Stable One-Dimensional Periodic Wave in Kerr-Type and Quadratic Nonlinear Media
Directory of Open Access Journals (Sweden)
Roxana Savastru
2012-01-01
Full Text Available We present the propagation of optical beams and the properties of one-dimensional (1D spatial solitons (“bright” and “dark” in saturated Kerr-type and quadratic nonlinear media. Special attention is paid to the recent advances of the theory of soliton stability. We show that the stabilization of bright periodic waves occurs above a certain threshold power level and the dark periodic waves can be destabilized by the saturation of the nonlinear response, while the dark quadratic waves turn out to be metastable in the broad range of material parameters. The propagation of (1+1 a dimension-optical field on saturated Kerr media using nonlinear Schrödinger equations is described. A model for the envelope one-dimensional evolution equation is built up using the Laplace transform.
Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media
Energy Technology Data Exchange (ETDEWEB)
Kartashov, Yaroslav V [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, E-08034 Barcelona (Spain); Egorov, Alexey A [Physics Department, M V Lomonosov Moscow State University, 119899, Moscow (Russian Federation); Vysloukh, Victor A [Departamento de Fisica y Matematicas, Universidad de las Americas-Puebla, Santa Catarina Martir, 72820, Puebla, Cholula (Mexico); Torner, Lluis [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, E-08034 Barcelona (Spain)
2004-05-01
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.
Institute of Scientific and Technical Information of China (English)
YANG Yong; YAN Zhen-Ya
2002-01-01
In this letter the three-dimensional nonlinear Helmholtz equation is investigated, which describes electro-magnetic wave propagation in a nonlinear Kerr-type medium such that sixteen families of new Jacobi elliptic functionsolutions are obtained, by using our extended Jacobian elliptic function expansion method. When the modulus m → 1or0, the corresponding solitary waves including bright solitons, dark solitons and new line solitons and singly periodicsolutions can be also found.
Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Zhong, Wei-Ping, E-mail: zhongwp6@126.com [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Texas A and M University at Qatar, P.O. Box 23874 Doha (Qatar); Belić, Milivoj [Texas A and M University at Qatar, P.O. Box 23874 Doha (Qatar); Institute of Physics, University of Belgrade, P.O. Box 57, 11001 Belgrade (Serbia)
2014-12-15
We present a class of exact solutions to the coupled (2+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity and a special external potential, which describe the evolution of two-component vector solitons in defocusing Kerr-type media. We find a robust soliton solution, constructed with the help of Whittaker functions. For specific choices of the topological charge, the radial mode number and the modulation depth, the solitons may exist in various forms, such as the half-moon, necklace-ring, and sawtooth vortex-ring patterns. Our results show that the profile of such solitons can be effectively controlled by the topological charge, the radial mode number, and the modulation depth. - Highlights: • Two-component vector soliton clusters in defocusing Kerr-type media are reported. • These soliton clusters are constructed with the help of Whittaker functions. • The half-moon, necklace-ring and vortex-ring patterns are found. • The profile of these solitons can be effectively controlled by three soliton parameters.
Time delay in thin slabs with self-focusing Kerr-type nonlinearity
Isić, G.; Milanović, V.; Radovanović, J.; Ikonić, Z.; Indjin, D.; Harrison, P.
2008-03-01
Time delays for an intense transverse electric (TE) wave propagating through a Kerr-type nonlinear slab are investigated. The relation between the bidirectional group delay and the dwell time is derived and it is shown that the difference between them can be separated into three terms. The first one is the familiar self-interference time, due to the dispersion of the medium surrounding the slab. The other two terms are caused by the nonlinearity and oblique incidence of the TE wave. It is shown that the electric field distribution along the slab may be expressed in terms of Jacobi elliptic functions while the phase difference introduced by the slab is given in terms of incomplete elliptic integrals. The expressions for the field-intensity-dependent complex reflection and transmission coefficients are derived and the multivalued oscillatory behavior of the delay times for the case of a thin slab is demonstrated.
Energy Technology Data Exchange (ETDEWEB)
Xu Guoding, E-mail: guodingxu@163.co [Department of Physics, Suzhou University of Science and Technology, Suzhou 215009 (China); Zang Taocheng; Mao Hongmin; Pan Tao [Department of Physics, Suzhou University of Science and Technology, Suzhou 215009 (China)
2010-07-26
As the surface polaritons are excited in Kretschmann configuration with a Kerr-type substrate, the nonlinear Goos-Haenchen (GH) shifts exhibit the optically hysteretic response to the intensity of incident light. For thicker metal films, the GH shifts become very sensitive to the intensity of incident light and the angle of incidence.
Kerr nonlinearity and plasmonic bistability in graphene nanoribbons
DEFF Research Database (Denmark)
Christensen, Thomas; Yan, Wei; Jauho, Antti-Pekka;
2015-01-01
We theoretically examine the role of Kerr nonlinearities for graphene plasmonics in nanostructures, specifically in nanoribbons. The nonlinear Kerr interaction is included semiclassically in the intraband approximation. The resulting electromagnetic problem is solved numerically by self-consisten...
Modulational instability in nonlocal nonlinear Kerr media
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Juul Rasmussen, Jens
2001-01-01
We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespective of the particular profile of the nonlocal response function....... For a defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media...... for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose...
Sadhu, Arunangshu; Sarkar, Somenath
2016-08-01
We investigate the Kerr nonlinear optical processes (NOPs) in the case of a single-mode trapezoidal index fiber based on recently formulated and appropriate Marcuse-type relations for spot size in terms of normalized frequency corresponding to such fiber having various aspect ratios. With the help of these relations, we have analyzed the maximum NOP in these fibers having prospective the merits of tight light confinement in the subwavelength diameter waveguiding region. The comparative investigation reveals that the aspect ratio having a value of 0.7 is the most promising candidate for maximum optical nonlinearity, constructional convenience, and less diffraction. The analysis should be attractive for system users as a ready reference.
Enhanced Kerr nonlinearity via quantum interference from spontaneous emission
Energy Technology Data Exchange (ETDEWEB)
Asadpour, S.H., E-mail: S.Hosein.Asadpour@gmail.com [Young Researchers Club, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali (Iran, Islamic Republic of); Sahrai, M. [Research Institute for Applied Physics and Astronomy, University of Tabriz, Tabriz (Iran, Islamic Republic of); Soltani, A. [School of Engineering and Emerging Technologies, University of Tabriz, Tabriz (Iran, Islamic Republic of); Hamedi, H.R. [Research Institute for Applied Physics and Astronomy, University of Tabriz, Tabriz (Iran, Islamic Republic of)
2012-01-02
A novel atom configuration is proposed for a giant Kerr nonlinearity in zero linear and nonlinear probe absorption. It is shown that without coherent control field and just by quantum interference of spontaneous emission, a giant Kerr nonlinearity can be obtained. -- Highlights: ► The quantum interference from spontaneous emission is considered in a four-level medium. ► The giant Kerr nonlinearity in the zero linear and nonlinear absorption is obtained. ► The quantum interference effect on group velocity is then investigated.
Yarmoghaddam, Elahe; Rakheja, Shaloo
2017-08-01
We theoretically model the dispersion characteristics of surface plasmons in a graphene-based parallel-plate waveguide geometry using nonlinear Kerr-type core (inter-plate) dielectric. The optical nonlinearity of graphene in the terahertz band under high light intensity is specifically included in the analysis. By solving Maxwell's equations and applying appropriate boundary conditions, we show that the waveguide supports four guided plasmon modes, each of which can be categorized as either symmetric or anti-symmetric based on the electric field distribution in the structure. Of the four guided modes, two modes are similar in characteristics to the modes obtained in the structure with linear graphene coating, while the two new modes have distinct characteristics as a result of the nonlinearity of graphene. We note that the group velocity of one of the plasmon modes acquires a negative value under high light intensity. Additionally, the optical nonlinearity of the core dielectric leads to a significant enhancement in the localization length of various plasmon modes. The description of the intra-band optical conductivity of graphene incorporates effects of carrier scatterings due to charged impurities, resonant scatterers, and acoustic phonons at 300 K. The proposed structure offers flexibility to tune the waveguide characteristics and the mode index by changing light intensity and electrochemical potential in graphene for reconfigurable plasmonic devices.
Measurement of the Kerr nonlinear refractive index of Cs vapor
Araújo, Michelle O; Oriá, Marcos; Chevrollier, Martine; de Silans, Thierry Passerat; Castro, Romeu; Moretti, Danieverton
2014-01-01
Atomic vapors are systems well suited for nonlinear optics studies but very few direct measurements of their nonlinear refractive index have been reported. Here we use the z-scan technique to measure the Kerr coefficient, $n_2$, for a Cs vapor. Our results are analyzed through a four-level model, and we show that coherence between excited levels as well as cross-population effects contribute to the Kerr-nonlinearity.
Kerr-lens Mode Locking Without Nonlinear Astigmatism
Yefet, Shi; Pe'er, Avi
2013-01-01
We demonstrate a Kerr-lens mode locked folded cavity using a planar (non-Brewster) Ti:sapphire crystal as a gain and Kerr medium, thus cancelling the nonlinear astigmatism caused by a Brewster cut Kerr medium. Our method uses a novel cavity folding in which the intra-cavity laser beam propagates in two perpendicular planes such that the astigmatism of one mirror is compensated by the other mirror, enabling the introduction of an astigmatic free, planar-cut gain medium. We demonstrate that this configuration is inherently free of nonlinear astigmatism, which in standard cavity folding needs a special power specific compensation.
Dark Spatial Soliton Interaction in Nonlinear Kerr Medium
Institute of Scientific and Technical Information of China (English)
LuchuanWANG; QinliangFAN
1998-01-01
The dark spatial soliton interaction in nonlinear Kerr medium has been studied in this paper.The problem has been solved by the use of the slowly varying envelope approximation in solving coupled nonlinear Schroedinger equations.The perturbation nature of dark spatial soliton interaction has been described and some of their key properties has been discussed as well in the paper.
Enhanced Kerr electro-optic nonlinearity through cascaded Pockels effects
Li, Guang-Zhen; Jiang, Hao-Wei; Chen, Xian-Feng
2015-01-01
We demonstrated a large enhancement of Kerr electro-optic nonlinearity through cascaded Pockels effects in a domain inversion ferroelectric crystal. We designed a structure that can implement the cascaded Pockels effects and second-harmonic generation simultaneously. The energy coupling between the fundamental lights of different polarizations led to a large nonlinear phase shift, and thus an effective electro-optic nonlinear refractive index. The effective nonlinearity can be either positive or negative, causing the second-harmonic spectra to move towards the coupling center, which in turn, offered us a way to measure the effective electro-optic nonlinear refractive index. The corresponding enhanced Kerr electro-optic nonlinearity is more than three orders of magnitude higher than the intrinsic value. These results open a door to manipulate the nonlinear phase by applying external electric field instead of light intensity in noncentrosymmetric crystals.
Thermodynamics of Phase Transitions of a Kerr Nonlinear Blackbody
Institute of Scientific and Technical Information of China (English)
CHENG Ze
2008-01-01
We study the thermodynamics of phase transitions of a blackbody whose interior is filled by a Kerr nonlinear crystal. There is a transition temperature To, above which the Kerr nonlinear blackbody is in the normal thermal radiation state, and below which it is in the squeezed thermal radiation state. At To, the Gibbs free energy of the two phases is continuous but the entropy density of the two phases is discontinuous. Hence, there is a jump in the entropy density and this leads to a latent heat density. The photon system undergoes a first-order phase transition from the normal to the squeezed thermal radiation state.
The anisotropic Kerr nonlinear refractive index of \\beta-BaB_2O_4
Bache, Morten; Zhou, Binbin; Zeng, Xianglong
2012-01-01
We study the anisotropic nature of the Kerr nonlinear response in a \\beta-BaB_2O_4 (BBO) crystal. The focus is on determining the relevant $\\chi^{(3)}$ cubic tensor component in connection with type I cascaded quadratic interaction, which is done by analyzing various experiments in the literature. We correct the data from some of the experiments for contributions from cascading as well as for updated material parameters, and find that the Kerr nonlinear refractive index used to model self-phase modulation in cascading is considerably larger than what has been used to date.
Non-linear Q-clouds around Kerr black holes
Directory of Open Access Journals (Sweden)
Carlos Herdeiro
2014-12-01
Full Text Available Q-balls are regular extended ‘objects’ that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces – existence lines – of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q-clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q-cloud reduces to a linear cloud. Thus, Q-clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q-clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family.
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A.; Carvalho, Márcio; Leblond, Hervé; Malomed, Boris A.
2016-11-01
We elaborate a solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water, and optical glasses at sufficiently high intensities. We also show that the tubular, rotating, and specklelike filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A; Leblond, Hervé; Malomed, Boris A
2016-01-01
We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water and optical glasses at sufficiently high intensities. We also show that the tubular, rotating and speckle-like filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Nonlinear plasmonics with Kerr-like media for sensing
Crutcher, Sihon H.; Ruffin, Paul B.; Edwards, Eugene; Brantley, Christina L.
2014-04-01
Sensing technologies are currently needed for better maintainability, reliability, safety, and monitoring small variable changes on microscopic and nanoscale systems. Plasmonic sensor research has contributed to chemical and biological sensing needs by monitoring ultrafast temporal and spatial changes in optoelectronic systems. Nonlinear plasmonic waveguides with subwavelength confinement can further enhance the capabilities of plasmonic devices. Results in this paper highlight the derivation of the full-vector Maxwell Equations for the single metal- dielectric slot waveguide and the metal -dielectric -metal waveguide with the dielectric having a Kerr-like nonlinearity. These waveguides, typically have metallic losses that compete with nonlinearity at certain frequencies that can hinder surface plasmon wave propagation. By considering temporal and spatial beam propagation in these waveguides one expects to observe novel effects that could be used for sensing applications such as femtosecond pulse propagation with plasmon self-focusing, self-trapping, and frequency conversion with reduction in metallic losses.
DEFF Research Database (Denmark)
Bache, Morten; Guo, Hairun; Zhou, Binbin
2013-01-01
We study the anisotropic nature of the Kerr nonlinear response in a beta-barium borate (β-BaB2O4, BBO) nonlinear crystal. The focus is on determining the relevant χ(3) cubic tensor components that affect interaction of type I cascaded second-harmonic generation. Various experiments in the literat...
Plasmon-enhanced Kerr nonlinearity via subwavelength-confined anisotropic Purcell factors
Ren, Juanjuan; Chen, Hongyi; Gu, Ying; Zhao, Dongxing; Zhou, Haitao; Zhang, Junxiang; Gong, Qihuang
2016-10-01
We theoretically investigate the enhancement of Kerr nonlinearity through anisotropic Purcell factors provided by plasmon nanostructures. In a three-level atomic system with crossing damping, larger anisotropism of Purcell factors leads to more enhanced Kerr nonlinearity in electromagnetically induced transparency windows. While for fixed anisotropic Purcell factors, Kerr nonlinearity with orthogonal dipole moments increases with the decrease of its crossing damping, and Kerr nonlinearity with nonorthogonal dipole moments is very sensitive to both the value of crossing damping and the orientation of the dipole moments. We design the non-resonant gold nanorods array, which only provides subwavelength-confined anisotropic Purcell factors, and demonstrate that the Kerr nonlinearity of cesium atoms close to the nanorods array can be modulated at the nanoscale. These findings should have potential application in ultracompact quantum logic devices.
Zhu, Chengjie; Huang, Guoxiang
2011-11-07
We study linear and nonlinear propagations of probe and signal pulses in a multiple quantum-well structure with a four-level, double Λ-type configuration. We show that slow, mutually matched group velocities and giant Kerr nonlinearity of the probe and the signal pulses may be achieved with nearly vanishing optical absorption. Based on these properties we demonstrate that two-qubit quantum polarization phase gates can be constructed and highly entangled photon pairs may be produced. In addition, we show that coupled slow-light soliton pairs with very low generation power can be realized in the system.
Naseri, Tayebeh; Moradi, Ronak
2017-01-01
Some optical properties including the linear and nonlinear susceptibility and electromagnetically induced phase grating (EIG) in graphene under Raman excitation is studied. A single-layer graphene nanostructure driven by coherent and incoherent fields is investigated theoretically. It is revealed that by adjusting the amplitude of control and incoherent fields, the linear and nonlinear absorption as well as Kerr nonlinearity of the medium can be optimized. It is realized that the enhanced Kerr nonlinearity can occur with zero linear absorption and nonlinear amplification. Furthermore, it should be noted that EIG in graphene is studied for the first time. The results indicate that the diffraction efficiency of the phase grating is dramatically enhanced by controlling the amplitude of coherent and incoherent fields, and an efficient electromagnetically induced phase grating can be obtained. A novel result shows a considerable improvement of the intensity of higher-order diffractions and switching between different orders of grating via incoherent pumping field. Therefore, this model can be used in real experiments for the development of new types of nanoelectronic devices used for the realization of all-optical switching processes.
Bacha, Bakht Amin; Nazmidinov, Rashid G
2014-01-01
A Field Generated Coherence (FGC)' based 3-field cyclically-driven 4-level atomic system, which is an extended version of $\\Lambda$ type schemes, is investigated for Autler-Townes triplet absorption (ATT) spectroscopy. Two dark lines which appear in the ATT spectrum, are the essence of the generated multiple controllable EIT windows for a superluminal Gaussian light pulse. We also investigate enhancement in the group velocity for the Gaussian light pulse, using a nonlinear coherence Kerr effect. Consequently, the superluminal probing pulse leaves a steep anomalous region of the medium by $28 \\mu s$ sooner than the light pulse of the Kerr-free system. A co-linear propagation of the driving fields is suggested to minimize our explored Doppler broadening incoherence effect on the probe pulse. Indeed, the analytically observed undistorted retrieved light pulse, which is a necessary and useful requirement for realization of the results in laboratory, is also shown and analyzed explicitly.
Negative Kerr Nonlinearity of Graphene as seen via Chirped-Pulse-Pumped Self-Phase Modulation
Vermeulen, Nathalie; Castelló-Lurbe, David; Cheng, JinLuo; Pasternak, Iwona; Krajewska, Aleksandra; Ciuk, Tymoteusz; Strupinski, Wlodek; Thienpont, Hugo; Van Erps, Jürgen
2016-10-01
We experimentally demonstrate a negative Kerr nonlinearity for quasiundoped graphene. Hereto, we introduce the method of chirped-pulse-pumped self-phase modulation and apply it to graphene-covered silicon waveguides at telecom wavelengths. The extracted Kerr-nonlinear index for graphene equals n2 ,gr=-10-13 m2 /W . Whereas the sign of n2 ,gr turns out to be negative in contrast to what has been assumed so far, its magnitude is in correspondence with that observed in earlier experiments. Graphene's negative Kerr nonlinearity strongly impacts how graphene should be exploited for enhancing the nonlinear response of photonic (integrated) devices exhibiting a positive nonlinearity. It also opens up the possibility of using graphene to annihilate unwanted nonlinear effects in such devices, to develop unexplored approaches for establishing Kerr processes, and to extend the scope of the "periodic poling" method often used for second-order nonlinearities towards third-order Kerr processes. Because of the generic nature of the chirped-pulse-pumped self-phase modulation method, it will allow fully characterizing the Kerr nonlinearity of essentially any novel (2D) material.
Enhancement of Kerr nonlinearity and its application to entangled state discrimination
Institute of Scientific and Technical Information of China (English)
NIU Yue-ping; QIAN Jun; FENG Xun-li; GONG Shang-qing
2007-01-01
In this paper, the recent research on the enhan-ced Kerr nonlinearity and its application in entangled state discrimination is reported. Two kinds of dynamics, including interacting double dark resonances and spontaneously gen-erated coherence, are presented to enhance the Kerr nonlin-earity. The application of Kerr nonlinearity in quantum state discrimination is also discussed. An arbitrary Greenberger-Horne-Zeilinger state can be discriminated using two-photon polarization parity detection which resorts to cross-Kerr no-nlinearity between a single-photon qubit and probe field. In addition, a scheme for Greenberger-Home-Zeilinger state discrimination of matter qubits is also proposed using the dipole induced transparency in a cavity-dipole system.
Negative Kerr nonlinearity of graphene as seen via chirped-pulse-pumped self-phase modulation
Vermeulen, Nathalie; Cheng, JinLuo; Pasternak, Iwona; Krajewska, Aleksandra; Ciuk, Tymoteusz; Strupinski, Wlodek; Thienpont, Hugo; Van Erps, Jurgen
2016-01-01
We experimentally demonstrate a negative Kerr nonlinearity for quasi-undoped graphene. Hereto, we introduce the method of chirped-pulse-pumped self-phase modulation and apply it to graphene-covered silicon waveguides at telecom wavelengths. The extracted Kerr-nonlinear index for graphene equals n2,gr = -10^(-13) m^2/W. Whereas the sign of n2,gr turns out to be negative in contrast to what has been assumed so far, its magnitude is in correspondence with that observed in earlier experiments. Graphene's negative Kerr nonlinearity strongly impacts how graphene should be exploited for enhancing the nonlinear response of photonic (integrated) devices exhibiting a positive nonlinearity. It also opens up the possibility of using graphene to annihilate unwanted nonlinear effects in such devices, to develop unexplored approaches for establishing Kerr processes, and to extend the scope of the "periodic poling" method often used for second-order nonlinearities towards third-order Kerr processes. Because of the generic na...
The global non-linear stability of the Kerr-de Sitter family of black holes
Hintz, Peter
2016-01-01
We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta, and without any symmetry assumptions on the initial data. We achieve this by extending the linear and non-linear analysis on black hole spacetimes described in a sequence of earlier papers by the authors: We develop a general framework which enables us to deal systematically with the diffeomorphism invariance of Einstein's equations. In particular, the iteration scheme used to solve Einstein's equations automatically finds the parameters of the Kerr-de Sitter black hole that the solution is asymptotic to, the exponentially decaying tail of the solution, and the gauge in which we are able to find the solution; the gauge here is a wave map/DeTurck type gauge, modified by source terms which are treated as unknowns, lying in a suitable finite-dimensional space.
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...
Chaos control in the nonlinear Schrödinger equation with Kerr law nonlinearity
Yin, Jiu-Li; Zhao, Liu-Wei; Tian, Li-Xin
2014-02-01
The nonlinear Schrödinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions.
Z-scan technique for investigation of the noninstantaneous optical Kerr nonlinearity.
Gu, Bing; Wang, Hui-Tian; Ji, Wei
2009-09-15
By treating laser-induced optical Kerr nonlinearity as a noninstantaneous decaying process, we present the pulse-duration-dependent Z-scan analytical expressions for an arbitrary aperture and an arbitrary nonlinear magnitude. This theory has the capacity to characterize the third-order nonlinear refraction induced by a laser pulse with its temporal duration being much longer than or comparable to the recovery time of the nonlinear effect. Through Z-scan measurements at different pulse durations, the nonlinear refractive coefficient and the recovery time could be determined unambiguously and simultaneously. Furthermore, the theory can be utilized to confirm whether the measured optical Kerr nonlinearity is instantaneous or noninstantaneous with respect to the given pulse duration.
Double-dark-resonance-enhanced Kerr nonlinearity in a single layer of graphene nanostructure
Solookinejad, Gh.; Panahi, M.; Ahmadi Sangachin, E.; Hossein Asadpour, Seyyed
2016-08-01
In this paper, a novel scheme is proposed for the giant enhanced Kerr nonlinearity in a single layer of graphene nanostructure based on quantum optics and nonlinear optical sciences. The linear and the nonlinear susceptibility of the monolayer graphene system are presented in details by using the density matrix method and perturbation theory. After deriving the equations of motion in the steady-state regime, we analytically solve the linear and nonlinear susceptibility of the system. Our numerical results show that the giant enhanced Kerr nonlinearity can be obtained in the double-dark-resonance condition with zero linear and nonlinear absorption. Our results may have potential applications in quantum information science in infrared and terahertz regimes.
Enhanced Kerr nonlinearity in a quantized four-level graphene nanostructure
Ghahraman, Solookinejad; M, Panahi; E, Ahmadi; Seyyed, Hossein Asadpour
2016-07-01
In this paper, a new model is proposed for manipulating the Kerr nonlinearity of right-hand circular probe light in a monolayer of graphene nanostructure. By using the density matrix equations and quantum optical approach, the third-order susceptibility of probe light is explored numerically. It is realized that the enhanced Kerr nonlinearity with zero linear absorption can be provided by selecting the appropriate quantities of controllable parameters, such as Rabi frequency and elliptical parameter of elliptical polarized coupling field. Our results may be useful applications in future all-optical system devices in nanostructures.
Johansson, Magnus; Derevyanko, Stanislav A
2013-01-01
We investigate the mobility of nonlinear localized modes in a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping, described by a generalized discrete Ginzburg-Landau type model. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations, and slower, large-oscillation modes. The velocities and the oscillation periods are typically related...
Phase stabilization of Kerr frequency comb internally without nonlinear optical interferometry
Huang, S -W; Yang, J; Yu, M; Kwong, D -L; Wong, C W
2016-01-01
Optical frequency comb (OFC) technology has been the cornerstone for scientific breakthroughs such as precision frequency metrology, redefinition of time, extreme light-matter interaction, and attosecond sciences. While the current mode-locked laser-based OFC has had great success in extending the scientific frontier, its use in real-world applications beyond the laboratory setting remains an unsolved challenge. Microresonator-based OFCs, or Kerr frequency comb, have recently emerged as a candidate solution to the challenge because of their preferable size, weight, and power consumption (SWaP). On the other hand, the current phase stabilization technology requires either external optical references or power-demanding nonlinear processes, overturning the SWaP benefit of Kerr frequency combs. Introducing a new concept in phase control, here we report an internally phase stabilized Kerr frequency comb without the need of any optical references or nonlinear processes. We describe the comb generation analytically ...
Measurement-Induced Strong Kerr Nonlinearity for Weak Quantum States of Light
Costanzo, Luca S.; Coelho, Antonio S.; Biagi, Nicola; Fiurášek, Jaromír; Bellini, Marco; Zavatta, Alessandro
2017-07-01
Strong nonlinearity at the single photon level represents a crucial enabling tool for optical quantum technologies. Here we report on experimental implementation of a strong Kerr nonlinearity by measurement-induced quantum operations on weak quantum states of light. Our scheme coherently combines two sequences of single photon addition and subtraction to induce a nonlinear phase shift at the single photon level. We probe the induced nonlinearity with weak coherent states and characterize the output non-Gaussian states with quantum state tomography. The strong nonlinearity is clearly witnessed as a change of sign of specific off-diagonal density matrix elements in the Fock basis.
Multiple four-wave mixing and Kerr combs in a bichromatically pumped nonlinear fiber ring cavity.
Ceoldo, D; Bendahmane, A; Fatome, J; Millot, G; Hansson, T; Modotto, D; Wabnitz, S; Kibler, B
2016-12-01
We report numerical and experimental studies of multiple four-wave mixing processes emerging from dual-frequency pumping of a passive nonlinear fiber ring cavity. We observe the formation of a periodic train of nearly background-free soliton pulses associated with Kerr frequency combs. The generation of resonant dispersive waves is also reported.
Comparative Study of FDTD-Adopted Numerical Algorithms for Kerr Nonlinearities
DEFF Research Database (Denmark)
Maksymov, Ivan S.; Sukhorukov, Andrey A.; Lavrinenko, Andrei
2011-01-01
Accurate finite-difference time-domain (FDTD) modeling of optical pulse propagation in nonlinear media usually implies the use of auxiliary differential equation (ADE) techniques. The updating of electric field in full-vectorial 3-D ADE FDTD modeling of the optical Kerr effect and two-photon abso...... approaches. Such schemes can significantly reduce the CPU time for nonlinear computations, especially in 3-D models....
DEFF Research Database (Denmark)
Bache, Morten; Guo, Hairun; Zhou, Binbin;
2013-01-01
We study the anisotropic nature of the Kerr nonlinear response in a beta-barium borate (β-BaB2O4, BBO) nonlinear crystal. The focus is on determining the relevant χ(3) cubic tensor components that affect interaction of type I cascaded second-harmonic generation. Various experiments...... a complete list that we propose as reference of the four major cubic tensor components in BBO. We finally discuss the impact of using the cubic anisotropic response in ultrafast cascading experiments in BBO....
Comparative Study of FDTD-Adopted Numerical Algorithms for Kerr Nonlinearities
DEFF Research Database (Denmark)
Maksymov, Ivan S.; Sukhorukov, Andrey A.; Lavrinenko, Andrei;
2011-01-01
Accurate finite-difference time-domain (FDTD) modeling of optical pulse propagation in nonlinear media usually implies the use of auxiliary differential equation (ADE) techniques. The updating of electric field in full-vectorial 3-D ADE FDTD modeling of the optical Kerr effect and two-photon abso......Accurate finite-difference time-domain (FDTD) modeling of optical pulse propagation in nonlinear media usually implies the use of auxiliary differential equation (ADE) techniques. The updating of electric field in full-vectorial 3-D ADE FDTD modeling of the optical Kerr effect and two......-photon absorption in optical media is proceeded conventionally through the iterative solution of nonlinear algebraic equations. Here, we study three approaches for the field update including simple noniterative explicit schemes. By comparing them to the analytical results for optical pulse propagation in long...
Vukovic, N.; Healy, N.; Suhailin, F. H.; Mehta, P.; Day, T. D.; Badding, J. V.; Peacock, A. C.
2013-10-01
Microresonators are ideal systems for probing nonlinear phenomena at low thresholds due to their small mode volumes and high quality (Q) factors. As such, they have found use both for fundamental studies of light-matter interactions as well as for applications in areas ranging from telecommunications to medicine. In particular, semiconductor-based resonators with large Kerr nonlinearities have great potential for high speed, low power all-optical processing. Here we present experiments to characterize the size of the Kerr induced resonance wavelength shifting in a hydrogenated amorphous silicon resonator and demonstrate its potential for ultrafast all-optical modulation and switching. Large wavelength shifts are observed for low pump powers due to the high nonlinearity of the amorphous silicon material and the strong mode confinement in the microcylindrical resonator. The threshold energy for switching is less than a picojoule, representing a significant step towards advantageous low power silicon-based photonic technologies.
Energy Technology Data Exchange (ETDEWEB)
Torres-Torres, C., E-mail: crstorres@yahoo.com.mx [Seccion de Estudios de Posgrado e Investigacion, ESIME-Z, Instituto Politecnico Nacional, Mexico, DF 07738 (Mexico); Garcia-Cruz, M.L. [Centro de Investigacion en Dispositivos Semiconductores, Benemerita Universidad Autonoma de Puebla, A. P. J-48, Puebla 72570, Mexico (Mexico); Castaneda, L., E-mail: luisca@sirio.ifuap.buap.mx [Instituto de Fisica, Benemerita Universidad Autonoma de Puebla, A. P. J-48, Puebla 72570, Mexico (Mexico); Rangel Rojo, R. [CICESE/Depto. de Optica, A. P. 360, Ensenada, BC 22860 (Mexico); Tamayo-Rivera, L. [Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Mexico, DF 01000 (Mexico); Maldonado, A. [Depto. de Ing. Electrica, CINVESTAV IPN-SEES, A. P. 14740, Mexico DF 07000 (Mexico); Avendano-Alejo, M., E-mail: imax_aa@yahoo.com.mx [Centro de Ciencias Aplicadas y Desarrollo Tecnologico, Universidad Nacional Autonoma de Mexico, A. P. 70-186, 04510, DF (Mexico); and others
2012-04-15
Chromium doped zinc oxide thin solid films were deposited on soda-lime glass substrates. The photoconductivity of the material and its influence on the optical behavior was evaluated. A non-alkoxide sol-gel synthesis approach was used for the preparation of the samples. An enhancement of the photoluminescence response exhibited by the resulting photoconductive films with embedded chromium nanoclusters is presented. The modification in the photoconduction induced by a 445 nm wavelength was measured and then associated with the participation of the optical absorptive response. In order to investigate the third order optical nonlinearities of the samples, a standard time-resolved Optical Kerr Gate configuration with 80 fs pulses at 830 nm was used and a quasi-instantaneous pure electronic nonlinearity without the contribution of nonlinear optical absorption was observed. We estimate that from the inclusion of Cr nanoclusters into the sample results a strong optical Kerr effect originated by quantum confinement. The large photoluminescence response and the important refractive nonlinearity of the photoconductive samples seem to promise potential applications for the development of multifunctional all-optical nanodevices. - Highlights: Black-Right-Pointing-Pointer Enhancement in photoluminescence for chromium doped zinc oxide films is presented. Black-Right-Pointing-Pointer A strong and ultrafast optical Kerr effect seems to result from quantum confinement. Black-Right-Pointing-Pointer Photoconductive properties for optical and optoelectronic functions were observed.
Indian Academy of Sciences (India)
Zaiyun Zhang; Jianhua Huang; Juan Zhong; Sha-Sha Dou; Jiao Liu; Dan Peng; Ting Gao
2014-06-01
In this paper, we construct the travelling wave solutions to the perturbed nonlinear Schrödinger’s equation (NLSE) with Kerr law non-linearity by the extended (′/)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with Kerr law nonlinearity with arbitrary parameters. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.
Institute of Scientific and Technical Information of China (English)
Su Shi-Lei; Wang Yuan; Guo Qi; Wang Hong-Fu; Zhang Shou
2012-01-01
We propose a protocol to generate a four-photon polarization-entangled cluster state with cross-Kerr nonlinearity by using the interference of polarized photons. The protocol is based on optical elements,cross-Kerr nonlinearity,and homodyne measurement,therefore it is feasible with current experimental technology.The success probability of our protocol is optimal,this property makes our protocol more efficient than others in the applications of quantum communication.
Energy Squeeze of Ultrashort Light Pulse by Kerr Nonlinear Photonic Crystals
Institute of Scientific and Technical Information of China (English)
LIU Ye; ZHOU Fei; ZHANG Dao-Zhong; LI Zhi-Yuan
2009-01-01
Self-phase modulation can efficiently shape the spectrum of an optical pulse propagating along an optical material with Kerr nonlinearity. In this work we show that a one-dimensional Kerr nonlinear photonic crystal can impose anomalous spectrum modulation to a high-power ultrashort light pulse. The spectrum component at the photonic band gap edge can be one order of magnitude enhanced in addition to the ordinary spectrum broadening due to self-phase modulation. The enhancement is strictly pinned at the band gap edge by changing the sample length, the intensity or central wavelength of the incident pulse. The phenomenon is attributed to band gap induced enhancement of light-matter interaction.
Plasmon beams interaction at interface between metal and dielectric with saturable Kerr nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Ignatyeva, Daria O.; Sukhorukov, Anatoly P. [Lomonosov Moscow State University, Moscow (Russian Federation)
2012-12-15
We present a novel theory of surface plasmon polariton interaction on the surface of dielectric with saturable Kerr nonlinearity. The effect of the total internal reflection of a weak signal plasmon beam from a high-power reference beam is discussed. Both ray and wave theories are used to describe signal propagation. The effect of the signal tunneling through the narrow inhomogeneity induced by the reference beam is considered. (orig.)
Indian Academy of Sciences (India)
Hari Prakash; Devendra K Singh
2010-03-01
It is shown that all optical polarization states of light except plane and circular polarization states undergo an intensity-dependent change in normal incidence of light in an isotropic nonlinear Kerr medium. This effect should be detectable and we propose an experiment for detecting nonlinear susceptibility involved in that part of nonlinear polarization, which depends on the polarization state of light also.
Theoretical investigation on Raman induced Kerr effect spectroscopy in nonlinear confocal microscopy
Institute of Scientific and Technical Information of China (English)
Gun LiNa; TANG ZhiLie; XING Da
2008-01-01
The imaging theory of Raman induced Kerr effect spectroscopy (RIKES) in nonlinear confocal microscopy is presented in this paper. Three-dimensional point spread function (3D-PSF) of RIKES nonlinear confocal microscopy in isotropic media is derived with Fourier imaging theory and RIKES theory. The impact of nonlinear property of RIKES on the spatial resolution and imaging properties of confocal microscopy have been analyzed in detail. It is proved that RIKES nonlinear confocal microscopy can simultaneously provide more information than twophoton confocal microscopy concerning molecular vibration mode, vibration orientation and optically induced molecular reorientation, etc. It is shown that RIKES nonlinear confocal microscopy significantly enhances the spatial resolution and imaging quality of confocal microscopy and achieves much higher resolution than that of two-photon confocal microscopy.
Theoretical investigation on Raman induced Kerr effect spectroscopy in nonlinear confocal microscopy
Institute of Scientific and Technical Information of China (English)
2008-01-01
The imaging theory of Raman induced Kerr effect spectroscopy (RIKES) in nonlinear confocal microscopy is presented in this paper. Three-dimensional point spread function (3D-PSF) of RIKES nonlinear confocal microscopy in isotropic media is derived with Fourier imaging theory and RIKES theory. The impact of nonlinear property of RIKES on the spatial resolution and imaging properties of confocal microscopy have been analyzed in detail. It is proved that RIKES nonlinear confocal microscopy can simultaneously provide more information than two-photon confocal microscopy concerning molecular vibration mode, vibration orientation and optically induced molecular reorientation, etc. It is shown that RIKES nonlinear confocal microscopy significantly enhances the spatial resolution and imaging quality of confocal microscopy and achieves much higher resolution than that of two-photon confocal microscopy.
