conditions of the second type which employ the electric charge and the mass of the system as seen by a distant observer. The relations between results obtained within the framework of each method are briefly discussed

  13. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2002-01-01

    Lambda-lifting is a program transformation used in compilers and in partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one for each...... local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters that yields the cubic factor in the traditional formulation of lambda-lifting, which...... is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity of lambda-lifting from O(n 3 log n)toO(n2 log n), where n is the size of the program. Since a lambda-lifter can output...

  14. Low-rank quadratic semidefinite programming

    KAUST Repository

    Yuan, Ganzhao; Zhang, Zhenjie; Ghanem, Bernard; Hao, Zhifeng

    2013-01-01

    Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.

  15. A ''quadratized'' augmented plane wave method

    International Nuclear Information System (INIS)

    Smrcka, L.

    1982-02-01

    The exact radial solution inside the muffin-tin sphere is replaced by its Taylor expansion with respect to the energy, truncated after the quadratic term. Making use of it the energy independent augmented plane waves are formed which lead to the secular equations linear in energy. The method resembles the currently used linearized APW method but yields higher accuracy. The analysis of solution inside one muffin-tin sphere shows that the eigenvalue error is proportional to (E-E 0 ) 6 as compared with (E-E 0 ) 4 for LAPW. The error of eigenfunctions is (E-E 0 ) 3 ((E-E 0 ) 2 for LAPW). These conclusions are confirmed by direct numerical calculation of band structure of Cu and Al. (author)

  16. Quadratic gravity in first order formalism

    Energy Technology Data Exchange (ETDEWEB)

    Alvarez, Enrique; Anero, Jesus; Gonzalez-Martin, Sergio, E-mail: enrique.alvarez@uam.es, E-mail: jesusanero@gmail.com, E-mail: sergio.gonzalez.martin@uam.es [Departamento de Física Teórica and Instituto de Física Teórica (IFT-UAM/CSIC), Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid (Spain)

    2017-10-01

    We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the gravitational field; in particular, there are no propagators falling down faster than 1/ p {sup 2}. The drawback is of course that the parameter space of the theory is too big, so that in many cases will be far away from a theory of gravity alone. In order to analyze this issue, the interaction between external sources was examined in some detail. We find that this interaction is conveyed mainly by propagation of the three-index connection field. At any rate the theory as it stands is in the conformal invariant phase; only when Weyl invariance is broken through the coupling to matter can an Einstein-Hilbert term (and its corresponding Planck mass scale) be generated by quantum corrections.

  17. Nonlinear Optics and Applications

    Science.gov (United States)

    Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)

    2007-01-01

    Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.

  18. High power and spectral purity continuous-wave photonic THz source tunable from 1 to 4.5 THz for nonlinear molecular spectroscopy

    Science.gov (United States)

    Kiessling, J.; Breunig, I.; Schunemann, P. G.; Buse, K.; Vodopyanov, K. L.

    2013-10-01

    We report a diffraction-limited photonic terahertz (THz) source with linewidth OP) gallium arsenide (GaAs) via intracavity frequency mixing between the two closely spaced resonating signal and idler waves of an optical parametric oscillator (OPO) operating near λ = 2 μm. The doubly resonant type II OPO is based on a periodically poled lithium niobate (PPLN) pumped by a single-frequency Yb:YAG disc laser at 1030 nm. We take advantage of the enhancement of both optical fields inside a high-finesse OPO cavity: with 10 W of 1030 nm pump, 100 W of intracavity power near 2 μm was attained with GaAs inside cavity. This allows dramatic improvement in terms of generated THz power, as compared to the state-of-the art CW methods. We achieved >25 μW of single-frequency tunable CW THz output power scalable to >1 mW with proper choice of pump laser wavelength.

  19. Understanding the dynamics of photoionization-induced nonlinear effects and solitons in gas-filled hollow-core photonic crystal fibers

    Energy Technology Data Exchange (ETDEWEB)

    Saleh, Mohammed F.; Biancalana, Fabio [Max Planck Institute for the Science of Light, Guenther-Scharowsky Str. 1, DE-91058 Erlangen (Germany)

    2011-12-15

    We present the details of our previously formulated model [Saleh et al., Phys. Rev. Lett. 107, 203902 (2011)] that governs pulse propagation in hollow-core photonic crystal fibers filled by an ionizable gas. By using perturbative methods, we find that the photoionization process induces the opposite phenomenon of the well-known Raman self-frequency redshift of solitons in solid-core glass fibers, as was recently experimentally demonstrated [Hoelzer et al., Phys. Rev. Lett. 107, 203901 (2011)]. This process is only limited by ionization losses, and leads to a constant acceleration of solitons in the time domain with a continuous blueshift in the frequency domain. By applying the Gagnon-Belanger gauge transformation, multipeak ''inverted gravitylike'' solitary waves are predicted. We also demonstrate that the pulse dynamics shows the ejection of solitons during propagation in such fibers, analogous to what happens in conventional solid-core fibers. Moreover, unconventional long-range nonlocal interactions between temporally distant solitons, unique of gas plasma systems, are predicted and studied. Finally, the effects of higher-order dispersion coefficients and the shock operator on the pulse dynamics are investigated, showing that the conversion efficiency of resonant radiation into the deep UV can be improved via plasma formation.

  20. Photon technology. Hard photon technology; Photon technology. Hard photon gijutsu

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1996-03-01

    Research results of hard photon technology have been summarized as a part of novel technology development highly utilizing the quantum nature of photon. Hard photon technology refers to photon beam technologies which use photon in the 0.1 to 200 nm wavelength region. Hard photon has not been used in industry due to the lack of suitable photon sources and optical devices. However, hard photon in this wavelength region is expected to bring about innovations in such areas as ultrafine processing and material synthesis due to its atom selective reaction, inner shell excitation reaction, and spatially high resolution. Then, technological themes and possibility have been surveyed. Although there are principle proposes and their verification of individual technologies for the technologies of hard photon generation, regulation and utilization, they are still far from the practical applications. For the photon source technology, the laser diode pumped driver laser technology, laser plasma photon source technology, synchrotron radiation photon source technology, and vacuum ultraviolet photon source technology are presented. For the optical device technology, the multi-layer film technology for beam mirrors and the non-spherical lens processing technology are introduced. Also are described the reduction lithography technology, hard photon excitation process, and methods of analysis and measurement. 430 refs., 165 figs., 23 tabs.

  1. A sequential quadratic programming algorithm using an incomplete solution of the subproblem

    Energy Technology Data Exchange (ETDEWEB)

    Murray, W. [Stanford Univ., CA (United States). Systems Optimization Lab.; Prieto, F.J. [Universidad `Carlos III` de Madrid (Spain). Dept. de Estadistica y Econometria

    1993-05-01

    We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is not assumed that the iterates lie on a compact set.

  2. Newton-Raphson based modified Laplace Adomian decomposition method for solving quadratic Riccati differential equations

    Directory of Open Access Journals (Sweden)

    Mishra Vinod

    2016-01-01

    Full Text Available Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known Newton-Raphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method, HPM (Homotopy perturbation method, Taylor series method and the proposed scheme.

  3. Coupled Photonic Crystal Cavity Array Laser

    DEFF Research Database (Denmark)

    Schubert, Martin

    in the quadratic lattice. Processing techniques are developed and optimized in order fabricate photonic crystals membranes in gallium arsenide with quantum dots as gain medium and in indium gallium arsenide phosphide with quantum wells as gain medium. Several key issues in process to ensure good quality....... The results are in good agreement with standard coupled mode theory. Also a novel type of photonic crystal structure is proposed called lambda shifted cavity which is a twodimensional photonic crystal laser analog of a VCSEL laser. Detailed measurements of the coupled modes in the photonic crystals...... with quantum dots are carried out. In agreement with a simple gain model the structures do not show stimulated emission. The spectral splitting due to the coupling between single cavities as well as arrays of cavities is studied theoretically and experimentally. Lasing is observed for photonic crystal cavity...

  4. Vagal activity is quadratically related to prosocial traits, prosocial emotions, and observer perceptions of prosociality.

    Science.gov (United States)

    Kogan, Aleksandr; Oveis, Christopher; Carr, Evan W; Gruber, June; Mauss, Iris B; Shallcross, Amanda; Impett, Emily A; van der Lowe, Ilmo; Hui, Bryant; Cheng, Cecilia; Keltner, Dacher

    2014-12-01

    In the present article, we introduce the quadratic vagal activity-prosociality hypothesis, a theoretical framework for understanding the vagus nerve's involvement in prosociality. We argue that vagus nerve activity supports prosocial behavior by regulating physiological systems that enable emotional expression, empathy for others' mental and emotional states, the regulation of one's own distress, and the experience of positive emotions. However, we contend that extremely high levels of vagal activity can be detrimental to prosociality. We present 3 studies providing support for our model, finding consistent evidence of a quadratic relationship between respiratory sinus arrhythmia--the degree to which the vagus nerve modulates the heart rate--and prosociality. Individual differences in vagal activity were quadratically related to prosocial traits (Study 1), prosocial emotions (Study 2), and outside ratings of prosociality by complete strangers (Study 3). Thus, too much or too little vagal activity appears to be detrimental to prosociality. The present article provides the 1st theoretical and empirical account of the nonlinear relationship between vagal activity and prosociality.

  5. Orthogonal and Scaling Transformations of Quadratic Functions with ...

    African Journals Online (AJOL)

    In this paper we present a non-singular transformation that can reduce a given quadratic function defined on Rn to another simpler quadratic function and study the impact of the transformation in relation to the problem of minimization of the function. In particular, we construct a non-singular transformation that can reduce a ...

  6. Quadratic Twists of Rigid Calabi–Yau Threefolds Over

    DEFF Research Database (Denmark)

    Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko

    2013-01-01

    of weight 4 on some Γ 0(N). We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples. The question is motivated by the deeper question of which newforms of weight 4 on some Γ 0(N...

  7. Approximate *-derivations and approximate quadratic *-derivations on C*-algebras

    Directory of Open Access Journals (Sweden)

    Park Choonkil

    2011-01-01

    Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.

  8. A Linear Programming Reformulation of the Standard Quadratic Optimization Problem

    NARCIS (Netherlands)

    de Klerk, E.; Pasechnik, D.V.

    2005-01-01

    The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO).It is NPhard, and contains the maximum stable set problem in graphs as a special case.In this note we show that the SQO problem may be reformulated as an (exponentially

  9. Effects of Classroom Instruction on Students' Understanding of Quadratic Equations

    Science.gov (United States)

    Vaiyavutjamai, Pongchawee; Clements, M. A.

    2006-01-01

    Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

  10. Analysis of Students' Error in Learning of Quadratic Equations

    Science.gov (United States)

    Zakaria, Effandi; Ibrahim; Maat, Siti Mistima

    2010-01-01

    The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…

  11. Sketching the General Quadratic Equation Using Dynamic Geometry Software

    Science.gov (United States)

    Stols, G. H.

    2005-01-01

    This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

  12. Tangent Lines without Derivatives for Quadratic and Cubic Equations

    Science.gov (United States)

    Carroll, William J.

    2009-01-01

    In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

  13. Visualising the Roots of Quadratic Equations with Complex Coefficients

    Science.gov (United States)

    Bardell, Nicholas S.

    2014-01-01

    This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

  14. Polychromatic photons

    DEFF Research Database (Denmark)

    Keller, Ole

    2002-01-01

    train quantum electrodynamics. A brief description of particle (photon) position operators is given, and it is shown that photons usually are only algebraically confined in an emission process. Finally, it is demonstrated that the profile of the birth domain of a radio-frequency photon emitted...

  15. The photon and the vacuum cleaner

    International Nuclear Information System (INIS)

    Walmsley, I.A.

    2005-01-01

    Quantum technologies based on optics often rely on photon bunching and measurement with feed forward to achieve an effective nonlinear interaction between otherwise transparent particles. The efficacy of this strategy for implementing nonlinear interactions requires pure state single photon wave packets. These, however, are not so easy to come by. In this talk I will discussed some methods and tools that enable the preparation of such state. (author)

  16. Two-photon-induced hot-electron transfer to a single molecule in a scanning tunneling microscope

    International Nuclear Information System (INIS)

    Wu, S. W.; Ho, W.

    2010-01-01

    The junction of a scanning tunneling microscope (STM) operating in the tunneling regime was irradiated with femtosecond laser pulses. A photoexcited hot electron in the STM tip resonantly tunnels into an excited state of a single molecule on the surface, converting it from the neutral to the anion. The electron-transfer rate depends quadratically on the incident laser power, suggesting a two-photon excitation process. This nonlinear optical process is further confirmed by the polarization measurement. Spatial dependence of the electron-transfer rate exhibits atomic-scale variations. A two-pulse correlation experiment reveals the ultrafast dynamic nature of photoinduced charging process in the STM junction. Results from these experiments are important for understanding photoinduced interfacial charge transfer in many nanoscale inorganic-organic structures.

  17. Isochronous Liénard-type nonlinear oscillators of arbitrary dimensions

    Indian Academy of Sciences (India)

    2015-10-13

    Oct 13, 2015 ... Isochronous system; Liénard-type system; singular and nonsingular Hamiltonian. ... Liénard-type nonlinear oscillators exhibiting isochronous properties, including linear, quadratic and ... Pramana – Journal of Physics | News.