Bacha, Bakhtt A; Ahmad, Iftikhar
2013-01-01
We investigate the behavior of light pulse propagation in a 4-level double Lambda atomic system under condition of electromagnetically induced transparency. The Fano type interference effect and spectral hole burning appears in the the dynamics of the absorption-dispersion spectra caused by the joint nonlinear coherence Kerr effect and Doppler broadening. The coherent Kerr effect exhibits an enhancement (reduction) in superluminal (subluminal) in negative (in positive) group index while the Doppler broadening generates multiple hole burning in the Autler-Townes like spectra of this system. The hole burning in addition with coherent Kerr effect on the spectral profile influences the dynamics of subluminal and superluminal of the probe pulse through the medium. The characteristics of superluminality and subluminality modified by considering cold-Kerr-free medium and hot-Kerr-dependent mediums. The light pulse delays and advances in different regions of dispersion medium with the Doppler broadening and coherent ...
Propagation of Gaussian beams family through a Kerr-type left-handed metamaterial
Institute of Scientific and Technical Information of China (English)
A. Keshavarz; M. Naseri
2015-01-01
In this paper the propagation of elegant Hermite-cosh-Gaussian, elegant Laguerre Gaussian, and Bessel Gaussian beams through a Kerr left-handed metamaterial (LHM) slab have been studied. A split-step Fourier method is used to investigate the propagation of laser beams through this media. Numerical simulation shows that Gaussian beams have different focusing behaviors in a Kerr LHM slab with positive or negative nonlinearity. Beam focusing happens in slabs with positive nonlinearity and not in slabs with negative nonlinearity;however, negative nonlinearity is required for a Kerr LHM slab to act like a lens. Additionally, the focusing properties of beams can be controlled by controlling the thickness of the slab or the input power of the incident beam. A multilayer structure is also proposed to have beam focusing by thinner slabs and passing longer distances.
Schrödinger plasmon-solitons in Kerr nonlinear heterostructures with magnetic manipulation.
Davydova, M D; Dodonov, D V; Kalish, A N; Belotelov, V; Zvezdin, A K
2015-12-01
We investigate surface plasmon-soliton (SPS) propagation in transverse magnetic field in heterostructures with Kerr nonlinearity. The nonlinear Schrödinger equation in the framework of perturbation theory has been derived for three cases: a single-interface metal/nonlinear-dielectric structure and double-interface structures of nonlinear-dielectric/metal/dielectric with either ferromagnetic or nonmagnetic dielectric. The effect of the magneto-optical nonreciprocity in the Schrödinger equation is found. The estimations show that the effect is the strongest for the double-interface structure with a magnetic substrate in the vicinity of the resonant plasmonic frequency. We have also shown that the external magnetic field modifies SPS amplitude and width.
Solitons supported by singular spatial modulation of the Kerr nonlinearity
Borovkova, Olga V; Malomed, Boris A
2012-01-01
We introduce a setting based on the one-dimensional (1D) nonlinear Schroedinger equation (NLSE) with the self-focusing (SF) cubic term modulated by a singular function of the coordinate, |x|^{-a}. It may be additionally combined with the uniform self-defocusing (SDF) nonlinear background, and with a similar singular repulsive linear potential. The setting, which can be implemented in optics and BEC, aims to extend the general analysis of the existence and stability of solitons in NLSEs. Results for fundamental solitons are obtained analytically and verified numerically. The solitons feature a quasi-cuspon shape, with the second derivative diverging at the center, and are stable in the entire existence range, which is 0 < a < 1. Dipole (odd) solitons are found too. They are unstable in the infinite domain, but stable in the semi-infinite one. In the presence of the SDF background, there are two subfamilies of fundamental solitons, one stable and one unstable, which exist together above a threshold value ...
Pump induced normal mode splittings in phase conjugation in a Kerr nonlinear waveguide
Indian Academy of Sciences (India)
S Dutta Gupta
2000-03-01
Phase conjugation in a Kerr nonlinear waveguide is studied with counter-propagating normally incident pumps and a probe beam at an arbitrary angle of incidence. Detailed numerical results for the specular and phase conjugated reﬂectivities are obtained with full account of pump depletion. For sufﬁcient strengths of the pump a normal mode splitting is demonstrated in both the specular and the phase conjugated reﬂectivities of the probe wave. The splitting is explained in terms of a simple model under undepleted pump approximation.
Strong micro-macro entanglement from a weak cross-Kerr nonlinearity
Wang, Tian; Kaviani, Hamidreza; Ghobadi, Roohollah; Simon, Christoph
2014-01-01
We study the entanglement generated by a weak cross-Kerr nonlinearity between two initial coherent states, one of which has an amplitude close to the single-photon level, while the other one is macroscopic. We show that strong micro-macro entanglement is possible for weak phase shifts by choosing the amplitude of the macroscopic beam sufficiently large. We analyze the effects of loss and discuss possible experimental demonstrations of the micro-macro entanglement based on homodyne tomography and on a new entanglement witness.
Generation of squeezed-state superpositions via time-dependent Kerr nonlinearities
León-Montiel, R de J
2015-01-01
We put forward an experimental scheme for direct generation of optical squeezed coherent-state superpositions. The proposed setup makes use of an optical cavity, filled with a nonlinear Kerr medium, whose frequency is allowed to change during time evolution. By exactly solving the corresponding time-dependent anharmonic-oscillator Hamiltonian, we demonstrate that squeezed-state superpositions can be generated in an optical cavity. Furthermore, we show that the squeezing degree of the produced states can be tuned by properly controlling the frequency shift of the cavity, a feature that could be useful in many quantum information protocols, such as quantum teleportation and quantum computing.
Measuring the nonlinear refractive index of graphene using the optical Kerr effect method.
Dremetsika, Evdokia; Dlubak, Bruno; Gorza, Simon-Pierre; Ciret, Charles; Martin, Marie-Blandine; Hofmann, Stephan; Seneor, Pierre; Dolfi, Daniel; Massar, Serge; Emplit, Philippe; Kockaert, Pascal
2016-07-15
By means of the ultrafast optical Kerr effect method coupled to optical heterodyne detection (OHD-OKE), we characterize the third-order nonlinear response of graphene and compare it to experimental values obtained by the Z-scan method on the same samples. From these measurements, we estimate a negative nonlinear refractive index for monolayer graphene, n2=-1.1×10-13 m2/W. This is in contradiction to previously reported values, which leads us to compare our experimental measurements obtained by the OHD-OKE and the Z-scan method with theoretical and experimental values found in the literature and to discuss the discrepancies, taking into account parameters such as doping.
Measuring the Nonlinear Refractive Index of Graphene using the Optical Kerr Effect Method
Dremetsika, Evdokia; Gorza, Simon-Pierre; Ciret, Charles; Martin, Marie-Blandine; Hofmann, Stephan; Seneor, Pierre; Dolfi, Daniel; Massar, Serge; Emplit, Philippe; Kockaert, Pascal
2016-01-01
By means of the ultrafast optical Kerr effect method coupled to optical heterodyne detection (OHD-OKE), we characterize the third order nonlinear response of graphene at telecom wavelength, and compare it to experimental values obtained by the Z-scan method on the same samples. From these measurements, we estimate a negative nonlinear refractive index for monolayer graphene, $n_2 = - 1.1\\times 10^{-13} m^2/W$. This is in contradiction to previously reported values, which leads us to compare our experimental measurements obtained by the OHD-OKE and the Z-scan method with theoretical and experimental values found in the literature, and to discuss the discrepancies, taking into account parameters such as doping.
Brillouin/Raman compensation of the Kerr-effect-induced bias in a nonlinear ring laser gyroscope.
Luo, Zhang; Yuan, Xiaodong; Zhu, Zhihong; Liu, Ken; Ye, Weimin; Zeng, Chun; Ji, Jiarong
2013-04-01
In this Letter, the beat frequency at rest of a ring laser gyroscope with nonlinear effects is discussed in detail. Even without an additional intensity-stabilizing system, the random nullshift bias induced by the Kerr effect is compensated by the phase shift associated with the stimulated Brillouin/Raman scattering. And the nonlinear stimulated scattering also serves as the gain mechanism of the gyroscope. And thus the influence of the fluctuation of the injected pump intensity on the beat frequency is eliminated.
Yu, Xiang-xiang; Wang, Yu-hua
2014-01-13
Silver nanoparticles synthesized in a synthetic sapphire matrix were fabricated by ion implantation using the metal vapor vacuum arc ion source. The optical absorption spectrum of the Ag: Al2O3 composite material has been measured. The analysis of the supercontinuum spectrum displayed the nonlinear refractive property of this kind of sample. Nonlinear optical refraction index was identified at 800 nm excitation using the Kerr-lens autocorrelation (KLAC) technique. The spectrum showed that the material possessed self-defocusing property (n(2) = -1.1 × 10(-15) cm(2)W). The mechanism of nonlinear refraction has been discussed.
Sadhu, Arunangshu; Sarkar, Somenath
2016-05-01
We report a simple and straightforward approximate analysis to investigate the effect of Kerr type nonlinear optical processes in sub-wavelength diameter step index optical fibers based on Marcuse method in single mode region. Optimum core diameters of such fibers, predicted by us, together with relevant core nonlinearity coefficient and effective area are seen to be compatible with the analytical values indicating the validity of this novel application of the elegant approximate method. However, the corresponding values, obtained by earlier variational method, show larger discrepancy with analytical findings in comparison with ours. Also, maximum enhancement of nonlinear processes within single mode region, confirming almost the analytical method, assures less diffraction. Formulations, coupled with simplicity and novelty of the present analysis, should find wide use by system users and experimentalists in this emerging area.
Mechanical Kerr nonlinearities due to bipolar optical forces between deformable silicon waveguides.
Ma, Jing; Povinelli, Michelle L
2011-05-23
We use an analytical method based on the perturbation of effective index at fixed frequency to calculate optical forces between silicon waveguides. We use the method to investigate the mechanical Kerr effect in a coupled-waveguide system with bipolar forces. We find that a positive mechanical Kerr coefficient results from either an attractive or repulsive force. An enhanced mechanical Kerr coefficient several orders of magnitude larger than the intrinsic Kerr coefficient is obtained in waveguides for which the optical mode approaches the air light line, given appropriate design of the waveguide dimensions.
Röken, Christian
2015-01-01
The separability of the massive Dirac equation in a rotating Kerr black hole background in advanced Eddington-Finkelstein-type coordinates is shown. To this end, the Kerr spacetime is described in the framework of the Newman-Penrose formalism by a local Carter tetrad, and the Dirac wave functions are given on a spin bundle in a chiral Newman-Penrose dyad representation. Applying mode analysis techniques, the Dirac equation is separated into coupled systems of radial and angular ordinary differential equations. Asymptotic radial solutions at infinity and the event and Cauchy horizons are explicitly derived and, by means of error estimates, the decay properties are analyzed. Solutions of the angular ordinary differential equations matching the Chandrasekhar-Page equation are discussed. These solutions are used in order to study the scattering of Dirac waves by the gravitational field of a Kerr black hole for an observer described by a frame without coordinate singularities at the inner horizon boundaries such t...
One-photon controlled two-photon not gate contributed by weak cross-Kerr nonlinearities
Xiu, Xiao-Ming; Li, Qing-Yang; Lin, Yan-Fang; Dong, Li; Dong, Hai-Kuan; Gao, Ya-Jun
2017-06-01
A quantum logic gate is an indispensable fundamental element for completing tasks of quantum information processing, such as quantum computation and scalable quantum networks. With the help of weak cross-Kerr nonlinearities, we propose an efficient optical one-photon controlled two-photon not gate, where polarization modes of photons act as quantum bits, aiming to construct the practical and scalable quantum logic circuits. By adopting one-time nondestructive measurement, this gate can realize the function of two two-photon controlled-not gates, where the polarization bits of two target photons will be flipped when the controlled photon is in the vertical polarization state. After measuring on the coherent state, the suitable operations including swapping of photon states and single-photon transformations are carried out by classical feed forward, conditioned on the measurement outcomes. Simple linear optical elements, and mature techniques containing Homodyne measurement and classical feed forward are applied to enhance the feasibility of the scheme presented here and other scalable logic gates.
Wang, Meiyu; Yan, Fengli; Gao, Ting
2017-08-01
We present a new scheme to provide an arbitrary four-photon polarization-entangled state, which enables the encoding of single logical qubit information into a four-qubit decoherence-free subspace robustly against collective decoherence. With the assistance of the cross-Kerr nonlinearities, a spatial entanglement gate and a polarization entanglement gate are inserted into the circuit, where the X-quadrature homodyne measurement is properly performed. According to the outcomes of homodyne measurement in the spatial entanglement process, some swap gates are inserted into the corresponding paths of the photons to swap their spatial modes. Apart from Kerr media, some basic linear optical elements are necessary, which make it feasible with current experimental techniques.
Institute of Scientific and Technical Information of China (English)
YANGYong; YANZhen－Ya
2002-01-01
In this letter the three-dimensional nonlinear Helmholtz equation is investigated.which describes electromagnetic wave propagation in a nonlinear Kerr-type medium such that sixteen families of new Jacobi elliptic function solutions are obtained,by using our extended Jacobian elliptic function expansion method.When the modulus m-→1 or 0,the corresponding solitary waves including bright solitons,dark solitons and new line solitons and singly periodic solutions can be also found.
Institute of Scientific and Technical Information of China (English)
Ziming Meng; Xiaolan Zhong; Chen Wang; Zhiyuan Li
2012-01-01
Fabrication details of air-bridged Kerr nonlinear polymer photonic crystal slab structures are presented.Both the two-dimensional photonic crystal slab and the one-dimensional nanobeam structures are fabricated using direct focused ion beam etching and subsequent wet chemical etching.The scanning electron microscopy images show the uniformity and homogeneity of the cylindrical air holes.The optical measurement in the near-infrared region is implemented using the tapered fiber coupling method,and the results agree with the numerical calculations by using the three-dimensional finite-difference time-domain method.
Wang, Mei-Yu; Yan, Feng-Li; Gao, Ting
2016-07-01
We present two deterministic quantum entanglement distribution protocols for a four-photon Dicke polarization entangled state resorting to the frequency and spatial degrees of freedom, which are immune to an arbitrary collective-noise channel. Both of the protocols adopt the X homodyne measurement based on the cross-Kerr nonlinearity to complete the task of the single-photon detection with nearly unit probability in principle. After the four receivers share the photons, they add some local unitary operations to obtain a standard four-photon Dicke polarization entangled state.
Highly enhanced steady-state optomechanical entanglement via cross-Kerr nonlinearity
Chakraborty, Subhadeep
2016-01-01
We study steady-state optomechanical entanglement in presence of an additional cross-Kerr coupling between the optical and mechanical mode. We find that a significant enhancement of the steady-state entanglement can be achieved at a considerably lower driving power, which is also extremely robust with respect to system parameters and environmental temperature.
Nonlinear Goos–Hänchen shifts of reflected light from inhomogeneous Kerr-like slabs
Energy Technology Data Exchange (ETDEWEB)
Mao, Hongmin, E-mail: hongminmao@hotmail.com; Zang, Taocheng; Sun, Jian; Pan, Tao; Xu, Guoding
2013-09-02
We investigate the Goos–Hänchen (GH) shifts of reflected light from Kerr-like slabs, whose permittivities are inhomogeneous in space as well as light intensity dependent. The GH shifts exhibit bistable, multivalued properties or a more complicated hysteretic response to the input light intensity, and the different spatial dependences of the permittivity have a great effect on the hysteretic response. The bistable or multivalued GH shifts can be modulated by various parameters, such as the angle of incidence and the thickness of slab. - Highlights: • The Goos–Hänchen (GH) shifts of reflected light from inhomogeneous Kerr-like slabs are investigated. • The GH shifts exhibit bistable, multivalued properties or a more complicated hysteretic response to the input light intensity. • The bistable or multivalued GH shifts can be modulated by the angle of incidence and the thickness of slab.
Hopkins, James; Gaudette, Jamie; Mehta, Priyanth
2013-10-01
With the advent of digital signal processing (DSP) in optical transmitters and receivers, the ability to finely tune the ratio of pre and post dispersion compensation can be exploited to best mitigate the nonlinear penalties caused by the Kerr effect. A portion of the nonlinear penalty in optical communication channels has been explained by an increase in peak to average power ratio (PAPR) inherent in highly dispersed signals. The standard approach for minimizing these impairments applies 50% pre dispersion compensation and 50% post dispersion compensation, thereby decreasing average PAPR along the length of the cable, as compared with either 100% pre or post dispersion compensation. In this paper we demonstrate that simply considering the net accumulated dispersion, and applying 50/50 pre/post dispersion is not necessarily the best way to minimize PAPR and subsequent Kerr nonlinearities. Instead, we consider the cumulative dispersion along the entire length of the cable, and, taking into account this additional information, derive an analytic formula for the minimization of PAPR. Alignment with simulation and experimental measurements is presented using a commercially available 100Gb/s dual-polarization binary phase-shift-keying (DP-BPSK) coherent modem, with transmitter and receiver DSP. Measurements are provided from two different 5000km dispersion managed Submarine test-beds, as well as a 3800km terrestrial test-bed with a mixture of SMF-28 and TWRS optical fiber. This method is shown to deviate significantly from the conventional 50/50 method described above, in dispersion managed communications systems, and more closely aligns with results obtained from simulation and data collected from laboratory test-beds.
Institute of Scientific and Technical Information of China (English)
WANG Jun-Min
2011-01-01
With the aid of Mathematica, three auxiliary equations, i.e.the Riccati equation, the Lenard equation and the Hyperbolic equation, are employed to investigate traveling wave solutions of a cosh-Gaussian laser beam in both Kerr and cubic quintic nonlinear media. As a result, many traveling wave solutions are obtained, including soliton-like solutions, hyperbolic function solutions and trigonometric function solutions.
Directory of Open Access Journals (Sweden)
Shingo Takeuchi
2017-08-01
Full Text Available We carry out the Kerr/CFT correspondence in a four-dimensional extremal rotating regular black hole with a non-linear magnetic monopole (NLMM. One problem in this study would be whether our geometry can be a solution or not. We search for the way making our rotating geometry into a solution based on the fact that the Schwarzschild regular geometry can be a solution. However, in the attempt to extend the Schwarzschild case that we can naturally consider, it turns out that it is impossible to construct a model in which our geometry can be a exact solution. We manage this problem by making use of the fact that our geometry can be a solution approximately in the whole space-time except for the black hole's core region. As a next problem, it turns out that the equation to obtain the horizon radii is given by a fifth-order equation due to the regularization effect. We overcome this problem by treating the regularization effect perturbatively. As a result, we can obtain the near-horizon extremal Kerr (NHEK geometry with the correction of the regularization effect. Once obtaining the NHEK geometry, we can obtain the central charge and the Frolov–Thorne temperature in the dual CFT. Using these, we compute its entropy through the Cardy formula, which agrees with the one computed from the Bekenstein–Hawking entropy.
Comprehensive analysis of the optical Kerr coefficient of graphene
Soh, Daniel B. S.; Hamerly, Ryan; Mabuchi, Hideo
2016-08-01
We present a comprehensive analysis of the nonlinear optical Kerr effect in graphene. We directly solve the S -matrix element to calculate the absorption rate, utilizing the Volkov-Keldysh-type crystal wave functions. We then convert to the nonlinear refractive index coefficients through the Kramers-Kronig relation. In this formalism, the source of Kerr nonlinearity is the interplay of optical fields that cooperatively drive the transition from valence to conduction band. This formalism makes it possible to identify and compute the rates of distinct nonlinear processes that contribute to the Kerr nonlinear refractive index coefficient. The four identified mechanisms are two-photon absorption, Raman transition, self-coupling, and quadratic ac Stark effect. We also present a comparison of our theory with recent experimental and theoretical results.
Energy Technology Data Exchange (ETDEWEB)
Hamedi, Hamid Reza, E-mail: hamid.r.hamedi@gmail.com
2014-06-01
A novel solid configuration is proposed to achieve a giant Kerr nonlinearity with reduced absorption under conditions of slow light levels. It is shown that an enhanced Kerr nonlinearity accompanied with negligible absorption can be obtained just through the proper tuning of intensity of coherent driving field at C-band telecommunication wavelength which is practical for communication applications. Moreover, the impact of incoherent pump field as well as frequency detuning of coherent field on manipulating the linear and nonlinear optical properties of the yttrium–aluminum-garnet (YAG) crystal medium is discussed. The presented results may be of interest to researchers in the field of all-optical signal processing and solid-state quantum information science.
Nalegaev, Sergey S.; Belashov, Andrey V.; Petrov, Nikolay V.
2017-07-01
The methodology of Photothermal Interferometry implemented through off-axis digital holography for the nonlinear refractive index measurements of optical media with the thermal mechanism of nonlinearity is presented. An experimental appraisal is done on the example of chlorophyllin 1% solution in ethyl alcohol. It allows us to estimate the effective value of nonlinear refractive index as - 0.65 ·10-3 cm2/W. The comparison of the experimental result with data obtained by means of a reference approach was performed. Possible errors lead to a mismatch between them are highlighted and analyzed.
Institute of Scientific and Technical Information of China (English)
LUO Jin-Ming; LI Jia-Hua; XIE Xiao-Tao
2006-01-01
@@ Taking the intensity-dependent coupling between atoms and cavity mode into account, we investigate a system consisting of N homogeneously broadened two-level atoms interacting with the field inside a single-mode Fabry Perot cavity containing a nonlinear Kerr-like medium. We derive the steady-state bistable behaviour of the system, and further analyse in details the influence of several critical parameters on the bistable behaviour.
Kerr nonlinearity and multi-photon absorption in germanium at mid-infrared wavelengths
Sohn, B.-U.; Monmeyran, C.; Kimerling, L. C.; Agarwal, A. M.; Tan, D. T. H.
2017-08-01
Multiphoton absorption coefficients and nonlinear refractive indices of germanium in the near and mid-infrared (2-5 μm) are reported. The nonlinear coefficients are measured by open and closed aperture Z-scan with 150 fs pulses at a repetition rate of 1 kHz. The nonlinear refractive index of Ge has a peak value of 9.1 ×10-5cm2/GW at a wavelength of 3 μm. The effect of free electrons generated by multiphoton absorption is discussed by investigating the variation of multiphoton absorption coefficients at different input powers. Kramers-Kronig relations are also discussed with regard to the relationship between nonlinear refractive index and two photon absorption coefficient.
Fusion arrest and collapse phenomena due to Kerr-nonlinearity in quadratic media
DEFF Research Database (Denmark)
Johansen, Steffen Kjær; Bang, Ole; Sørensen, Mads Peter
2000-01-01
Emphasizing collapse phenomena it is investigated to what extend the always present cubic nonlinearity affects the properties of soliton interaction in quadratic bulk media. An effective particle approach is applied and verified by numerical simulations....
Yan-Chao, She; Ting-Ting, Luo; Wei-Xi, Zhang; Mao-Wu, Ran; Deng-Long, Wang
2016-01-01
The linear optical properties and Kerr nonlinear optical response in a four-level loop configuration GaAs/AlGaAs semiconductor quantum dot are analytically studied with the phonon-assisted transition (PAT). It is shown that the changes among a single electromagnetically induced transparency (EIT) window, a double EIT window and the amplification of the probe field in the absorption curves can be controlled by varying the strength of PAT κ. Meanwhile, double switching from the anomalous dispersion regime to the normal dispersion regime can likely be achieved by increasing the Rabi energy of the external optical control field. Furthermore, we demonstrate that the group velocity of the probe field can be practically regulated by varying the PAT and the intensity of the optical control field. In the nonlinear case, it is shown that the large SPM and XPM can be achieved as linear absorption vanishes simultaneously, and the PAT can suppress both third-order self-Kerr and the cross-Kerr nonlinear effect of the QD. Our study is much more practical than its atomic counterpart due to its flexible design and the controllable interference strength, and may provide some new possibilities for technological applications. Project supported by the National Natural Science Foundation of China (Grant No. 61367003), the Scientific Research Fund of Hunan Provincial Education Department, China (Grant No. 12A140), and the Scientific Research Fund of Guizhou Provincial Education Department, China (Grant Nos. KY[2015]384 and KY[2015]446).
Nonlinear self-focus of pulsed-wave beams in Kerr media
Energy Technology Data Exchange (ETDEWEB)
Judkins, J.B.
1992-12-31
A modified finite-difference time-domain method for solving Maxwell`s equations in nonlinear media is presented. This method allows for a finite response time to be incorporated in the medium, physically creating dispersion and absorption mechanisms. The technique models electromagnetic fields in two space dimensions and time and encompasses both the TE{sub z} and TM{sub z} set of decoupled field equations. Aspects of an ultra-short pulsed Gaussian beam are studied in a variety of linear and nonlinear environments to demonstrate that the methods developed here can be used efficaciously in the modeling of pulses in complex problem space geometries even when nonlinearities are present.
Energy Technology Data Exchange (ETDEWEB)
AbdelMalek, Fathi; Aroua, Walid [National Institute of Applied Science and Technology, University of Carthage, Tunis (Tunisia); Haxha, Shyqyri [Computer Science and Technology Department, Bedfordshire University, Luton (United Kingdom); Flint, Ian [Selex ES Ltd, Luton, Bedfordshire (United Kingdom)
2016-08-15
In this research work, we propose all-optical transistor based on metallic nanoparticle cross-chains geometry. The geometry of the proposed device consists of two silver nanoparticle chains arranged along the x- and z-axis. The x-chain contains a Kerr nonlinearity, the source beam is set at the left side of the later, while the control beam is located at the top side of the z-chain. The control beam can turn ON and OFF the light transmission of an incoming light. We report a theoretical model of a very small all-optical transistor proof-of-concept made of optical 'light switching light' concept. We show that the transmission efficiency strongly depends on the control beam and polarization of the incoming light. We investigate the influence of a perfect reflector and reflecting substrate on the transmission of the optical signal when the control beam is turned ON and OFF. These new findings make our unique design a potential candidate for future highly-integrated optical information processing chips. (copyright 2016 by WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Propagation of Weakly Guided Waves in a Kerr Nonlinear Medium using a Perturbation Approach
Energy Technology Data Exchange (ETDEWEB)
Dacles-Mariani, J; Rodrigue, G
2004-10-06
The equations are represented in a simplified format with only a few leading terms needed in the expansion. The set of equations are then solved numerically using vector finite element method. To validate the algorithm, they analyzed a two-dimensional rectangular waveguide consisting of a linear core and nonlinear identical cladding. The exact nonlinear solutions for three different modes of propagations, TE0, TE1, and TE2 modes are generated and compared with the computed solutions. Next, they investigate the effect of a more intense monochromatic field on the propagation of a 'weak' optical field in a fully three-dimensional cylindrical waveguide.
Stability Analysis of Fixed points in a Parity-time symmetric coupler with Kerr nonlinearity
Deka, Jyoti Prasad
2016-01-01
We report our study on nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. In the linear regime, the differential equations governing the dynamics of the coupler, under some parametric changes, can be solved exactly. But with the inclusion of nonlinearity, analytical solution of the system is a rather complicated job. And the sensitiveness of the system on the initial conditions is yet another critical issue. To circumvent the situation, we have employed the mathematical framework of nonlinear dynamics. Considering the parity-time threshold of the linear PT-coupler as the reference point, we find that in nonlinear coupler the parity-time symmetric threshold governs the existence of fixed points. We have found that the stability of the ground state undergoes a phase transition when the gain/loss coefficient is increased from zero to beyond the PT threshold. In the unbroken PT regime, we find that the instabilities in the initial launch conditions can trigger an exponential growth and dec...
Observation of optical-fiber Kerr nonlinearity at the single-photon level
Matsuda, Nobuyuki; Mitsumori, Yasuyoshi; Kosaka, Hideo; Edamatsu, Keiichi; 10.1038/nphoton.2008.292
2012-01-01
Optical fibers have been enabling numerous distinguished applications involving the operation and generation of light, such as soliton transmission, light amplification, all-optical switching and supercontinuum generation. The active function of optical fibers in the quantum regime is expected to be applicable to ultralow-power all-optical signal processing and quantum information processing. Here we demonstrate the first experimental observation of optical nonlinearity at the single-photon level in an optical fiber. Taking advantage of large nonlinearity and managed dispersion of a photonic crystal fiber, we have successfully measured very small (10^(-7) ~ 10^(-8)) conditional phase shifts induced by weak coherent pulses that contain one or less than one photon per pulse on average. In spite of its tininess, the phase shift was measurable using much (~10^6 times) stronger coherent probe pulses than the pump pulses. We discuss the feasibility of quantum information processing using optical fibers, taking into...
Two-beam nonlinear Kerr effect to stabilize laser frequency with sub-Doppler resolution
Martins, Weliton Soares; de Silans, Thierry Passerat; Oriá, Marcos; Chevrollier, Martine; 10.1364/AO.51.005080
2012-01-01
Avoiding laser frequency drifts is a key issue in many atomic physics experiments. Several techniques have been developed to lock the laser frequency using sub-Doppler dispersive atomic lineshapes as error signals in a feedback loop. We propose here a two-beam technique that uses non-linear properties of an atomic vapor around sharp resonances to produce sub-Doppler dispersive-like lineshapes that can be used as error signals. Our simple and robust technique has the advantage of not needing either modulation or magnetic fields.
Design of triply-resonant microphotonic parametric oscillators based on Kerr nonlinearity.
Zeng, Xiaoge; Popović, Miloš A
2014-06-30
We propose optimal designs for triply-resonant optical parametric oscillators (OPOs) based on degenerate four-wave mixing (FWM) in microcavities. We show that optimal designs in general call for different external coupling to pump and signal/idler resonances. We provide a number of normalized performance metrics including threshold pump power and maximum achievable conversion efficiency for OPOs with and without two-photon (TPA) and free-carrier absorption (FCA). We find that the maximum achievable conversion efficiency is bound to an upper limit by nonlinear and free-carrier losses independent of pump power, while linear losses only increase the pump power required to achieve a certain conversion efficiency. The results of this work suggest unique advantages in on-chip implementations that allow explicit engineering of resonances, mode field overlaps, dispersion, and wavelength-and mode-selective coupling. We provide universal design curves that yield optimum designs, and give example designs of microring-resonator-based OPOs in silicon at the wavelengths 1.55 μm (with TPA) and 2.3 μm (no TPA) as well as in silicon nitride (Si(3)N(4)) at 1.55 μm. For typical microcavity quality factor of 10(6), we show that the oscillation threshold in excitation bus can be well into the sub-mW regime for silicon microrings and a few mW for silicon nitride microrings. The conversion efficiency can be a few percent when pumped at 10 times of the threshold. Next, based on our results, we suggest a family of synthetic "photonic molecule"-like, coupled-cavity systems to implement optimum FWM, where structure design for control of resonant wavelengths can be separated from that of optimizing nonlinear conversion efficiency, and where furthermore pump, signal, and idler coupling to bus waveguides can be controlled independently, using interferometric cavity supermode coupling as an example. Finally, consideration of these complex geometries calls for a generalization of the nonlinear
Magneto-optical Kerr spectra and magnetic properties of Co-substituted M-type strontium ferrites
Energy Technology Data Exchange (ETDEWEB)
Liu Xiansong, E-mail: xiansongliu@ahu.edu.cn [Engineering Technology Research Center of Magnetic Materials, Anhui Province, School of Physics and Materials Science, Anhui University, Hefei 230039 (China); Fernandez-Garcia, Lucia [Centro de Investigacion en Nanomateriales y Nanotecnologia (CINN), Consejo superior de Investigaciones Cientificas (CSIC) - Universidad de Oviedo UO - Principado de Asturias, Parque Tecnologico de Asturias, 33428 Llanera, Asturias (Spain); Hu Feng; Zhu Deru [Engineering Technology Research Center of Magnetic Materials, Anhui Province, School of Physics and Materials Science, Anhui University, Hefei 230039 (China); Suarez, Marta; Menendez, Jose Luis [Centro de Investigacion en Nanomateriales y Nanotecnologia (CINN), Consejo superior de Investigaciones Cientificas (CSIC) - Universidad de Oviedo UO - Principado de Asturias, Parque Tecnologico de Asturias, 33428 Llanera, Asturias (Spain)
2012-04-16
Highlights: Black-Right-Pointing-Pointer Prepare single phase ferrites by substituted with Co{sup 2+}. Black-Right-Pointing-Pointer The magnetic properties were remarkably modified. Black-Right-Pointing-Pointer A very noticeable Kerr activity was obtained for the Co-substituted ferrites. - Abstract: M-type strontium ferrites SrFe{sub 12-x}Co{sub x}O{sub 19} (x = 0, 0.05, 0.10, 0.15, 0.20) were prepared by the conventional ceramic technology. The structure, magnetic properties and magneto-optical Kerr activity of the samples were investigated by X-ray diffraction (XRD), vibrating sample magnetometer (VSM) and magneto-optical ellipsometry, respectively. X-ray diffraction showed that all the samples were single phase ferrites. The magnetic properties, especially the coercive field, were remarkably modified due to the substitution of cobalt. Most importantly, a noticeable Kerr activity was demonstrated in the Co-substituted M-type strontium ferrites with x = 0.20.
DEFF Research Database (Denmark)
Sackey, I.; Da Ros, Francesco; Jazayerifar, M.;
2014-01-01
inversion of 5 × 28-GBd polarization-multiplexed 16- QAM signals. Signal quality factor (Q-factor) improvements of 1.1 dB and 0.8 dB were obtained in the cases of a single-channel and a five-channel wavelength-division multiplexing (WDM) system, respectively. The experimental results are compared......We present experimental and numerical investigations of Kerr nonlinearity compensation in a 400-km standard single-mode fiber link with distributed Raman amplification with backward pumping. A dual-pump polarization-independent fiber-based optical parametric amplifier is used for mid-link spectral...
DEFF Research Database (Denmark)
Sackey, Isaac; Da Ros, Francesco; Karl Fischer, Johannes;
2015-01-01
We experimentally investigate Kerr nonlinearity mitigation of a 28-GBd polarization-multiplexed 16-QAM signal in a five-channel 50-GHz spaced wavelength-division multiplexing (WDM) system. Optical phase conjugation (OPC) employing the mid-link spectral inversion technique is implemented by using...... a dual-pump polarization-independent fiber-optic parametric amplifier and compared to digital backpropagation (DBP) compensation over up to 800-km in a dispersion-managed link. In the single-channel case, the use of the DBP algorithm outperformed the OPC with a Q-factor improvement of 0.9 dB after 800-km...
DEFF Research Database (Denmark)
Sackey, Isaac; Da Ros, Francesco; Karl Fischer, Johannes
2015-01-01
a dual-pump polarization-independent fiber-optic parametric amplifier and compared to digital backpropagation (DBP) compensation over up to 800-km in a dispersion-managed link. In the single-channel case, the use of the DBP algorithm outperformed the OPC with a Q-factor improvement of 0.9 dB after 800-km......We experimentally investigate Kerr nonlinearity mitigation of a 28-GBd polarization-multiplexed 16-QAM signal in a five-channel 50-GHz spaced wavelength-division multiplexing (WDM) system. Optical phase conjugation (OPC) employing the mid-link spectral inversion technique is implemented by using...
Nguyen, A; Dechard, J; Thiele, I; Babushkin, I; Skupin, S; Berge, L
2016-01-01
We theoretically and numerically study the influence of both instantaneous and Raman-delayed Kerr nonlinearities as well as a long-wavelength pump in the terahertz (THz) emissions produced by two-color femtosecond filaments in air. Although the Raman-delayed nonlinearity induced by air molecules weakens THz generation, four-wave mixing is found to impact the THz spectra accumulated upon propagation via self-, cross-phase modulations and self-steepening. Besides, using the local current theory, we show that the scaling of laser-to-THz conversion efficiency with the fundamental laser wavelength strongly depends on the relative phase between the two colors, the pulse duration and shape, rendering a universal scaling law impossible. Scaling laws in powers of the pump wavelength may only provide a rough estimate of the increase in the THz yield. We confront these results with comprehensive numerical simulations of strongly focused pulses and of filaments propagating over meter-range distances.
Deser, S
2006-01-01
In this pedagogical note, we obtain and outline the physical content of the Kerr geometry in the linearized approximation to General Relativity. In particular, we derive its time-independence (Birkhoff's theorem) and relate its parameters to those of an effective localized spinning mass.
Heo, Jino; Hong, Chang-Ho; Yang, Hyung-Jin; Hong, Jong-Phil; Choi, Seong-Gon
2017-04-01
We demonstrate the advantages of an optical parity gate using weak cross-Kerr nonlinearities (XKNLs), quantum bus (qubus) beams, and photon number resolving (PNR) measurement through our analysis, utilizing a master equation under the decoherence effect (occurred the dephasing and photon loss). To generate Bell states, parity gates based on quantum non-demolition measurement using XKNL are extensively employed in quantum information processing. When designing a parity gate via XKNL, the parity gate can be diversely constructed according to the measurement strategies. In practice, the interactions of XKNLs in optical fiber are inevitable under the decoherence effect. Thus, by our analysis of the decoherence effect, we show that the designed parity gate employing homodyne measurement would not be expected to provide reliable quantum operation. Furthermore, compared with a parity gate using a displacement operator and PNR measurement, we conclude there is experimental benefit from implementation of a parity gate via qubus beams and PNR measurement under the decoherence effect.
Heo, Jino; Kang, Min-Sung; Hong, Chang-Ho; Yang, Hyeon; Choi, Seong-Gon
2016-12-01
We present a scheme for implementing discrete quantum Fourier transform (DQFT) with robustness against the decoherence effect using weak cross-Kerr nonlinearities (XKNLs). The multi-photon DQFT scheme can be achieved by operating the controlled path and merging path gates that are formed with weak XKNLs and linear optical devices. To enhance feasibility under the decoherence effect, in practice, we utilize a displacement operator and photon-number-resolving measurement in the optical gate using XKNLs. Consequently, when there is a strong amplitude of the coherent state, we demonstrate that it is possible to experimentally implement the DQFT scheme, utilizing current technology, with a certain probability of success under the decoherence effect.