  18. Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

    Directory of Open Access Journals (Sweden)

    Y. N. Pavlov

    2015-01-01

    Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

  19. Photonics activities at DTU Fotonik

    DEFF Research Database (Denmark)

    Jeppesen, Palle; Jepsen, Peter Uhd; Lodahl, Peter

    2010-01-01

    DTU Fotonik, Department of Photonics Engineering at the Technical University of Denmark has about 200 employees including 60 PhD students. The ambition is to be among the world’s leading University departments within photonics research, education and innovation. To fulfil this ambition, DTU Fotonik...... tries to attract excellent researchers and students from all over the world and to collaborate with world leading research institutes and companies. The activities span from quantum photonics, nanotechnology and metamaterials over nonlinear fiber optics, optical sensors and diode lasers & LED systems...

  20. Resonant Photonic States in Coupled Heterostructure Photonic Crystal Waveguides

    Directory of Open Access Journals (Sweden)

    Sabarinathan J

    2010-01-01

    Full Text Available Abstract In this paper, we study the photonic resonance states and transmission spectra of coupled waveguides made from heterostructure photonic crystals. We consider photonic crystal waveguides made from three photonic crystals A, B and C, where the waveguide heterostructure is denoted as B/A/C/A/B. Due to the band structure engineering, light is confined within crystal A, which thus act as waveguides. Here, photonic crystal C is taken as a nonlinear photonic crystal, which has a band gap that may be modified by applying a pump laser. We have found that the number of bound states within the waveguides depends on the width and well depth of photonic crystal A. It has also been found that when both waveguides are far away from each other, the energies of bound photons in each of the waveguides are degenerate. However, when they are brought close to each other, the degeneracy of the bound states is removed due to the coupling between them, which causes these states to split into pairs. We have also investigated the effect of the pump field on photonic crystal C. We have shown that by applying a pump field, the system may be switched between a double waveguide to a single waveguide, which effectively turns on or off the coupling between degenerate states. This reveals interesting results that can be applied to develop new types of nanophotonic devices such as nano-switches and nano-transistors.

  1. Nonlinear optics quantum computing with circuit QED.

    Science.gov (United States)

    Adhikari, Prabin; Hafezi, Mohammad; Taylor, J M

    2013-02-08

    One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation.

  2. Nonlinear optical properties of silicon waveguides

    International Nuclear Information System (INIS)

    Tsang, H K; Liu, Y

    2008-01-01

    Recent work on two-photon absorption (TPA), stimulated Raman scattering (SRS) and optical Kerr effect in silicon-on-insulator (SOI) waveguides is reviewed and some potential applications of these optical nonlinearities, including silicon-based autocorrelation detectors, optical amplifiers, high speed optical switches, optical wavelength converters and self-phase modulation (SPM), are highlighted. The importance of free carriers generated by TPA in nonlinear devices is discussed, and a generalized definition of the nonlinear effective length to cater for nonlinear losses is proposed. How carrier lifetime engineering, and in particular the use of helium ion implantation, can enhance the nonlinear effective length for nonlinear devices is also discussed

  3. AUTOJOM, Quadratic Equation Coefficient for Conic Volume, Parallelepipeds, Wedges, Pyramids. JOMREAD, Check of 3-D Geometry Structure from Quadratic Surfaces

    International Nuclear Information System (INIS)

    2005-01-01

    Nature of physical problem solved: AUTOJOM is a computer program that will generate the coefficients of any quadratic equation used to define conic volumes and also the coefficients of the planes needed to define parallelepipeds, wedges, and pyramids. JOMREAD is a computer code to check any 3D geometry composed of and constructed with quadratic surfaces

  4. Mismatch management for optical and matter-wave quadratic solitons

    International Nuclear Information System (INIS)

    Driben, R.; Oz, Y.; Malomed, B. A.; Gubeskys, A.; Yurovsky, V. A.

    2007-01-01

    We propose a way to control solitons in χ (2) (quadratically nonlinear) systems by means of periodic modulation imposed on the phase-mismatch parameter ('mismatch management', MM). It may be realized in the cotransmission of fundamental-frequency (FF) and second-harmonic (SH) waves in a planar optical waveguide via a long-period modulation of the usual quasi-phase-matching pattern of ferroelectric domains. In an altogether different physical setting, the MM may also be implemented by dint of the Feshbach resonance in a harmonically modulated magnetic field in a hybrid atomic-molecular Bose-Einstein condensate (BEC), with the atomic and molecular mean fields (MFs) playing the roles of the FF and SH, respectively. Accordingly, the problem is analyzed in two different ways. First, in the optical model, we identify stability regions for spatial solitons in the MM system, in terms of the MM amplitude and period, using the MF equations for spatially inhomogeneous configurations. In particular, an instability enclave is found inside the stability area. The robustness of the solitons is also tested against variation of the shape of the input pulse, and a threshold for the formation of stable solitons is found in terms of the power. Interactions between stable solitons are virtually unaffected by the MM. The second method (parametric approximation), going beyond the MF description, is developed for spatially homogeneous states in the BEC model. It demonstrates that the MF description is valid for large modulation periods, while, at smaller periods, non-MF components acquire gain, which implies destruction of the MF under the action of the high-frequency MM

  5. Are ghost surfaces quadratic-flux-minimizing?

    International Nuclear Information System (INIS)

    Hudson, S.R.; Dewar, R.L.

    2009-01-01

    Two candidates for 'almost-invariant' toroidal surfaces passing through magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost surfaces, use families of periodic pseudo-orbits (i.e. paths for which the action is not exactly extremal). QFMin pseudo-orbits, which are coordinate-dependent, are field lines obtained from a modified magnetic field, and ghost-surface pseudo-orbits are obtained by displacing closed field lines in the direction of steepest descent of magnetic action, ∫A.dl. A generalized Hamiltonian definition of ghost surfaces is given and specialized to the usual Lagrangian definition. A modified Hamilton's Principle is introduced that allows the use of Lagrangian integration for calculation of the QFMin pseudo-orbits. Numerical calculations show QFMin and Lagrangian ghost surfaces give very similar results for a chaotic magnetic field perturbed from an integrable case, and this is explained using a perturbative construction of an auxiliary poloidal angle for which QFMin and Lagrangian ghost surfaces are the same up to second order. While presented in the context of 3-dimensional magnetic field line systems, the concepts are applicable to defining almost-invariant tori in other 11/2 degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.

  6. Securing Digital Audio using Complex Quadratic Map

    Science.gov (United States)

    Suryadi, MT; Satria Gunawan, Tjandra; Satria, Yudi

    2018-03-01

    In This digital era, exchanging data are common and easy to do, therefore it is vulnerable to be attacked and manipulated from unauthorized parties. One data type that is vulnerable to attack is digital audio. So, we need data securing method that is not vulnerable and fast. One of the methods that match all of those criteria is securing the data using chaos function. Chaos function that is used in this research is complex quadratic map (CQM). There are some parameter value that causing the key stream that is generated by CQM function to pass all 15 NIST test, this means that the key stream that is generated using this CQM is proven to be random. In addition, samples of encrypted digital sound when tested using goodness of fit test are proven to be uniform, so securing digital audio using this method is not vulnerable to frequency analysis attack. The key space is very huge about 8.1×l031 possible keys and the key sensitivity is very small about 10-10, therefore this method is also not vulnerable against brute-force attack. And finally, the processing speed for both encryption and decryption process on average about 450 times faster that its digital audio duration.

  7. Designing Camera Networks by Convex Quadratic Programming

    KAUST Repository

    Ghanem, Bernard

    2015-05-04

    ​In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport). ​

  8. Universal formats for nonlinear ordinary differential systems

    International Nuclear Information System (INIS)

    Kerner, E.H.

    1981-01-01

    It is shown that very general nonlinear ordinary differential systems (embracing all that arise in practice) may, first, be brought down to polynomial systems (where the nonlinearities occur only as polynomials in the dependent variables) by introducing suitable new variables into the original system; second, that polynomial systems are reducible to ''Riccati systems,'' where the nonlinearities are quadratic at most; third, that Riccati systems may be brought to elemental universal formats containing purely quadratic terms with simple arrays of coefficients that are all zero or unity. The elemental systems have representations as novel types of matrix Riccati equations. Different starting systems and their associated Riccati systems differ from one another, at the final elemental level, in order and in initial data, but not in format

  9. Generation and growth rates of nonlinear distortions in a traveling wave tube

    International Nuclear Information System (INIS)

    Woehlbier, John G.; Dobson, Ian; Booske, John H.

    2002-01-01

    The structure of a steady state multifrequency model of a traveling wave tube amplifier is exploited to describe the generation of intermodulation frequencies and calculate their growth rates. The model describes the evolution of Fourier coefficients of circuit and electron beam quantities and has the form of differential equations with quadratic nonlinearities. Intermodulation frequencies are sequentially generated by the quadratic nonlinearities in a series solution of the differential equations. A formula for maximum intermodulation growth rates is derived and compared to simulation results

  10. On Stabilization of Nonautonomous Nonlinear Systems

    International Nuclear Information System (INIS)

    Bogdanov, A. Yu.

    2008-01-01

    The procedures to obtain the sufficient conditions of asymptotic stability for nonlinear nonstationary continuous-time systems are discussed. We consider different types of the following general controlled system: x = X(t,x,u) = F(t,x)+B(t,x)u, x(t 0 ) = x 0 . (*) The basis of investigation is limiting equations, limiting Lyapunov functions, etc. The improved concept of observability of the pair of functional matrices is presented. By these results the problem of synthesis of asymptotically stable control nonlinear nonautonomous systems (with linear parts) involving the quadratic time-dependent Lyapunov functions is solved as well as stabilizing a given unstable system with nonlinear control law.

  11. Generation of sub-Poissonian photon number distribution

    DEFF Research Database (Denmark)

    Grønbech-Jensen, N.; Ramanujam, P. S.

    1990-01-01

    An optimization of a nonlinear Mach-Zehnder interferometer to produce sub-Poissonian photon number distribution is proposed. We treat the system quantum mechanically and estimate the mirror parameters, the nonlinearity of the medium in the interferometer, and the input power to obtain minimal...... output uncertainty in the photon number. The power efficiency of the system is shown to be high....

  12. Single-shot measurement of nonlinear absorption and nonlinear refraction.

    Science.gov (United States)

    Jayabalan, J; Singh, Asha; Oak, Shrikant M

    2006-06-01

    A single-shot method for measurement of nonlinear optical absorption and refraction is described and analyzed. A spatial intensity variation of an elliptical Gaussian beam in conjugation with an array detector is the key element of this method. The advantages of this single-shot technique were demonstrated by measuring the two-photon absorption and free-carrier absorption in GaAs as well as the nonlinear refractive index of CS2 using a modified optical Kerr setup.

  13. Topology optimization of nonlinear optical devices

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard

    2011-01-01

    This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation and an incremen......This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation...... limiter. Here, air, a linear and a nonlinear material are distributed so that the wave transmission displays a strong sensitivity to the amplitude of the incoming wave....

  14. Nonlinear optics principles and applications

    CERN Document Server

    Li, Chunfei

    2017-01-01

    This book reflects the latest advances in nonlinear optics. Besides the simple, strict mathematical deduction, it also discusses the experimental verification and possible future applications, such as the all-optical switches. It consistently uses the practical unit system throughout. It employs simple physical images, such as "light waves" and "photons" to systematically explain the main principles of nonlinear optical effects. It uses the first-order nonlinear wave equation in frequency domain under the condition of “slowly varying amplitude approximation" and the classical model of the interaction between the light and electric dipole. At the same time, it also uses the rate equations based on the energy-level transition of particle systems excited by photons and the energy and momentum conservation principles to explain the nonlinear optical phenomenon. The book is intended for researchers, engineers and graduate students in the field of the optics, optoelectronics, fiber communication, information tech...

  15. A revisit to quadratic programming with fuzzy parameters

    International Nuclear Information System (INIS)

    Liu, S.-T.

    2009-01-01

    Quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the linear terms in objective function, constraint coefficients, and right-hand sides are fuzzy numbers [Liu ST. Quadratic programming with fuzzy parameters: a membership function approach. Chaos, Solitons and Fractals 2009;40:237-45]. In this paper, we generalize Liu's method to a more general fuzzy quadratic programming problem, where the cost coefficients in objective function, constraint coefficients, and right-hand sides are all fuzzy numbers. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. With the ability of calculating the fuzzy objective value developed in this paper, it might help initiate wider applications.

  16. Harmonic distortion in microwave photonic filters.

    Science.gov (United States)

    Rius, Manuel; Mora, José; Bolea, Mario; Capmany, José

    2012-04-09

    We present a theoretical and experimental analysis of nonlinear microwave photonic filters. Far from the conventional condition of low modulation index commonly used to neglect high-order terms, we have analyzed the harmonic distortion involved in microwave photonic structures with periodic and non-periodic frequency responses. We show that it is possible to design microwave photonic filters with reduced harmonic distortion and high linearity even under large signal operation.

  17. Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems

    International Nuclear Information System (INIS)

    Scott, D.S.; Ward, R.C.