Finster, Felix
2016-01-01
The massive Dirac equation is considered in the non-extreme Kerr geometry in horizon-penetrating Eddington-Finkelstein-type coordinates. We derive an integral representation for the Dirac propagator involving the solutions of the ODEs which arise in Chandrasekhar's separation of variables. This integral representation describes the dynamics of Dirac waves outside and across the event horizon, up to the Cauchy horizon. For the proof, we write the Dirac equation in Hamiltonian form. One of the main difficulties is that the time evolution is not unitary, because the wave may "hit" the singularity. This problem is resolved by imposing suitable Dirichlet-type boundary conditions inside the Cauchy horizon, having no effect on the outside dynamics. Another main difficulty is that the Dirac Hamiltonian fails to be elliptic at the horizons. Combining the theory of symmetric hyperbolic systems with elliptic methods near the boundary, we construct a self-adjoint extension of the resulting Hamiltonian. We finally apply S...
Institute of Scientific and Technical Information of China (English)
Liu Su-Mei; He An-Zhi; Ji Yun-Jing
2008-01-01
In this paper the evolution characteristics of the fidelity of quantum information for the Ⅴ-type three-level atom interacting with number state light field in Kerr medium are investigated. It shows that the periodicity of the evolutions of fidelity of quantum information is influenced by the Kerr coefficient, the photon number of the initial field and intensity of light. The evolutions of the fidelity of quantum information are modulated by the initial number state field. The Rabi oscillation frequency and the modulation frequency of fidelity for the field and the system vary with the value of the Kerr coefficient. The evolutions of fidelity of quantum information obviously show the quantum collapse and revival behaviours in the system of atom interacting with light field.
Tavousi, Alireza; Mansouri-Birjandi, Mohammad Ali; Saffari, Mehdi
2016-09-01
Implementing of photonic sampling and quantizing analog-to-digital converters (ADCs) enable us to extract a single binary word from optical signals without need for extra electronic assisting parts. This would enormously increase the sampling and quantizing time as well as decreasing the consumed power. To this end, based on the concept of successive approximation method, a 4-bit full-optical ADC that operates using the intensity-dependent Kerr-like nonlinearity in a two dimensional photonic crystal (2DPhC) platform is proposed. The Silicon (Si) nanocrystal is chosen because of the suitable nonlinear material characteristic. An optical limiter is used for the clamping and quantization of each successive levels that represent the ADC bits. In the proposal, an energy efficient optical ADC circuit is implemented by controlling the system parameters such as ring-to-waveguide coupling coefficients, the ring's nonlinear refractive index, and the ring's length. The performance of the ADC structure is verified by the simulation using finite difference time domain (FDTD) method.
Menezes, J. W. M.; Fraga, W. B.; Lima, F. T.; Guimarães, G. F.; Ferreira, A. C.; Lyra, M. L.; Sombra, A. S. B.
2011-06-01
Recently, much attention has been given to the influence of the relaxation process of the non-linear response, because the usual assumption of instantaneous non-linear response fails for ultra-short pulses, and additional contributions coming from non-linear dispersion and delayed non-linearity have to be taken into account. This article presents a numerical analysis of the symmetric planar and asymmetric planar three-core non-linear directional fiber couplers operating with a soliton pulse, where effects of both delayed and instantaneous non-linear Kerr responses are analyzed for implementation of an all-optical half-adder. To implement this all-optical half-adder, eight configurations were analyzed for the non-linear directional fiber coupler, with two symmetric and six asymmetric configurations. The half-adder is the key building block for many digital processing functions, such as shift register, binary counter, and serial parallel data converters. The optical coupler is an important component for applications in optical-fiber telecommunication systems and all integrated optical circuit because of its very high switching speeds. In this numerical simulation, the symmetric/asymmetric planar presents a structure with three cores in a parallel equidistant arrangement, three logical inputs, and two output energy. To prove the effectiveness of the theoretical model for generation of the all-optical half-adder, the best phase to be applied to the control pulse was sought, and a study was done of the extinction ratio level as a function of the Δ > parameter, the normalized time duration, and the Sum and Carry outputs of the (symmetric planar/asymmetric planar) non-linear directional fiber coupler. In this article, the interest is in transmission characteristics, extinction ratio level, normalized time duration, and pulse evolution along the non-linear directional fiber coupler. To compare the performance of the all-optical half-adders, the figure of merit of the
Soliton crystals in Kerr resonators
Cole, Daniel C; Del'Haye, Pascal; Diddams, Scott A; Papp, Scott B
2016-01-01
Solitons are pulses that propagate without spreading due to a balance between nonlinearity and dispersion (or diffraction), and are universal features of systems exhibiting these effects. Solitons play an important role in plasma physics, fluid dynamics, atomic physics, biology, and optics. In the context of integrated photonics, bright dissipative cavity solitons in Kerr-nonlinear resonators are envisioned to play an important role in next-generation communication, computation, and measurement systems. Here we report the discovery of soliton crystals in Kerr resonators-collectively ordered ensembles of co-propagating solitons with discrete allowed temporal separations. Through analysis of optical spectra, we identify a complicated but discrete space of interacting soliton configurations, including crystals exhibiting vacancies (Schottky defects), shifted pulses (Frenkel defects), and superstructure. Time-domain characterization of the output-coupled soliton pulse train directly confirms our inference of the ...
Rajan, M. S. Mani
2016-08-01
In this manuscript, the ultrashort soliton pulse propagation through nonlinear tunneling in cubic quintic media is investigated. The effect of chirping on propagation characteristics of the soliton pulse is analytically investigated using similarity transformation. In particular, we investigate the propagation dynamics of ultrashort soliton pulse through dispersion barrier for both chirp and chirp-free soliton. By investigating the obtained soliton solution, we found that chirping has strong influence on soliton dynamics such as pulse compression with amplification. These two important dynamics of chirped soliton in cubic quintic media open new possibilities to improve the solitonic communication system. Moreover, we surprisingly observe that a dispersion well is formed for the chirped case whereas a barrier is formed for the chirp-free case, which has certain applications in the construction of logic gate devices to achieve ultrafast switching.
Institute of Scientific and Technical Information of China (English)
刘丹; 洪伟毅; 郭旗
2016-01-01
In this paper, the propagation of a few-cycle femtosecond pulse in a nonlinear Kerr medium is studied by the method of time-transformation. The time-transformation approach can greatly improve the computational eﬃciency. Because the width of electric field of the few-cycle femtosecond pulse is less than the characteristic time of Raman response in a nonlinear medium, it is observed that the electric field of the pulse experiences a significant deformation and breaks into a Raman soliton and the dispersion waves during the propagation, which can be attributed to strongly nonlocal nonlinearity. A deeper investigation of the time-frequency distributions for both the Raman soliton and the dispersion waves is also included. Since the pulse contains only few cycles, the carrier-envelope phase (CEP) of the pulse plays an important role in the process of nonlinear propagation. The numerical results show the CEP-dependence in the process of nonlinear propagation: the phase changes for both the Raman soliton and the dispersive waves are just equal to the CEP change of the initial pulse, which indicates that the CEP of the pulse is linearly transmitted in the process of nonlinear propagation. This phenomenon can be attributed to the fact that the phase change due to the nonlinearity is only dependent on the intensities of the fields of both the Raman soliton and the dispersion wave, which are unchanged for all the CEPs.
Photon statistics of the micromaser with a Kerr medium
Institute of Scientific and Technical Information of China (English)
吴曙东; 詹志明; 金丽霞
2002-01-01
We have established the master equation for the micromaser with a Kerr medium. We have studied the photon statistics of the micromaser with a Kerr medium field and analysed the influence of the Kerr effect on the photon statistics. The influence of the Kerr effect on the photon statistics is different in two regimes. In the thermal-atom regime, the Kerr effect produces quantum noise, and decreases the mean photon number. In the ultracold-atom regime,with the increase of the nonlinear parameter of the Kerr medium, the stability of the mean photon number and the normalized variance enhances the mean photon number, and the normalized variance exhibits collapse-revival phenomena periodically, their resonance peaks become lower, and the photon statistics of more and more regions are sub-Poissonian.
Photon Rings around Kerr and Kerr-like Black Holes
Johannsen, Tim
2015-01-01
Very-long baseline interferometric observations have resolved structure on scales of only a few Schwarzschild radii around the supermassive black holes at the centers of our Galaxy and M87. In the near future, such observations are expected to image the shadows of these black holes together with a bright and narrow ring surrounding their shadows. For a Kerr black hole, the shape of this photon ring is nearly circular unless the black hole spins very rapidly. Whether or not, however, astrophysical black holes are truly described by the Kerr metric as encapsulated in the no-hair theorem still remains an untested assumption. For black holes that differ from Kerr black holes, photon rings have been shown numerically to be asymmetric for small to intermediate spins. In this paper, I calculate semi-analytic expressions of the shapes of photon rings around black holes described by a new Kerr-like metric which is valid for all spins. I show that photon rings in this spacetime are affected by two types of deviations f...
Single Kerr-Schild metrics: a double view
Energy Technology Data Exchange (ETDEWEB)
McIntosh, C.B.G.; Hickman, M.S.
1988-08-01
Real-vacuum single Kerr-Schild (ISKS) metrics are discussed and new results proved. It is shown that if they Weyl tensor of such a metric has a twist-free expanding principal null direction, then it belongs to the Schwarzchild family of metrics-there are no Petrov type-II Robinson-Trautman metrics of Kerr-Schild type. If such a metric has twist then it belongs either to the Kerr family or else its Weyl tensor is of Petrov type II. The main part of the paper is concerned with complexified versions of Kerr-Schild metrics. The general real ISKS metric is written in double Kerr-Schild (IDKS) form. The H and l potentials which generate IDKS metrics are determined for the general vacuum ISKS metric and given explicitly for the Schwarzchild and Kerr families of metrics.
A NONLINEAR LAVRENTIEV-BITSADZE MIXED TYPE EQUATION
Institute of Scientific and Technical Information of China (English)
Chen Shuxing
2011-01-01
In this paper the Tricomi problem for a nonlinear mixed type equation is studied.The coefficients of the mixed type equation are discontinuous on the line,where the equation changes its type.The existence of solution to this problem is proved.The method developed in this paper can be applied to study more difficult problems for nonlinear mixed type equations arising in gas dynamics.
Coherent data transmission with microresonator Kerr frequency combs
Pfeifle, Joerg; Wegner, Daniel; Brasch, Victor; Herr, Tobias; Hartinger, Klaus; Li, Jingshi; Hillerkuss, David; Schmogrow, Rene; Holzwarth, Ronald; Freude, Wolfgang; Leuthold, Juerg; Kippenberg, Tobias J; Koos, Christian
2013-01-01
Optical frequency combs enable coherent data transmission on hundreds of wavelength channels and have the potential to revolutionize terabit communications. Generation of Kerr combs in nonlinear integrated microcavities represents a particularly promising option enabling line spacings of tens of GHz, compliant with wavelength-division multiplexing (WDM) grids. However, Kerr combs may exhibit strong phase noise and multiplet spectral lines, and this has made high-speed data transmission impossible up to now. Recent work has shown that systematic adjustment of pump conditions allows generating low phase-noise Kerr combs with singlet spectral lines. Here, by employing an integrated Si3N4 microresonator, we demonstrate that Kerr combs are suited for coherent data transmission with advanced modulation formats that pose stringent requirements on the spectral purity of the optical source. In our experiment, we encode a data stream of 392 Gbit/s on subsequent lines of a Kerr comb using quadrature phase shift keying (...
Superradiant instability of the Kerr brane
Ishibashi, Akihiro; Gualtieri, Leonardo; Cardoso, Vitor
2015-01-01
We consider linear gravitational perturbations of the Kerr brane, an exact solution of vacuum Einstein's equations in dimensions higher than four and a low-energy solution of string theory. Decomposing the perturbations in tensor harmonics of the transverse Ricci-flat space, we show that tensor- and vector-type metric perturbations of the Kerr brane satisfy respectively a massive Klein-Gordon equation and a Proca equation on the four-dimensional Kerr space, where the mass term is proportional to the eigenvalue of the harmonics. Massive bosonic fields trigger a well-known superradiant instability on a Kerr black hole. We thus establish that Kerr branes in dimensions $D\\geq6$ are gravitationally unstable due to superradiance. These solutions are also unstable against the Gregory-Laflamme instability and we discuss the conditions for either instability to occur and their rather different nature. When the transverse dimensions are compactified and much smaller than the Kerr horizon, only the superradiant instabil...
Filamentation with nonlinear Bessel vortices.
Jukna, V; Milián, C; Xie, C; Itina, T; Dudley, J; Courvoisier, F; Couairon, A
2014-10-20
We present a new type of ring-shaped filaments featured by stationary nonlinear high-order Bessel solutions to the laser beam propagation equation. Two different regimes are identified by direct numerical simulations of the nonlinear propagation of axicon focused Gaussian beams carrying helicity in a Kerr medium with multiphoton absorption: the stable nonlinear propagation regime corresponds to a slow beam reshaping into one of the stationary nonlinear high-order Bessel solutions, called nonlinear Bessel vortices. The region of existence of nonlinear Bessel vortices is found semi-analytically. The influence of the Kerr nonlinearity and nonlinear losses on the beam shape is presented. Direct numerical simulations highlight the role of attractors played by nonlinear Bessel vortices in the stable propagation regime. Large input powers or small cone angles lead to the unstable propagation regime where nonlinear Bessel vortices break up into an helical multiple filament pattern or a more irregular structure. Nonlinear Bessel vortices are shown to be sufficiently intense to generate a ring-shaped filamentary ionized channel in the medium which is foreseen as opening the way to novel applications in laser material processing of transparent dielectrics.
Third-order chromatic dispersion stabilizes Kerr frequency combs
Parra-Rivas, Pedro; Leo, Francois; Coen, Stephane; Gelens, Lendert
2014-01-01
Using numerical simulations of an extended Lugiato-Lefever equation, we analyze the stability and nonlinear dynamics of Kerr frequency combs generated in microresonators and fiber resonators taking into account third-order dispersion effects. We show that cavity solitons underlying Kerr frequency combs, normally sensitive to oscillatory and chaotic instabilities, are stabilized in a wide range of parameter space by third-order dispersion. Moreover, we demonstrate how the snaking structure organizing compound states of multiple cavity solitons is qualitatively changed by third-order dispersion, promoting an increased stability of Kerr combs underlined by a single cavity soliton.
Third-order chromatic dispersion stabilizes Kerr frequency combs.
Parra-Rivas, Pedro; Gomila, Damià; Leo, François; Coen, Stéphane; Gelens, Lendert
2014-05-15
Using numerical simulations of an extended Lugiato-Lefever equation we analyze the stability and nonlinear dynamics of Kerr frequency combs generated in microresonators and fiber resonators, taking into account third-order dispersion effects. We show that cavity solitons underlying Kerr frequency combs, normally sensitive to oscillatory and chaotic instabilities, are stabilized in a wide range of parameter space by third-order dispersion. Moreover, we demonstrate how the snaking structure organizing compound states of multiple cavity solitons is qualitatively changed by third-order dispersion, promoting an increased stability of Kerr combs underlined by a single cavity soliton.
Electromagnetic source for the Kerr-Newman geometry
Dymnikova, Irina
2015-01-01
Source-free equations of nonlinear electrodynamics minimally coupled to gravity (NED-GR) admit regular axially symmetric asymptotically Kerr-Newman solutions, which describe electrically charged rotating black holes and spinning solitons. Asymptotic analysis of solutions shows the existence of de Sitter vacuum interior which has the properties of a perfect conductor and an ideal diamagnetic. The Kerr ring singularity (a naked singularity in the case without horizons) is replaced with a superconducting current, which serves as a nondissipative source of the Kerr-Newman fields and can be responsible for an unlimited life time of a spinning object.
Modulational instability in nonlocal Kerr media with a sine-oscillatory response
Wang, Zhuo; Guo, Qi; Hong, Weiyi; Hu, Wei
2017-07-01
We discuss modulational instability (MI) in nonlocal optical Kerr media with a sine-oscillatory response which can model nematic liquid crystals with negative dielectric anisotropy. In the framework of nonlocal nonlinear Schrödinger equation, MI in this type of media is found to have two unique properties different from those in other media discussed previously. First, MI exists both when the Kerr coefficient is positive and when it is negative. Second, the maximum gain points of MI do not shift with light intensity. We also explore the physical mechanism behind MI in local and nonlocal optical Kerr media by utilizing the theory of four-wave mixing. Through introducing a phase mismatch term (Δk) and a growth factor (γ), we deduce that the necessary and sufficient condition for MI to occur is that the phase mismatching during the four-wave-mixing process should be small enough such that | Δk | optical Kerr media obtained in the current work as well as those presented in previous work by others.
Elsawy, Mahmoud M R
2016-01-01
Two distinct models are developed to investigate the transverse magnetic stationary solutions propagating in one-dimensional anisotropic nonlinear plasmonic structures made from a nonlinear metamaterial core of Kerr-type embedded between two semi-infinite metal claddings. The first model is semi-analytical, in which we assumed that the anisotropic nonlinearity depends only on the transverse component of the electric field and that the nonlinear refractive index modification is small compared to the linear one. This method allows us to derive analytically the field profiles and the nonlinear dispersion relations in terms of the Jacobi elliptical functions. The second model is fully numerical, it is based on the finite-element method in which all the components of the electric field are considered in the Kerr-type nonlinearity with no presumptions on the nonlinear refractive index change. Our finite-element based model is valid beyond weak nonlinearity regime and generalize the well-known single-component fixed...
DEFF Research Database (Denmark)
Oster, Michael; Gaididei, Yuri B.; Johansson, Magnus
2004-01-01
We study the continuum limit of a nonlinear Schrodinger lattice model with both on-site and inter-site nonlinearities, describing weakly coupled optical waveguides or Bose-Einstein condensates. The resulting continuum nonlinear Schrodinger-type equation includes both nonlocal and nonlinear...
Dynamic gain aperture modelocking in picosecond regime based on cascaded second-order nonlinearity.
Mondal, Shyamal; Mukherjee, Shouvik; Singh, Satya Pratap; Rand, Stephen C; Bhattacharya, Sayantan; Das, Amit C; Datta, Prasanta Kumar
2016-07-11
The operation of a cascaded second-order mode-locked Nd:YVO4 laser has been investigated considering it as a soft-aperture Kerr lens type and using complex beam parameters. A self consistent complex beam propagation method is used to incorporate the effect of cascaded Kerr nonlinearity on radially varying gain aperturing. The analysis deduces a stable pulsewidth of ~9.5 ps which agrees well with the experimental value of 10.3 ps.
Power Series Solution for Solving Nonlinear Burgers-Type Equations
Directory of Open Access Journals (Sweden)
E. López-Sandoval
2015-01-01
Full Text Available Power series solution method has been traditionally used to solve ordinary and partial linear differential equations. However, despite their usefulness the application of this method has been limited to this particular kind of equations. In this work we use the method of power series to solve nonlinear partial differential equations. The method is applied to solve three versions of nonlinear time-dependent Burgers-type differential equations in order to demonstrate its scope and applicability.
Power Series Solution for Solving Nonlinear Burgers-Type Equations
López-Sandoval, E.; Mello, A.; Godina-Nava, J. J.; Samana, A. R.
2015-01-01
Power series solution method has been traditionally used to solve ordinary and partial linear differential equations. However, despite their usefulness the application of this method has been limited to this particular kind of equations. In this work we use the method of power series to solve nonlinear partial differential equations. The method is applied to solve three versions of nonlinear time-dependent Burgers-type differential equations in order to demonstrate its scope and applicability.
DEFF Research Database (Denmark)
Tuz, Vladimir R.; Novitsky, Denis V.; Prosvirnin, Sergey L.
2014-01-01
Optical properties of one-dimensional photonic structures consisting of Kerr-type nonlinear and magnetic layers under the action of an external static magnetic field in the Faraday geometry are investigated. The structure is a periodic arrangement of alternating nonlinear and magnetic layers (a one...
Sturm-Picone type theorems for nonlinear differential systems
Directory of Open Access Journals (Sweden)
Aydin Tiryaki
2015-06-01
Full Text Available In this article, we establish a Picone-type inequality for a pair of first-order nonlinear differential systems. By using this inequality, we give Sturm-Picone type comparison theorems for these systems and a special class of second-order half-linear equations with damping term.
Nonlinear Spinor Fields in Bianchi type-III spacetime
Saha, Bijan
2016-01-01
Within the scope of Bianchi type-III spacetime we study the role of spinor field on the evolution of the Universe as well as the influence of gravity on the spinor field. In doing so we have considered a polynomial type of nonlinearity. In this case the spacetime remains locally rotationally symmetric and anisotropic all the time. It is found that depending on the sign of nonlinearity the models allows both accelerated and oscillatory modes of expansion. The non-diagonal components of energy-momentum tensor though impose some restrictions on metric functions and components of spinor field, unlike Bianchi type I, V and $VI_0$ cases, they do not lead to vanishing mass and nonlinear terms of the spinor field.
Teukolsky, Saul A
2014-01-01
This review describes the events leading up to the discovery of the Kerr metric in 1963 and the enormous impact the discovery has had in the subsequent 50 years. The review discusses the Penrose process, the four laws of black hole mechanics, uniqueness of the solution, and the no-hair theorems. It also includes Kerr perturbation theory and its application to black hole stability and quasi-normal modes. The Kerr metric's importance in the astrophysics of quasars and accreting stellar-mass black hole systems is detailed. A theme of the review is the "miraculous" nature of the solution, both in describing in a simple analytic formula the most general rotating black hole, and in having unexpected mathematical properties that make many calculations tractable. Also included is a pedagogical derivation of the solution suitable for a first course in general relativity.
Cross-Kerr-effect induced by coupled Josephson qubits in circuit quantum electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Hu Yong; Ge Guoqin; Chen Shi; Yang Xiaofei; Chen Youling [School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074 (China); Department of Electronic Science and Technology, Huazhong University of Science and Technology, Wuhan, Hubei 430074 (China); Department of Physics, Peking University, Beijing 100871 (China)
2011-07-15
We propose a scheme for implementing cross-Kerr nonlinearity between two superconducting transmission line resonators (TLRs) via their interactions with a coupler constructed by two superconducting transmon qubits connected to each other through a superconducting quantum interference device. When suitably driven, the coupler can induce very strong cross phase modulation (XPM) between the two TLRs due to its N-type level structure and the consequent electromagnetically induced transparency in its lowest states. The flexibility of our design can lead to various inter-TLR coupling configurations. The obtained cross-Kerr coefficient is large enough to allow many important quantum operations in which only few photons are involved. We further show that this scheme is very robust against fluctuations in solid-state quantum circuits. Our numerical calculations imply that the absorption and the dispersion of the TLRs resulting from the decoherence of the coupler are very small compared with the proposed XPM strength.
Nonlinear dynamic analysis of traveling wave-type ultrasonic motors.
Nakagawa, Yosuke; Saito, Akira; Maeno, Takashi
2008-03-01
In this paper, nonlinear dynamic response of a traveling wave-type ultrasonic motor was investigated. In particular, understanding the transient dynamics of a bar-type ultrasonic motor, such as starting up and stopping, is of primary interest. First, the transient response of the bar-type ultrasonic motor at starting up and stopping was measured using a laser Doppler velocimeter, and its driving characteristics are discussed in detail. The motor is shown to possess amplitude-dependent nonlinearity that greatly influences the transient dynamics of the motor. Second, a dynamical model of the motor was constructed as a second-order nonlinear oscillator, which represents the dynamics of the piezoelectric ceramic, stator, and rotor. The model features nonlinearities caused by the frictional interface between the stator and the rotor, and cubic nonlinearity in the dynamics of the stator. Coulomb's friction model was employed for the interface model, and a stick-slip phenomenon is considered. Lastly, it was shown that the model is capable of representing the transient dynamics of the motor accurately. The critical parameters in the model were identified from measured results, and numerical simulations were conducted using the model with the identified parameters. Good agreement between the results of measurements and numerical simulations is observed.
Josephson junction-embedded transmission-line resonators: from Kerr medium to in-line transmon
Bourassa, J; Gambetta, Jay M; Blais, A
2012-01-01
We provide a general method to find the Hamiltonian of a linear circuit in the presence of a nonlinearity. Focussing on the case of a Josephson junction embedded in a transmission-line resonator, we solve for the normal modes of the system by taking into account exactly the effect of the quadratic (i.e. inductive) part of the Josephson potential. The nonlinearity is then found to lead to self and cross-Kerr effect, as well as beam-splitter type interactions between modes. By adjusting the parameters of the circuit, the Kerr coefficient K can be made to reach values that are weak (K \\kappa) or even very strong (K >> \\kappa) with respect to the photon-loss rate \\kappa. In the latter case, the resonator+junction circuit corresponds to an in-line version of the transmon. By replacing the single junction by a SQUID, the Kerr coefficient can be tuned in-situ, allowing for example the fast generation of Schr\\"odinger cat states of microwave light. Finally, we explore the maximal strength of qubit-resonator coupling...
Nonlinear Discrete Inequalities of Bihari-type and Applications
Institute of Scientific and Technical Information of China (English)
Yu WU
2013-01-01
Discrete Bihari-type inequalities with n nonlinear terms are discussed,which generalize some known results and may be used in the analysis of certain problems in the theory of difference equations.Examples to illustrate the boundedness of solutions of a difference equation are also given.
Stabilization of spatiotemporal solitons in Kerr media by dispersive coupling
Kartashov, Yaroslav V; Konotop, Vladimir V; Lobanov, Valery E; Torner, Lluis
2015-01-01
We introduce a mechanism to stabilize spatiotemporal solitons in Kerr nonlinear media, based on the dispersion of linear coupling between the field components forming the soliton states. Specifically, we consider solitons in a two-core guiding structure with inter-core coupling dispersion (CD). We show that CD profoundly affects properties of the solitons, causing the complete stabilization of the otherwise highly unstable spatiotemporal solitons in Kerr media with focusing nonlinearity. We also find that the presence of CD stimulates the formation of bound states, which however are unstable.
Kerr black holes with Proca hair
Herdeiro, Carlos; Radu, Eugen; Rúnarsson, Helgi
2016-08-01
Bekenstein proved that in Einstein's gravity minimally coupled to one (or many) real, Abelian, Proca field, stationary black holes (BHs) cannot have Proca hair. Dropping Bekenstein's assumption that matter inherits spacetime symmetries, we show this model admits asymptotically flat, stationary, axi-symmetric, regular on and outside an event horizon BHs with Proca hair, for an even number of real (or an arbitrary number of complex) Proca fields. To establish it, we start by showing that a test, complex Proca field can form bound states, with real frequency, around Kerr BHs: stationary Proca clouds. These states exist at the threshold of superradiance. It was conjectured in [1, 2], that the existence of such clouds at the linear level implies the existence of a new family of BH solutions at the nonlinear level. We confirm this expectation and explicitly construct examples of such Kerr BHs with Proca hair (KBHsPH). For a single complex Proca field, these BHs form a countable number of families with three continuous parameters (ADM mass, ADM angular momentum and Noether charge). They branch off from the Kerr solutions that can support stationary Proca clouds and reduce to Proca stars [3] when the horizon size vanishes. We present the domain of existence of one family of KBHsPH, as well as its phase space in terms of ADM quantities. Some physical properties of the solutions are discussed; in particular, and in contrast with Kerr BHs with scalar hair, some spacetime regions can be counter-rotating with respect to the horizon. We further establish a no-Proca-hair theorem for static, spherically symmetric BHs but allowing the complex Proca field to have a harmonic time dependence, which shows BHs with Proca hair in this model require rotation and have no static limit. KBHsPH are also disconnected from Kerr-Newman BHs with a real, massless vector field.
Nonlinear Spinor Fields in Bianchi type-V spacetime
Saha, Bijan
2016-01-01
A self-consistent system of nonlinear spinor and Bianchi type-V anisotropic gravitational fields are investigated. It is found that the presence of nontrivial non-diagonal components of the energy-momentum tensor of the spinor field imposes some severe restrictions to the system. As a result two different solutions are found. In one case the metric functions are similar to each other, i.e., $a_1 \\sim a_2 \\sim a_3$ and the spinor mass and spinor field nonlinearity do not disappear from the system. In this case the spacetime expands with acceleration in case of a positive self-coupling constant $\\lambda$. A negative $\\lambda$ gives rise to a cyclic or periodical mode of expansion. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly with time.
Second-order nonlinear optical metamaterials: ABC-type nanolaminates
Energy Technology Data Exchange (ETDEWEB)
Alloatti, L., E-mail: alloatti@mit.edu; Kieninger, C.; Lauermann, M.; Köhnle, K. [Institute of Photonics and Quantum Electronics (IPQ), Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); Froelich, A.; Wegener, M. [Institute of Applied Physics, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), 76021 Karlsruhe (Germany); Frenzel, T. [Institute of Applied Physics, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); Freude, W. [Institute of Photonics and Quantum Electronics (IPQ), Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); Institute for Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), 76344 Eggenstein-Leopoldshafen (Germany); Leuthold, J.; Koos, C., E-mail: christian.koos@kit.edu [Institute of Photonics and Quantum Electronics (IPQ), Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); Institute for Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), 76344 Eggenstein-Leopoldshafen (Germany)
2015-09-21
We demonstrate a concept for second-order nonlinear metamaterials that can be obtained from non-metallic centrosymmetric constituents with inherently low optical absorption. The concept is based on iterative atomic-layer deposition of three different materials, A = Al{sub 2}O{sub 3}, B = TiO{sub 2}, and C = HfO{sub 2}. The centrosymmetry of the resulting ABC stack is broken since the ABC and the inverted CBA sequences are not equivalent—a necessary condition for non-zero second-order nonlinearity. In our experiments, we find that the bulk second-order nonlinear susceptibility depends on the density of interfaces, leading to a nonlinear susceptibility of 0.26 pm/V at a wavelength of 800 nm. ABC-type nanolaminates can be deposited on virtually any substrate and offer a promising route towards engineering of second-order optical nonlinearities at both infrared and visible wavelengths.
Various Newton-type iterative methods for solving nonlinear equations
Directory of Open Access Journals (Sweden)
Manoj Kumar
2013-10-01
Full Text Available The aim of the present paper is to introduce and investigate new ninth and seventh order convergent Newton-type iterative methods for solving nonlinear equations. The ninth order convergent Newton-type iterative method is made derivative free to obtain seventh-order convergent Newton-type iterative method. These new with and without derivative methods have efficiency indices 1.5518 and 1.6266, respectively. The error equations are used to establish the order of convergence of these proposed iterative methods. Finally, various numerical comparisons are implemented by MATLAB to demonstrate the performance of the developed methods.
Collapse suppression and soliton stabilization through nonlocality in bulk Kerr media
DEFF Research Database (Denmark)
Bang, Ole; Chemineau, E. T.; Krolikowski, Wieslaw
2000-01-01
We show that self-focusing cannot occur in bulk Kerr media with a nonlocal nonlinear response. We find the stationary solutions and show that nonlocality makes them stable. The results are verified numerically....
Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials
Energy Technology Data Exchange (ETDEWEB)
Tsitsas, N.L. [School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Zografos, Athens 15773 (Greece); Horikis, T.P. [Department of Mathematics, University of Ioannina, Ioannina 45110 (Greece); Shen, Y.; Kevrekidis, P.G.; Whitaker, N. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Frantzeskakis, D.J., E-mail: dfrantz@phys.uoa.g [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84 (Greece)
2010-03-01
We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. Two short-pulse equations (SPEs) are derived for the high- and low-frequency 'band gaps' (where linear electromagnetic waves are evanescent) with linear effective permittivity epsilon<0 and permeability mu>0. The structure of the solutions of the SPEs is also briefly discussed, and connections with the soliton solutions of the nonlinear Schroedinger equation are made.
Generation of Kerr Frequency Combs in Resonators with Normal GVD
Matsko, Andrey B; Maleki, Lute
2011-01-01
We show via numerical simulation that Kerr frequency combs can be generated in a nonlinear resonator characterized with normal group velocity dispersion (GVD). We find the spectral shape of the comb and temporal envelope of the corresponding optical pulses formed in the resonator.
Hard and Soft Excitation Regimes of Kerr Frequency Combs
Matsko, Andrey B; Ilchenko, Vladimir S; Seidel, David; Maleki, Lute
2011-01-01
We theoretically study the stability conditions and excitation regimes of hyper-parametric oscillation and Kerr frequency comb generation in continuously pumped nonlinear optical resonators possessing anomalous group velocity dispersion. We show that both hard and soft excitation regimes are possible in the resonators. Selection between the regimes is achieved via change in the parameters of the pumping light.
Self-Frequency Shift of Cavity Soliton in Kerr Frequency Comb
Zhang, Lin; Kimerling, Lionel C; Michel, Jurgen
2014-01-01
We show that the ultrashort cavity soliton in octave-spanning Kerr frequency comb generation exhibits striking self-adaptiveness and robustness to external perturbations, resulting in a novel frequency shifting/cancellation mechanism and gigantic dispersive wave generation in response to the strong frequency dependence of Kerr nonlinearity, Raman scattering, chromatic dispersion, and cavity Q. These observations open up a great avenue towards versatile manipulation of nonlinear soliton dynamics, flexible spectrum engineering of mode-locked Kerr frequency combs, and highly efficient frequency translation of optical waves.
Comment on "Saturation of the All-Optical Kerr Effect"
Wahlstrand, J K
2011-01-01
Br\\'ee, Demircan, and Steinmeyer [Phys. Rev. Lett. 106, 183902 (2011)] recently calculated higher-order Kerr effect (HOKE) coefficients using the nonlinear Kramers-Kronig relations. We show that the saturated and negative nonlinear index of refraction obtained by Br\\'ee et al. is an artifact of their use of a perturbative theory of ionization in an intensity region where it breaks down.
Unconventional Hamilton-type variational principles for nonlinear coupled thermoelastodynamics
Institute of Scientific and Technical Information of China (English)
罗恩; 邝君尚; 黄伟江; 罗志国
2002-01-01
According to the basic idea of classical yin-yang complementarity and modem dual-com plementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type vari ational principles for geometrically nonlinear coupled thermoelastodynamics can be established system atically. The new unconventional Hamilton-type variational principle can fully characterize the initia boundary-value problem of this dynamics. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for geometrically nonlin ear coupled thermodynamics. Based on this relation, it is possible not only to obtain the principle of vir tual work in geometrically nonlinear coupled thermodynamics, but also to derive systematically the complementary functionals for eight-field, six-field, four-field and two-field unconventional Hamilton type variational principles by the generalized Legendre transformations given in this paper. Further more, with this approach, the intrinsic relationship among various principles can be explained clearly.
Nonlinear system PID-type multi-step predictive control
Institute of Scientific and Technical Information of China (English)
Yan ZHANG; Zengqiang CHEN; Zhuzhi YUAN
2004-01-01
A compound neural network was constructed during the process of identification and multi-step prediction. Under the PlD-type long-range predictive cost function, the control signal was calculated based on gradient algorithm. The nonlinear controller' s structure was similar to the conventional PID controller. The parameters of this controller were tuned by using a local recurrent neural network on-line. The controller has a better effect than the conventional PID controller. Simulation study shows the effectiveness and good performance.
Few-cycle nonlinear mid-IR pulse generated with cascaded quadratic nonlinearities
DEFF Research Database (Denmark)
Bache, Morten; Liu, Xing; Zhou, Binbin
change Δn = ncascI, where ncase ∝ −d2eff/Δk, and deff is the effective quadratic nonlinearity. Due to competing material nonlinearities nKerr the total nonlinear refractive is ncubic = ncasc + nKerr. Interestingly ncubic can become negative (self-defocusing), elegantly avoiding self-focusing problems...
Eliminating material constraints for nonlinearity with plasmonic metamaterials
Neira, Andres D.; Olivier, Nicolas; Nasir, Mazhar E.; Dickson, Wayne; Wurtz, Gregory A.; Zayats, Anatoly V.
2015-01-01
Nonlinear optical materials comprise the foundation of modern photonics, offering functionalities ranging from ultrafast lasers to optical switching, harmonic and soliton generation. Optical nonlinearities are typically strong near the electronic resonances of a material and thus provide limited tuneability for practical use. Here we show that in plasmonic nanorod metamaterials, the Kerr-type nonlinearity is not limited by the nonlinear properties of the constituents. Compared with gold's nonlinearity, the measured nonlinear absorption and refraction demonstrate more than two orders of magnitude enhancement over a broad spectral range that can be engineered via geometrical parameters. Depending on the metamaterial's effective plasma frequency, either a focusing or defocusing nonlinearity is observed. The ability to obtain strong and fast optical nonlinearities in a given spectral range makes these metamaterials a flexible platform for the development of low-intensity nonlinear applications. PMID:26195182
Influence of Kerr-like medium on the dynamics of a two-mode Raman coupled model
Singh, Sudha; Gilhare, Karuna
2016-08-01
We study the quantum dynamics of an effective two-level atom interacting with two modes via Raman process inside an ideal cavity in the presence of Kerr non-linearity. The cavity modes interact both with the atom as well as the Kerr-like medium. The unitary transformation method presented here, not only solves the time-dependent problem, but also provides the eigensolutions of the interacting Hamiltonian at the same time. We study the atomic-population dynamics and the dynamics of the photon statistics in the two cavity modes. The influence of the Kerr-like medium on the statistics of the field is explored and it is observed that Kerr medium introduces antibunching in mode 1 and this effect is enhanced by a stronger interaction with the non-linear medium. In the high non-linear coupling regime anticorrelated beam become correlated. Kerr medium also introduces non-classical correlation between the two modes.