    1981-01-01

    Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda 2 + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices

  18. Observation of an octave-spanning supercontinuum in the mid-infrared using ultrafast cascaded nonlinearities

    DEFF Research Database (Denmark)

    Bache, Morten; Liu, Xing; Zhou, Binbin

    2014-01-01

    An octave-spanning mid-IR supercontinuum is observed experimentally using ultrafast cascaded nonlinearities in an LiInS2 quadratic nonlinear crystal pumped with 70 fs energetic mid-IR pulses and cut for strongly phase-mismatched second-harmonic generation. ©OSA 2014.......An octave-spanning mid-IR supercontinuum is observed experimentally using ultrafast cascaded nonlinearities in an LiInS2 quadratic nonlinear crystal pumped with 70 fs energetic mid-IR pulses and cut for strongly phase-mismatched second-harmonic generation. ©OSA 2014....

  19. Octave-Spanning Mid-IR Supercontinuum Generation with Ultrafast Cascaded Nonlinearities

    DEFF Research Database (Denmark)

    Zhou, Binbin; Guo, Hairun; Liu, Xing

    2014-01-01

    An octave-spanning mid-IR supercontinuum is observed experimentally using ultrafast cascaded nonlinearities in an LiInS2 quadratic nonlinear crystal pumped with 70 fs energetic mid-IR pulses and cut for strongly phase-mismatched second-harmonic generation.......An octave-spanning mid-IR supercontinuum is observed experimentally using ultrafast cascaded nonlinearities in an LiInS2 quadratic nonlinear crystal pumped with 70 fs energetic mid-IR pulses and cut for strongly phase-mismatched second-harmonic generation....

  20. Photonic Hypercrystals

    Directory of Open Access Journals (Sweden)

    Evgenii E. Narimanov

    2014-10-01

    Full Text Available We introduce a new “universality class” of artificial optical media—photonic hypercrystals. These hyperbolic metamaterials, with periodic spatial variation of dielectric permittivity on subwavelength scale, combine the features of optical metamaterials and photonic crystals. In particular, surface waves supported by a hypercrystal possess the properties of both the optical Tamm states in photonic crystals and surface-plasmon polaritons at the metal-dielectric interface.

  1. Time-resolved Femtosecond Photon Echo Probes Bimodal Solvent Dynamics

    NARCIS (Netherlands)

    Pshenichnikov, M.S; Duppen, K.; Wiersma, D. A.

    1995-01-01

    We report on time-resolved femtosecond photon echo experiments of a dye molecule in a polar solution. The photon echo is time resolved by mixing the echo with a femtosecond gate pulse in a nonlinear crystal. It is shown that the temporal profile of the photon echo allows separation of the

  2. Microwave photonics

    CERN Document Server

    Lee, Chi H

    2006-01-01

    Wireless, optical, and electronic networks continue to converge, prompting heavy research into the interface between microwave electronics, ultrafast optics, and photonic technologies. New developments arrive nearly as fast as the photons under investigation, and their commercial impact depends on the ability to stay abreast of new findings, techniques, and technologies. Presenting a broad yet in-depth survey, Microwave Photonics examines the major advances that are affecting new applications in this rapidly expanding field.This book reviews important achievements made in microwave photonics o

  3. Integrable Hamiltonian systems and interactions through quadratic constraints

    International Nuclear Information System (INIS)

    Pohlmeyer, K.

    1975-08-01

    Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de

  4. A perturbative solution for gravitational waves in quadratic gravity

    International Nuclear Information System (INIS)

    Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de

    2003-01-01

    We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin

  5. The Kerr nonlinearity of the beta-barium borate crystal

    DEFF Research Database (Denmark)

    Bache, Morten; Guo, Hairun; Zhou, Binbin

    2013-01-01

    A popular crystal for ultrafast cascading experiments is beta-barium-borate (β-BaB2O4, BBO). It has a decent quadratic nonlinear coefficient, and because the crystal is anisotropie it can be birefringence phase-matched for type I (oo → e) second-harmonic generation (SHG). For femtosecond experime......A popular crystal for ultrafast cascading experiments is beta-barium-borate (β-BaB2O4, BBO). It has a decent quadratic nonlinear coefficient, and because the crystal is anisotropie it can be birefringence phase-matched for type I (oo → e) second-harmonic generation (SHG). For femtosecond...

  6. Resolving Actuator Redundancy - Control Allocation vs. Linear Quadratic Control

    OpenAIRE

    Härkegård, Ola

    2004-01-01

    When designing control laws for systems with more inputs than controlled variables, one issue to consider is how to deal with actuator redundancy. Two tools for distributing the control effort among a redundant set of actuators are control allocation and linear quadratic control design. In this paper, we investigate the relationship between these two design tools when a quadratic performance index is used for control allocation. We show that for a particular class of linear systems, they give...

  7. Scale-Invariant Rotating Black Holes in Quadratic Gravity

    Directory of Open Access Journals (Sweden)

    Guido Cognola

    2015-07-01

    Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.

  8. Staff turnover in hotels : exploring the quadratic and linear relationships.

    OpenAIRE

    Mohsin, A.; Lengler, J.F.B.; Aguzzoli, R.L.

    2015-01-01

    The aim of this study is to assess whether the relationship between intention to leave the job and its antecedents is quadratic or linear. To explore those relationships a theoretical model (see Fig. 1) and eight hypotheses are proposed. Each linear hypothesis is followed by an alternative quadratic hypothesis. The alternative hypotheses propose that the relationship between the four antecedent constructs and intention to leave the job might not be linear, as the existing literature suggests....

  9. On wave-packet dynamics in a decaying quadratic potential

    DEFF Research Database (Denmark)

    Møller, Klaus Braagaard; Henriksen, Niels Engholm

    1997-01-01

    We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics.......We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics....

  10. The stability of quadratic-reciprocal functional equation

    Science.gov (United States)

    Song, Aimin; Song, Minwei

    2018-04-01

    A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.

  11. Burgers' turbulence problem with linear or quadratic external potential

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.

    2005-01-01

    We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....

  12. Quadratic programming with fuzzy parameters: A membership function approach

    International Nuclear Information System (INIS)

    Liu, S.-T.

    2009-01-01

    Quadratic programming has been widely applied to solving real world problems. The conventional quadratic programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper discusses the fuzzy quadratic programming problems where the cost coefficients, constraint coefficients, and right-hand sides are represented by convex fuzzy numbers. Since the parameters in the program are fuzzy numbers, the derived objective value is a fuzzy number as well. Using Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. An example illustrates method proposed in this paper.

  13. Broadband Nonlinear Signal Processing in Silicon Nanowires

    DEFF Research Database (Denmark)

    Yvind, Kresten; Pu, Minhao; Hvam, Jørn Märcher

    The fast non-linearity of silicon allows Tbit/s optical signal processing. By choosing suitable dimensions of silicon nanowires their dispersion can be tailored to ensure a high nonlinearity at power levels low enough to avoid significant two-photon abso We have fabricated low insertion...