H, R. Baghshahi; M, K. Tavassoly; A, Behjat
2014-07-01
The interaction between a two-level atom and a single-mode field in the k-photon Jaynes—Cummings model (JCM) in the presence of the Stark shift and a Kerr medium is studied. All terms in the Hamiltonian, such as the single-mode field, its interaction with the atom, the contribution of the Stark shift and the Kerr medium effects are considered to be f-deformed. In particular, the effect of the initial state of the radiation field on the dynamical evolution of some physical properties such as atomic inversion and entropy squeezing are investigated by considering different initial field states (coherent, squeezed and thermal states).
Gibson, C H
2003-01-01
A quantum gravitational instability is identified at Planck scales between non-spinning extreme Schwarzschild black holes and spinning extreme Kerr black holes, which produces a turbulent Planck particle gas. Planck inertial vortex forces balance gravitational forces as the Planck turbulence cascades to larger scales and the universe expands and cools. Turbulent mixing of temperature fluctuations and viscous dissipation of turbulent kinetic energy provide irreversibilities necessary to sustain the process to the strong force freeze out temperature where inflation begins. Turbulent temperature fluctuations are fossilized when they are stretched by inflation beyond the horizon scale of causal connection. As the horizon of the expanding universe grows, the fluctuations seed patterns of nucleosynthesis, and these seed the formation of structure in the plasma epoch. Fossil big bang turbulence is supported by extended self similarity coefficients computed for cosmic microwave background temperature anisotropies tha...
Quasilocal Energy in Kerr Spacetime
Liu, Jian-Liang
2016-01-01
In this work we study the quasilocal energy as in [11] for a constant radius surface in Kerr spacetime in Boyer-Lindquist coordinates. We show that under suitable conditions for isometric embedding, for a stationary observer the quasilocal energy defined in [11] for constant radius in a Kerr like spacetime is exactly equal to the Brown-York quasilocal energy [2]. By some careful estimations, we show that for a constant radius surface in the Kerr spacetime which is outside the ergosphere the embedding conditions for the previous result are satisfied. Finally we discuss extremal solutions as described in [14] and show that near the horizon of the Kerr spacetime for the small rotation case the extremal solutions are trivial.
Higher-order Kerr effect and harmonic cascading in gases
Bache, Morten; Minardi, Stefano
2012-01-01
The higher-order Kerr effect (HOKE) has been recently advocated to explain measurements of the saturation of the nonlinear refractive index in gases. Here we show that cascaded third-harmonic generation results in an effective fifth order nonlinearity that is negative and significant. Higher-order harmonic cascading will also occur from the HOKE, and the cascading contributions may significantly modify the observed nonlinear index change. At lower wavelengths cascading increases the HOKE saturation intensity, while for longer wavelengths cascading will decrease the HOKE saturation intensity.
Abdalla, M. Sebawe; Khalil, E. M.; Obada, A. S.-F.
2017-01-01
In the present communication, we consider the problem of two quantum systems with the Kerr-like medium nonlinearity. The system is cast form of an interaction between two operators of the form su(1 , 1) Lie algebra and su(2) Lie algebra. We obtain the wave function via the evolution operator where we use the Heisenberg equations of motion to derive the constants of motion. We discuss the atomic inversion. It is found that the Kerr-like medium decreases the amplitude and increases the fluctuations. Also we consider different types of squeezing, it is shown that the entropy squeezing is pronounced in the second quadrature, but it shows a small amount in the first quadrature. For the variance squeezing, a small amount occurs in the presence of the Kerr-like medium. However, the normal squeezing occurs in the first quadrature where the squeezing is sensitive to both the Kerr-like medium parameter and the initial state. Furthermore, the degree of entanglement is examined through the linear entropy. It is shown that the function decreases besides rapid fluctuations. The correlation function displays nonclassical behavior in addition to an increase in the amplitude of the fluctuations.
Robust Absolute Stability of General Interval Lur'e Type Nonlinear Control Systems
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper, Lyapunov function method isused to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matrix inequality form are obtained for the general interval Lur'e type nonlinear control systems, thus the relationship between the stability of symmetrical interval matrix and the robust absolute stability of general interval Lur'e type nonlinear control systems is established.
Optical Kerr effect of tRNA solution induced by femtosecond laser pulses
Kucia, Weronika E.; Sharma, Gargi; Joseph, Cecil S.; Sarbak, Szymon; Oliver, Cameron; Dobek, Andrzej; Giles, Robert H.
2016-10-01
The optical Kerr effect (OKE) in a transfer ribonucleic acid (tRNA) solution induced by femtosecond pulses of linearly polarized pump light (λi = 800 nm) and sounded by probe light (λp = 800 nm) was studied. The measurements were performed to find nonlinear optical parameters describing a single molecule (molecular Kerr constant K, mean nonlinear third order optical polarizability cpi) and to compare them with our previous OKE results obtained in ns and ps time range. The OKE experiment has proven to be an efficient method to obtain the nonlinear parameters of single molecules in solution, which reflects dynamic structure changes.
Quantum Popov robust stability analysis of an optical cavity containing a saturated Kerr medium
Petersen, Ian R.
2017-09-01
This paper applies results of the robust stability of nonlinear quantum systems to a system consisting of an optical cavity containing a saturated Kerr medium. The system is characterised by a Hamiltonian operator that contains a non-quadratic term involving a quartic function of the annihilation and creation operators. A saturated version of the Kerr nonlinearity leads to a sector-bounded nonlinearity that enables a quantum small gain theorem to be applied to this system in order to analyse its stability. Also, a non-quadratic version of a quantum Popov stability criterion is presented and applied to analyse the stability of this system.
Kerr black holes with Proca hair
Herdeiro, Carlos; Runarsson, Helgi
2016-01-01
Bekenstein proved that in Einstein's gravity minimally coupled to one (or many) real, Abelian, Proca field, stationary black holes (BHs) cannot have Proca hair. Dropping Bekenstein's assumption that matter inherits spacetime symmetries, we show this model admits asymptotically flat, stationary, axi-symmetric, regular on and outside an event horizon BHs with Proca hair, for an even number of real (or an arbitrary number of complex) Proca fields. To establish it, we start by showing that a test, complex Proca field can form bound states, with real frequency, around Kerr BHs: stationary Proca clouds. These states exist at the threshold of superradiance. It was conjectured in arXiv:1403.2757, that the existence of such clouds at the linear level implies the existence of a new family of BH solutions at the non-linear level. We confirm this expectation and explicitly construct examples of such Kerr black holes with Proca hair (KBHsPH). For a single complex Proca field, these BHs form a countable number of families ...
Optical lattice trap for Kerr solitons
Taheri, Hossein; Matsko, Andrey B.; Maleki, Lute
2017-06-01
We show theoretically and numerically that dichromatic pumping of a nonlinear microresonator by two continuous wave coherent optical pumps creates an optical lattice trap that results in the localization of intra-cavity Kerr solitons with soliton positions defined by the beat frequency of the two pumps. This phenomenon corresponds to the stabilization of the comb repetition rate. The locking of the second pump, through adiabatic tuning of its frequency, to the comb generated by the first pump allows transitioning to single-soliton states, manipulating the position of Kerr solitons in the cavity, and tuning the frequency comb repetition rate within the locking range. It also explains soliton crystal formation in resonators supporting a dispersive wave emitted as a result of higher-order group velocity dispersion or avoided mode crossing. We show that dichromatic pumping by externally stabilized pumps can be utilized for stabilization of microresonator-based optical frequency combs when the comb span does not cover an octave or a significant fraction thereof and standard self-referencing techniques cannot be employed. Our findings have significant ramifications for high-precision applications of optical frequency combs in spectrally pure signal generation, metrology, and timekeeping.
Spatial synchronization between optical waveguides in arrays of Kerr fibers
Pando, L C L
2002-01-01
We study a new family of solutions of the discrete nonlinear Schroedinger equation (DNLSE), whose initial conditions are close to the resonances of a suitable area preserving map. We show that some of these solutions are stable. We study the DNLSE in the context of arrays consisting of a finite number of coupled Kerr waveguides. Partial as well as complete spatial synchronization arises between the electric fields of some waveguides as light propagates.
Spatial synchronization between optical waveguides in arrays of Kerr fibers
Pando, L C L
2002-01-01
We study a new family of solutions of the discrete nonlinear Schr\\"{o}dinger equation (DNLSE), whose initial conditions are close to the resonances of a suitable area preserving map. We show that some of these solutions are stable. We study the DNLSE in the context of arrays consisting of a finite number of coupled Kerr waveguides. Partial as well as complete spatial synchronization arises between the electric fields of some waveguides as light propagates.
Miranowicz, A; Miranowicz, Adam; Leonski, Wieslaw
2006-01-01
Schemes for optical-state truncation of two cavity modes are analysed. The systems, referred to as the nonlinear quantum scissors devices, comprise two coupled nonlinear oscillators (Kerr nonlinear coupler) with one or two of them pumped by external classical fields. It is shown that the quantum evolution of the pumped couplers can be closed in a two-qubit Hilbert space spanned by vacuum and single-photon states only. Thus, the pumped couplers can behave as a two-qubit system. Analysis of time evolution of the quantum entanglement shows that Bell states can be generated. A possible implementation of the couplers is suggested in a pumped double-ring cavity with resonantly enhanced Kerr nonlinearities in an electromagnetically-induced transparency scheme. The fragility of the generated states and their entanglement due to the standard dissipation and phase damping are discussed by numerically solving two types of master equations.
Elsawy, Mahmoud M. R.; Renversez, Gilles
2017-07-01
Two distinct models are developed to investigate the transverse magnetic stationary solutions propagating in one-dimensional anisotropic nonlinear plasmonic structures made from a Kerr-type nonlinear metamaterial core embedded between two semi-infinite metal claddings. The first model is semi-analytical, in which we assume that the anisotropic nonlinearity depends only on the transverse component of the electric field and that the nonlinear refractive index modification is small compared to the linear one. This method allows us to derive analytically the field profiles and nonlinear dispersion relations in terms of the Jacobi elliptical functions. The second model is fully numerical and is based on the finite element method in which all the components of the electric field are considered in the Kerr-type nonlinearity, with no presumptions as to the nonlinear refractive index change. Our finite-element-based model is valid beyond the weak nonlinearity regime and generalizes the well-known single-component fixed power algorithm that is usually used. Examples of the main cases are investigated, including those with strong spatial nonlinear effects at low power. Loss issues are reduced through the use of a gain medium in the nonlinear metamaterial core. Using anisotropic nonlinear FDTD simulations, we provide some results for the properties of the main solution.
Multiple scales analysis and travelling wave solutions for KdV type nonlinear evolution equations
Ayhan, Burcu; Ozer, M. Naci; Bekir, Ahmet
2017-01-01
Nonlinear evolution equations are the mathematical models of problems that arise in many field of science. These equations has become an important field of study in applied mathematics in recent years. We apply exact solution methods and multiple scale method which is known as a perturbation method to nonlinear evolution equations. Using exact solution methods we get travelling wave solutions expressed by hyperbolic functions, trigonometric functions and rational functions. Also we derive Nonlinear Schrödinger (NLS) type equations from Korteweg-de Vries (KdV) type nonlinear evolution equations and we get approximate solutions for KdV type equations using multiple scale method. The proposed methods are direct and effective and can be used for many nonlinear evolution equations. It is shown that these methods provide a powerful mathematical tool to solve nonlinear evolution equations in mathematical physics.
On the convergence of nonlinear Beltrami type operators
Directory of Open Access Journals (Sweden)
Riccardo De Arcangelis
1986-11-01
Full Text Available One of the results proved is the following: if (fh is a sequence of K-quasiregular mappings, converging to f in L1loc , whose jacobians verify a weak integrability condition, then the solutions of Dirichlet problems for the nonlinear Laplace-Beltrami operator associated to each fh converge to the solution of the Dirichlet problem for the nonlinear Laplace-Beltrami operator associated to f. Such result is deduced as a particular case of a more general theorem concerning nonlinear operators. The case of K-quasiconformal functions fh is also treated. A class of weighted Sobolev spaces associated to quasiconformal mappings is studied.
Unstable Fields in Kerr Spacetimes
Dotti, Gustavo; Ranea-Sandoval, Ignacio F
2011-01-01
We present a generalization of previous results regarding the stability under gravitational perturbations of nakedly singular super extreme Kerr spacetime and Kerr black hole interior beyond the Cauchy horizon. To do so we study solutions to the radial and angular Teukolsky's equations with different spin weights, particulary $s=\\pm 1$ representing electromagnetic perturbations, $s=\\pm 1/2$ representing a perturbation by a Dirac field and $s=0$ representing perturbations by a scalar field. By analizing the properties of radial and angular eigenvalues we prove the existence of an infinite family of unstable modes.
Institute of Scientific and Technical Information of China (English)
Jeong Ja Bae
2012-01-01
In this article,we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials,one component is a Kirchhoff type wave equation with nonlinear time dependent localized dissipation which is effective only on a neighborhood of certain part of the boundary,while the other is a Kirchhoff type wave equation with nonlinear memory.
Optical nonlinearities of excitonic states in atomically thin 2D transition metal dichalcogenides.
Energy Technology Data Exchange (ETDEWEB)
Soh, Daniel Beom Soo
2017-09-01
We calculated the optical nonlinearities of the atomically thin monolayer transition metal dichalcogenide material (particularly MoS 2 ), particularly for those linear and nonlinear tran- sition processes that utilize the bound exciton states. We adopted the bound and the unbound exciton states as the basis for the Hilbert space, and derived all the dynamical density matri- ces that provides the induced current density, from which the nonlinear susceptibilities can be drawn order-by-order via perturbative calculations. We provide the nonlinear susceptibil- ities for the linear, the second-harmonic, the third-harmonic, and the kerr-type two-photon processes.
Vectorial spatial solitons in bulk periodic quadratically nonlinear media
Energy Technology Data Exchange (ETDEWEB)
Panoiu, N-C [Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 (United States); Mihalache, D [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Mazilu, D [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Lederer, F [Institute of Solid State Theory and Theoretical Optics, Friedrich Schiller University Jena, Max-Wien-Platz 1, Jena, D-07743 (Germany); Osgood, R M Jr [Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 (United States)
2004-05-01
We present a comprehensive analysis of the generation, propagation and characteristic properties of two-dimensional spatial solitons formed in quasi-phase-matched gratings through type-II vectorial interaction. By employing an averaging approach based on asymptotic expansion theory, we show that the dynamics of soliton propagation in the grating and their stability properties are strongly influenced by induced Kerr-like nonlinearities. Finally, through extensive numerical simulations, we verify the validity of our theoretical predictions.
Universality of the quasinormal spectrum of near-extremal Kerr-Newman black holes
Energy Technology Data Exchange (ETDEWEB)
Hod, Shahar [The Ruppin Academic Center, Emeq Hefer (Israel); The Hadassah Institute, Jerusalem (Israel)
2015-06-15
Our current knowledge about the quasinormal resonance spectrum of charged and rotating Kerr-Newman black holes is quite poor. This unsatisfactory situation is a direct consequence of the fact that all attempts to decouple the gravitational and electromagnetic perturbations of generic Kerr-Newman black holes have failed thus far. Recently, Zilhao et al. (Phys Rev D 90:12, 124088, 2014. arXiv:1410.0694) have studied the nonlinear stability of Kerr-Newman black holes. We show here that their numerical results for the time evolutions of the spacetime deformations of near-extremal Kerr-Newman black holes are described extremely well by a simple and universal analytical formula for the quasinormal resonances of the black holes. This formula is expressed in terms of the black-hole physical parameters: the horizon angular velocity Ω{sub H} and the Bekenstein-Hawking temperature T{sub BH}. (orig.)
Nonlinear optical response in Kronig-Penney type graphene superlattice in terahertz regime
Jiang, Lijuan; Yuan, Rui-Yang; Zhao, Xin; Lv, Jing; Yan, Hui
2015-05-01
The terahertz nonlinear optical response in Kronig-Penney (KP) type graphene superlattice is demonstrated. The single-, triple- and quintuple-frequencies of the fifth-order nonlinear responses are investigated for different frequencies and temperatures with the angle φ along the periodicity of the superlattice toward the external field tuning from 0 to π/2. The results show that the fifth-order nonlinear optical conductance of graphene superlattice is enhanced in the terahertz regime when φ = 0, i.e. an external field is applied along the periodicity of the superlattice. The fifth-order nonlinear optical conductances at φ = 0 for different frequencies and temperatures are calculated. The results show that the nonlinear optical conductance is enhanced in low frequency and low temperature. Our results suggest that KP type graphene superlattices are preferred structures for developing graphene-based nonlinear photonics and optoelectronics devices.
Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers
Directory of Open Access Journals (Sweden)
Nicolás Peréz Alvarez
2015-11-01
Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.
Kerr optical frequency combs: theory, applications and perspectives
Chembo, Yanne K.
2016-06-01
The optical frequency comb technology is one of the most important breakthrough in photonics in recent years. This concept has revolutionized the science of ultra-stable lightwave and microwave signal generation. These combs were originally generated using ultrafast mode-locked lasers, but in the past decade, a simple and elegant alternativewas proposed,which consisted in pumping an ultra-high-Q optical resonator with Kerr nonlinearity using a continuous-wave laser. When optimal conditions are met, the intracavity pump photons are redistributed via four-wave mixing to the neighboring cavity modes, thereby creating the so-called Kerr optical frequency comb. Beyond being energy-efficient, conceptually simple, and structurally robust, Kerr comb generators are very compact devices (millimetric down to micrometric size) which can be integrated on a chip. They are, therefore, considered as very promising candidates to replace femtosecond mode-locked lasers for the generation of broadband and coherent optical frequency combs in the spectral domain, or equivalently, narrow optical pulses in the temporal domain. These combs are, moreover, expected to provide breakthroughs in many technological areas, such as integrated photonics, metrology, optical telecommunications, and aerospace engineering. The purpose of this review article is to present a comprehensive survey of the topic of Kerr optical frequency combs.We provide an overview of the main theoretical and experimental results that have been obtained so far. We also highlight the potential of Kerr combs for current or prospective applications, and discuss as well some of the open challenges that are to be met at the fundamental and applied level.
Kerr optical frequency combs: theory, applications and perspectives
Directory of Open Access Journals (Sweden)
Chembo Yanne K.
2016-06-01
Full Text Available The optical frequency comb technology is one of the most important breakthrough in photonics in recent years. This concept has revolutionized the science of ultra-stable lightwave and microwave signal generation. These combs were originally generated using ultrafast mode-locked lasers, but in the past decade, a simple and elegant alternativewas proposed,which consisted in pumping an ultra-high-Q optical resonator with Kerr nonlinearity using a continuous-wave laser. When optimal conditions are met, the intracavity pump photons are redistributed via four-wave mixing to the neighboring cavity modes, thereby creating the so-called Kerr optical frequency comb. Beyond being energy-efficient, conceptually simple, and structurally robust, Kerr comb generators are very compact devices (millimetric down to micrometric size which can be integrated on a chip. They are, therefore, considered as very promising candidates to replace femtosecond mode-locked lasers for the generation of broadband and coherent optical frequency combs in the spectral domain, or equivalently, narrow optical pulses in the temporal domain. These combs are, moreover, expected to provide breakthroughs in many technological areas, such as integrated photonics, metrology, optical telecommunications, and aerospace engineering. The purpose of this review article is to present a comprehensive survey of the topic of Kerr optical frequency combs.We provide an overview of the main theoretical and experimental results that have been obtained so far. We also highlight the potential of Kerr combs for current or prospective applications, and discuss as well some of the open challenges that are to be met at the fundamental and applied level.
Measurement of high order Kerr refractive index of major air components.
Loriot, V; Hertz, E; Faucher, O; Lavorel, B
2009-08-03
We measure the instantaneous electronic nonlinear refractive index of N(2), O(2) and Ar at room temperature for a 90 fs and 800 nm laser pulse. Measurements are calibrated by post-pulse molecular alignment through a polarization technique. At low intensity, quadratic coefficients n(2) are determined. At higher intensities, a strong negative contribution with a higher nonlinearity appears, which leads to an overall negative nonlinear Kerr refractive index in air above 26 TW/cm(2).
Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types
Remillieux, Marcel C.; Guyer, Robert A.; Payan, Cédric; Ulrich, T. J.
2016-03-01
In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. This result could lead to further understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.
On nonlinear equation of Schrödinger type
Soltanov, Kamal N.
2012-11-01
In this paper we study a mixed problem for the nonlinear Schrödinger equation that have a nonlinear adding, in which the coefficient is a generalized function. Here is proved a solvability theorem of the considered problem with use of the general solvability theorem of the article [28]. Furthermore here is investigated also the behaviour of the solution of the studied problem. aipproc class produce a paper with the correct layout for AIP Conference Proceedings 8.5in × 11in double column.
Rigorous theory of molecular orientational nonlinear optics
Directory of Open Access Journals (Sweden)
Chong Hoon Kwak
2015-01-01
Full Text Available Classical statistical mechanics of the molecular optics theory proposed by Buckingham [A. D. Buckingham and J. A. Pople, Proc. Phys. Soc. A 68, 905 (1955] has been extended to describe the field induced molecular orientational polarization effects on nonlinear optics. In this paper, we present the generalized molecular orientational nonlinear optical processes (MONLO through the calculation of the classical orientational averaging using the Boltzmann type time-averaged orientational interaction energy in the randomly oriented molecular system under the influence of applied electric fields. The focal points of the calculation are (1 the derivation of rigorous tensorial components of the effective molecular hyperpolarizabilities, (2 the molecular orientational polarizations and the electronic polarizations including the well-known third-order dc polarization, dc electric field induced Kerr effect (dc Kerr effect, optical Kerr effect (OKE, dc electric field induced second harmonic generation (EFISH, degenerate four wave mixing (DFWM and third harmonic generation (THG. We also present some of the new predictive MONLO processes. For second-order MONLO, second-order optical rectification (SOR, Pockels effect and difference frequency generation (DFG are described in terms of the anisotropic coefficients of first hyperpolarizability. And, for third-order MONLO, third-order optical rectification (TOR, dc electric field induced difference frequency generation (EFIDFG and pump-probe transmission are presented.
El-Menoufi, Basem Kamal
2015-01-01
In the context of effective field theory, we consider quantum gravity with minimally coupled massless particles. Fixing the background geometry to be of the Kerr-Schild type, we fully determine the one-loop effective action of the theory whose finite non-local part is induced by the long-distance portion of quantum loops. This is accomplished using the non-local expansion of the heat kernel in addition to a non-linear completion technique through which the effective action is expanded in gravitational curvatures. Via Euclidean methods, we identify a logarithmic correction to the Bekenstein-Hawking entropy of Schwarzschild black hole. Using dimensional transmutation the result is shown to exhibit an interesting interplay between the UV and IR properties of quantum gravity.
Interactive optomechanical coupling with nonlinear polaritonic systems
Bobrovska, N; Liew, T C H; Kyriienko, O
2016-01-01
We study a system of interacting matter quasiparticles strongly coupled to photons inside an optomechanical cavity. The resulting normal modes of the system are represented by hybrid polaritonic quasiparticles, which acquire effective nonlinearity. Its strength is influenced by the presence of the mechanical mode and depends on the resonance frequency of the cavity. This leads to an interactive type of optomechanical coupling, being distinct from the previously studied dispersive and dissipative couplings in optomechanical systems. The emergent interactive coupling is shown to generate effective optical nonlinearity terms of high order, being quartic in the polariton number. We consider particular systems of exciton-polaritons and dipolaritons, and show that the induced effective optical nonlinearity due to the interactive coupling can exceed in magnitude the strength of Kerr nonlinear terms, such as those arising from polariton-polariton interactions. As applications, we show that the higher order terms give...
USTIFICATION OF A TWO-DIMENSIONAL NONLINEAR SHELL MODEL OF KOITER'S TYPE
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A two-dimensional nonlinear shell model"of Koiter's type"has recently been proposed by the first author. It is shown here that, according to two mutually exclusive sets of assumptions bearing on the associated manifold of admissible inextensional displacements, the leading term of a formal asymptotic expansion of the solution of this two-dimensional model, with the thickness as the"small" parameter, satisfies either the two-dimensional equations of a nonlinearly elastic "membrane" shell or those of a nonlinearly elastic "flexural" shell. These conclusions being identical to those recently drawn by B. Miara, then by V. Lods and B. Miara, for the leading term of a formal asymptotic expansion of the solution of the equations of three-dimensional nonlinear elasticity, again with the thickness as the "small" parameter, the nonlinear shell model of Koiter's type considered here is thus justified, at least formally.
Picone-type inequalities for nonlinear elliptic equations and their applications
Directory of Open Access Journals (Sweden)
Takaŝi Kusano
2001-01-01
Full Text Available Picone-type inequalities are derived for nonlinear elliptic equations, and Sturmian comparison theorems are established as applications. Oscillation theorems for forced super-linear elliptic equations and superlinear-sublinear elliptic equations are also obtained.
MULTIPLE POSITIVE SOLUTIONS TO A SYSTEM OF NONLINEAR HAMMERSTEIN TYPE INTEGRAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Wang Feng; Zhang Fang; Liu Chunhan
2009-01-01
In this paper, we use cone theory and a new method of computation of fixed point index to study a system of nonlinear Hammerstein type integral equations, and the existence of multiple positive solutions to the system is discussed.
Maslov-type index and brake orbits in nonlinear Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian systems.
Indian Academy of Sciences (India)
K Balachandran; K Uchiyama
2000-05-01
In this paper we prove the existence of mild and strong solutions of a nonlinear integrodifferential equation of Sobolev type with nonlocal condition. The results are obtained by using semigroup theory and the Schauder fixed point theorem.
Preparation of the Inclusion Complex-Type Nonlinear Optical Polymer
Directory of Open Access Journals (Sweden)
Li-Fen Wang
2013-01-01
Full Text Available This study uses the inclusion complex method to import nonlinear optical (NLO chromophores, disperse red1 (DR1, and spiropyran (SP, into the γ-CD cavity of the γ-cyclodextrin polymer (γ-CDP to prepare orderly aligned nonphotocontrollable and photocontrollable nonlinear optical polymers. Calculations support the ultraviolet/visible analyses and suggest the formation of the 1 : 2 DR1/γ-CDP and 1 : 2 SP/γ-CDP inclusion complexes. Upon complexation, the DR1 and SP molecules are free to align themselves along an applied electric field and show high order parameters of approximately 0.48 and 0.20, respectively. Reversible photochromic reactions exhibit that the SP/γ-CDP complex still retains the photochromic properties following corona poling.
Photons co- and counter-propagating through $N$ cross-Kerr sites
Brod, Daniel J
2016-01-01
A cross-Kerr interaction produces a phase shift on two modes of light proportional to the number of photons in both modes, and is sometimes called cross-phase modulation. Cross-Kerr nonlinearities have many applications in classical and quantum nonlinear optics, including the possibility of a deterministic and all-optical controlled-phase gate. We calculate the one- and two-photon S-matrix for fields propagating in a medium where the cross-Kerr interaction is spatially distributed at discrete interaction sites comprised of atoms. For the interactions considered, we analyze the cases where the photons co-propagate and counter-propagate through the medium and give a physical interpretation to the differences between the two cases.
Kerr black hole thermodynamical fluctuations
Pavon, D.; Rubi, J. M.
1985-04-01
The near-equilibrium thermodynamical (TD) fluctuations of a massive rotating uncharged Kerr black hole immersed in a uniformly corotating radiation bath at its temperature are investigated theoretically, generalizing Schwarzschild-black-hole analysis of Pavon and Rubi(1983), based on Einstein fluctuation theory. The correlations for the energy and angular moment fluctuations and the second moments of the other TD parameters are obtained, and the generalized second law of black-hole TD and the Bekenstein (1975) interpretation of black-hole entropy are seen as functioning well in this case. A local-stability criterion and relation for TD equilibrium between the Kerr hole and its own radiation in the flat-space-time limit are derived, and a restriction between C and Lambda is deduced.
Massive vector particles tunneling from Kerr and Kerr-Newman black holes
Li, Xiang-Qian
2015-01-01
In this paper, we investigate the Hawking radiation of massive spin-1 particles from 4-dimensional Kerr and Kerr-Newman black holes. By applying the Hamilton-Jacobi ansatz and the WKB approximation to the field equations of the massive bosons in Kerr and Kerr-Newman space-time, the quantum tunneling method is successfully implemented. As a result, we obtain the tunneling rate of the emitted vector particles and recover the standard Hawking temperature of both the two black holes.
Kerr-induced all-optical switching in a GaInP photonic crystal Fabry-Perot resonator.
Eckhouse, V; Cestier, I; Eisenstein, G; Combrié, S; Lehoucq, G; De Rossi, A
2012-04-09
We describe nonlinear properties of a GaInP photonic crystal Fabry-Perot resonator containing integrated reflectors. The device exhibits an extremely large static nonlinearity due to a thermal effect. Dynamical measurements were used to discriminate between the thermal and Kerr contributions to the nonlinearity. The high frequency nonlinear response is strictly due to the Kerr effect and the efficiency is similar to that obtained in self-phase modulation and four wave mixing experiments. The waveguide dispersion and the wavelength dependent integrated reflectors yield a series of transmission peaks with varying widths which determine the maximum speed at which the device can operate. Switching and wavelength conversion experiments with 92ps and 30ps wide pulses were demonstrated using pulse energies of a few pJ. The switching process is Kerr dominated with the fundamental response being essentially instantaneous so that the obtainable switching speed is strictly determined by the resonator structure.
Nonlinear THz spectroscopy on n-type GaAs
Energy Technology Data Exchange (ETDEWEB)
Gaal, Peter
2008-06-23
In this thesis, the ultrafast dynamics of conduction band electrons in semiconductors are investigated by nonlinear terahertz (THz) spectroscopy. In particular, n-doped gallium arsenide samples with doping concentrations in the range of 10{sup 16} cm{sup -3} to 10{sup 17} cm{sup -3} are studied. A novel source for the generation of intense THz radiation is developed which yields single-cycle THz transients with field amplitudes of more then 400 kV/cm. The THz source uses ultrashort optical laser pulses provided by a Ti:sapphire oscillator. In addition, a two-color THz-pump mid-infrared-probe setup is implemented, which allows for two-dimensional time-resolved experiments in the far-infrared wavelength range. Field ionization of neutral shallow donors in gallium arsenide with intense, ultrashort THz pulses and subsequent coherent radiative recombination of electrons to impurity ground states is observed at room temperature. The superradiant decay of the nonlinear polarization results in the emission of a coherent signal with picosecond lifetimes. Such nonlinear signals, which exhibit a lifetime ten times longer than in the linear regime are observed for the first time. At low temperatures and THz field strengths below 5 kV/cm, Rabi flopping on shallow donor transitions is demonstrated. For the first time, the polar electron-LO phonon interaction is directly measured in the quantum kinetic transport regime. Quasi-instantaneous acceleration of conduction band electrons in the polar gallium arsenide lattice by the electric field of intense THz pulses and subsequent probing of the mid-infrared transmission reveals a modulation of the transmission along the THz-mid-infrared delay coordinate with the frequency of the LO phonon. These modulations directly display the relative phase between the electron motion and its surrounding virtual phonon cloud. Quantum kinetic model calculations fully account for the observed phenomena. (orig.)
Stray-field-induced Faraday contributions in wide-field Kerr microscopy and -magnetometry
Energy Technology Data Exchange (ETDEWEB)
Markó, D.; Soldatov, I. [Leibniz Institute for Solid State and Materials Research (IFW) Dresden, Institute for Metallic Materials, PO 270116, D-01171 Dresden (Germany); Dresden University of Technology, Institute for Materials Science, D-01062 Dresden (Germany); Tekielak, M. [Institute of Experimental Physics, University of Bialystok, Lipowa 41, Bialystok 15-424 Poland (Poland); Schäfer, R., E-mail: r.schaefer@ifw-dresden.de [Leibniz Institute for Solid State and Materials Research (IFW) Dresden, Institute for Metallic Materials, PO 270116, D-01171 Dresden (Germany); Dresden University of Technology, Institute for Materials Science, D-01062 Dresden (Germany)
2015-12-15
The magnetic domain contrast in wide-field Kerr microscopy on bulk specimens can be substantially distorted by non-linear, field-dependent Faraday rotations in the objective lens that are caused by stray-field components emerging from the specimen. These Faraday contributions, which were detected by Kerr-magnetometry on grain-oriented iron–silicon steel samples, are thoroughly elaborated and characterized. They express themselves as a field-dependent gray-scale offset to the domain contrast and in highly distorted surface magnetization curves if optically measured in a wide field Kerr microscope. An experimental method to avoid such distortions is suggested. In the course of these studies, a low-permeability part in the surface magnetization loop of slightly misoriented (110)-surfaces in iron–silicon sheets was discovered that is attributed to demagnetization effects in direction perpendicular to the sheet surface. - Highlights: • Magnetizing a finite sample in a Kerr microscope leads to sample-generated stray-fields. • They cause non-linear, field- and position-dependent Faraday rotations in the objective. • This leads to a modulation of the Kerr contrast and to distorted MOKE loops. • A method to compensate these Faraday rotations is presented.
Energy Technology Data Exchange (ETDEWEB)
Liu Chunping
2003-06-02
Using a direct algebraic method, more new exact solutions of the Kolmogorov-Petrovskii-Piskunov equation are presented by formula form. Then a theorem concerning the relation between the kink-type solution and the kink-bell-type solution of nonlinear evolution equations is given. Finally, the applications of the theorem to several well-known equations in physics are also discussed.
Nonlinear Optics in AlGaAs on Insulator
DEFF Research Database (Denmark)
Pu, Minhao; Ottaviano, Luisa; Semenova, Elizaveta;
2016-01-01
AlGaAs on insulator is a powerful nonlinear platform sporting a high effective nonlinearity and the possibility to fabricate complex designs. We will present low loss waveguides enabling efficient optical signal processing and Kerr comb generation.......AlGaAs on insulator is a powerful nonlinear platform sporting a high effective nonlinearity and the possibility to fabricate complex designs. We will present low loss waveguides enabling efficient optical signal processing and Kerr comb generation....
a Scaling Law for Amplitude-Squared Squeezing in Kerr Effect
Prakash, Hari; Kumar, Pankaj
We study amplitude-squared squeezing in interaction of coherent light with a nonlinear Kerr medium modelled as an anharmonic oscillator with interaction Hamiltonian H = ½ λ a+2 a2, where λ is proportional to χ(3) of the nonlinear medium and a is annihilation operator for the interacting field. We find the squeezing parameter S ( τ, r) in terms of a dimensionless interaction time τ = λ t and Kerr parameter r, which is product of, τ and the average number of photons and obtain almost complete amplitude-squared squeezing (i.e., S ≈ 0) for very small interaction time and very large intensity of the interacting light. We optimize squeezing parameter S ( τ, r) by an analytic estimation assuming high intensity of the interacting light and realistic values of Kerr nonlinearity following J.Bajer et al. [Czech. J. Phy. 52, 1313 (2002)] and obtain a scaling law for optimal amplitude-squared squeezing with minimum value Smin, at r = rmin for a given τ. The validity of the scaling law is checked numerically and analytically in the region of realistic values of Kerr nonlinearity and intensity of the interacting light.
Higher-order nonlinear effects in a Josephson parametric amplifier
Kochetov, Bogdan A.; Fedorov, Arkady
2015-12-01
Nonlinearity of the current-phase relationship of a Josephson junction is the key resource for a Josephson parametric amplifier (JPA) as well as for a Josephson traveling-wave parametric amplifier, the only devices in which the quantum limit for added noise has so far been approached at microwave frequencies. A standard approach to describe JPA takes into account only the lowest order (cubic) nonlinearity resulting in a Duffing-like oscillator equation of motion or in a Kerr-type nonlinearity term in the Hamiltonian. In this paper we derive the quantum expression for the gain of JPA including all orders of the Josephson junction nonlinearity in the linear response regime. We then analyze gain saturation effect for stronger signals within a semiclassical approach. Our results reveal nonlinear effects of higher orders and their implications for operation of a JPA.
Nonlinear absorption due to linear loss and magnetic permeability in metamaterials.
Xiang, Yuanjiang; Dai, Xiaoyu; Wen, Shuangchun; Guo, Jun
2012-06-01
We predict theoretically that linear magnetic permeability induces nonlinear absorption (NA) of an electric field in lossy metamaterials (MMs) with Kerr-type nonlinear polarization even when the imaginary part of the nonlinear polarization is absent. The nonlinear magnetic susceptibility, if it exists and although it may be real, enhances or reduces the NA of the electric field, depending on the relative values of the electric and magnetic losses. In particular, it is shown that the NA effect can be tuned by the figure of merit (FOM) of the MM: generally, MMs with a better FOM have a weaker NA effect. Moreover, the nonlinear coefficient can also be enhanced greatly due to the combined effect of the linear losses and the nonlinear magnetization of MMs. The control of the tunable NA and nonlinear coefficients by the structural parameters of MMs is also discussed.
Energy Technology Data Exchange (ETDEWEB)
Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics
2017-06-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
Zou, Li; Liang, Songxin; Li, Yawei; Jeffrey, David J.
2017-03-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
Smoothing and Decay Estimates for Nonlinear Diffusion Equations Equations of Porous Medium Type
Vázquez, Juan Luis
2006-01-01
This text is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of Physics, Chemistry, Biology, and Engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis.Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity ("equations of porou
Oscillatory dynamics in nanocavities with noninstantaneous Kerr response
Energy Technology Data Exchange (ETDEWEB)
Armaroli, Andrea; Malaguti, Stefania; Bellanca, Gaetano; Trillo, Stefano; Rossi, Alfredo de; Combrie, Sylvain [Department of Engineering, University of Ferrara, Via Saragat 1, IT 44122 Ferrara (Italy); Thales Research and Technology, Palaiseau Cedex FR 91767 (France)
2011-11-15
We investigate the impact of a finite response time of Kerr nonlinearities over the onset of spontaneous oscillations (self-pulsing) occurring in a nanocavity. The complete characterization of the underlying Hopf bifurcation in the full parameter space allows us to show the existence of a critical value of the response time and to envisage different regimes of competition with bistability. The transition from a stable oscillatory state to chaos is found to occur only in cavities which are detuned far off-resonance, which turns out to be mutually exclusive with the region where the cavity can operate as a bistable switch.