  14. Photonics an introduction

    CERN Document Server

    Reider, Georg A

    2016-01-01

    This book provides a comprehensive introduction into photonics, from the electrodynamic and quantum mechanic fundamentals to the level of photonic components and building blocks such as lasers, amplifiers, modulators, waveguides, and detectors. The book will serve both as textbook and as a reference work for the advanced student or scientist. Theoretical results are derived from basic principles with convenient, yet state-of-the-art mathematical tools, providing not only deeper understanding but also familiarization with formalisms used in the relevant technical literature and research articles. Among the subject matters treated are polarization optics, pulse and beam propagation, waveguides, light–matter interaction, stationary and transient behavior of lasers, semiconductor optics and lasers (including low-dimensional systems such as quantum wells), detector technology, photometry, and colorimetry. Nonlinear optics are elaborated comprehensively. The book is intended for both students of physics and elect...

  15. Nonlinear dynamics in photonic crystal nanocavity lasers

    DEFF Research Database (Denmark)

    Skovgård, Troels Suhr; Kristensen, Philip Trøst; Frandsen, Lars Hagedorn

    2009-01-01

    We model coupled nanolasers by adding phase-dependent coupling terms to the Purcell-enhanced laser rate equations. Transitions between phase-locking and complex oscillatory behavior are observed at critical coupling strengths in detuned two-laser systems....

  16. Two-photon interference : spatial aspects of two-photon entanglement, diffraction, and scattering

    NARCIS (Netherlands)

    Peeters, Wouter Herman

    2010-01-01

    This dissertation contains scientific research within the realm of quantum optics, which is a branch of physics. An experimental and theoretical study is made of two-photon interference phenomena in various optical systems. Spatially entangled photon pairs are produced via the nonlinear optical

  17. Nonlinear optics

    International Nuclear Information System (INIS)

    Boyd, R.W.

    1992-01-01

    Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics

  18. Nonlinear optical interactions in silicon waveguides

    Directory of Open Access Journals (Sweden)

    Kuyken B.

    2017-03-01

    Full Text Available The strong nonlinear response of silicon photonic nanowire waveguides allows for the integration of nonlinear optical functions on a chip. However, the detrimental nonlinear optical absorption in silicon at telecom wavelengths limits the efficiency of many such experiments. In this review, several approaches are proposed and demonstrated to overcome this fundamental issue. By using the proposed methods, we demonstrate amongst others supercontinuum generation, frequency comb generation, a parametric optical amplifier, and a parametric optical oscillator.

  19. Photon technology. Hard photon technology; Photon technology. Hard photon gijutsu

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1997-03-01

    For the application of photon to industrial technologies, in particular, a hard photon technology was surveyed which uses photon beams of 0.1-200nm in wavelength. Its features such as selective atom reaction, dense inner shell excitation and spacial high resolution by quantum energy are expected to provide innovative techniques for various field such as fine machining, material synthesis and advanced inspection technology. This wavelength region has been hardly utilized for industrial fields because of poor development of suitable photon sources and optical devices. The developmental meaning, usable time and issue of a hard photon reduction lithography were surveyed as lithography in ultra-fine region below 0.1{mu}m. On hard photon analysis/evaluation technology, the industrial use of analysis, measurement and evaluation technologies by micro-beam was viewed, and optimum photon sources and optical systems were surveyed. Prediction of surface and surface layer modification by inner shell excitation, the future trend of this process and development of a vacuum ultraviolet light source were also surveyed. 383 refs., 153 figs., 17 tabs.

  20. Inverse photon-photon processes

    International Nuclear Information System (INIS)

    Carimalo, C.; Crozon, M.; Kesler, P.; Parisi, J.

    1981-12-01

    We here consider inverse photon-photon processes, i.e. AB → γγX (where A, B are hadrons, in particular protons or antiprotons), at high energies. As regards the production of a γγ continuum, we show that, under specific conditions the study of such processes might provide some information on the subprocess gg γγ, involving a quark box. It is also suggested to use those processes in order to systematically look for heavy C = + structures (quarkonium states, gluonia, etc.) showing up in the γγ channel. Inverse photon-photon processes might thus become a new and fertile area of investigation in high-energy physics, provided the difficult problem of discriminating between direct photons and indirect ones can be handled in a satisfactory way

  1. Polarization-insensitive all-optical dual pump-phase transmultiplexing from 2 x 10-GBd OOKs to 10-GBd RZ-QPSK using cross-phase modulation in a passive nonlinear birefringent photonic crystal fiber

    Science.gov (United States)

    Mahmood, Tanvir

    Considering the network size, bit rate, spectral and channel capacity limitations, different modulation formats may be selectively used in future optical networks. Although the traditional metropolitan area networks (MANs) still uses the non-return-to-zero on-off keying (NRZ-OOK) modulation format due to its technical simplicity and therefore low cost, QPSK format is more advantageous in spectrally efficient long-haul fiber optic transmission systems because of its constant power envelope, and robustness to various transmission impairments. Consequently, an important problem may arise, in particular how to route the OOK-data streams from MANs to long-haul backbone networks when the state of polarization (SOP) of the remotely generated OOK is unpredictable. Hence, the focus of this dissertation was to investigate a polarization insensitive (PI) all-optical nonlinear optical signal processing (NOSP) method that can be implemented at the network cross-connect (X-connect) to transfer data from a remotely and a locally generated OOK data simultaneously to more effectual QPSK format for long-haul transmission. By utilizing cross-phase modulation (XPM) and inherent birefringence of the device, the work demonstrated, for the first time, PI all-optical data transfer utilizing dual pump-phase transmultiplexing (DPTM) from 2 x 10-GBd OOKs to 10-GBd RZ-QPSK in a passive nonlinear birefringent photonic crystal fiber (PCF). Polarization insensitivity was achieved by scrambling the SOP of the remotely generated OOK pump and launching the locally generated OOK pump and the probe off-axis. To mitigate polarization induced power fluctuations and detrimental effects due to nearby partially degenerate and non-degenerate four wave mixings, an optimum pump-probe detuning was also utilized. The PI DPTM RZ-QPSK demonstrated a pre-amplified receiver sensitivity penalty < 5.5 dB at 10--9 bit-error-rate (BER), relative to relative to the FPGA-precoded RZ-DQPSK baseline in ASE

  2. On the analysis of clonogenic survival data: Statistical alternatives to the linear-quadratic model

    International Nuclear Information System (INIS)

    Unkel, Steffen; Belka, Claus; Lauber, Kirsten

    2016-01-01

    The most frequently used method to quantitatively describe the response to ionizing irradiation in terms of clonogenic survival is the linear-quadratic (LQ) model. In the LQ model, the logarithm of the surviving fraction is regressed linearly on the radiation dose by means of a second-degree polynomial. The ratio of the estimated parameters for the linear and quadratic term, respectively, represents the dose at which both terms have the same weight in the abrogation of clonogenic survival. This ratio is known as the α/β ratio. However, there are plausible scenarios in which the α/β ratio fails to sufficiently reflect differences between dose-response curves, for example when curves with similar α/β ratio but different overall steepness are being compared. In such situations, the interpretation of the LQ model is severely limited. Colony formation assays were performed in order to measure the clonogenic survival of nine human pancreatic cancer cell lines and immortalized human pancreatic ductal epithelial cells upon irradiation at 0-10 Gy. The resulting dataset was subjected to LQ regression and non-linear log-logistic regression. Dimensionality reduction of the data was performed by cluster analysis and principal component analysis. Both the LQ model and the non-linear log-logistic regression model resulted in accurate approximations of the observed dose-response relationships in the dataset of clonogenic survival. However, in contrast to the LQ model the non-linear regression model allowed the discrimination of curves with different overall steepness but similar α/β ratio and revealed an improved goodness-of-fit. Additionally, the estimated parameters in the non-linear model exhibit a more direct interpretation than the α/β ratio. Dimensionality reduction of clonogenic survival data by means of cluster analysis was shown to be a useful tool for classifying radioresistant and sensitive cell lines. More quantitatively, principal component analysis allowed

  3. Microsphere imaging with confocal microscopy and two photon microscopy

    International Nuclear Information System (INIS)

    Chun, Hyung Su; An, Kyung Won; Lee, Jai Hyung

    2002-01-01

    We have acquired images of polystyrene and fused-silica microsphere by using conventional optical microscopy, confocal microscopy and two-photon microscopy, and performed comparative analysis of these images. Different from conventional optical microscopy, confocal and two-photon microscopy had good optical sectioning capability. In addition, confocal microscopy and two-photon microscopy had better lateral resolution than conventional optical microscopy. These results are attributed to confocality and nonlinearity of confocal microscopy and two photon microscopy, respectively.

  4. Nonlinear optics

    CERN Document Server

    Bloembergen, Nicolaas

    1996-01-01

    Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe

  5. Engineering high-order nonlinear dissipation for quantum superconducting circuits

    Science.gov (United States)

    Mundhada, S. O.; Grimm, A.; Touzard, S.; Shankar, S.; Minev, Z. K.; Vool, U.; Mirrahimi, M.; Devoret, M. H.

    Engineering nonlinear driven-dissipative processes is essential for quantum control. In the case of a harmonic oscillator, nonlinear dissipation can stabilize a decoherence-free manifold, leading to protected quantum information encoding. One possible approach to implement such nonlinear interactions is to combine the nonlinearities provided by Josephson circuits with parametric pump drives. However, it is usually hard to achieve strong nonlinearities while avoiding undesired couplings. Here we propose a scheme to engineer a four-photon drive and dissipation in a harmonic oscillator by cascading experimentally demonstrated two-photon processes. We also report experimental progress towards realization of such a scheme. Work supported by: ARO, ONR, AFOSR and YINQE.

  6. Comparison between linear quadratic and early time dose models

    International Nuclear Information System (INIS)

    Chougule, A.A.; Supe, S.J.

    1993-01-01

    During the 70s, much interest was focused on fractionation in radiotherapy with the aim of improving tumor control rate without producing unacceptable normal tissue damage. To compare the radiobiological effectiveness of various fractionation schedules, empirical formulae such as Nominal Standard Dose, Time Dose Factor, Cumulative Radiation Effect and Tumour Significant Dose, were introduced and were used despite many shortcomings. It has been claimed that a recent linear quadratic model is able to predict the radiobiological responses of tumours as well as normal tissues more accurately. We compared Time Dose Factor and Tumour Significant Dose models with the linear quadratic model for tumour regression in patients with carcinomas of the cervix. It was observed that the prediction of tumour regression estimated by the Tumour Significant Dose and Time Dose factor concepts varied by 1.6% from that of the linear quadratic model prediction. In view of the lack of knowledge of the precise values of the parameters of the linear quadratic model, it should be applied with caution. One can continue to use the Time Dose Factor concept which has been in use for more than a decade as its results are within ±2% as compared to that predicted by the linear quadratic model. (author). 11 refs., 3 figs., 4 tabs

  7. Fitness analysis method for magnesium in drinking water with atomic absorption using quadratic curve calibration

    Directory of Open Access Journals (Sweden)

    Esteban Pérez-López

    2014-11-01

    Full Text Available Because of the importance of quantitative chemical analysis in research, quality control, sales of services and other areas of interest , and the limiting of some instrumental analysis methods for quantification with linear calibration curve, sometimes because the short linear dynamic ranges of the analyte, and sometimes by limiting the technique itself, is that there is a need to investigate a little more about the convenience of using quadratic curves for analytical quantification, which seeks demonstrate that it is a valid calculation model for chemical analysis instruments. To this was taken as an analysis method based on the technique and atomic absorption spectroscopy in particular a determination of magnesium in a sample of drinking water Tacares sector Northern Grecia, employing a nonlinear calibration curve and a curve specific quadratic behavior, which was compared with the test results obtained for the same analysis with a linear calibration curve. The results show that the methodology is valid for the determination referred to, with all confidence, since the concentrations are very similar, and as used hypothesis testing can be considered equal.

  8. Quadratic Polynomial Regression using Serial Observation Processing:Implementation within DART

    Science.gov (United States)

    Hodyss, D.; Anderson, J. L.; Collins, N.; Campbell, W. F.; Reinecke, P. A.

    2017-12-01

    Many Ensemble-Based Kalman ltering (EBKF) algorithms process the observations serially. Serial observation processing views the data assimilation process as an iterative sequence of scalar update equations. What is useful about this data assimilation algorithm is that it has very low memory requirements and does not need complex methods to perform the typical high-dimensional inverse calculation of many other algorithms. Recently, the push has been towards the prediction, and therefore the assimilation of observations, for regions and phenomena for which high-resolution is required and/or highly nonlinear physical processes are operating. For these situations, a basic hypothesis is that the use of the EBKF is sub-optimal and performance gains could be achieved by accounting for aspects of the non-Gaussianty. To this end, we develop here a new component of the Data Assimilation Research Testbed [DART] to allow for a wide-variety of users to test this hypothesis. This new version of DART allows one to run several variants of the EBKF as well as several variants of the quadratic polynomial lter using the same forecast model and observations. Dierences between the results of the two systems will then highlight the degree of non-Gaussianity in the system being examined. We will illustrate in this work the differences between the performance of linear versus quadratic polynomial regression in a hierarchy of models from Lorenz-63 to a simple general circulation model.