Generic features of modulational instability in nonlocal Kerr media
DEFF Research Database (Denmark)
Wyller, John; Krolikowski, Wieslaw; Bang, Ole
2002-01-01
The modulational instability (MI) of plane waves in nonlocal Kerr media is studied for a general response function. Several generic properties are proven mathematically, with emphasis on how new gain bands are formed through a bifurcation process when the degree of nonlocality, sigma, passes...... the nonlocality tends to suppress MI, but can never remove it completely, irrespectively of the shape of the response function. For a defocusing nonlinearity the stability properties depend sensitively on the profile of the response function. For response functions with a positive-definite spectrum...
Optical Kerr Frequency Comb Generation in Overmoded Resonators
Matsko, A B; Liang, W; Ilchenko, V S; Seidel, D; Maleki, L
2012-01-01
We show that scattering-based interaction among nearly degenerate optical modes is the key factor in low threshold generation of Kerr frequency combs in nonlinear optical resonators possessing small group velocity dispersion (GVD). The mode interaction is capable of producing drastic change in the local GVD, resulting in either a significant reduction or increase of the oscillation threshold. It is also responsible for the majority of observed combs in resonators characterized with large normal GVD. We present results of our numerical simulations as well as supporting experimental data.
Generalized Jacobi Elliptic Function Solution to a Class of Nonlinear Schrödinger-Type Equations
Directory of Open Access Journals (Sweden)
Zeid I. A. Al-Muhiameed
2011-01-01
Full Text Available With the help of the generalized Jacobi elliptic function, an improved Jacobi elliptic function method is used to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Lin equation are investigated, and the exact solutions are derived with the aid of the homogenous balance principle.
Directory of Open Access Journals (Sweden)
Jessada Tariboon
2014-01-01
Full Text Available We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative, and Leray-Schauder’s degree theory. Enlightening examples illustrating the obtained results are also presented.
Directory of Open Access Journals (Sweden)
Oscar Castillo
2013-01-01
Full Text Available Neural networks (NNs, type-1 fuzzy logic systems (T1FLSs, and interval type-2 fuzzy logic systems (IT2FLSs have been shown to be universal approximators, which means that they can approximate any nonlinear continuous function. Recent research shows that embedding an IT2FLS on an NN can be very effective for a wide number of nonlinear complex systems, especially when handling imperfect or incomplete information. In this paper we show, based on the Stone-Weierstrass theorem, that an interval type-2 fuzzy neural network (IT2FNN is a universal approximator, which uses a set of rules and interval type-2 membership functions (IT2MFs for this purpose. Simulation results of nonlinear function identification using the IT2FNN for one and three variables and for the Mackey-Glass chaotic time series prediction are presented to illustrate the concept of universal approximation.
Optical diode behavior of photonic crystal structure with asymmetric Kerr defect
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Optical diode behavior of asymmetric one-dimensional photonic crystal with Kerr defect is numerically investigated using nonlinear transfer matrix method. In the linear case, the intensity and the phase of transmitted field are the same for the forward and backward operations. In the nonlinear case, however, the transmitted intensities are much different for the two operations, which display diode characteristic. Physical origin of the anisotropic transmission lies in the different localizations in the defect layer of the two operations.
Quantum teleportation and Kerr-Newman spacetime
Institute of Scientific and Technical Information of China (English)
Ge Xian-Hui; Shen You-Gen
2005-01-01
We consider the teleportation in the background of Kerr-Newman spacetime. Because of the Hawking effect, the fidelity of the teleportation is reduced. The results also show the fidelity is closely related to the mass, charge and rotating velocity of the black hole: high fidelity can be reached for massive, slowly rotating Kerr-Newman black holes.
Noether-Type Symmetries and Associated Conservation Laws of Some Systems of Nonlinear PDEs
Institute of Scientific and Technical Information of China (English)
MEI Jian-Qin
2009-01-01
The algorithm for constructing conservation laws of Etder-Lagrange--type equations via Noether-type symmetry operators associated with partial Lagrangian has been presented. As applications, many new conservation laws of some important systems of nonlinear partial differential equations have been obtained.
Pattern Formation in Double-Layer Kerr Resonators with Coupled Modes
Bois, Antoine
2016-01-01
A double-layer Kerr resonator in which both coupled modes are excited and interact with each other via incoherent cross-phase modulation is investigated to reveal stable localized solutions beyond the usual formation mechanism involving a single mode. Periodic solutions from modulational instability are found to occur at a slight penalty on the nonlinear efficiency, but they stabilize the spatial dynamics, leading to dissipative solitons in previously unattainable regimes. Numerical simulations show paired breather solitons in addition to temporally stable solutions. The results demonstrate coupled modes can increase the stability of Kerr frequency comb generation.
The Kerr-Schild ansatz revised
Bini, Donato; Kerr, Roy P
2014-01-01
Kerr-Schild metrics have been introduced as a linear superposition of the flat spacetime metric and a squared null vector field, say $\\boldsymbol{k}$, multiplied by some scalar function, say $H$. The basic assumption which led to Kerr solution was that $\\boldsymbol{k}$ be both geodesic and shearfree. This condition is relaxed here and Kerr-Schild ansatz is revised by treating Kerr-Schild metrics as {\\it exact linear perturbations} of Minkowski spacetime. The scalar function $H$ is taken as the perturbing function, so that Einstein's field equations are solved order by order in powers of $H$. It turns out that the congruence must be geodesic and shearfree as a consequence of third and second order equations, leading to an alternative derivation of Kerr solution.
The effect of surface modification on femtosecond optical Kerr effect of PBS nanoparticles
Institute of Scientific and Technical Information of China (English)
XichengAi; LinGuo; 等
1999-01-01
PbS nanoparticles modified by a polymer (P-PbS) was prepared,and the transient nonlinear optical properties studied by femtosecond optical Kerr effect(OKE) spectroscopy for the first time.A very large nonlinear optical effect(X(3)-5.6×10-12esu) with response time comparable to the laser pulse(-165fs) was observed.Comparing with PbS nonoparticles stabilized with PVA and coated with sodium dodecyle benzene sulphonate(DBS).the optical nonlinearity of the PbS nanoparticles modified by the polymer is much larger than those of them.Thereafter.the corresponding nonlinearity mechanism was interpreted.
First-order D-type Iterative Learning Control for Nonlinear Systems with Unknown Relative Degree
Institute of Scientific and Technical Information of China (English)
SONGZhao-Qing; MAOJian-Qin; DAIShao-Wu
2005-01-01
The classical D-type iterative learning control law depends crucially on the relative degree of the controlled system, high order differential iterative learning law must be taken for systems with high order relative degree. It is very difficult to ascertain the relative degree of the controlled system for uncertain nonlinear systems. A first-order D-type iterative learning control design method is presented for a class of nonlinear systems with unknown relative degree based on dummy model in this paper. A dummy model with relative degree 1 is constructed for a class of nonlinear systems with unknown relative degree. A first-order D-type iterative learning control law is designed based on the dummy model, so that the dummy model can track the desired trajectory perfectly, and the controlled system can track the desired trajectory within a certain error. The simulation example demonstrates the feasibility and effectiveness of the presented method.
Advances in quantitative Kerr microscopy
Soldatov, I. V.; Schäfer, R.
2017-01-01
An advanced wide-field Kerr microscopy approach to the vector imaging of magnetic domains is demonstrated. Utilizing the light from eight monochrome light emitting diodes, guided to the microscope by glass fibers, and being properly switched in synchronization with the camera exposure, domain images with orthogonal in-plane sensitivity are obtained simultaneously at real time. After calibrating the Kerr contrast under the same orthogonal sensitivity conditions, the magnetization vector field of complete magnetization cycles along the hysteresis loop can be calculated and plotted as a coded color or vector image. In the pulsed mode also parasitic, magnetic field-dependent Faraday rotations in the microscope optics are eliminated, thus increasing the accuracy of the measured magnetization angles to better than 5∘. The method is applied to the investigation of the magnetization process in a patterned Permalloy film element. Furthermore it is shown that the effective magnetic anisotropy axes in a GaMnAs semiconducting film can be quantitatively measured by vectorial analysis of the domain structure.
Fully Nonlinear Boussinesq-Type Equations with Optimized Parameters for Water Wave Propagation
Institute of Scientific and Technical Information of China (English)
荆海晓; 刘长根; 龙文; 陶建华
2015-01-01
For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Boussinesq-type equations has been a practical problem for engineers. In this paper, approaches of improving the characteristics of the equations, i.e. linear dispersion, shoaling gradient and nonlinearity, are reviewed and the advantages and disadvantages of several different Boussinesq-type equations are compared for the applications of these Boussinesq-type equations in coastal engineering with relatively large sea areas. Then for improving the properties of Boussinesq-type equations, a new set of fully nonlinear Boussinseq-type equations with modified representative velocity are derived, which can be used for better linear dispersion and nonlinearity. Based on the method of minimizing the overall error in different ranges of applications, sets of parameters are determined with optimized linear dispersion, linear shoaling and nonlinearity, respectively. Finally, a test example is given for validating the results of this study. Both results show that the equations with optimized parameters display better characteristics than the ones obtained by matching with padé approximation.
Fully nonlinear Boussinesq-type equations with optimized parameters for water wave propagation
Jing, Hai-xiao; Liu, Chang-gen; Long, Wen; Tao, Jian-hua
2015-06-01
For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Boussinesq-type equations has been a practical problem for engineers. In this paper, approaches of improving the characteristics of the equations, i.e. linear dispersion, shoaling gradient and nonlinearity, are reviewed and the advantages and disadvantages of several different Boussinesq-type equations are compared for the applications of these Boussinesq-type equations in coastal engineering with relatively large sea areas. Then for improving the properties of Boussinesq-type equations, a new set of fully nonlinear Boussinseq-type equations with modified representative velocity are derived, which can be used for better linear dispersion and nonlinearity. Based on the method of minimizing the overall error in different ranges of applications, sets of parameters are determined with optimized linear dispersion, linear shoaling and nonlinearity, respectively. Finally, a test example is given for validating the results of this study. Both results show that the equations with optimized parameters display better characteristics than the ones obtained by matching with padé approximation.
Quantum stability of nonlinear wave type solutions with intrinsic mass parameter in QCD
Kim, Youngman; Lee, Bum-Hoon; Pak, D. G.; Park, Chanyong; Tsukioka, Takuya
2017-09-01
The problem of the existence of a stable vacuum field in pure QCD is revised. Our approach is based on using classical stationary nonlinear wave type solutions with an intrinsic mass scale parameter. Such solutions can be treated as quantum-mechanical wave functions describing massive spinless states in quantum theory. We verify whether nonlinear wave type solutions can form a stable vacuum field background within the framework of the effective action formalism. We demonstrate that there is a special class of stationary generalized Wu-Yang monopole solutions that are stable against quantum gluon fluctuations.
Self-referencing of an on-chip soliton Kerr frequency comb without external broadening
Brasch, Victor; Jost, John D; Geiselmann, Michael; Kippenberg, Tobias J
2016-01-01
Self-referencing turns pulsed laser systems into self-referenced frequency combs. Such frequency combs allow counting of optical frequencies and have a wide range of applications. The required optical bandwidth to implement self-referencing is typically obtained via nonlinear broadening in optical fibers. Recent advances in the field of Kerr frequency combs have provided a path towards the development of compact frequency comb sources that provide broadband frequency combs, exhibit microwave repetition rates and that are compatible with on-chip photonic integration. These devices have the potential to significantly expand the use of frequency combs. Yet to date self-referencing of such Kerr frequency combs has only been attained by applying conventional, fiber based broadening techniques. Here we demonstrate external broadening-free self-referencing of a Kerr frequency comb. An optical spectrum that spans two-thirds of an octave is directly synthesized from a continuous wave laser-driven silicon nitride micro...
THEORETICAL EVALUATION OF NONLINEAR EFFECTS ON OPTICAL WDM NETWORKS WITH VARIOUS FIBER TYPES
Directory of Open Access Journals (Sweden)
YASIN M. KARFAA
2010-09-01
Full Text Available A theoretical study is carried out to evaluate the performance of an opticalwavelength division multiplexing (WDM network transmission system in the presenceof crosstalk due to optical fiber nonlinearities. The most significant nonlinear effects inthe optical fiber which are Cross-Phase Modulation (XPM, Four-Wave Mixing (FWM,and Stimulated Raman Scattering (SRS are investigated. Four types of optical fiber areincluded in the analysis; these are: single-mode fiber (SMF, dispersion compensationfiber (DCF, non-zero dispersion fiber (NZDF, and non-zero dispersion shifted fiber(NZDSF. The results represent the standard deviation of nonlinearity induced crosstalknoise power due to FWM and SRS, XPM power penalty for SMF, DCF, NZDF, andNZDSF types of fiber, besides the Bit Error Rate (BER for the three nonlinear effectsusing standard fiber type (SMF. It is concluded that three significant fiber nonlinearitiesare making huge limitations against increasing the launched power which is desired,otherwise, lower values of launched power limit network expansion including length,distance, covered areas, and number of users accessing the WDM network, unlesssuitable precautions are taken to neutralize the nonlinear effects. Besides, various fibertypes are not behaving similarly towards network parameters.
Comparison of different Kerr-lens mode locking laser design techniques
Moreno-Larios, José Agustín.; Rosete-Aguilar, Martha; Garduño-Mejía, Jesús
2016-04-01
Three numerical methods for the design of Kerr Lens Mode-Locking (KLML) ultrashort pulse cavities that use a solid state Brewster-cut nonlinear gain medium are compared. The nonlinear medium is modeled first deploying a matrix approximation that considers non-coupled (tangential analysis is independent of sagittal analysis) Kerr and thermal self-focusing; and second with a differential equation that relates the real and imaginary parts of the inverse of the complex Gaussian beam parameter. The third comparison is against a matrix analysis method that considers the coupling between the sagittal and tangential modes inside the nonlinear medium in order to determine the impact of this effect. The three methods search the self-consistency condition for the complex beam parameter and the results are compared.
Finite thickness lens model for self-focusing (defocusing) in Kerr medium
Institute of Scientific and Technical Information of China (English)
Shi-fang GUO; Qiang TIAN
2009-01-01
A "finite thickness lens" model for self-focusing (defocusing) in Kerr medium is presented. An onaxis normalization transmittance formula is presented for arbitrary nonlinear phase shift for the finite thickness Kerr medium by introducing a nonlinear ABCD-matrix for the transition of a Gaussian beam from linear to nonlinear medium, without complex calculation for the beam radius at the far field aperture. The variation of the peak and valley transmittance difference is found to enhance linearly as the phase shift at the focus increases by increasing the thickness of the medium. If the ratio of the Rayleigh distance divided by the thickness of the medium (d/zo) is constant and small enough, the peak and valley transmittance difference stays constant. Finally, a qualitative formula is presented to express the relationship between the system parameters and the on-axis phase shift at the focus.
PI-type Iterative Learning Control for Nonlinear Electro-hydraulic Servo Vibrating System
Institute of Scientific and Technical Information of China (English)
LUO Xiaohui; ZHU Yuquan; HU Junhua
2009-01-01
For the electro-hydraulic servo vibrating system(ESVS) with the characteristics of non-linearity and repeating motion, a novel method, PI-type iterative learning control(ILC), is proposed on the basis of traditional PID control. By using memory ability of computer, the method keeps last time's tracking error of the system and then applies the error information to the next time's control process. At the same time, a forgetting factor and a D-type learning law of feedforward fuzzy-inferring referenced displacement error under the optimal objective are employed to enhance the systemic robustness and tracking accuracy. The results of simulation and test reveal that the algorithm has a trait of high repeating precision, and could restrain the influence of nonlinear factors like leaking, external disturbance, aerated oil, etc. Compared with traditional PID control, it could better meet the requirement of nonlinear electro-hydraulic servo vibrating system.
Three types magnetic moment distribution of nonlinear excitations in a Heisenberg helimagnet
Energy Technology Data Exchange (ETDEWEB)
Qi, Jian-Wen [School of Physics, Northwest University, Xi' an 710069 (China); Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi' an 710069 (China); Li, Zai-Dong [Department of Applied Physics, Hebei University of Technology, Tianjin 300401 (China); Yang, Zhan-Ying, E-mail: zyyang@nwu.edu.cn [School of Physics, Northwest University, Xi' an 710069 (China); Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi' an 710069 (China); Yang, Wen-Li [Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi' an 710069 (China); Institute of Modern Physics, Northwest University, Xi' an 710069 (China)
2017-06-15
Highlights: • Three different types of soliton excitations under the spin-wave background are demonstrated in spin chain system. • The magnetic moment distributions corresponding to these solitons are characterized in detail. • The formation mechanisms of those excitations are explained by the magnon density distribution. - Abstract: We study the nonlinear spin dynamics of an anisotropic Heisenberg helimagnet in a fourth-order integrable nonlinear Schrödinger equation. We demonstrate that there are three types of nonlinear spin excitations on a spin-wave background in the Heisenberg helimagnet, notably including anti-dark soliton, W-shaped soliton, and multi-peak soliton. The magnetic moment distribution that corresponds to each of these are characterized in detail. Additionally, the formation mechanism is clarified by the magnon density distribution.
Nonlinear graphene plasmonics (Conference Presentation)
Cox, Joel D.; Marini, Andrea; Garcia de Abajo, Javier F.
2016-09-01
The combination of graphene's intrinsically-high nonlinear optical response with its ability to support long-lived, electrically tunable plasmons that couple strongly with light has generated great expectations for application of the atomically-thin material to nanophotonic devices. These expectations are mainly reinforced by classical analyses performed using the response derived from extended graphene, neglecting finite-size and nonlocal effects that become important when the carbon layer is structured on the nanometer scale in actual device designs. Based on a quantum-mechanical description of graphene using tight-binding electronic states combined with the random-phase approximation, we show that finite-size effects produce large contributions that increase the nonlinear response associated with plasmons in nanostructured graphene to significantly higher levels than previously thought, particularly in the case of Kerr-type optical nonlinearities. Motivated by this finding, we discuss and compare saturable absorption in extended and nanostructured graphene, with or without plasmonic enhancement, within the context of passive mode-locking for ultrafast lasers. We also explore the possibility of high-harmonic generation in doped graphene nanoribbons and nanoislands, where illumination by an infrared pulse of moderate intensity, tuned to a plasmon resonance, is predicted to generate light at harmonics of order 13 or higher, extending over the visible and UV regimes. Our atomistic description of graphene's nonlinear optical response reveals its complex nature in both extended and nanostructured systems, while further supporting the exceptional potential of this material for nonlinear nanophotonic devices.
The role of symmetries in the Kerr-Schild derivation of the Kerr black hole
Ayón-Beato, Eloy; Higuita-Borja, Daniel
2015-01-01
In this work we explore the consequences of considering from the very beginning the stationary and axisymmetric properties of the Kerr black hole as one attempts to derive this solution through the Kerr-Schild ansatz. The first consequence is kinematical and is based on a new stationary and axisymmetric version of the Kerr theorem that yields to the precise shearfree and geodesic null congruence of flat spacetime characterizing the Kerr solution. An straightforward advantage of this strategy is concerned with the parameter $a$ which appears naturally as associated to the conserved angular momentum of the geodesics due to axisymmetry. The second consequence is dynamical and takes into account the circularity theorem. In fact, a stationary-axisymmetric Kerr-Schild ansatz is in general incompatible with the circularity property warranted by vacuum Einstein equations unless the remaining angular dependence in the Kerr-Schild profile appears fixed in a precise way. Thank to these two ingredients, the integration o...
Scaling dimensions in hidden Kerr/CFT
Lowe, David A; Skanata, Antun
2011-01-01
It has been proposed that a hidden conformal field theory (CFT) governs the dynamics of low frequency scattering in a general Kerr black hole background. We further investigate this correspondence by mapping higher order corrections to the massless wave equations in a Kerr background to an expansion within the CFT in terms of higher dimension operators. This implies the presence of infinite towers of CFT primary operators with positive conformal dimensions compatible with unitarity. The exact Kerr background softly breaks the conformal symmetry and the scaling dimensions of these operators run with frequency. The scale-invariant fixed point is dual to a degenerate case of flat spacetime.
Coherence properties of Kerr frequency combs
Erkintalo, Miro
2014-01-01
We use numerical simulations based on an extended Lugiato-Lefever equation (LLE) to investigate the stability properties of Kerr frequency combs generated in microresonators. In particular, we show that an ensemble average calculated over sequences of output fields separated by a fixed number of resonator roundtrips allows the coherence of Kerr combs to be quantified in terms of the complex-degree of first-order coherence. We identify different regimes of comb coherence, linked to the solutions of the LLE. Our approach provides a practical and unambiguous way of assessing the stability of Kerr combs that is directly connected to an accessible experimental quantity.
Coherence properties of Kerr frequency combs.
Erkintalo, Miro; Coen, Stéphane
2014-01-15
We use numerical simulations based on an extended Lugiato-Lefever equation (LLE) to investigate the stability properties of Kerr frequency combs generated in microresonators. In particular, we show that an ensemble average calculated over sequences of output fields separated by a fixed number of resonator roundtrips allows the coherence of Kerr combs to be quantified in terms of the complex degree of first-order coherence. We identify different regimes of comb coherence, linked to the solutions of the LLE. Our approach provides a practical and unambiguous way of assessing the stability of Kerr combs that is directly connected to an accessible experimental quantity.
Miranda, Galaxia; García, Nadiezhda Motelongo
2013-01-01
In this work we study a Kerr-like wormhole with phantom matter as source. It has three parameters: mass, angular momentum and scalar field charge. This wormhole has a naked ring singularity, other wise it is regular everywhere. The mean feature of this wormhole is that the mouth of the throat lie on a sphere of the same radius as the ring singularity an avoids any observer to see or to reach the singularity, it behaves like an anti-horizon. We analyse the geodesics of the wormhole and find that an observer can go through the geodesics without troubles, but the equator presents an infinity potential barrier which avoids to reach the throat. From an analysis of the Riemann tensor we obtain that the tidal forces permits the wormhole to be traversable for an observer like a human being.
Rational extension and Jacobi-type X{sub m} solutions of a quantum nonlinear oscillator
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, Axel [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Roy, Barnana [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)
2013-12-15
We construct a rational extension of a recently studied nonlinear quantum oscillator model. Our extended model is shown to retain exact solvability, admitting a discrete spectrum and corresponding closed-form solutions that are expressed through Jacobi-type X{sub m} exceptional orthogonal polynomials.
Institute of Scientific and Technical Information of China (English)
LI Wei-hua; LUO En; HUANG Wei-jiang
2007-01-01
According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically, which can fully characterize the initial-boundary-value problem of this kind of dynamics. An important integral relation is made, which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechanics. Based on such relationship, it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures, but also to derive systematically the complementary functionals for five-field, four-field, three-field and two-field unconventional Hamilton-type variational principles, and the functional for the unconventional Hamilton-type variational principle in phase space and the potential energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the generalized Legendre transformation given in this paper. Furthermore, the intrinsic relationship among various principles can be explained clearly with this approach.
Institute of Scientific and Technical Information of China (English)
Yepeng Xing; Qiong Wang; Valery G. Romanovski
2009-01-01
We prove several new comparison results and develop the monotone iterative tech-nique to show the existence of extremal solutions to a kind of periodic boundary value problem (PBVP) for nonlinear integro-differential equation of mixed type on time scales.
Spatial nonlinearity in anisotropic metamaterial plasmonic slot waveguides
Elsawy, Mahmoud M R
2016-01-01
We study the main nonlinear solutions of plasmonic slot waveguides made from an anisotropic metamaterial core with a positive Kerr-type nonlinearity surrounded by two semi-infinite metal regions. First, we demonstrate that for a highly anisotropic diagonal elliptical core, the bifurcation threshold of the asymmetric mode is reduced from GW/m threshold for the isotropic case to 50 MW/m one indicating a strong enhancement of the spatial nonlinear effects, and that the slope of the dispersion curve of the asymmetric mode stays positive, at least near the bifurcation, suggesting a stable mode. Second, we show that for the hyperbolic case there is no physically meaningful asymmetric mode, and that the sign of the effective nonlinearity can become negative.
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
Second-harmonic generation (SHG) in the limit of large phase mismatch, given by Deltabeta=beta2-2beta1 effectively induces a Kerr-like nonlinear phase shift on the fundamental wave (FW). The phase mismatch determines the sign and magnitude of the effective Kerr nonlinearity, making large negative...
Generalized Hyperbolic Function Solution to a Class of Nonlinear Schrödinger-Type Equations
Directory of Open Access Journals (Sweden)
Zeid I. A. Al-Muhiameed
2012-01-01
Full Text Available With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Liu equation are investigated and the exact solutions are derived with the aid of the homogenous balance principle and generalized hyperbolic functions. We study the effect of the generalized hyperbolic function parameters p and q in the obtained solutions by using the computer simulation.
Kim, Daewook; Kim, Dojin; Hong, Keum-Shik; Jung, Il Hyo
2014-01-01
The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku'' + M(|A (1/2) u|(2))Au + g(u') = 0 under suitable assumptions on K, A, M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations in order to verify the analytical results are given.
Identification of Nonlinear Dynamic Systems Using Hammerstein-Type Neural Network
Directory of Open Access Journals (Sweden)
Hongshan Yu
2014-01-01
Full Text Available Hammerstein model has been popularly applied to identify the nonlinear systems. In this paper, a Hammerstein-type neural network (HTNN is derived to formulate the well-known Hammerstein model. The HTNN consists of a nonlinear static gain in cascade with a linear dynamic part. First, the Lipschitz criterion for order determination is derived. Second, the backpropagation algorithm for updating the network weights is presented, and the stability analysis is also drawn. Finally, simulation results show that HTNN identification approach demonstrated identification performances.
Energy Technology Data Exchange (ETDEWEB)
Stalin, S. [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620024, Tamil Nadu (India); Senthilvelan, M., E-mail: velan@cnld.bdu.ac.in [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620024, Tamil Nadu (India)
2011-10-17
In this Letter, we formulate an exterior differential system for the newly discovered cubically nonlinear integrable Camassa-Holm type equation. From the exterior differential system we establish the integrability of this equation. We then study Cartan prolongation structure of this equation. We also discuss the method of identifying conservation laws and Baecklund transformation for this equation from the identified exterior differential system. -- Highlights: → An exterior differential system for a cubic nonlinear integrable equation is given. → The conservation laws from the exterior differential system is derived. → The Baecklund transformation from the Cartan-Ehresmann connection is obtained.
Energy Technology Data Exchange (ETDEWEB)
Bejarano, Cecilia; Guzman, Maria Jose [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Ferraro, Rafael [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)
2015-02-01
Null tetrads are shown to be a valuable tool in teleparallel theories of modified gravity. We use them to prove that Kerr geometry remains a solution for a wide family of f(T) theories of gravity. (orig.)
Kerr Naked Singularities as Particle Accelerators
Patil, Mandar
2011-01-01
We investigate here the particle acceleration by Kerr naked singularities. We consider a collision between particles dropped in from infinity at rest, which follow geodesic motion in the equatorial plane, with angular momentum of one of the particles in an appropriate finite range of values. The absence of an event horizon and the repulsive nature of angular momentum makes it possible for the initially infalling particle to turn back as an outgoing particle and then collide with another infalling particle. When these particles collide at a location close to what would have been the event horizon in the extremal Kerr blackhole case, the center of mass energy of collision turns out to be arbitrarily large depending on how close is the Kerr naked singularity to extremality. We briefly discuss the possible astrophysical consequences of this process and suggest that the fast rotating Kerr configurations could provide a good cosmic laboratory to probe ultra-high-energy physics.
High-order Boussinesq-type modelling of nonlinear wave phenomena in deep and shallow water
DEFF Research Database (Denmark)
Madsen, Per A.; Fuhrman, David R.
2010-01-01
In this work, we start with a review of the development of Boussinesq theory for water waves covering the period from 1872 to date. Previous reviews have been given by Dingemans,1 Kirby,2,3 and Madsen & Schäffer.4 Next, we present our most recent high-order Boussinesq-type formulation valid...... for fully nonlinear and highly dispersive waves traveling over a rapidly varying bathymetry. Finally, we cover applications of this Boussinesq model, and we study a number of nonlinear wave phenomena in deep and shallow water. These include (1) Kinematics in highly nonlinear progressive deep-water waves; (2......) Kinematics in progressive solitary waves; (3) Reflection of solitary waves from a vertical wall; (4) Reflection and diffraction around a vertical plate; (5) Quartet and quintet interactions and class I and II instabilities; (6) Extreme events from focused directionally spread waveelds; (7) Bragg scattering...
Particular solutions to multidimensional PDEs with KdV-type nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Zenchuk, A.I., E-mail: zenchuk@itp.ac.ru
2014-03-01
We consider a class of particular solutions to the (2+1)-dimensional nonlinear partial differential equation (PDE) u{sub t}+∂{sub x{sub 2}{sup n}}u{sub x{sub 1}}−u{sub x{sub 1}}u=0 (here n is any integer) reducing it to the ordinary differential equation (ODE). In a simplest case, n=1, the ODE is solvable in terms of elementary functions. Next choice, n=2, yields the cnoidal waves for the special case of Zakharov–Kuznetsov equation. The proposed method is based on the deformation of the characteristic of the equation u{sub t}−uu{sub x{sub 1}}=0 and might also be useful in study of the higher-dimensional PDEs with arbitrary linear part and KdV-type nonlinearity (i.e. the nonlinear term is u{sub x{sub 1}}u).
Material and Geometric Nonlinear Analysis of Functionally Graded Plate-Shell Type Structures
Moita, J. S.; Araújo, A. L.; Mota Soares, C. M.; Mota Soares, C. A.; Herskovits, J.
2016-08-01
A nonlinear formulation for general Functionally Graded Material plate-shell type structures is presented. The formulation accounts for geometric and material nonlinear behaviour of these structures. Using the Newton-Raphson incremental-iterative method, the incremental equilibrium path is obtained, and in case of snap-through occurrence the automatic arc-length method is used. This simple and fast element model is a non-conforming triangular flat plate/shell element with 24 degrees of freedom for the generalized displacements. It is benchmarked in the solution of some illustrative plate- shell examples and the results are presented and discussed with numerical alternative models. Benchmark tests with material and geometrically nonlinear behaviour are also proposed.
High-order Boussinesq-type modelling of nonlinear wave phenomena in deep and shallow water
DEFF Research Database (Denmark)
Madsen, Per A.; Fuhrman, David R.
2010-01-01
In this work, we start with a review of the development of Boussinesq theory for water waves covering the period from 1872 to date. Previous reviews have been given by Dingemans,1 Kirby,2,3 and Madsen & Schäffer.4 Next, we present our most recent high-order Boussinesq-type formulation valid...... for fully nonlinear and highly dispersive waves traveling over a rapidly varying bathymetry. Finally, we cover applications of this Boussinesq model, and we study a number of nonlinear wave phenomena in deep and shallow water. These include (1) Kinematics in highly nonlinear progressive deep-water waves; (2......) Kinematics in progressive solitary waves; (3) Reflection of solitary waves from a vertical wall; (4) Reflection and diffraction around a vertical plate; (5) Quartet and quintet interactions and class I and II instabilities; (6) Extreme events from focused directionally spread waveelds; (7) Bragg scattering...
Xu, Run; Ma, Xiangting
2017-01-01
In this paper, we establish some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two independent variables, and we present the applications to research the boundedness of solutions to retarded nonlinear Volterra-Fredholm type integral equations.
Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi
2017-05-01
This paper studies the dynamics of solitons to the nonlinear Schrödinger’s equation (NLSE) with spatio-temporal dispersion (STD). The integration algorithm that is employed in this paper is the Riccati-Bernoulli sub-ODE method. This leads to dark and singular soliton solutions that are important in the field of optoelectronics and fiber optics. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. There are four types of nonlinear media studied in this paper. They are Kerr law, power law, parabolic law and dual law. The conservation laws (Cls) for the Kerr law and parabolic law nonlinear media are constructed using the conservation theorem presented by Ibragimov.
Lucas, Erwan; Kippenberg, Tobias J
2016-01-01
Temporal dissipative Kerr solitons in a continuous-wave laser-driven nonlinear optical microresonator enable compact, high-repetition rate sources of ultrashort pulses and coherent broadband optical frequency combs. A central parameter in the soliton formation process, is the effective detuning of the pump laser to the thermally- and Kerr-shifted cavity resonance, which, together with the free spectral range and dispersion, governs the soliton pulse duration. Here, we introduce a technique to probe, stabilize, and control the effective detuning of a driven nonlinear crystalline resonator while monitoring the dissipative Kerr soliton properties, which enables to study the detuning-dependent soliton properties and accurate comparisons of the theoretical predictions with experiments. We demonstrate that the experimentally measured relation between detuning and soliton duration deviates by less than 1% from the analytical solution, demonstrating its excellent predictive power. In contrast, avoided mode crossings,...
Optical vortex solitons in self-defocusing Kerr-type nonlocal medium∗%自散焦非局域非线性材料中的光学涡旋孤子
Institute of Scientific and Technical Information of China (English)
欧阳世根
2013-01-01
通过数值模拟的方法对非局域非线性自散焦材料中的光学涡旋孤子的传输特性以及相互作用特性进行了研究。研究表明，拓扑荷|m|=1的非局域涡旋孤子是稳定的，而拓扑荷|m|>1的非局域涡旋孤子均具有拓扑不稳定性。在微扰存在的情况下以及在近距离相互作用的过程中，|m|>1的涡旋孤子会分裂成一系列的|m|=1的涡旋孤子。非局域涡旋孤子与局域涡旋孤子具有相同的长距离相互作用模式，即点涡旋相互作用模式。但两者的短距离相互作用存在一些差别，在相同的距离下，两涡旋间的相互绕转的周期随着材料的非局域响应长度增大而增大。%The propagation and interaction properties of optical vortex solitons in a self-defocusing Kerr-type nonlocal medium are investi-gated by the numerical simulation method. It is indicated that the singly charged vortices are stable and the multicharged vortices are topologically unstable in both the nonlocal and local cases. And in the nonlocal and local cases the point vortices model is applicable for describing the interactions of vortices provided that the interval distances between vortices are much larger than the size of the core of the vortices. However, vortices interact differently in short distance, depending on the nonlocality, and the larger the characteristic nonlocal respond length, the larger the rotating period of two singly charged vortices.
Off-diagonal deformations of Kerr metrics and black ellipsoids in heterotic supergravity
Energy Technology Data Exchange (ETDEWEB)
Vacaru, Sergiu I. [Quantum Gravity Research, Topanga, CA (United States); University ' ' Al. I. Cuza' ' , Project IDEI, Iasi (Romania); Irwin, Klee [Quantum Gravity Research, Topanga, CA (United States)
2017-01-15
Geometric methods for constructing exact solutions of equations of motion with first order α{sup '} corrections to the heterotic supergravity action implying a nontrivial Yang-Mills sector and six-dimensional, 6-d, almost-Kaehler internal spaces are studied. In 10-d spacetimes, general parametrizations for generic off-diagonal metrics, nonlinear and linear connections, and matter sources, when the equations of motion decouple in very general forms are considered. This allows us to construct a variety of exact solutions when the coefficients of fundamental geometric/physical objects depend on all higher-dimensional spacetime coordinates via corresponding classes of generating and integration functions, generalized effective sources and integration constants. Such generalized solutions are determined by generic off-diagonal metrics and nonlinear and/or linear connections; in particular, as configurations which are warped/compactified to lower dimensions and for Levi-Civita connections. The corresponding metrics can have (non-) Killing and/or Lie algebra symmetries and/or describe (1+2)-d and/or (1+3)-d domain wall configurations, with possible warping nearly almost-Kaehler manifolds, with gravitational and gauge instantons for nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants encoding string gravity effects. A series of examples of exact solutions describing generic off-diagonal supergravity modifications to black hole/ellipsoid and solitonic configurations are provided and analyzed. We prove that it is possible to reproduce the Kerr and other type black solutions in general relativity (with certain types of string corrections) in the 4-d case and to generalize the solutions to non-vacuum configurations in (super-) gravity/string theories. (orig.)
Off-diagonal deformations of Kerr metrics and black ellipsoids in heterotic supergravity
Vacaru, Sergiu I.; Irwin, Klee
2017-01-01
Geometric methods for constructing exact solutions of equations of motion with first order α ^' } corrections to the heterotic supergravity action implying a nontrivial Yang-Mills sector and six-dimensional, 6-d, almost-Kähler internal spaces are studied. In 10-d spacetimes, general parametrizations for generic off-diagonal metrics, nonlinear and linear connections, and matter sources, when the equations of motion decouple in very general forms are considered. This allows us to construct a variety of exact solutions when the coefficients of fundamental geometric/physical objects depend on all higher-dimensional spacetime coordinates via corresponding classes of generating and integration functions, generalized effective sources and integration constants. Such generalized solutions are determined by generic off-diagonal metrics and nonlinear and/or linear connections; in particular, as configurations which are warped/compactified to lower dimensions and for Levi-Civita connections. The corresponding metrics can have (non-) Killing and/or Lie algebra symmetries and/or describe (1+2)-d and/or (1+3)-d domain wall configurations, with possible warping nearly almost-Kähler manifolds, with gravitational and gauge instantons for nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants encoding string gravity effects. A series of examples of exact solutions describing generic off-diagonal supergravity modifications to black hole/ellipsoid and solitonic configurations are provided and analyzed. We prove that it is possible to reproduce the Kerr and other type black solutions in general relativity (with certain types of string corrections) in the 4-d case and to generalize the solutions to non-vacuum configurations in (super-) gravity/string theories.
Morozov-type discrepancy principle for nonlinear ill-posed problems under -condition
Indian Academy of Sciences (India)
M Thamban Nair
2015-05-01
For proving the existence of a regularization parameter under a Morozov-type discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems, it is required to impose additional nonlinearity assumptions on the forward operator. Lipschitz continuity of the Freéchet derivative and requirement of the Lipschitz constant to depend on a source condition is one such restriction (Ramlau P, Numer. Funct. Anal. Optim. 23(1&22) (2003) 147–172). Another nonlinearity condition considered by Scherzer (Computing, 51 (1993) 45–60) was by requiring the forward operator to be close to a linear operator in a restricted sense. A seemingly natural nonlinear assumption which appears in many applications which attracted attention in various contexts of the study of nonlinear problems is the so-called -condition. However, a Morozov-type discrepancy principle together with -condition does not seem to have been studied, except in a recent paper by the author (Bull. Aust. Math. Soc. 79 (2009) 337–342), where error estimates under a general source condition is derived, by assuming the existence of the parameter. In this paper, the existence of the parameter satisfying a Morozov-type discrepancy principle is proved under the -condition on the forward operator, by assuming the source condition as in the papers of Scherzer (Computing, 51 (1993) 45–60) and Ramlau (Numer. Funct. Anal. Optim. 23(1&22) (2003) 147–172). This source condition is, in fact, a special case of the source condition in the author’s paper (Bull. Aust. Math. Soc. 79 (2009) 337–342).
Nonlinear interaction of two trapped-mode resonances in a bilayer "fish-scale" metamaterial
Tuz, Vladimir R; Mladyonov, Pavel L; Prosvirnin, Sergey L; Novitsky, Andrey V
2014-01-01
We report on a bistable light transmission through a bilayer "fish-scale" (meander-line) metamaterial. It is demonstrated that an all-optical switching may be achieved nearly the frequency of the high-quality-factor Fano-shaped trapped-mode resonance excitation. The nonlinear interaction of two closely spaced trapped-mode resonances in the bilayer structure composed with a Kerr-type nonlinear dielectric slab is analyzed in both frequency and time domains. It is demonstrated that these two resonances react differently on the applied intense light which leads to destination of a multistable transmission.
Quantum correlations and entanglement in a model comprised of a short chain of nonlinear oscillators
Kalaga, J. K.; Kowalewska-Kudłaszyk, A.; Leoński, W.; Barasiński, A.
2016-09-01
We discuss a model comprised of a chain of three Kerr-like nonlinear oscillators pumped by two modes of external coherent field. We show that the system can be treated as nonlinear quantum scissors and behave as a three-qubit model. For such situation, different types of tripartite entangled states can be generated, even when damping effects are present in the system. Some amount of such entanglement can survive even in a long-time limit. The flow of bipartite entanglement between subsystems of the model and relations among first-order correlations, second-order correlations, and the entanglement are discussed.
Determination of Kerr and two-photon absorption coefficients of indandione derivatives
Bundulis, Arturs; Mihailovs, Igors; Nitiss, Edgars; Busenbergs, Janis; Rutkis, Martins
2017-05-01
We studied nonlinear optical properties of two different aminobenziliden-1,3-indandione derivatives - DDMABI and DMABI-OH by employing the Z-scan method. Through this we described how different donor and acceptor groups influence third-order nonlinear optical properties such as Kerr effect and two-photon absorption. During experimental measurements we used 1064 nm Nd:YAG laser with 30 ps pulse duration and 10 Hz repetition rate. From acquired values of Kerr and two-photon absorption coefficients we calculated values for real and imaginary parts of third-order susceptibility, as well as second-order hyperpolarizability. Quantum chemical calculations were carried out for secondorder hyperpolarizability to study how well calculations correlate with experimental values. Acquired data for DDMABI and DMABI-OH were compared with data for other ABI derivatives studied previously.
Non-Bragg-gap solitons in one-dimensional Kerr-metamaterial Fibonacci heterostructures.
Reyes-Gómez, E; Cavalcanti, S B; Oliveira, L E
2015-06-01
A detailed study of non-Bragg-gap solitons in one-dimensional Kerr-metamaterial quasiperiodic Fibonacci heterostructures is performed. The transmission coefficient is numerically obtained by combining the transfer-matrix formalism in the metamaterial layers with a numerical solution of the nonlinear differential equation in the Kerr slabs, and by considering the loss effects in the metamaterial slabs. A switching from states of no transparency in the linear regime to high-transparency states in the nonlinear regime is observed for both zero-order and plasmon-polariton gaps. The spatial localization of the non-Bragg-gap solitons is also examined, and the symmetry properties of the soliton waves are briefly discussed.
A wavy way leading to the Kerr metric
Gurtug, O
2015-01-01
From inherent non-linearity two gravitational waves, unless they are unidirectional, fail to satisfy a superposition law. They collide to develop a new spacetime carrying the imprints of the incoming waves. Same behaviour is valid also for any massless lightlike field. As a result of the violent collision process either a naked singularity or a Cauchy horizon (CH) develops. It was shown by Chandrasekhar and Xanthopoulos (CX) that a particular class of colliding gravitational waves (CGW) spacetime is locally isometric to the Kerr metric for rotating black holes. This relation came to be known as the CX duality. Such a duality can be exploited as an alternative derivation for the Kerr metric as we do herein. We claim at the same time that the duality points to the deeper rooted wave - particle correlation in a futuristic quantum gravity. In such a scenario black hole acts as the representative of a particle while CGW spacetime stands for its wavelike complementary partner. Not each case gives rise to a CH but t...
Spatial Kerr solitons in optical fibres of finite size cross section: beyond the Townes soliton
Drouart, F.; Renversez, G.; Nicolet, A.; Geuzaine, C.
2008-12-01
We propose a new and efficient numerical method to find spatial solitons in optical fibres with a nonlinear Kerr effect including microstructured ones. A nonlinear non-paraxial scalar model of the electric field in the fibre is used (nonlinear Helmholtz equation) and an iterative algorithm is proposed to obtain the nonlinear solutions using the finite element method. The field is supposed to be harmonic in time and along the direction of invariance of the fibre but inhomogeneous in the cross section. In our approach, we solve a nonlinear eigenvalue problem in which the propagation constant is the eigenvalue. Several examples dealing with step-index fibres and microstructured optical fibres with a finite size cross section are described. In each geometry, a single self-coherent nonlinear solution is obtained. This solution, which also depends on the size of the structure, is different from the Townes soliton—but converges towards it at small wavelengths.
APPLIED OPTICS. Overcoming Kerr-induced capacity limit in optical fiber transmission.
Temprana, E; Myslivets, E; Kuo, B P-P; Liu, L; Ataie, V; Alic, N; Radic, S
2015-06-26
Nonlinear optical response of silica imposes a fundamental limit on the information transfer capacity in optical fibers. Communication beyond this limit requires higher signal power and suppression of nonlinear distortions to prevent irreversible information loss. The nonlinear interaction in silica is a deterministic phenomenon that can, in principle, be completely reversed. However, attempts to remove the effects of nonlinear propagation have led to only modest improvements, and the precise physical mechanism preventing nonlinear cancellation remains unknown. We demonstrate that optical carrier stability plays a critical role in canceling Kerr-induced distortions and that nonlinear wave interaction in silica can be substantially reverted if optical carriers possess a sufficient degree of mutual coherence. These measurements indicate that fiber information capacity can be notably increased over previous estimates.
Kutev, N.; Kolkovska, N.; Dimova, M.
2013-10-01
The Cauchy problem to the generalized Boussinesq equation with Bernoulli type nonlinearities is studied. Global solvability of the solutions with sub-critical initial energy is proved by means of different techniques - nonstandard potential well method and method of the conservation low of the energy. In the framework of the nonstandard potential well method a new critical energy constant is introduced and estimated. The performed numerical experiments support the theoretical results.
Institute of Scientific and Technical Information of China (English)
刘安平; 何猛省
2002-01-01
By making use of the integral inequalities and some results of the functional differential equations, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations of neutral type with multi-delays were investigated and a series of sufficient conditions for oscillations of the equations were established. The results fully indicate that the oscillations are caused by delay and hence reveal the difference between these equations and those equations without delay.
Directory of Open Access Journals (Sweden)
Xiaofei Cao
2016-11-01
Full Text Available In this article, we consider the multiplicity of positive solutions for a class of Kirchhoff type problems with concave and convex nonlinearities. Under appropriate assumptions, we prove that the problem has at least two positive solutions, moreover, one of which is a positive ground state solution. Our approach is mainly based on the Nehari manifold, Ekeland variational principle and the theory of Lagrange multipliers.
Estimates for solutions to a class of nonlinear time-delay systems of neutral type
Directory of Open Access Journals (Sweden)
Gennadii V. Demidenko
2015-02-01
Full Text Available We consider nonlinear time-delay systems of neutral type with constant coefficients in the linear terms, $$ \\frac{d}{dt}\\big(y(t + D y(t-\\tau\\big = A y(t + B y(t-\\tau + F(t, y(t, y(t-\\tau. $$ We obtain estimates characterizing the exponential decay of solutions at infinity, and dependending on the norms of the powers of D.
Exact solutions to a class of nonlinear Schrödinger-type equations
Indian Academy of Sciences (India)
Jin-Liang Zhang; Ming-Liang Wing
2006-12-01
A class of nonlinear Schrödinger-type equations, including the Rangwala–Rao equation, the Gerdjikov–Ivanov equation, the Chen–Lee–Lin equation and the Ablowitz–Ramani–Segur equation are investigated, and the exact solutions are derived with the aid of the homogeneous balance principle, and a set of subsidiary higher order ordinary differential equations (sub-ODEs for short).
Switching behaviour of nonlinear Mach–Zehnder interferometer based on photonic crystal geometry
Indian Academy of Sciences (India)
Man Mohan Gupta; S Medhekar
2014-06-01
Nonlinear Mach–Zehnder interferometer (NMZI) created with photonic crystal waveguides (PCW) and with Kerr-type nonlinearity has been investigated in this paper. The NMZI has been simulated using two-dimensional finite difference time domain (2D-FDTD) method. Input verses output (I/O) characteristics have been obtained for different lengths of the nonlinear arm, nonlinear coefficients of the nonlinear arm, wavelengths of the input beam, sizes of defect rods and NMZI offset. The results obtained are compared with earlier published results of NMZI created with conventional step index waveguides (SIW). It is shown that all useful features of light switching offered by SIW-based NMZIs are also possible with PCW-based NMZIs of extremely small dimensions. Moreover, PCW-based NMZIs offer additional useful feature not available with SIW-based NMZIs.
Directory of Open Access Journals (Sweden)
Mohammad A. Assareh
2008-01-01
Full Text Available The operation for offshore oil has become an important issue in the recent years. Offshore platforms are some of those structures which are built to withstand environmental and accidental loads during oil exploitation operation. One of the most usual types of these platforms is the Jacket Type Offshore Platform (JTOP which can be divided into three important parts, which are Deck, Jacket and piles. In order to increase the safety, particular attention should be paid to earthquake excitations which are directly applied to the piles of these structures. Nonlinearity in piles and buckling of the struts are important issues which have to be considered by the designers of offshore platforms. The case of nonlinearity in piles and failure capture in these members has not effectively been covered by researchers. Incremental Dynamic Analysis (IDA is a powerful tool to assess the capacity of a structure upon seismic loads. In this paper incremental dynamic analysis has been implemented on single piles considering soil-pile interactions and free field site response. The use of nonlinear materials and lateral load resisting elements in the incremental dynamic analysis done in this paper has made it possible to get promising insights for incorporation of appropriate limit states and applications of performance based engineering. Special Engineering Demand Parameters (EDP and Intensity Measures (IM have been introduced for the single pile dynamic analysis in jacket type offshore platforms.
Energy spectrum of the Dirac equation for the Scharzschild and Kerr fields
Energy Technology Data Exchange (ETDEWEB)
Ternov, I.M.; Gaina, A.B.
1988-08-01
We consider the effect of relativistic corrections and rotation of the central body on the structure of the energy spectrum of a particle with spin in the Schwarzchild and Kerr fields. A splitting of levels is obtained, which corresponds to the classical shift of the perihelion of the orbit and precession of the plane of the gravitational spin-orbit interaction and several nonlinear spin effects are calculated.
Nonlinearly Coupled Superconducting Lumped Element Resonators
Collodo, Michele C.; Potočnik, Anton; Rubio Abadal, Antonio; Mondal, Mintu; Oppliger, Markus; Wallraff, Andreas
We study SQUID-mediated tunable coupling between two superconducting on-chip resonators in the microwave frequency range. In this circuit QED implementation, we employ lumped-element type resonators, which consist of Nb thin film structured into interdigitated finger shunt capacitors and meander inductors. A SQUID, functioning as flux dependent and intrinsically nonlinear inductor, is placed as a coupling element together with an interdigitated capacitor between the two resonators (cf. A. Baust et al., Phys Rev. B 91 014515 (2015)). We perform a spectroscopic measurement in a dilution refrigerator and find the linear photon hopping rate between the resonators to be widely tunable as well as suppressible for an appropriate choice of parameters, which is made possible due to the interplay of inductively and capacitively mediated coupling. Vanishing linear coupling promotes nonlinear effects ranging from onsite- to cross-Kerr interaction. A dominating cross-Kerr interaction related to this configuration is notable, as it induces a unique quantum state. In the course of analog quantum simulations, such elementary building blocks can serve as a precursor for more complex geometries and thus pave the way to a number of novel quantum phases of light
The polar Kerr effect in superconductors
Energy Technology Data Exchange (ETDEWEB)
Robbins, Joshua; Annett, James F.; Gradhand, Martin [University of Bristol (United Kingdom)
2016-07-01
The polar Kerr effect is an optical phenomenon which arises in states with broken time-reversal symmetry. This effect has recently been observed in a series of unconventional superconductors, including the layered perovskite compound Sr{sub 2}RuO{sub 4}. Confirmation of a Kerr signal below T{sub c} supports the hypothesis of chiral p-wave superconductivity in this material. However, the nature of the unconventional superconducting state remains a source of controversy. Here, we present calculations for the chiral superconducting state including spin-orbit coupling (SOC) by extending the three dimensional, multiband model considered previously. SOC was found to induce strong mixing of the orbital characters within the bandstructure. This mixing is essential for the existence of the polar Kerr effect and the large increase due to SOC has a significant influence on the frequency dependence of the predicted Kerr signal. We will extend and apply the model to other unconventional superconductors which have displayed the Kerr effect in recent years. This will allow a detailed study of the symmetry properties of these systems and will provide valuable insight into the pairing mechanism of superconductors.
Investigation on the formation of intense fringe near nonlinear medium slab in nonlinear imaging
Hu, Yonghua; Qiu, Yaqiong; Peng, Xue
2016-11-01
It is well known that hot images of small-scale scatterers can be formed. For phase-typed scatterers, hot image and second-order hot-image can be formed. However, when the number of scatterer is larger than one, the interaction between the scatterered waves will lead to new nonlinear propagation results. In this paper, the propagation of flat-topped intense laser beam through Kerr medium slab is investigated, with the incident beam modulated by two parallel wirelike phase-typed scatterers. We demonstrate that an intense fringe together with hot image and second-order hot image can be formed when the distance of the two scatterers is several millimeters. It is found that the on-axis position of the plane of this intense fringe is in the middle part between the exit surface of the Kerr medium slab and the secondorder hot image plane. This intense fringe shows the following basic properties: Firstly, its intensity is apparently higher than that of corresponding second-order hot image and can be comparable with that of corresponding hot image; Secondly, the distances between it and the in-beam positions of the scatterers are identical. The intensity profile shows that this intense fringe is the only prominent bright fringe in the corresponding plane, and thus it is not a nonlinear image of any scatterer. Besides, the influences of the properties of scatterer on the intensity of the fringe are discussed.
On the sharp front-type solution of the Nagumo equation with nonlinear diffusion and convection
Indian Academy of Sciences (India)
M B A Mansour
2013-03-01
This paper is concerned with the Nagumo equation with nonlinear degenerate diffusion and convection which arises in several problems of population dynamics, chemical reactions and others. A sharp front-type solution with a minimum speed to this model equation is analysed using different methods. One of the methods is to solve the travelling wave equations and compute an exact solution which describes the sharp travelling wavefront. The second method is to solve numerically an initial-moving boundary-value problem for the partial differential equation and obtain an approximation for this sharp front-type solution.
Directory of Open Access Journals (Sweden)
Baiyu Liu
2014-01-01
Full Text Available We consider a class of coupled nonlinear Schrödinger systems with potential terms and combined power-type nonlinearities. We establish the existence of ground states, by using a variational method. As an application, some symmetry results for ground states of Schrödinger systems with harmonic potential terms are obtained.
Analytic study of a coupled Kerr-SBS system
Conte, Robert; Gandarias, Maria Luz
2017-01-01
In order to describe the coupling between the Kerr nonlinearity and the stimulated Brillouin scattering, Mauger et al. recently proposed a system of partial differential equations in three complex amplitudes. We perform here its analytic study by two methods. The first method is to investigate the structure of singularities, in order to possibly find closed form single-valued solutions obeying this structure. The second method is to look at the infinitesimal symmetries of the system in order to build reductions to a lesser number of independent variables. Our overall conclusion is that the structure of singularities is too intricate to obtain closed form solutions by the usual methods. One of our results is the proof of the nonexistence of traveling waves.
Analytic study of a coupled Kerr-SBS system
Conte, Robert
2016-01-01
In order to describe the coupling between the Kerr nonlinearity and the stimulated Brillouin scattering, Mauger et alii recently proposed a system of partial differential equations in three complex amplitudes. We perform here its analytic study by two methods. The first method is to investigate the structure of singularities, in order to possibly find closed form singlevalued solutions obeying this structure. The second method is to look at the infinitesimal symmetries of the system in order to build reductions to a lesser number of independent variables. Our overall conclusion is that the structure of singularities is too intricate to obtain closed form solutions by the usual methods. One of our results is the proof of the nonexistence of traveling waves.
Dissipative Kerr solitons in optical microresonators
Herr, Tobias; Kippenberg, Tobias J
2015-01-01
This chapter describes the discovery and stable generation of temporal dissipative Kerr solitons in continuous-wave (CW) laser driven optical microresonators. The experimental signatures as well as the temporal and spectral characteristics of this class of bright solitons are discussed. Moreover, analytical and numerical descriptions are presented that do not only reproduce qualitative features but can also be used to accurately model and predict the characteristics of experimental systems. Particular emphasis lies on temporal dissipative Kerr solitons with regard to optical frequency comb generation where they are of particular importance. Here, one example is spectral broadening and self-referencing enabled by the ultra-short pulsed nature of the solitons. Another example is dissipative Kerr soliton formation in integrated on-chip microresonators where the emission of a dispersive wave allows for the direct generation of unprecedentedly broadband and coherent soliton spectra with smooth spectral envelope.
Kerr-Newman Black Hole In Quintessence
Xu, Zhaoyi
2016-01-01
We study the Kerr-Newman solutions of the Einstein-Maxwell equation in quintessence field around a black hole by Newman-Janis algorithm. From the horizon structure and stationary limit surfaces, we find that Kerr-Newman black hole exists an ergosphere with $r^{+} < r < r^{L}$, which is related to the parameters $\\omega$ and $\\alpha$. We obtain the general expression between $\\alpha$ and $\\omega$ if the cosmological horizon exists, in which for $\\omega=-1/2$, $\\alpha\\leq\\sqrt{2}/5$, and for $\\omega=-2/3$, $\\alpha\\leq 1/6$. For $\\omega=-2/3$, the result is same with rotational black hole in quintessence. The singularity of the black holes is the same with that of Kerr black hole. We also discuss the rotation velocity of the black holes on the equatorial plane for $\\omega =-2/3$ and $-1/2$.
Searching for non-Kerr objects
Energy Technology Data Exchange (ETDEWEB)
Apostolatos, Theocharis A; Lukes-Gerakopoulos, Georgios [Section of Astrophysics, Astronomy, and Mechanics, Department of Physics, University of Athens, Panepistimiopolis Zografos GR15783, Athens (Greece); Contopoulos, George, E-mail: thapostol@phys.uoa.gr [Academy of Athens, Research Center for Astronomy, Soranou Efesiou 4, GR-11527, Athens (Greece)
2011-02-01
We suggest a method that could be used to discriminate a Kerr black hole from any other supermassive axisymmetric astrophysical object by analyzing the gravitational-wave signal from an extreme mass ratio inspiral (EMRI). The method is based on the quite distinct qualitative features that characterize a slightly nonintegrable system. According to the Poincare-Birkhoff theorem, whenever a resonance of frequencies arise in an axisymmetric perturbed Kerr metric, instead of the anticipated KAM curves of the integrable Kerr case, a Birkhoff chain of islands appears on a surface of sections. The orbits of this chain of islands have a fixed ratio of frequencies. The idea is to exploit this feature to check if the inspiraling low-mass object spends a finite interval of time to cross this resonance, while its orbit evolves adiabatically due to the radiation of gravitational waves.
HIGH SPEED KERR CELL FRAMING CAMERA
Goss, W.C.; Gilley, L.F.
1964-01-01
The present invention relates to a high speed camera utilizing a Kerr cell shutter and a novel optical delay system having no moving parts. The camera can selectively photograph at least 6 frames within 9 x 10/sup -8/ seconds during any such time interval of an occurring event. The invention utilizes particularly an optical system which views and transmits 6 images of an event to a multi-channeled optical delay relay system. The delay relay system has optical paths of successively increased length in whole multiples of the first channel optical path length, into which optical paths the 6 images are transmitted. The successively delayed images are accepted from the exit of the delay relay system by an optical image focusing means, which in turn directs the images into a Kerr cell shutter disposed to intercept the image paths. A camera is disposed to simultaneously view and record the 6 images during a single exposure of the Kerr cell shutter. (AEC)
Analogue Kerr-like geometries in a MHD inflow
Noda, Sousuke; Takahashi, Masaaki
2016-01-01
We present a model of the analogue black hole in magnetohydrodynamic (MHD) flow. For a two dimensional axisymmetric stationary trans-magnetosonic inflow with a sink, using the dispersion relation of the MHD waves, we introduce the effective geometries for magnetoacoustic waves propagating in the MHD flow. Investigating the properties of the effective potentials for magnetoacoustic rays, we find that the effective geometries can be classified into five types which include analogue spacetimes of the Kerr black hole, ultra spinning stars with ergoregions and spinning stars without ergoregions. We address the effects of the magnetic pressure and the magnetic tension on each magnetoacoustic geometries.
Ayhan, Burcu; Özer, M. Naci; Bekir, Ahmet
2016-08-01
In this article, we applied the method of multiple scales for Korteweg-de Vries (KdV) type equations and we derived nonlinear Schrödinger (NLS) type equations. So we get a relation between KdV type equations and NLS type equations. In addition, exact solutions were found for KdV type equations. The ( G'} over G )-expansion methods and the ( {G'} over G, {1 over G}} )-expansion methods were proposed to establish new exact solutions for KdV type differential equations. We obtained periodic and hyperbolic function solutions for these equations. These methods are very effective for getting travelling wave solutions of nonlinear evolution equations (NEEs).
Liang, Wei; Ilchenko, Vladimir S; Eliyahu, Danny; Seidel, David; Matsko, Andrey B; Maleki, Lute
2014-01-01
We demonstrate experimentally, and explain theoretically, generation of a wide, fundamentally phase locked Kerr frequency comb in a nonlinear resonator with a normal group velocity dispersion. A magnesium fluoride whispering gallery resonator characterized with 10 GHz free spectral range and pumped either at 780 nm or 795 nm is used in the experiment. The envelope of the observed frequency comb differs significantly from the Kerr frequency comb spectra reported previously. We show via numerical simulation that, while the frequency comb does not correspond to generation of short optical pulses, the relative phases of the generated harmonics are fixed.
Nonlinear Michelson interferometer for improved quantum metrology
Luis, Alfredo; Rivas, Ángel
2015-08-01
We examine quantum detection via a Michelson interferometer embedded in a gas with Kerr nonlinearity. This nonlinear interferometer is illuminated by pulses of classical light. This strategy combines the robustness against practical imperfections of classical light with the improvement provided by nonlinear processes. Regarding ultimate quantum limits, we stress that, as a difference with linear schemes, the nonlinearity introduces pulse duration as a new variable into play along with the energy resources.
Nonlinear Michelson interferometer for improved quantum metrology
Luis Aina, Alfredo; Rivas Vargas, Ángel
2015-01-01
We examine quantum detection via a Michelson interferometer embedded in a gas with Kerr nonlinearity. This nonlinear interferometer is illuminated by pulses of classical light. This strategy combines the robustness against practical imperfections of classical light with the improvement provided by nonlinear processes. Regarding ultimate quantum limits, we stress that, as a difference with linear schemes, the nonlinearity introduces pulse duration as a new variable into play along with the ene...
Normal-dispersion microresonator Kerr frequency combs
Directory of Open Access Journals (Sweden)
Xue Xiaoxiao
2016-06-01
Full Text Available Optical microresonator-based Kerr frequency comb generation has developed into a hot research area in the past decade. Microresonator combs are promising for portable applications due to their potential for chip-level integration and low power consumption. According to the group velocity dispersion of the microresonator employed, research in this field may be classified into two categories: the anomalous dispersion regime and the normal dispersion regime. In this paper, we discuss the physics of Kerr comb generation in the normal dispersion regime and review recent experimental advances. The potential advantages and future directions of normal dispersion combs are also discussed.
Late time tails in the Kerr spacetime
Gleiser, Reinaldo J; Pullin, Jorge
2008-01-01
Outside a black hole, perturbation fields die off in time as $1/t^n$. For spherical holes $n=2\\ell+3$ where $\\ell$ is the multipole index. In the nonspherical Kerr spacetime there is no coordinate-independent meaning of "multipole," and a common sense viewpoint is to set $\\ell$ to the lowest radiatiable index, although theoretical studies have led to very different claims. Numerical results, to date, have been controversial. Here we show that expansion for small Kerr spin parameter $a$ leads to very definite numerical results confirming previous theoretical analyses.
Fast plunges into Kerr black holes
Energy Technology Data Exchange (ETDEWEB)
Hadar, Shahar [Racah Institute of Physics, Hebrew University,Jerusalem 91904 (Israel); Porfyriadis, Achilleas P.; Strominger, Andrew [Center for the Fundamental Laws of Nature, Harvard University,Cambridge, MA 02138 (United States)
2015-07-15
Most extreme-mass-ratio-inspirals of small compact objects into supermassive black holes end with a fast plunge from an eccentric last stable orbit. For rapidly rotating black holes such fast plunges may be studied in the context of the Kerr/CFT correspondence because they occur in the near-horizon region where dynamics are governed by the infinite dimensional conformal symmetry. In this paper we use conformal transformations to analytically solve for the radiation emitted from fast plunges into near-extreme Kerr black holes. We find perfect agreement between the gravity and CFT computations.
Institute of Scientific and Technical Information of China (English)
易文辉; 李春永; 郑建邦; 吴洪才; 张治国
2003-01-01
合成了一系列聚芳香杂环甲烯,包括聚吡咯甲烯和聚噻吩甲烯.采用四波混频法研究材料的共振三阶非线性光学效应(λ＝532 nm),其共振二阶超分子极化率γ三阶非线性光学系数分别达到10-30esu和10-8esu.选择具有良好溶解性、成膜性的聚吡咯对二甲氨基苯甲烯(PPDMAB),采用飞秒时间分辨光克尔效应方法研究材料的非共振三阶非线性光学效应(λ＝790 nm).实验表明,翠绿亚胺碱溶液的光克尔信号仅表现一超快响应的成分,归功于π电子云扭转产生的非共振激发.PPDMAB的非共振二阶超分子极化率γ三阶非线性光学系数分别达到γ=5.78×10-32esu和χ(3) =1.26×10-10esu.%A series of poly(heteroarylene methines) containing one pyrrole or thiophene ring alternating with a carbon atom in the main chain were synthesized. The resonant third-order optical nonlinearity at 532 nm was studied by using degenerate four-wave mixing (DFWM) techique. The resonant second-order hyperpolarizabilities γ and third-order nonlinear optical susceptibility χ(3) were up to 10-30esu and 10-8esu respectively. Poly{pyrrole-[2,5-diyl(p-N,N-dimethlamino)benzylidene]} (PPDMAB) was chosen to be further studied mainly due to its good solubility and film forming performance.Time-resolved Optical Kerr effect (OKE) of PPDMAB was investigated with femtosecond laser pulses at 790 nm. Only an ultrafast component of OKE of PPDMAB was observed and its dephasing time was 84.7 fs, which is attributed to π-electron-cloud distortion occurring upon the non-resonant excitation. The off-resonant second-order hyperpolarizabilities γ and third-order nonlinear optical susceptibility χ(3) of PPDMAB were also determined by transient OKE. The results show that PPDMAB exhibit large off-resonant nonlinearities γ as large as γ=5.78×10-32esu, for each structural units and χ(3) as large as χ(3)=1.26×10-10esu for the material have been obtained.
DEFF Research Database (Denmark)
Bang, Ole; Graversen, T. W.; Clausen, Carl A. Balslev
2000-01-01
Quasi-phase-matching gratings induces Kerr effects in quadratic nonlinear materials. We show analytically and confirm numerically how modulating the grating changes the effective quadratic and cubic nonlinearities and allows for multi-wavelength second-harmonic generation....
A geometric invariant characterising initial data for the Kerr-Newman spacetime
Cole, Michael J
2016-01-01
We describe the construction of a geometric invariant characterising initial data for the Kerr-Newman spacetime. This geometric invariant vanishes if and only if the initial data set corresponds to exact Kerr-Newman initial data, and so characterises this type of data. We first illustrate the characterisation of the Kerr-Newman spacetime in terms of Killing spinors. The space spinor formalism is then used to obtain a set of four independent conditions on an initial Cauchy hypersurface that guarantee the existence of a Killing spinor on the development of the initial data. Following a similar analysis in the vacuum case, we study the properties of solutions to the approximate Killing spinor equation and use them to construct the geometric invariant.
Controllable cross-Kerr interaction between microwave photons in circuit quantum electrodynamics
Institute of Scientific and Technical Information of China (English)
Wu Qin-Qin; Liao Jie-Qiao; Kuang Le-Man
2011-01-01
We propose a scheme to enable a controllable cross-Kerr interaction between microwave photons in a circuit quantum electrodynamics (QED) system. In this scheme we use two transmission-line resonators (TLRs) and one superconducting quantum interference device (SQUID) type charge qubit, which acts as an artificial atom. It is shown that in the dispersive regime of the circuit-QED system, a controllable cross-Kerr interaction can be obtained by properly preparing the initial state of the qubit, and a large cross-phase shift between two microwave fields in the two TLRs can then be reached. Based on this cross-Kerr interaction, we show how to create a macroscopic entangled state between the two TLRs.
High-resolution nonlinear ellipse rotation measurements for 3D microscopy
Miguez, M. L.; Barbano, E. C.; Coura, J. A.; Zilio, S. C.; Misoguti, L.
2015-03-01
Nonlinear optical effects have been widely explored for microscopy due to the possibility of three-dimension (3D) image acquisition. Harmonic generation and nonlinear absorption, for instance, were used for this purpose. Each nonlinear effect has its own characteristic, complexity, type of contrast, advantage and disadvantage, etc. Recently, we developed a new simple and sensitive method for measuring nonlinear ellipse rotation (NER) using a dual-phase lock-in amplifier, which could be successfully applied for measuring local nonlinearity distribution on a sample and, consequently, the image acquisition. The NER is a particular refractive nonlinear effect which appears when strong elliptical polarized laser beam propagates along one nonlinear material. It is type of refractive Kerr nonlinearity similar to self-focalization responsible for the signal in the Z-scan technique. The self-focalization is one of the most important refractive effects, but it cannot be used for image acquisition. On the other hand, NER does. Furthermore, such refractive nonlinearities signal can be very strong and serves as a new contrast for nonlinear microscopy.
Weakly nonlinear analysis and localised structures in nonlinear cavities with metamaterials
Slimani, N.; Makhoute, A.; Tlidi, M.
2016-04-01
We consider an optical ring cavity filled with a metamaterial and with a Kerr medium. The cavity is driven by a coherent radiation beam. The modelling of this device leads to the well known Lugiato-Lefever equation with high order diffraction term. We assume that both left-handed and right-handed materials possess a Kerr focusing type of nonlinearity. We show that close to the zero-diffraction regime, high-order diffraction effect allows us to stabilise dark localised structures in this device. These structures consist of dips or holes in the transverse profile of the intracavity field and do not exist without high-order diffraction effects. We show that high order diffraction effects alter in depth the space-time dynamics of this device. A weakly nonlinear analysis in the vicinity of the first threshold associated with the Turing instability is performed. This analysis allows us to determine the parameter regime where the transition from super- to sub-critical bifurcation occurs. When the modulational instability appears subcritically, we show that bright localised structures of light may be generated in two-dimensional setting. Close to the second threshold associated with the Turing instability, dark localised structures are generated.
General radiation via tunneling in Kerr and Kerr-Newman black holes
Institute of Scientific and Technical Information of China (English)
2008-01-01
Hawking radiation can be viewed as a process of quantum tunneling near the black hole horizon. When a particle with angular momentum L≠ω a tunnels across the event horizon of Kerr or Kerr-Newman black hole, the angular momentum per unit mass a should be changed. The emission rate of the massless particles under this general case is calculated, and the result is consistent with an underlying unitary theory.
STUDIES ON NONLINEAR STABILITY OF THREE-DIMENSIONAL H-TYPE DISTURBANCE
Institute of Scientific and Technical Information of China (English)
王伟志; 唐登斌
2003-01-01
The three-dimensional H-type nonlinear evolution process for the problem of boundary layer stability is studied by using a newly developed method called parabolic stability equations (PSE).The key initial conditions for sub-harmonic disturbances are obtained by means of the secondary instability theory. The initial solutions of two-dimensional harmonic waves are expressed in Landau expansions. The numerical techniques developed in this paper, including the higher order spectrum method and the more effective algebraic mapping for dealing with the problem of an infinite region,increase the numerical accuracy and the rate of convergence greatly. With the predictor-corrector approach in the marching procedure, the normalization, which is very important for PSE method, is satisfied and the stability of the numerical calculation can be assured. The effects of different pressure gradients, including the favorable and adverse pressure gradients of the basic flow, on the "H-type"evolution are studied in detail. The results of the three-dimensional nonlinear "H-type" evolution are given accurately and show good agreement with the data of the experiment and the results of the DNS from the curves of the amplitude variation, disturbance velocity profile and the evolution of velocity.
Directory of Open Access Journals (Sweden)
Mourad Kerboua
2014-12-01
Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.
Jameson, A.
1976-01-01
A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.
A new Liu-Storey type nonlinear conjugate gradient method for unconstrained optimization problems
Zhang, Li
2009-03-01
Although the Liu-Storey (LS) nonlinear conjugate gradient method has a similar structure as the well-known Polak-Ribière-Polyak (PRP) and Hestenes-Stiefel (HS) methods, research about this method is very rare. In this paper, based on the memoryless BFGS quasi-Newton method, we propose a new LS type method, which converges globally for general functions with the Grippo-Lucidi line search. Moreover, we modify this new LS method such that the modified scheme is globally convergent for nonconvex minimization if the strong Wolfe line search is used. Numerical results are also reported.
PD-type iterative learning control for nonlinear time-delay system with external disturbance
Institute of Scientific and Technical Information of China (English)
Zhang Baolin; Tang Gongyou; Zheng Shi
2006-01-01
The PD-type iterative learning control design of a class of affine nonlinear time-delay systems with external disturbances is considered. Sufficient conditions guaranteeing the convergence of the n-norm of the tracking error are derived. It is shown that the system outputs can be guaranteed to converge to desired trajectories in the absence of external disturbances and output measurement noises. And in the presence of state disturbances and measurement noises, the tracking error will be bounded uniformly. A numerical simulation example is presented to validate the effectiveness of the proposed scheme.
Isochronous Liénard-type nonlinear oscillators of arbitrary dimensions
Indian Academy of Sciences (India)
Ajey K Tiwari; A Durga Devi; R Gladwin Pradeep; V K Chandrasekar
2015-11-01
In this paper, we briefly present an overview of the recent developments made in identifying/generating systems of Liénard-type nonlinear oscillators exhibiting isochronous properties, including linear, quadratic and mixed cases and their higher-order generalizations. There exists several procedures/methods in the literature to identify/generate isochronous systems. The application of local as well as nonlocal transformations and -modified Hamiltonian method in identifying and generating systems exhibiting isochronous properties of arbitrary dimensions is also discussed in detail. The identified oscillators include singular and nonsingular Hamiltonian systems and PT-symmetric systems.
NONLINEAR OPTICAL FREQUENCY CONVERTER OF LASER RADIATION ON THE LBO TYPE I CRYSTALS
Directory of Open Access Journals (Sweden)
N. V. Kondratyuk
2014-01-01
Full Text Available Describes nonlinear optical frequency converter of laser radiation based on the two LBO type I crystals allowing to receive pulses of radiation at three wavelengths of 1064 nm, 532 nm and 355 nm with an adjustable pulse energy. For fine adjustment of the output pulse energy used two dual phase plates that change the orientation of the plane of polarization of the two waves in cascade third harmonic generation. Measured the efficiency of the generation of harmonics of the intensity of radiation at 1064 nm.