  9. Photon generator

    Science.gov (United States)

    Srinivasan-Rao, Triveni

    2002-01-01

    A photon generator includes an electron gun for emitting an electron beam, a laser for emitting a laser beam, and an interaction ring wherein the laser beam repetitively collides with the electron beam for emitting a high energy photon beam therefrom in the exemplary form of x-rays. The interaction ring is a closed loop, sized and configured for circulating the electron beam with a period substantially equal to the period of the laser beam pulses for effecting repetitive collisions.

  10. Optimal linear-quadratic control of coupled parabolic-hyperbolic PDEs

    Science.gov (United States)

    Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

    2017-10-01

    This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances.

  11. Management of linear quadratic regulator optimal control with full-vehicle control case study

    Directory of Open Access Journals (Sweden)

    Rodrigue Tchamna

    2016-09-01

    Full Text Available Linear quadratic regulator is a powerful technique for dealing with the control design of any linear and nonlinear system after linearization of the system around an operating point. For small systems, which have fewer state variables, the transformation of the performance index from scalar to matrix form can be straightforward. On the other hand, as the system becomes large with many state variables and controllers, appropriate design and notations should be defined to make it easy to automatically implement the technique for any large system without the need to redesign from scratch every time one requires a new system. The main aim of this article was to deal with this issue. This article shows how to automatically obtain the matrix form of the performance index matrices from the scalar version of the performance index. Control of a full-vehicle in cornering was taken as a case study in this article.

  12. On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study

    KAUST Repository

    Lima, Ricardo

    2016-06-16

    This paper addresses the solution of a cardinality Boolean quadratic programming problem using three different approaches. The first transforms the original problem into six mixed-integer linear programming (MILP) formulations. The second approach takes one of the MILP formulations and relies on the specific features of an MILP solver, namely using starting incumbents, polishing, and callbacks. The last involves the direct solution of the original problem by solvers that can accomodate the nonlinear combinatorial problem. Particular emphasis is placed on the definition of the MILP reformulations and their comparison with the other approaches. The results indicate that the data of the problem has a strong influence on the performance of the different approaches, and that there are clear-cut approaches that are better for some instances of the data. A detailed analysis of the results is made to identify the most effective approaches for specific instances of the data. © 2016 Springer Science+Business Media New York

  13. On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study

    KAUST Repository

    Lima, Ricardo; Grossmann, Ignacio E.

    2016-01-01

    This paper addresses the solution of a cardinality Boolean quadratic programming problem using three different approaches. The first transforms the original problem into six mixed-integer linear programming (MILP) formulations. The second approach takes one of the MILP formulations and relies on the specific features of an MILP solver, namely using starting incumbents, polishing, and callbacks. The last involves the direct solution of the original problem by solvers that can accomodate the nonlinear combinatorial problem. Particular emphasis is placed on the definition of the MILP reformulations and their comparison with the other approaches. The results indicate that the data of the problem has a strong influence on the performance of the different approaches, and that there are clear-cut approaches that are better for some instances of the data. A detailed analysis of the results is made to identify the most effective approaches for specific instances of the data. © 2016 Springer Science+Business Media New York

  14. The application of LQR synthesis techniques to the turboshaft engine control problem. [Linear Quadratic Regulator

    Science.gov (United States)

    Pfeil, W. H.; De Los Reyes, G.; Bobula, G. A.

    1985-01-01

    A power turbine governor was designed for a recent-technology turboshaft engine coupled to a modern, articulated rotor system using Linear Quadratic Regulator (LQR) and Kalman Filter (KF) techniques. A linear, state-space model of the engine and rotor system was derived for six engine power settings from flight idle to maximum continuous. An integrator was appended to the fuel flow input to reduce the steady-state governor error to zero. Feedback gains were calculated for the system states at each power setting using the LQR technique. The main rotor tip speed state is not measurable, so a Kalman Filter of the rotor was used to estimate this state. The crossover of the system was increased to 10 rad/s compared to 2 rad/sec for a current governor. Initial computer simulations with a nonlinear engine model indicate a significant decrease in power turbine speed variation with the LQR governor compared to a conventional governor.

  15. The quadratic reciprocity law a collection of classical proofs

    CERN Document Server

    Baumgart, Oswald

    2015-01-01

    This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.

  16. Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems

    International Nuclear Information System (INIS)

    Marquette, Ian

    2011-01-01

    There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.

  17. The bounds of feasible space on constrained nonconvex quadratic programming

    Science.gov (United States)

    Zhu, Jinghao

    2008-03-01

    This paper presents a method to estimate the bounds of the radius of the feasible space for a class of constrained nonconvex quadratic programmingsE Results show that one may compute a bound of the radius of the feasible space by a linear programming which is known to be a P-problem [N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373-395]. It is proposed that one applies this method for using the canonical dual transformation [D.Y. Gao, Canonical duality theory and solutions to constrained nonconvex quadratic programming, J. Global Optimization 29 (2004) 377-399] for solving a standard quadratic programming problem.

  18. Ultra-Low Power Optical Transistor Using a Single Quantum Dot Embedded in a Photonic Wire

    DEFF Research Database (Denmark)

    Nguyen, H.A.; Grange, T.; Malik, N.S.

    2017-01-01

    Using a single InAs quantum dot embedded in a GaAs photonic wire, we realize a giant non-linearity between two optical modes to experimentally demonstrate an all-optical transistor triggered by 10 photons.......Using a single InAs quantum dot embedded in a GaAs photonic wire, we realize a giant non-linearity between two optical modes to experimentally demonstrate an all-optical transistor triggered by 10 photons....

  19. Bound-Electron Nonlinearity Beyond the Ionization Threshold

    Science.gov (United States)

    Wahlstrand, J. K.; Zahedpour, S.; Bahl, A.; Kolesik, M.; Milchberg, H. M.

    2018-05-01

    We present absolute space- and time-resolved measurements of the ultrafast laser-driven nonlinear polarizability in argon, krypton, xenon, nitrogen, and oxygen up to ionization fractions of a few percent. These measurements enable determination of the strongly nonperturbative bound-electron nonlinear polarizability well beyond the ionization threshold, where it is found to remain approximately quadratic in the laser field, a result normally expected at much lower intensities where perturbation theory applies.

  20. On the vibrations of a simply supported square plate on a weakly nonlinear elastic foundation

    NARCIS (Netherlands)

    Zarubinskaya, M.A.; Van Horssen, W.T.

    2003-01-01

    In this paper an initial-boundary value problem for a weakly nonlinear plate equation with a quadratic nonlinearity will be studied. This initial-boundary value problem can be regarded as a simple model describing free oscillations of a simply supported square plate on an elastic foundation. It is