Sturm-Picone type theorems for second-order nonlinear differential equations
Directory of Open Access Journals (Sweden)
Aydin Tiryaki
2014-06-01
Full Text Available The aim of this article is to give Sturm-Picone type theorems for the pair of second-order nonlinear differential equations $$\\displaylines{ (p_1(t|x'|^{\\alpha-1}x''+q_1(tf_1(x=0 \\cr (p_2(t|y'|^{\\alpha-1}y''+q_2(tf_2(y=0,\\quad t_1
Numerical Solutions of a New Type of Fractional Coupled Nonlinear Equations
Institute of Scientific and Technical Information of China (English)
WANG Ling; CHEN Yong; DONG Zhong-Zhou; AN Hong-Li
2008-01-01
In this paper, we investigate a new type of fractional coupled nonlinear equations. By introducing the frac-tional derivative that satisfies the Caputo's definition, we directly extend the applications of the Adomian decomposition method to the new system. As a result, with the aid of Maple, the realistic and convergent rapidly series solutions are obtained with easily computable components. Two famous fractional coupled examples: KdV and mKdV equations, are used to illustrate the efficiency and accuracy of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
1992-01-01
This publicity brochure profiles the Kerr-McGee Coal Corporation, one of the largest coal companies in the US and a major producer in the Powder River Basin. Aspects covered include: Corporate profiles; Jacobs Ranch Mine (Wyoming); Galatia Mine (Illinois); the subsidiary Pioneer Fuel Corporation; Clovis Point Mine (Wyoming); environment; people; and marketing.
Kerr black holes with scalar hair.
Herdeiro, Carlos A R; Radu, Eugen
2014-06-06
We present a family of solutions of Einstein's gravity minimally coupled to a complex, massive scalar field, describing asymptotically flat, spinning black holes with scalar hair and a regular horizon. These hairy black holes (HBHs) are supported by rotation and have no static limit. Besides mass M and angular momentum J, they carry a conserved, continuous Noether charge Q measuring the scalar hair. HBHs branch off from the Kerr metric at the threshold of the superradiant instability and reduce to spinning boson stars in the limit of vanishing horizon area. They overlap with Kerr black holes for a set of (M, J) values. A single Killing vector field preserves the solutions, tangent to the null geodesic generators of the event horizon. HBHs can exhibit sharp physical differences when compared to the Kerr solution, such as J/M^{2}>1, a quadrupole moment larger than J^{2}/M, and a larger orbital angular velocity at the innermost stable circular orbit. Families of HBHs connected to the Kerr geometry should exist in scalar (and other) models with more general self-interactions.
Universal scaling laws of Kerr frequency combs.
Coen, Stéphane; Erkintalo, Miro
2013-06-01
Using the known solutions of the Lugiato-Lefever equation, we derive universal trends of Kerr frequency combs. In particular, normalized properties of temporal cavity soliton solutions lead us to a simple analytic estimate of the maximum attainable bandwidth for given pump resonator parameters. The result is validated via comparison with past experiments encompassing a diverse range of resonator configurations and parameters.
Universal scaling laws of Kerr frequency combs
Coen, Stephane
2013-01-01
Using the known solutions of the Lugiato-Lefever equation, we derive universal trends of Kerr frequency combs. In particular, normalized properties of temporal cavity soliton solutions lead us to a simple analytic estimate of the maximum attainable bandwidth for given pump-resonator parameters. The result is validated via comparison with past experiments encompassing a diverse range of resonator configurations and parameters.
Kerr-Newman Electron as Spinning Soliton
Burinskii, Alexander
2015-10-01
Measurable parameters of the electron indicate that its background should be described by the Kerr-Newman (KN) solution. The spin/mass ratio of the electron is extreme large, and the black hole horizons disappear, opening a topological defect of space-time - the Kerr singular ring of Compton size, which may be interpreted as a closed fundamental string of low energy string theory. The singular and two-sheeted structure of the corresponding Kerr space has to be regularised, and we consider the old problem of regularising the source of the KN solution. As a development of the earlier Keres-Israel-Hamity-López model, we describe the model of smooth and regular source forming a gravitating and relativistically rotating soliton based on the chiral field model and the Higgs mechanism of broken symmetry. The model reveals some new remarkable properties: (1) the soliton forms a relativistically rotating bubble of Compton radius, which is filled by the oscillating Higgs field in a pseudo-vacuum state; (2) the boundary of the bubble forms a domain wall which interpolates between the internal flat background and the external exact Kerr-Newman (KN) solution; (3) the phase transition is provided by a system of chiral fields; (4) the vector potential of the external the KN solution forms a closed Wilson loop which is quantised, giving rise to a quantised spin of the soliton; (5) the soliton is bordered by a closed string, which is a part of the general complex stringy structure.
Nonthermal nature of extremal Kerr black holes
Rothman, T
2000-01-01
Liberati, Rothman and Sonego have recently showed that objects collapsing into extremal Reissner-Nordstrom black holes do not behave as thermal objects at any time in their history. In particular, a temperature, and hence thermodynamic entropy, are undefined for them. I demonstrate that the analysis goes through essentially unchanged for Kerr black holes.
Where is the extremal Kerr ISCO?
Jacobson, Ted
2011-01-01
Although the circular photon orbit and ISCO for the Kerr black hole remain distinct from each other and from the horizon in the extremal spin limit on a constant Boyer-Lindquist time slice, on a horizon-crossing slice they both coincide with the null generators of the horizon.
Limits of noise squeezing in Kerr effect
Bajer, J; Tanas, R
2002-01-01
It is well known that the optical Kerr effect can be a source of highly squeezed light, however the analytical limit of the noise suppression has not been found yet. The process is reconsidered and an analytical estimation of the optimal quadrature noise level is presented. The validity of the new scaling law is checked numerically and analytically.
Directory of Open Access Journals (Sweden)
Alexander Burinskii
2013-01-01
Full Text Available The 4D Kerr geometry displays many wonderful relations with quantum world and, in particular, with superstring theory. The lightlike structure of fields near the Kerr singular ring is similar to the structure of Sen solution for a closed heterotic string. Another string, open and complex, appears in the complex representation of the Kerr geometry initiated by Newman. Combination of these strings forms a membrane source of the Kerr geometry which is parallel to the structure of M-theory. In this paper we give one more evidence of this relationship, emergence of the Calabi-Yau twofold (K3 surface in twistorial structure of the Kerr geometry as a consequence of the Kerr theorem. Finally, we indicate that the Kerr stringy system may correspond to a complex embedding of the critical N = 2 superstring.
Intelligent control for nonlinear inverted pendulum based on interval type-2 fuzzy PD controller
Directory of Open Access Journals (Sweden)
Ahmad M. El-Nagar
2014-03-01
Full Text Available The interval type-2 fuzzy logic controller (IT2-FLC is able to model and minimize the numerical and linguistic uncertainties associated with the inputs and outputs of a fuzzy logic system (FLS. This paper proposes an interval type-2 fuzzy PD (IT2F-PD controller for nonlinear inverted pendulum. The proposed controller uses the Mamdani interval type-2 fuzzy rule based, interval type-2 fuzzy sets (IT2-FSs with triangular membership function, and the Wu–Mendel uncertainty bound method to approximate the type-reduced set. The proposed controller is able to minimize the effect of the structure uncertainties and the external disturbances for the inverted pendulum. The results of the proposed controller are compared with the type-1 fuzzy PD (T1F-PD controller in order to investigate the effectiveness and the robustness of the proposed controller. The simulation results show that the performance of the proposed controller is significantly improved compared with the T1F-PD controller. Also, the results show good performance over a wide range of the structure uncertainties and the effect of the external disturbances.
Asymptotic behavior of zero mass spin 2 fields propagating in Kerr spacetime
Caciotta, Giulio; Raparelli, Tiziana
2016-08-01
We introduce D(0)νW νμρσ = hμρσ, the inhomogeneous equation suitable to describe the solution of the linearized version of the conformal part of the Riemann tensor connected to the perturbations of the Kerr spacetime far from the origin. Then we find the right decays we have to impose to the source term hμρσ to obtain the peeling decays for this linearized solution. We explain how these decays are compatible with the ones we need to attack the full nonlinear problem following the Christodoulou-Klainerman approach, see [7, 11]. This result is expressed explicitly in Theorem 1.1 and requires some new detailed estimates for the connection coefficients related to the null cone foliation in Kerr, see [10], which could be considered as a useful result by itself.
Spatiotemporal Model for Kerr Comb Generation in Whispering Gallery Mode Resonators
Chembo, Yanne K
2012-01-01
We establish an exact partial differential equation to model Kerr comb generation in whispering-gallery mode resonators. This equation is a variant of the Lugiato-Lefever equation that includes higher-order dispersion and nonlinearity. This spatio-temporal model, whose main variable is the total intracavity field, is significantly more suitable than the modal expansion approach for the theoretical understanding and the numerical simulation of wide-span combs. It allows us to explore pulse formation in which a large number of modes interact cooperatively. This versatile approach can be straightforwardly extended to include higher-order dispersion, as well as other phenomena like Raman, Brillouin and Rayleigh scattering. We demonstrate for the first time that when the dispersion is anomalous, Kerr comb generation can arise as the spectral signature of dissipative cavity solitons, leading to wide-span combs with low pumping.
Parra-Rivas, P.; Gomila, D.; Matias, M. A.; Leo, F.; Coen, S.; Gelens, L.
2014-05-01
Optical frequency combs can be used to measure light frequencies and time intervals more easily and precisely than ever before, opening a large avenue for applications. Traditional frequency combs are usually associated with trains of evenly spaced, very short pulses. More recently, a new generation of comb sources has been demonstrated in compact high-Q optical microresonators with a Kerr nonlinearity pumped by continuous-wave laser light. These combs are now referred to as Kerr frequency combs and have attracted a lot of interest in the last few years. Kerr frequency combs can be modeled in a way that is strongly reminiscent of temporal cavity solitons (CSs) in nonlinear cavities. Temporal CSs have been experimentally studied in fiber resonators and their description is based on a now classical equation, the Lugiato-Lefever equation, that describes pattern formation in optical systems. In this work, we first perform a theoretical study of the correspondence between the CSs and patterns with frequency combs. It is known that the CSs appear in reversible systems that present bistability between a pattern and a homogeneous steady state through what it is called a homoclinic snaking structure. In this snaking region, single and multi-peak CSs coexist with patterns and homogeneous solutions, creating a largely multistable landscape. We study the changes of the homoclinic snaking for different parameter regimes in the Lugiato-Lefever equation and determine the stability and shape of the frequency combs through comparison with the underlying CSs and patterns. Secondly, we include third order dispersion in the system and study its effect on the multistable snaking structure. For high dispersion strengths the CS structures and the corresponding Kerr frequency combs disappear.
Topological nature of nonlinear optical effects in solids
Morimoto, Takahiro; Nagaosa, Naoto
2015-01-01
There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by the strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by the nonlinear suscepti...
Cho, Yonggeun
2016-05-04
This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrödinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method. © 2015 World Scientific Publishing Company
Directory of Open Access Journals (Sweden)
Yi-Xiang Chen
Full Text Available Two families of Gaussian-type soliton solutions of the (n+1-dimensional Schrödinger equation with cubic and power-law nonlinearities in PT-symmetric potentials are analytically derived. As an example, we discuss some dynamical behaviors of two dimensional soliton solutions. Their phase switches, powers and transverse power-flow densities are discussed. Results imply that the powers flow and exchange from the gain toward the loss regions in the PT cell. Moreover, the linear stability analysis and the direct numerical simulation are carried out, which indicates that spatial Gaussian-type soliton solutions are stable below some thresholds for the imaginary part of PT-symmetric potentials in the defocusing cubic and focusing power-law nonlinear medium, while they are always unstable for all parameters in other media.
Bayad, A.; Kim, T.
2016-04-01
We introduce a special nonlinear differential operator and, using its properties, reduce higher-order Frobenius-Euler Apostol-type polynomials to a finite series of first-order Apostol-type Frobenius-Euler polynomials and Stirling numbers. Interesting identities are established.
An Adaptive Nonlinear Basal-Bolus Calculator for Patients With Type 1 Diabetes.
Boiroux, Dimitri; Aradóttir, Tinna Björk; Nørgaard, Kirsten; Poulsen, Niels Kjølstad; Madsen, Henrik; Jørgensen, John Bagterp
2017-01-01
Bolus calculators help patients with type 1 diabetes to mitigate the effect of meals on their blood glucose by administering a large amount of insulin at mealtime. Intraindividual changes in patients physiology and nonlinearity in insulin-glucose dynamics pose a challenge to the accuracy of such calculators. We propose a method based on a continuous-discrete unscented Kalman filter to continuously track the postprandial glucose dynamics and the insulin sensitivity. We augment the Medtronic Virtual Patient (MVP) model to simulate noise-corrupted data from a continuous glucose monitor (CGM). The basal rate is determined by calculating the steady state of the model and is adjusted once a day before breakfast. The bolus size is determined by optimizing the postprandial glucose values based on an estimate of the insulin sensitivity and states, as well as the announced meal size. Following meal announcements, the meal compartment and the meal time constant are estimated, otherwise insulin sensitivity is estimated. We compare the performance of a conventional linear bolus calculator with the proposed bolus calculator. The proposed basal-bolus calculator significantly improves the time spent in glucose target ( P < .01) compared to the conventional bolus calculator. An adaptive nonlinear basal-bolus calculator can efficiently compensate for physiological changes. Further clinical studies will be needed to validate the results.
Insights from Melvin-Kerr-Newman spacetimes
Booth, Ivan; Palomo-Lozano, Alberto; Kunduri, Hari K
2015-01-01
We examine several aspects of black hole physics using the Melvin-Kerr-Newman (MKN) family of spacetimes. Roughly speaking these are black holes immersed in a distorting background magnetic field and unlike the standard Kerr-Newman (KN) family they are not asymptotically flat. Among other properties we see that their angular momentum and charge are bounded by horizon area in exactly the same way as KN and also that they obey the uniqueness theorems for extremal horizons: these properties are in accord with standard theorems but are seen to be satisfied in interesting and non-trivial ways. Horizon geometries are compared to KN horizons with equal area, charge and angular momentum. Finally we calculate the energy of these distorted black holes using the isolated horizon, Komar and recently proposed Gibbons-Pang-Pope procedures. Disagreements between these methods highlight the inherent ambiguities in attempting to define energy and other physical properties for a non-asymptotically flat spacetime.
Properties of the distorted Kerr black hole
Abdolrahimi, Shohreh; Nedkova, Petya; Tzounis, Christos
2015-01-01
We investigate the properties of the ergoregion and the location of the curvature singularities for the Kerr black hole distorted by the gravitational field of external sources. The particular cases of quadrupole and octupole distortion are studied in detail. We also investigate the scalar curvature invariants of the horizon and compare their behaviour with the case of the isolated Kerr black hole. In a certain region of the parameter space the ergoregion consists of a compact region encompassing the horizon and a disconnected part extending to infinity. The curvature singularities in the domain of outer communication, when they exist, are always located on the boundary of the ergoregion. We present arguments that they do not lie on the compact ergosurface. For quadrupole distortion the compact ergoregion size is negatively correlated with the horizon angular momentum when the external sources are varied. For octupole distortion infinitely many ergoregion configurations can exist for a certain horizon angular...
Spinning Particle Motion in a Kerr Geometry
Jones, A.; Baker, W. M.; Staton, R.
1999-12-01
The physics of particle motion in a Kerr geometry has been extensively studied. The case of motion of particles with spin is not as well investigated. We have studied the case of the motion of a spinning particle by applying the Papapetrou equation, which includes a spin-curvature coupling term, and an equation that describes the evolution of the spin of the particle. The motion is considered for a Kerr geometry in the weak field limit. We have obtained numerical solutions to this system of equations. Our results suggest that spin orientation is important for particle trajectories in a manner that is similar to the Stern-Gerlach effect. This could be important for the study of the motion of very low mass neutrinos. Project funded by a grant from the South Carolina Independent Colleges and Universities, and the Furman Advantage Program.
SOLUCIÓN DE LA ECUACIÓN NO LINEAL DE SCHRODINGER (1+1 EN UN MEDIO KERR
Directory of Open Access Journals (Sweden)
Francis Armando Segovia
2015-12-01
Full Text Available Se presenta un marco teórico y se muestra una simulación numérica de la propagación de solitones. Con especial atención a los solitones ópticos espaciales, se calcula analíticamente el perfil de solitón correspondiente a la ecuación Schrodinger no-lineal para un medio Kerr. Los resultados muestran que los solitones ópticos son pulsos estables cuya forma y espectro son preservados en grandes distancias.Solution of the nonlinear Schrodinger equation (1+1 in a Kerr mediumABSTRACTThis document presents a theoretical framework and shows a numerical simulation for the propagation of solitons. With special attention to the spatial optical solitons, we calculates analytically the profile of solitón corresponding to the non-linear Schrodinger equation for a Kerr medium. The results show that the optical solitons are stable pulses whose shape and spectrum are preserved at great distances.Keywords: nonlinear optics, nonlinear Schrodinger equation, solitons.
The Kerr-Newman metric: A Review
Adamo, Tim
2014-01-01
The Kerr-Newman metric describes a very special rotating, charged mass and is the most general of the asymptotically flat stationary 'black hole' solutions to the Einstein-Maxwell equations of general relativity. We review the derivation of this metric from the Reissner-Nordstrom solution by means of a complex transformation algorithm and provide a brief overview of its basic geometric properties. We also include some discussion of interpretive issues, related metrics, and higher-dimensional analogues.
Fast plunges into Kerr black holes
Hadar, Shahar; Porfyriadis, Achilleas; Strominger, Andrew E.
2015-01-01
Most extreme-mass-ratio-inspirals of small compact objects into supermassive black holes end with a fast plunge from an eccentric last stable orbit. For rapidly rotating black holes such fast plunges may be studied in the context of the Kerr/CFT correspondence because they occur in the near-horizon region where dynamics are governed by the infinite dimensional conformal symmetry. In this paper we use conformal transformations to analytically solve for the radiation emitted from fast plunges i...
Characterization of Null Geodesics on Kerr Spacetimes
Paganini, Claudio F; Oancea, Marius A
2016-01-01
We consider null geodesics in the domain of outer communication of a sub-extremal Kerr spacetime. We show, that most fundamental properties of null geodesics can be represented in one plot. In particular one can see immediately that the ergoregion and trapping are separated in phase space. Furthermore we show that from the point of view of any timelike observer outside of a black hole, trapping can be understood as a smooth set of spacelike directions on the observers' celestial sphere.
Wavefronts and Light Cones for Kerr Spacetimes
Frutos-Alfaro, Francisco; Mueller, Thomas; Adis, Daria
2014-01-01
We investigate the light propagation by means of simulations of wavefronts and light cones for Kerr spacetimes. Simulations of this kind give us a new insight to better understand the light propagation in presence of massive rotating black holes. A relevant result is that wavefronts are back scattered with winding around the black hole. To generate these visualizations, an interactive computer program with a graphical user interface, called JWFront, was written in Java.
Kerr-Newman electron as spinning soliton
Burinskii, Alexander
2014-01-01
Measurable parameters of the electron indicate that its background should be described by the Kerr-Newman (KN) solution. Spin/mass ratio of the electron is extreme large, and the black hole horizons disappear, opening a topological defect of spacetime -- the Kerr singular ring of the Compton size, which may be interpreted as a closed fundamental string to the low energy string theory. The singular and twosheeted structure of the corresponding Kerr space has to be regularized, and we consider the old problem of regular source of the KN solution. As a development of the earlier Keres-Israel-Hamity-L\\'opez model, we describe the model of smooth and regular source forming a gravitating and relativistically rotating soliton based on the chiral field model and the Higgs mechanism of broken symmetry. The model reveals some new remarkable properties: 1) the soliton forms a relativistically rotating bubble of the Compton radius, which is filled by the oscillating Higgs field in pseudo-vacuum state, 2) boundary of the ...
Neutral test particle orbits in the Kerr--Newman spacetime
Pugliese, Daniela; Ruffini, Remo
2013-01-01
We present a detailed analysis of the orbital circular motion of electrically neutral test particles on the equatorial plane of the Kerr-Newman spacetime. Many details of the motion in the cases of black hole and naked singularity sources are pointed out. We identify four different types of orbital regions, which depend on the properties of the orbital angular momentum, and define four different kinds of naked singularities, according to the values of the charge-to-mass ratio of the source. It is shown that the presence of a particular type of counter-rotating test particles is sufficient to uniquely identify naked singularities. It is pointed out that the structure of the stability regions can be used to differentiate between black holes and naked singularities.
Periodic solutions of fully nonlinear autonomous equations of Benjamin-Ono type
Baldi, Pietro
2012-01-01
We prove the existence of time-periodic, small amplitude solutions of autonomous quasilinear or fully nonlinear completely resonant pseudo-PDEs of Benjamin-Ono type in Sobolev class. The result holds for frequencies in a Cantor set that has asymptotically full measure as the amplitude goes to zero. At the first order of amplitude, the solutions are the superposition of an arbitrarily large number of waves that travel with different velocities (multimodal solutions). The equation can be considered as a Hamiltonian, reversible system plus a non-Hamiltonian (but still reversible) perturbation that contains derivatives of the highest order. The main difficulties of the problem are: an infinite-dimensional bifurcation equation, and small divisors in the linearized operator, where also the highest order derivatives have nonconstant coefficients. The main technical step of the proof is the reduction of the linearized operator to constant coefficients up to a regularizing rest, by means of changes of variables and co...
Yokoyama, Kazuto; Takahashi, Masaki
2015-02-01
A dynamics-based non-linear controller with energy shaping to accelerate a pendulum-type mobility is proposed. The concept of this study is to control translational acceleration of the vehicle in a dynamically reasonable manner. The body angle is controlled to maintain a reference state where the vehicle is statically unstable but dynamically stable, which leads to a constant translational acceleration due to instability of the system. The accelerating motion is like a sprinter moving from crouch start and it fully exploits dynamics of the vehicle. To achieve it, the total energy of the system is shaped to have the minimum at a given reference state and the system is controlled to converge to it. The controller can achieve various properties through the energy shaping procedure. Especially, an energy function that will lead to safe operation of the vehicle is proposed. The effectiveness of the controller is verified in simulations and experiments.
An implicit meshless scheme for the solution of transient non-linear Poisson-type equations
Bourantas, Georgios
2013-07-01
A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.
A kinetic formulation of piezoresistance in N-type silicon: Application to non-linear effects
Charbonnieras, A. R.; Tellier, C. R.
1999-07-01
This paper is devoted to the theoretical study of the influence of the temperature and of the doping on the piezoresistance of N-type silicon. In the first step the fractional change in the resistivity caused by stresses is calculated in the framework of a multivalley model using a kinetic transport formulation based on the Boltzmann transport equation. In the second step shifts in the minima of the conduction band and the resulting shift of the Fermi level are expressed in terms of deformation potentials and of stresses. General expressions for the fundamental linear, π_{11} and π_{12}, and non-linear, π_{111}, π_{112}, π_{122} and π_{123}, piezoresistance coefficients are then derived. Plots of the non-linear piezoresistance coefficients against the reduced shift of the Fermi level or against temperature allow us to characterize the influence of doping and temperature. Finally some attempts are made to estimate the non-linearity for heavily doped semiconductor gauges. Cette publication est consacrée à l'étude théorique de l'influence de la température et du dopage sur la piezorésistivité du silicium type N. Dans une première étape nous adoptons le modèle de vallées et nous utilisons une formulation cinétique du transport électronique faisant appel à l'équation de transport de Boltzmann pour calculer la variation de la résistivité du semiconducteur sous contrainte. Dans la deuxième étape nous exprimons les déplacements des minima de la bande de conduction et du niveau de Fermi en termes de potentiels de déformation et de contraintes. Nous proposons ensuite des expressions générales pour les coefficients piezorésistifs fondamentaux linéaires, π_{11} et π_{12}, et non-linéaires, π_{111}, π_{112}, π_{122} et π_{123}. Des représentations graphiques des variations des coefficients non-linéaires permettent de caractériser l'influence du dopage et de la température. Enfin nous fournissons une première pré-estimation des effets
Computational study on Kerr constants of neutral and ionized gases
Sato, M.; Kumada, A.; Hidaka, K.
2015-08-01
In order to quantitatively examine the measurement capability of Poisson's field using electro-optic Kerr-effect (EOKE), Kerr constants of neutral molecules and ions are examined by means of first principle calculations. We have systematically computed Kerr constants of neutral molecules and ions of several molecular symmetry groups, with consistent theory level and basis sets. Computed Kerr constants of neutral molecules (N2, CO2, SF6, and CF3I) ranging across two orders of magnitudes are within 50% error of the experimental values, which are comparable to the scattering between experimental values itself. The results show that SF6 has smaller Kerr constant due to its high molecular symmetry compared to those of N2 and CO2. In contrast, CF3I has large Kerr constant due to its permanent dipole. Computed Kerr constants for anions are larger by two orders of magnitude than those of neutral molecules, probably due to the shielding effect. For cations, the opposite holds true; however, due to anisotropic polarizability, computed Kerr constants for some cations are comparable to neutral molecules, while others show smaller values. The ratio of Kerr constants of ions to those of neutral molecules are at most 102; EOKE is valid for measuring electric field in weakly ionized gas whose ionization degree is smaller than 10-3.
A matrix method for quasinormal modes: Kerr and Kerr-Sen black holes
Lin, Kai; Qian, Wei-Liang; Pavan, Alan B.; Abdalla, Elcio
2017-08-01
In this paper, a matrix method is employed to study the scalar quasinormal modes of Kerr as well as Kerr-Sen black holes. Discretization is applied to transfer the scalar perturbation equation into a matrix form eigenvalue problem, where the resulting radial and angular equations are derived by the method of separation of variables. The eigenvalues, quasinormal frequencies ω and angular quantum numbers λ, are then obtained by numerically solving the resultant homogeneous matrix equation. This work shows that the present approach is an accurate, as well as efficient method for investigating quasinormal modes.
Gaur, Poonam; Sharma, Dimple; Singh, Nageshwar; Malik, B P; Gaur, Arun
2012-11-01
A systematic investigation on nonlinear optical properties such as three photon absorption (3PA) wavelength dependent of Kerr type nonlinear refraction in direct and indirect band gap crystals has been reported in the present work. The Z-scan measurements are recorded for both ZnO and CdI(2) with femtosecond laser pulses while the wavelength dependent of the Kerr nonlinearity are in agreement with a two band model. The wavelength dependence of the 3PA is determined by [(3E(photon)/E(g))-1](5/2)[(3E(photon)/E(g))](-9) in the case of direct band gap crystal and [(3E(photon)±ℏΩ/E(g))-1](5/2)[(3E(photon)±ℏΩ/E(g))](-9) in the case of indirect band gap crystal. In the present investigation the value of 3PA in the case of indirect band gap crystal is lower than the direct band gap crystal which is due to the phonon assisted transition. The materials of large band gap with optical nonlinearity and fast response speed should be dominating factor for further photonic devices such as optical limiters, optical switches and optical modulators. The higher order nonlinear optical effects have also been determined in the present study. Copyright © 2012 Elsevier B.V. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Chen Yong E-mail: chenyong@dlut.edu.cn; Li Biao E-mail: libiao@dlut.edu.cn
2004-03-01
Applying the improved generalized method, which is a direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear partial differential equations and implemented in a computer algebraic system, we consider the KdV-type equations and KdV-Burgers-type equations with nonlinear terms of any order. As a result, we can not only successfully recover the previously known travelling wave solutions found by existing various tanh methods and other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions.
A low-phase-noise 18 GHz Kerr frequency microcomb phase-locked over 65 THz
Huang, S -W; Zhou, H; Yu, M; Kwong, D -L; Wong, C W
2015-01-01
Laser frequency combs are coherent light sources that simultaneously provide pristine frequency spacings for precision metrology and the fundamental basis for ultrafast and attosecond sciences. Recently, nonlinear parametric conversion in high-Q microresonators has been suggested as an alternative platform for optical frequency combs, though almost all in 100 GHz frequencies or more. Here we report a low-phase-noise on-chip Kerr frequency comb with mode spacing compatible with high-speed silicon optoelectronics. The waveguide cross-section of the silicon nitride spiral resonator is designed to possess small and flattened group velocity dispersion, so that the Kerr frequency comb contains a record-high number of 3,600 phase-locked comb lines. We study the single-sideband phase noise as well as the long-term frequency stability and report the lowest phase noise floor achieved to date with -130 dBc/Hz at 1 MHz offset for the 18 GHz Kerr comb oscillator, along with feedback stabilization to achieve frequency Alla...
Nonlinear plasmonic amplification via dissipative soliplasmons
Ferrando, Albert
2016-01-01
In this contribution we introduce a new strategy for the compensation of plasmonic losses based on a recently proposed nonlinear mechanism: the resonant interaction between surface plasmon polaritons and spatial solitons propagating in parallel along a metal/dielectric/Kerr structure. This mechanism naturally leads to the generation of a quasi-particle excitation, the so-called soliplasmon resonance. We analyze the role played by the effective nonlinear coupling inherent to this system and how this can be used to provide a new mechanism of quasi-resonant nonlinear excitation of surface plasmon polaritons. We will pay particular attention to the introduction of asymmetric linear gain in the Kerr medium. The unique combination of nonlinear propagation, nonlinear coupling and gain give rise to a new scenario for the excitation of long- range surface plasmon polaritons with distinguishing characteristics. The connection between plasmonic losses and soliplasmon resonances in the presence of gain will be discussed.
Dynamics of self-focusing and self-phase modulation of elliptic Gaussian laser beam in a Kerr-medium
Indian Academy of Sciences (India)
Tarsem Singh; Nareshpal Singh Saini; Shyam Sunder Kaul
2000-09-01
Using a direct variational technique involving elliptic Gaussian laser beam trial function, the combined effect of non-linearity and diffraction on wave propagation of optical beam in a homogeneous bulk Kerr-medium is presented. Particular emphasis is put on the variation of beam width and longitudinal phase delay with the distance of propagation. It is observed that no stationary self-trapping is possible. The regularized phase is also seen to be always negative.
An analytic toy model for relativistic accretion in Kerr spacetime
Tejeda, Emilio; Miller, John C
2013-01-01
We present a relativistic model for the stationary axisymmetric accretion flow of a rotating cloud of non-interacting particles falling onto a Kerr black hole. Based on a ballistic approximation, streamlines are described analytically in terms of timelike geodesics, while a simple numerical scheme is introduced for calculating the density field. A novel approach is presented for describing all of the possible types of orbit by means of a single analytic expression. This model is a useful tool for highlighting purely relativistic signatures in the accretion flow dynamics coming from a strong gravitational field with frame-dragging. In particular, we explore the coupling due to this between the spin of the black hole and the angular momentum of the infalling matter. Moreover, we demonstrate how this analytic solution may be used for benchmarking general relativistic numerical hydrodynamics codes by comparing it against results of smoothed particle hydrodynamics simulations for a collapsar-like setup. These simu...
Chembo, Yanne K.; Menyuk, Curtis R.
2013-05-01
We demonstrate that frequency (Kerr) comb generation in whispering-gallery-mode resonators can be modeled by a variant of the Lugiato-Lefever equation that includes higher-order dispersion and nonlinearity. This spatiotemporal model allows us to explore pulse formation in which a large number of modes interact cooperatively. Pulse formation is shown to play a critical role in comb generation, and we find conditions under which single pulses (dissipative solitons) and multiple pulses (rolls) form. We show that a broadband comb is the spectral signature of a dissipative soliton, and we also show that these solitons can be obtained by using a weak anomalous dispersion and subcritical pumping.
Generation of Kerr non-Gaussian motional states of trapped ions
Stobińska, Magdalena; Leuchs, Gerd
2010-01-01
Non-Gaussian states represent a powerful resource for quantum information protocols in the continuous variables regime. Cat states, in particular, have been produced in the motional degree of freedom of trapped ions by controlled displacements dependent on the ionic internal state. An alternative method harnesses the Kerr nonlinearity naturally existent in this kind of system. We present detailed calculations confirming its feasibility for typical experimental conditions. Additionally, this method permits the generation of complex non-Gaussian states with negative Wigner functions. Especially, superpositions of many coherent states are achieved at a fraction of the time necessary to produce the cat state.
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
Lin Xiao-Gang; Liu Wen-Jun; Lei Ming
2016-03-01
Oscillating solitons are obtained in nonlinear optics. Analytical study of the variable coefficient nonlinear Schrödinger equation, which is used to describe the soliton propagation in those systems, is carried out using the Hirota’s bilinear method. The bilinear forms and analytic soliton solutions are derived, and the relevant properties and features of oscillating solitons are illustrated. Oscillating solitons are controlled by the reciprocal of the group velocity and Kerr nonlinearity. Results of this paper will be valuable to the study of dispersion-managed optical communication system and mode-locked fibre lasers.
Nonpoint Symmetry and Reduction of Nonlinear Evolution and Wave Type Equations
Directory of Open Access Journals (Sweden)
Ivan Tsyfra
2015-01-01
Full Text Available We study the symmetry reduction of nonlinear partial differential equations with two independent variables. We propose new ansätze reducing nonlinear evolution equations to system of ordinary differential equations. The ansätze are constructed by using operators of nonpoint classical and conditional symmetry. Then we find solution to nonlinear heat equation which cannot be obtained in the framework of the classical Lie approach. By using operators of Lie-Bäcklund symmetries we construct the solutions of nonlinear hyperbolic equations depending on arbitrary smooth function of one variable too.
Femtosecond filamentation in air and higher-order nonlinearities
Kolesik, M; Moloney, J V
2010-01-01
According to a recent experiment, the instantaneous electronic Kerr effect in air exhibits a strong intensity dependence, the nonlinear refractive index switching sign and crossing over from a self-focusing to a de-focusing nonlinearity. A subsequent theoretical work has demonstrated that this has paradigm-changing consequences for the understanding of filamentation in air, so it is important to subject the idea of higher-order nonlinearities to stringent tests. Here we use numerical modeling to propose an experiment capable of discriminating between the standard and the new intensity-dependent Kerr-effect models.
DEFF Research Database (Denmark)
Boiroux, Dimitri; Hagdrup, Morten; Mahmoudi, Zeinab
2016-01-01
This paper presents a novel ensemble nonlinear model predictive control (NMPC) algorithm for glucose regulation in type 1 diabetes. In this approach, we consider a number of scenarios describing different uncertainties, for instance meals or metabolic variations. We simulate a population of 9 pat...
Dynamics of a movable micro-mirror in a nonlinear optical cavity
Kumar, Tarun; ManMohan,
2009-01-01
We consider the dynamics of a movable mirror (cantilever) of a nonlinear optical cavity. We show that a $\\chi^{(3)}$ medium with a strong Kerr nonlinearity placed inside a cavity inhibits the normal mode splitting (NMS) due to the photon blockade mechanism. This study demonstrates that NMS could be used as a tool to observe the photon blockade effect. We also found that the backaction cooling of the movable mirror is reduced in the presence of the Kerr medium.
Chirped Peregrine solitons in a class of cubic-quintic nonlinear Schrödinger equations
Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M.; Liu, Yi; Grelu, Philippe
2016-06-01
We shed light on the fundamental form of the Peregrine soliton as well as on its frequency chirping property by virtue of a pertinent cubic-quintic nonlinear Schrödinger equation. An exact generic Peregrine soliton solution is obtained via a simple gauge transformation, which unifies the recently-most-studied fundamental rogue-wave species. We discover that this type of Peregrine soliton, viable for both the focusing and defocusing Kerr nonlinearities, could exhibit an extra doubly localized chirp while keeping the characteristic intensity features of the original Peregrine soliton, hence the term chirped Peregrine soliton. The existence of chirped Peregrine solitons in a self-defocusing nonlinear medium may be attributed to the presence of self-steepening effect when the latter is not balanced out by the third-order dispersion. We numerically confirm the robustness of such chirped Peregrine solitons in spite of the onset of modulation instability.
Anderson localization and saturable nonlinearity in one-dimensional disordered lattices
Nguyen, Ba Phi
2016-01-01
We investigate numerically the propagation and the Anderson localization of plane waves in a one-dimensional lattice chain, where disorder and saturable nonlinearity are simultaneously present. Using a calculation scheme for solving the stationary discrete nonlinear Schr\\"{o}dinger equation in the fixed input case, the disorder-averaged logarithmic transmittance and the localization length are calculated in a numerically precise manner. The localization length is found to be a nonmonotonic function of the incident wave intensity, acquiring a minimum value at a certain finite intensity, due to saturation effects. For low incident intensities where the saturation effect is ineffective, the enhancement of localization due to Kerr-type nonlinearity occurs in a way similar to the case without saturation. For sufficiently high incident intensities, we find that the localization length is an increasing function of the incident wave intensity, which implies that localization is suppressed for stronger input intensiti...
The extended Kerr-Schild approach to general relativity
Wang, Xun
2016-01-01
We study in some detail the "extended Kerr-Schild" formulation of general relativity, which decomposes the gauge-independent degrees of freedom of a generic metric into two arbitrary functions and the choice of a flat background tetrad. We recast Einstein's equations and spacetime curvatures in the extended Kerr-Schild form and discuss their properties, illustrated with simple examples.
Transient Regime of Kerr Frequency Comb Formation
Savchenkov, Anatoliy A; Liang, Wei; Ilchenko, Vladimir S; Seidel, David; Maleki, Lute
2011-01-01
Temporal growth of an optical Kerr frequency comb generated in a microresonator is studied both experimentally and numerically. We find that the comb emerges from vacuum fluctuations of the electromagnetic field on timescales significantly exceeding the ringdown time of the resonator modes. The frequency harmonics of the comb spread starting from the optically pumped mode if the microresonator is characterized with anomalous group velocity dispersion. The harmonics have different growth rates resulting from sequential four-wave mixing process that explains intrinsic modelocking of the comb.
Rotating Black Holes and the Kerr Metric
Kerr, Roy Patrick
2008-10-01
Since it was first discovered in 1963 the Kerr metric has been used by relativists as a test-bed for conjectures on worm-holes, time travel, closed time-like loops, and the existence or otherwise of global Cauchy surfaces. More importantly, it has also used by astrophysicists to investigate the effects of collapsed objects on their local environments. These two groups of applications should not be confused. Astrophysical Black Holes are not the same as the Kruskal solution and its generalisations.
The geometry of Kerr black holes
O'Neill, Barrett
2014-01-01
This unique monograph by a noted UCLA professor examines in detail the mathematics of Kerr black holes, which possess the properties of mass and angular momentum but carry no electrical charge. Suitable for advanced undergraduates and graduate students of mathematics, physics, and astronomy as well as professional physicists, the self-contained treatment constitutes an introduction to modern techniques in differential geometry. The text begins with a substantial chapter offering background on the mathematics needed for the rest of the book. Subsequent chapters emphasize physical interpretation
High-order tail in Kerr spacetime
Casals, Marc; Ottewill, Adrian C
2016-01-01
We investigate the late-time tail of the retarded Green function for the dynamics of a linear field perturbation of Kerr spacetime. We develop an analytical formalism for obtaining the late-time tail up to arbitrary order for general integer spin of the field. We then apply this formalism to obtain the details of the first five orders in the late-time tail of the Green function for the case of a scalar field: to leading order we recover the known power law tail $t^{-2\\ell-3}$, and at third order we obtain a logarithmic correction, $t^{-2\\ell-5}\\ln t$, where $\\ell$ is the field multipole.
Hidden Kerr/CFT at finite frequencies
Lowe, David A; Skanata, Antun
2013-01-01
Massless fields propagating in a generic Kerr black hole background enjoy a hidden SL(2,R)xSL(2,R) symmetry. We determine how the exact mode functions decompose into representations of this symmetry group. This extends earlier results on the low frequency limit of the massless scalar case to finite frequencies and general spin. As an application, we numerically determine the parameters of the representations that appear in quasinormal modes. These results represent a first step to formulating a more precise mapping to a holographic dual conformal field theory for generic black holes.
Shadows of Kerr black holes with and without scalar hair
Cunha, Pedro V P; Radu, Eugen; Runarsson, Helgi F
2016-01-01
For an observer, the Black Hole (BH) shadow is the BH's apparent image in the sky due to the gravitational lensing of nearby radiation, emitted by an external source. A recent class of solutions dubbed Kerr BHs with scalar hair possess smaller shadows than the corresponding Kerr BHs and, under some conditions, novel exotic shadow shapes can arise. Thus, these hairy BHs could potentially provide new shadow templates for future experiments such as the Event Horizon Telescope. In order to obtain the shadows, the backward ray-tracing algorithm is briefly introduced, followed by numerical examples of shadows of Kerr BHs with scalar hair contrasting with the Kerr analogues. Additionally, an analytical solution for the Kerr shadow is derived in closed form for a ZAMO observer at an arbitrary position.
Evolution of Kerr superspinars due to accretion counterrotating thin discs
Energy Technology Data Exchange (ETDEWEB)
StuchlIk, Zdenek; HledIk, Stanislav; Truparova, Kamila, E-mail: zdenek.stuchlik@fpf.slu.cz, E-mail: stanislav.hledik@fpf.slu.cz [Faculty of Philosophy and Science, Institute of Physics, Silesian University in Opava, Bezrucovo nam. 13, CZ-74601 Opava (Czech Republic)
2011-08-07
String theory predicts the existence of extremely compact objects spinning faster than Kerr black holes. The spacetime exterior to such superspinars is described by Kerr naked singularity geometry breaking the black-hole limit on the internal angular momentum. We demonstrate that the conversion of Kerr superspinars into a near-extreme black hole due to an accretion counterrotating Keplerian disc is much more effective in comparison with the case of a corotating one since both the accreted rest mass necessary for conversion and the evolution time of conversion are by orders smaller for counterrotating discs. The conversion time of Kerr superspinars is given for several accretion regimes, and it is shown that the self-regulated accretion flow implies fastest evolution to the black-hole state. In the final stages of the conversion, Kerr superspinars can serve as very efficient particle accelerators in the region where the black-hole horizon forms.
Shadows of Kerr black holes with and without scalar hair
Cunha, Pedro V. P.; Herdeiro, Carlos A. R.; Radu, Eugen; Rúnarsson, Helgi F.
2016-06-01
For an observer, the Black Hole (BH) shadow is the BHs apparent image in the sky due to the gravitational lensing of nearby radiation, emitted by an external source. A recent class of solutions dubbed Kerr BHs with scalar hair possess smaller shadows than the corresponding Kerr BHs and, under some conditions, novel exotic shadow shapes can arise. Thus, these hairy BHs could potentially provide new shadow templates for future experiments such as the Event Horizon Telescope. In order to obtain the shadows, the backward ray-tracing algorithm is briefly introduced, followed by numerical examples of shadows of Kerr BHs with scalar hair contrasting with the Kerr analogues. Additionally, an analytical solution for the Kerr shadow is derived in closed form for a ZAMO observer at an arbitrary position.
Xu, Tian; Chen, Guo Chong; Zhai, Lin; Ke, Kai Fu
2015-07-01
Observational studies between magnesium int- ake and risk of type 2 diabetes yielded inconsistent results. We conducted a system literature search of PubMed database through March 2015 for prospective cohort studies of magnesium intake and type 2 diabetes risk. Study-specific results were pooled in a random-effects model. Subgroup and sensitivity analysis were performed to assess the potential sources of heterogeneity and the robustness of the pooled estimation. Generalized least squares trend estimation was used to investigate the dose-response relationship. A total of 15 papers with 19 analyses were identified with 539,735 participants and 25,252 incident diabetes cases. Magnesium intake was associated with a significant lower risk of type 2 diabetes (RR: 0.77; 95% CI: 0.71-0.82) for the highest compared with lowest category. This association was not significantly modified by the pre-specified study characteristics. In the dose-response analysis, a magnesium intake increment of 100 mg/day was associated with a 16% reduction in type 2 diabetes risk (RR: 0.84; 95% CI: 0.80-0.88). A nonlinear relationship existed between magnesium intake and type 2 diabetes (P-nonlinearity=0.003). This meta-analysis further verified a protective effect of magnesium intake on type 2 diabetes in a nonlinear dose-response manner.
Phantom expansion with non-linear Schr\\"{o}dinger-type formulation of scalar field cosmology
Phetnora, Theerakarn; Gumjudpai, Burin
2008-01-01
We describe non-flat standard Friedmann cosmology of canonical scalar field with barotropic fluid in form of non-linear Schr\\"{o}dinger-type (NLS) formulation in which all cosmological dynamical quantities are expressed in term of Schr\\"{o}dinger quantities as similar to those in time-independent quantum mechanics. We assume the expansion to be superfast, i.e. phantom expansion. We report all Schr\\"{o}dinger-analogous quantities to scalar field cosmology. Effective equation of state coefficient is analyzed and illustrated. We show that in a non-flat universe, there is no fixed $w_{\\rm eff}$ value for the phantom divide. In a non-flat universe, even $w_{\\rm eff} > -1$, the expansion can be phantom. Moreover, in open universe, phantom expansion can happen even with $w_{\\rm eff} > 0$. We also report scalar field exact solutions within frameworks of the Friedmann formulation and the NLS formulation in non-flat universe cases.
Survey of non-linear hydrodynamic models of type-II Cepheids
Smolec, R
2015-01-01
We present a grid on non-linear convective type-II Cepheid models. The dense model grids are computed for 0.6M_Sun and a range of metallicities ([Fe/H]=-2.0,-1.5,-1.0), and for 0.8M_Sun ([Fe/H]=-1.5). Two sets of convective parameters are considered. The models cover the full temperature extent of the classical instability strip, but are limited in luminosity; for the most luminous models violent pulsation leads to the decoupling of the outermost model shell. Hence, our survey reaches only the shortest period RV Tau domain. In the Hertzsprung-Russel diagram we detect two domains in which period doubled pulsation is possible. The first extends through the BL Her domain and low luminosity W Vir domain (pulsation periods ~2-6.5 d). The second domain extends at higher luminosities (W Vir domain; periods >9.5d). Some models within these domains display period-4 pulsation. We also detect very narrow domains (~10 K wide) in which modulation of pulsation is possible. Another interesting phenomenon we detect is double...
Solitons in nonlocal nonlinear media: Exact solutions
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole
2001-01-01
We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties...
The harmonic structure of generic Kerr orbits
Grossman, Rebecca; Perez-Giz, Gabe
2011-01-01
Generic Kerr orbits exhibit intricate three-dimensional motion. We offer a classification scheme for these intricate orbits in terms of periodic orbits. The crucial insight is that for a given effective angular momentum $L$ and angle of inclination $\\iota$, there exists a discrete set of orbits that are geometrically $n$-leaf clovers in a precessing {\\it orbital plane}. When viewed in the full three dimensions, these orbits are periodic in $r-\\theta$. Each $n$-leaf clover is associated with a rational number, $1+q_{r\\theta}=\\omega_\\theta/\\omega_r$, that measures the degree of perihelion precession in the precessing orbital plane. The rational number $q_{r\\theta}$ varies monotonically with the orbital energy and with the orbital eccentricity. Since any bound orbit can be approximated as near one of these periodic $n$-leaf clovers, this special set offers a skeleton that illuminates the structure of all bound Kerr orbits, in or out of the equatorial plane.
Quantum cascade laser Kerr frequency comb
Lecaplain, Caroline; Lucas, Erwan; Jost, John D; Kippenberg, Tobias J
2015-01-01
The mid-infrared (mid-IR) regime (typically the wavelength regime of $\\lambda \\sim 2.5-20 \\ \\mathrm{\\mu m}$) is an important spectral range for spectroscopy as many molecules have their fundamental rotational-vibrational absorption in this band. Recently optical frequency combs based on optical microresonators ("Kerr" combs) at the onset of the mid-IR region have been generated using crystalline resonators and integrated planar silicon micro-resonators. Here we extend for the first time Kerr combs deep into the mid-IR i.e. the 'molecular fingerprint' region. This is achieved by combining an ultra high quality (Q) factor mid-IR microresonator based on crystalline $\\mathrm{MgF_{2}}$ with the quantum cascade laser (QCL) technology. Using a tapered chalgogenide (ChG) fiber and a QCL continuous wave pump laser, frequency combs at $\\lambda\\sim 4.4\\ \\mathrm{\\mu m}$ (i.e. 2270cm$^{-1}$) are generated, that span over 600nm (i.e. 300cm$^{-1}$) in bandwidth, with a mode spacing of 14.3GHz (0.5cm$^{-1}$), corresponding t...
Black Ring and Kerr Ellipsoid - Solitonic Configurations in Modified Finsler Gravity
Rajpoot, Subhash
2015-01-01
We study an effective Einstein-Finsler theory on tangent Lorentz bundle constructed as a "minimal" extension of general relativity. Black ring and Kerr like ellipsoid exact solutions and soliton configurations are presented. In this endeavor the relevant metric depends not only on four dimensional spacetime coordinates and also on velocity type variables that can be interpreted as additional coordinates in the space of "extra dimensions".
Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime
Shlapentokh-Rothman, Yakov
2013-01-01
We give a quantitative refinement and simple proofs of mode stability type statements for the wave equation on Kerr backgrounds in the full sub-extremal range (|a| < M). As an application, we are able to quantitatively control the energy flux along the horizon and null infinity and establish integrated local energy decay for solutions to the wave equation in any bounded-frequency regime.
Gravitational Waves from a Pseudo-Newtonian Kerr Field with Halos
Institute of Scientific and Technical Information of China (English)
王颖; 伍歆
2011-01-01
A close relation between gravitational waveforms and the types of trajectories in a superposed field between a pseudo-Newtonian Kerr black hole and quadrupolar halos is shown in detail The gravitational waveforms emitted from circular, KAM tori and chaotic orbits must be periodic, quasiperiodic and stochastic, respectively. The chaotic motion can maximally enhance both the amplitudes and the energy emission rates of the waves.
Directory of Open Access Journals (Sweden)
Jong-Yun Yoon
2015-08-01
Full Text Available Torsional systems with gear pairs such as the gearbox of wind turbines or vehicle driveline systems inherently show impact phenomena due to clearance-type nonlinearities when the system experiences sinusoidal excitation. This research investigates the vibro-impact energy of unloaded gears in geared systems using the harmonic balance method (HBM in both the frequency and time domains. To achieve accurate simulations, nonlinear models with piecewise and clearance-type nonlinearities and drag torques are defined and implemented in the HBM. Next, the nonlinear frequency responses are examined by focusing on the resonance areas where the impact phenomena occur, along with variations in key parameters such as clutch stiffness, drag torque, and inertias of the flywheel and the unloaded gear. Finally, the effects of the parameters on the vibro-impacts at a specific excitation frequency are explained using bifurcation diagrams. The results are correlated with prior research by defining the gear rattle criteria with key parameters. This article suggests a method to simulate the impact phenomena in torsional systems using the HBM and successfully assesses vibro-impact energy using bifurcation diagrams.
X-ray spectropolarimetric measurements of the Kerr metric
Liu, Dan; Cheng, Yifan; Bambi, Cosimo
2015-01-01
It is thought that the spacetime geometry around black hole candidates is described by the Kerr solution, but an observational confirmation is still missing. Today, the continuum-fitting method and the analysis of the iron K$\\alpha$ line cannot unambiguously test the Kerr paradigm because of the degeneracy among the parameters of the system, in the sense that it is impossible with current X-ray data to distinguish a Kerr black hole from a non-Kerr object with different spin and observed from a different viewing angle. In this paper, we study the possibility of testing the Kerr nature of black hole candidates with X-ray spectropolarimetric measurements. As a preliminary study, we employ a model with some simplifications, but our conclusions can unlikely change with a more sophisticated description. We find that -- even in the case of high quality data -- it is impossible to test the Kerr metric and the problem is still the strong correlation between the spin and possible deviations from the Kerr geometry. The ...
Modulational instability in nonlocal Kerr media with sine-oscillatory response
Wang, Zhuo; Hong, Weiyi; Hu, Wei
2016-01-01
We discuss the modulational instability (MI) of plane waves in nonlocal Kerr media with the sine-oscillation response function, which can model the nematic liquid crystal with negative dielectric anisotropy. The results in the framework of the nonlocal nonlinear Schr\\"{o}dinger equation show that the MI in this system has two extraordinary properties. First, MI exists in both cases of negative Kerr coefficient $(n_{2}0)$. Second, the maximum gain of MI is not affected by the intensity of the plane wave, and the wave number %spatial frequency of the maximum gain depends on the oscillation period of the response function. We also explore, for the first time to the best of our knowledge, the physical mechanism of MI in the framework of the four-wave mixing (FWM). %FWM interaction. By introducing a phase mismatch term $\\triangle k$ and a (nonlinear) growth factor $\\gamma$ (both of them have clear physical meanings), we find that the necessary and sufficient condition for the MI appearance is that the phase mismat...
Survey of non-linear hydrodynamic models of type-II Cepheids
Smolec, R.
2016-03-01
We present a grid of non-linear convective type-II Cepheid models. The dense model grids are computed for 0.6 M⊙ and a range of metallicities ([Fe/H] = -2.0, -1.5, -1.0), and for 0.8 M⊙ ([Fe/H] = -1.5). Two sets of convective parameters are considered. The models cover the full temperature extent of the classical instability strip, but are limited in luminosity; for the most luminous models, violent pulsation leads to the decoupling of the outermost model shell. Hence, our survey reaches only the shortest period RV Tau domain. In the Hertzsprung-Russell diagram, we detect two domains in which period-doubled pulsation is possible. The first extends through the BL Her domain and low-luminosity W Vir domain (pulsation periods ˜2-6.5 d). The second domain extends at higher luminosities (W Vir domain; periods >9.5 d). Some models within these domains display period-4 pulsation. We also detect very narrow domains (˜10 K wide) in which modulation of pulsation is possible. Another interesting phenomenon we detect is double-mode pulsation in the fundamental mode and in the fourth radial overtone. Fourth overtone is a surface mode, trapped in the outer model layers. Single-mode pulsation in the fourth overtone is also possible on the hot side of the classical instability strip. The origin of the above phenomena is discussed. In particular, the role of resonances in driving different pulsation dynamics as well as in shaping the morphology of the radius variation curves is analysed.
Nonlinear decline-rate dependence and intrinsic variation of typeIa supernova luminosities
Energy Technology Data Exchange (ETDEWEB)
Wang, Lifan; Strovink, Mark; Conley, Alexander; Goldhaber,Gerson; Kowalski, Marek; Perlmutter, Saul; Siegrist, James
2005-12-14
Published B and V fluxes from nearby Type Ia supernova are fitted to light-curve templates with 4-6 adjustable parameters. Separately, B magnitudes from the same sample are fitted to a linear dependence on B-V color within a post-maximum time window prescribed by the CMAGIC method. These fits yield two independent SN magnitude estimates B{sub max} and B{sub BV}. Their difference varies systematically with decline rate {Delta}m{sub 15} in a form that is compatible with a bilinear but not a linear dependence; a nonlinear form likely describes the decline-rate dependence of B{sub max} itself. A Hubble fit to the average of B{sub max} and B{sub BV} requires a systematic correction for observed B-V color that can be described by a linear coefficient R = 2.59 {+-} 0.24, well below the coefficient R{sub B} {approx} 4.1 commonly used to characterize the effects of Milky Way dust. At 99.9% confidence the data reject a simple model in which no color correction is required for SNe that are clustered at the blue end of their observed color distribution. After systematic corrections are performed, B{sub max} and B{sub BV} exhibit mutual rms intrinsic variation equal to 0.074 {+-} 0.019 mag, of which at least an equal share likely belongs to B{sub BV}. SN magnitudes measured using maximum-luminosity or cmagic methods show comparable rms deviations of order {approx}0.14 mag from the Hubble line. The same fit also establishes a 95% confidence upper limit of 486 km s{sup -1} on the rms peculiar velocity of nearby SNe relative to the Hubble flow.
Dirac-Point Solitons in Nonlinear Optical Lattices
Xie, Kang; Boardman, Allan D; Guo, Qi; Shi, Zhiwei; Jiang, Haiming; Hu, Zhijia; Zhang, Wei; Mao, Qiuping; Hu, Lei; Yang, Tianyu; Wen, Fei; Wang, Erlei
2015-01-01
The discovery of a new type of solitons occuring in periodic systems without photonic bandgaps is reported. Solitons are nonlinear self-trapped wave packets. They have been extensively studied in many branches of physics. Solitons in periodic systems, which have become the mainstream of soliton research in the past decade, are localized states supported by photonic bandgaps. In this Letter, we report the discovery of a new type of solitons located at the Dirac point beyond photonic bandgaps. The Dirac point is a conical singularity of a photonic band structure where wave motion obeys the famous Dirac equation. These new solitons are sustained by the Dirac point rather than photonic bandgaps, thus provides a sort of advance in conceptual understanding over the traditional gap solitons. Apart from their theoretical impact within soliton theory, they have many potential uses because such solitons have dramatic stability characteristics and are possible in both Kerr material and photorefractive crystals that poss...
Collinear, two-color optical Kerr effect shutter for ultrafast time-resolved imaging
Purwar, Harsh; Rozé, Claude; Sedarsky, David; Blaisot, Jean-Bernard
2015-01-01
Imaging with ultrashort exposure times is generally achieved with a crossed-beam geometry. In the usual arrangement, an off-axis gating pulse induces birefringence in a medium exhibiting a strong Kerr response (commonly carbon disulfide) which is followed by a polarizer aligned to fully attenuate the on-axis imaging beam. By properly timing the gate pulse, imaging light experiences a polarization change allowing time-dependent transmission through the polarizer to form an ultrashort image. The crossed-beam system is effective in generating short gate times, however, signal transmission through the system is complicated by the crossing angle of the gate and imaging beams. This work presents a robust ultrafast time-gated imaging scheme based on a combination of type-I frequency doubling and a collinear optical arrangement in carbon disulfide. We discuss spatial effects arising from crossed-beam Kerr gating, and examine the imaging spatial resolution and transmission timing affected by collinear activation of th...
Boundary conditions for Maxwell fields in Kerr-AdS spacetimes
Wang, Mengjie
2016-05-01
Perturbative methods are useful to study the interaction between black holes and test fields. The equation for a perturbation itself, however, is not complete to study such a composed system if we do not assign physically relevant boundary conditions. Recently we have proposed a new type of boundary conditions for Maxwell fields in Kerr-anti-de Sitter (Kerr-AdS) spacetimes, from the viewpoint that the AdS boundary may be regarded as a perfectly reflecting mirror, in the sense that energy flux vanishes asymptotically. In this paper, we prove explicitly that a vanishing energy flux leads to a vanishing angular momentum flux. Thus, these boundary conditions may be dubbed as vanishing flux boundary conditions.
High resolution polar Kerr magnetometer for nanomagnetism and nanospintronics.
Cormier, M; Ferré, J; Mougin, A; Cromières, J-P; Klein, V
2008-03-01
A new high resolution polar magneto-optical (MO) Kerr magnetometer, devoted to the study of nanometer sized elements with perpendicular magnetic anisotropy, is described. The unique performances of this setup in terms of sensitivity (1.2x10(-15) emu), stability (lateral drift +/-35 nm over 3 h), and resolution (laser spot full width at half maximum down to 470 nm) are demonstrated, and illustrated by Kerr hysteresis loop measurements on a unique ultrathin magnetic nanodot, and over small segments of ultranarrow magnetic tracks. Large scanning MO Kerr microscopy images were also obtained with the same performances.
Multispectral Kerr frequency comb initiated by Faraday ripples
Huang, Shu-Wei
2016-01-01
In a uniform microresonator, the generation of a broadband Kerr frequency comb is triggered by Turing patterns. Here, we study a distinctly different route to initiate the Kerr frequency comb by Faraday ripples. Momentum conservation is ensured by azimuthal modulation of the cavity dispersion. With a good agreement with the theoretical analysis, we demonstrate a multispectral Kerr frequency comb covering telecommunication O, C, L, and 2 {\\mu}m bands. Comb coherence and absence of a subcomb offset are confirmed by cw heterodyne beat note and amplitude noise spectra measurements. The device can be used for achieving broadband optical frequency synthesizer and high-capacity coherent telecommunication.
Improved nonlinear plasmonic slot waveguide: a full study
Elsawy, Mahmoud M R; Chauvet, Mathieu; Renversez, Gilles
2016-01-01
We present a full study of an improved nonlinear plasmonic slot waveguides (NPSWs) in which buffer linear dielectric layers are added between the Kerr type nonlinear dielectric core and the two semi-infinite metal regions. For TM polarized waves, the inclusion of these supplementary layers have two consequences. First, they reduced the overall losses. Secondly, they modify the types of solutions that propagate in the NPSWs adding new profiles enlarging the possibilities offered by these nonlinear waveguides. Our structure also provides longer propagation length due to the decrease of the losses compared to the simple nonlinear slot waveguide and exhibits, for well-chosen refractive index or thickness of the buffer layer, a spatial transition of its main modes that can be controlled by the power. We provide a full phase diagram of the TM wave operating regimes of these improved NPSWs. The stability of the main TM modes is then demonstrated numerically using the FDTD. We also demonstrate the existence of TE wav...
Directory of Open Access Journals (Sweden)
Alsaedi Ahmed
2009-01-01
Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.
Magnetised accretion discs in Kerr spacetimes
Ranea-Sandoval, Ignacio F
2014-01-01
We study the effect caused by external magnetic fields on the observed thermal spectra and iron line profiles of thin accretion discs formed around Kerr black holes and naked singularities. We aim to provide a tool that can be used to estimate the presence of magnetic fields in the neighbourhood of a compact object and to probe the cosmic censorship conjecture in these particular astrophysical environments. We developed a numerical scheme able to calculate thermal spectra of magnetised Page-Thorne accretion discs formed around rotating black holes and naked singularities as seen by an arbitrary distant observer. We incorporated two different magnetic field configurations: uniform and dipolar, using a perturbative scheme in the coupling constant between matter and magnetic field strength. Under the same assumptions, we obtained observed synthetic line profiles of the 6.4 keV fluorescent iron line. We show that an external magnetic field produces potentially observable modifications on the thermal energy spectr...
Entropy Correction for Kerr Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; ZHANG Sheng-Li
2005-01-01
In this paper, we discuss leading-order corrections to the entropy of Kerr black hole due to thermal fluctuations in the finite cavity. Then temperature is constant, the solution of the black hole is obtained within a cavity, that is, the solution of the spacetime after considering the radiation of the black hole. Therefore, we derive that the location of the black hole horizon and specific heat are the functions of temperature and the radius of the cavity.Corrections to entropy also are related to the radius of the cavity. Through calculation, we obtain conditions of taking the value of the cavity's radius. We provide a new way for studying the corrections of complicated spacetimes.
Equatorial circular motion in Kerr spacetime
Pugliese, Daniela; Ruffini, Remo
2011-01-01
We analyze the properties of circular orbits of test particles on the equatorial plane of a rotating central mass whose gravitational field is described by the Kerr spacetime. For rotating black holes and naked singularities we explore all the spatial regions where circular orbits can exist and analyze the behavior of the energy and the angular momentum of the corresponding test particles. In particular, we find all the radii at which a test particle can have zero angular momentum due to the repulsive gravity effects generated by naked singularities. We classify all the stability zones of circular orbits. It is shown that the geometric structure of the stability zones of black holes is completely different from that of naked singularities.
Nonlinear optics quantum computing with circuit QED.
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.
Kato, Takumi; Chen-Jinnai, Akitoshi; Nagano, Takuma; Kobatake, Tomoya; Suzuki, Ryo; Yoshiki, Wataru; Tanabe, Takasumi
2016-07-01
A numerical and experimental study of Kerr frequency comb generation in a silica toroid microcavity is presented. We use a generalized mean-field Lugiato-Lefever equation and solve it with the split-step Fourier method. We observe that a stable mode-locked regime can be accessed when we reduce the input power after strong pumping due to the bistable nature of the nonlinear cavity system used. The experimental results agree well with the results of the numerical analysis, where we obtain a low-noise Kerr comb spectrum by gradually reducing the pumping input after strong pumping. This finding complements the results obtained by a previous wavelength scanning method and clarifies the procedure for achieving mode-locked states in such high-Q microcavity systems.
On the global stability of the wave-map equation in Kerr spaces with small angular momentum
Ionescu, A D
2014-01-01
This paper is motivated by the problem of the nonlinear stability of the Kerr solution for axially symmetric perturbations. We consider a model problem concerning the axially symmetric perturbations of a wave map $\\Phi$ defined from a fixed Kerr solution $\\KK(M,a)$, $0\\le a < M $, with values in the two dimensional hyperbolic space $\\HHH^2$. A particular such wave map is given by the complex Ernst potential associated to the axial Killing vectorfield $\\Z$ of $\\KK(M,a)$. We conjecture that this stationary solution is stable, under small axially symmetric perturbations, in the domain of outer communication (DOC) of $\\KK(M,a)$, for all $0\\le a
Optical nonlinearities in semiconductor-doped glasses near and below the band edge
Bindra, K. S.; Oak, S. M.; Rustagi, K. C.
1998-03-01
We present a brief review of our recent experimental results on optical nonlinearities in semiconductor-doped glasses. It is shown that even below the absorption edge the nonlinearities are determined by nonlinear absorption. The optical Kerr effect is found to have a susceptibility which is comparable to that for nonlinear refraction. We also find that in degenerate four-wave mixing the observed intensity dependence can be strongly influenced by nonlinear absorption.
A scalar hyperbolic equation with GR-type non-linearity
Khokhlov, A M
2003-01-01
We study a scalar hyperbolic partial differential equation with non-linear terms similar to those of the equations of general relativity. The equation has a number of non-trivial analytical solutions whose existence rely on a delicate balance between linear and non-linear terms. We formulate two classes of second-order accurate central-difference schemes, CFLN and MOL, for numerical integration of this equation. Solutions produced by the schemes converge to exact solutions at any fixed time $t$ when numerical resolution is increased. However, in certain cases integration becomes asymptotically unstable when $t$ is increased and resolution is kept fixed. This behavior is caused by subtle changes in the balance between linear and non-linear terms when the equation is discretized. Changes in the balance occur without violating second-order accuracy of discretization. We thus demonstrate that a second-order accuracy, althoug necessary for convergence at finite $t$, does not guarantee a correct asymptotic behavior...
AlGaAs-On-Insulator Nonlinear Photonics
Pu, Minhao; Semenova, Elizaveta; Yvind, Kresten
2015-01-01
The combination of nonlinear and integrated photonics has recently seen a surge with Kerr frequency comb generation in micro-resonators as the most significant achievement. Efficient nonlinear photonic chips have myriad applications including high speed optical signal processing, on-chip multi-wavelength lasers, metrology, molecular spectroscopy, and quantum information science. Aluminium gallium arsenide (AlGaAs) exhibits very high material nonlinearity and low nonlinear loss when operated below half its bandgap energy. However, difficulties in device processing and low device effective nonlinearity made Kerr frequency comb generation elusive. Here, we demonstrate AlGaAs-on-insulator as a nonlinear platform at telecom wavelengths. Using newly developed fabrication processes, we show high-quality-factor (Q>100,000) micro-resonators with integrated bus waveguides in a planar circuit where optical parametric oscillation is achieved with a record low threshold power of 3 mW and a frequency comb spanning 350 nm i...
Institute of Scientific and Technical Information of China (English)
鲁世平
2003-01-01
By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second-order Volterra functional differential equation was considered first. Then, by constructing the right-side layer function and the outer solution, a nonlinear boundary value problem subject to a kind of second- order Volterra functional differential equation with a small parameter was studied further. By using the differential mean value theorem and the technique of upper and lower solution, a new result on the existence of the solutions to the boundary value problem is obtained, and a uniformly valid asymptotic expansions of the solution is given as well.
Travelling Wave Solutions to a Special Type of Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
XU Gui-Qiong; LI Zhi-Bin
2003-01-01
A unified approach is presented for finding the travelling wave solutions to one kind of nonlinear evolution equation by introducing a concept of "rank". The key idea of this method is to make use of the arbitrariness of the manifold in Painleve analysis. We selected a new expansion variable and thus obtained a rich variety of travelling wave solutions to nonlinear evolution equation, which covered solitary wave solutions, periodic wave solutions, Weierstrass elliptic function solutions, and rational solutions. Three illustrative equations are investigated by this means, and abundant travelling wave solutions are obtained in a systematic way. In addition, some new solutions are firstly reported here.
Nonlinear optical properties of porphyrins compounds based on Cobalt and Zinc push-pull type
Chniti, Meherzia
2016-01-01
This study deals with the third-order nonlinear optical properties (NL) of tetraphenylporphyrins and some of its metallic derivatives (Zn, Co) dissolved in chlorobenzene. The solutions were exposed to a laser emitting at 1064 nm, 532 nm and 355 nm in the picosecond regime ( ≈ 10 ps) using D4σ-Z-scan method in a 4f setup and a new technique called Dark-Field Zscan. The latter provides to be very reliable for the direct determination of the nonlinear refractive signal in the presence of a stron...
The Quasinormal Modes of Weakly Charged Kerr-Newman Spacetimes
Mark, Zachary; Zimmerman, Aaron; Chen, Yanbei
2014-01-01
The resonant mode spectrum of the Kerr-Newman spacetime is presently unknown. These modes, called the quasinormal modes, play a central role in determining the stability of Kerr-Newman black holes and their response to perturbations. We present a new formalism, generalized from time-independent perturbation theory in quantum mechanics, for calculating the quasinormal mode frequencies of weakly charged Kerr-Newman spacetimes of arbitrary spin. Our method makes use of an original technique for applying perturbation theory to zeroth-order solutions that are not square- integrable, and it can be applied to other problems in theoretical physics. The new formalism reveals no unstable modes, which together with previous results in the slow-rotation limit strongly indicates the modal stability of the Kerr-Newman spacetime. Our techniques and results are of interest in the areas of holographic duality, foundational problems in General Relativity, and possibly in astrophysical systems.
Destroying Kerr-Sen black holes with test particles
Siahaan, Haryanto M
2015-01-01
By neglecting the self-force, self-energy, and radiative effects, it has been shown that an extremal or near-extremal Kerr-Newman black hole can turn to a naked singularity when it captures charged massive test particles with angular momentum. A straightforward question then arises, do charged and rotating black holes in string theory possess the same property? In this paper we adopt the Wald's gedanken experiment in an effort to destroy a Kerr-Newman black hole's horizon to the case of (near)-extremal Kerr-Sen black holes. We find that feeding a test particle into a (near)-extremal Kerr-Sen black hole could lead to a violation of the extremal bound for such black hole.
Gravitational Effects Near the Kerr-Newman Black Hole
Institute of Scientific and Technical Information of China (English)
王永久; 唐智明
2001-01-01
e have reached a solution of the Dirac equation and the energy spectrum of electrons in the gravitational field of the Kerr-Newman black hole. The results are interesting in astrophysics for observations of the black hole.
An Exact Expression for Photon Polarization in Kerr Geometry
Farooqui, Anusar; Panangaden, Prakash
2013-01-01
We analyze the transformation of the polarization of a photon propagating along an arbitrary null geodesic in Kerr geometry. The motivation comes from the problem of an observer trying to communicate quantum information to another observer in Kerr spacetime by transmitting polarized photons. It is essential that the observers understand the relationship between their frames of reference and also know how the photon's polarization transforms as it travels through Kerr spacetime. Existing methods to calculate the rotation of the photon polarization (Faraday rotation) depend on choices of coordinate systems, are algebraically complex and yield results only in the weak-field limit. We give a closed-form expression for a parallel propagated frame along an arbitrary null geodesic using Killing-Yano theory, and thereby solve the problem of parallel transport of the polarization vector in an intrinsic, geometrically-motivated fashion. The symmetries of Kerr geometry are utilized to obtain a remarkably compact express...
New schemes for manipulating quantum states using a Kerr cell
Genovèse, M
2000-01-01
In this proceeding we describe various proposals of application of an high coefficient Kerr cell to quantum states manipulation, ranging from fast modulation of quantum interference, GHZ states generation, Schroedinger cats creation, translucent eavesdropping, etc.
Spin precession of Dirac particles in Kerr geometry
Farooqui, Anusar
2017-01-01
We isolate and study the transformation of the intrinsic spin of Dirac particles as they propagate along timelike geodesics in Kerr geometry. Reference frames play a crucial role in the definition and measurement of the intrinsic spin of test particles. We show how observers located in the outer geometry of Kerr black holes may exploit the symmetries of the geometry to set up reference frames using purely geometric, locally-available information. Armed with these geometrically-defined reference frames, we obtain a closed-form expression for the geometrically-induced spin precession of Dirac particles in the outer geometry of Kerr black holes. We show that the spin of Dirac particles does not precess on the equatorial place of Kerr geometry; and hence, in Schwarzschild geometry.
Removal of Closed Timelike Curves in Kerr-Newman Spacetime
Kim, H
2002-01-01
A simple yet systematic new algorithm to investigate the global structure of Kerr-Newman spacetime is suggested. Namely, the global structure of \\theta=const. timelike submanifolds of Kerr-Newman metric are studied by introducing a new time coordinate slightly different from the usual Boyer-Lindquist time coordinate. In addition, it is demonstrated that the possible causality violation thus far regarded to occur near the ring singularity via the development of closed timelike curves there is not really an unavoidable pathology which has plagued the Kerr-Newman solution but simply a gauge (coordinate) artifact as it disappears upon transforming from Boyer-Lindquist to the new time coordinate. This last point appears to lend support to the fact that, indeed, the Kerr-Newman spacetime is a legitimate solution to represent the interior as well as the exterior regions of a rotating, charged black hole spacetime.
Constraining the Kerr parameters via X-ray reflection spectroscopy
Ghasemi-Nodehi, M
2016-01-01
In a recent paper [Ghasemi-Nodehi & Bambi, EPJC 76 (2016) 290], we have proposed a new parametrization for testing the Kerr nature of astrophysical black hole candidates. In the present work, we study the possibility of constraining the "Kerr parameters" of our proposal using X-ray reflection spectroscopy, the so-called iron line method. We simulate observations with the LAD instrument on board of the future eXTP mission assuming an exposure time of 200 ks. We fit the simulated data to see if the Kerr parameters can be constrained. If we have the correct astrophysical model, 200 ks observations with LAD/eXTP can constrain all the Kerr parameters with the exception of $b_{11}$, whose impact on the iron line profile is extremely weak and its measurement looks very challenging.
Directory of Open Access Journals (Sweden)
Weiguo Rui
2014-01-01
Full Text Available By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.
On the strength of the Kerr singularity and cosmic censorship
Rudnicki, W
2000-01-01
It has been suggested by Israel that the Kerr singularity cannot be strong in the sense of Tipler, for it tends to cause repulsive effects. We show here that, contrary to that suggestion, nearly all null geodesics reaching this singularity do in fact terminate in Tipler's strong curvature singularity. Implications of this result are discussed in the context of an earlier cosmic censorship theorem which constraints the occurrence of Kerr-like naked singularities in generic collapse situations.
Time-Periodic Einstein--Klein--Gordon Bifurcations of Kerr
Chodosh, Otis
2015-01-01
We construct one-parameter families of solutions to the Einstein--Klein--Gordon equations bifurcating off the Kerr solution such that the underlying family of spacetimes are each an asymptotically flat, stationary, axisymmetric, black hole spacetime, and such that the corresponding scalar fields are non-zero and time-periodic. An immediate corollary is that for these Klein--Gordon masses, the Kerr family is not asymptotically stable as a solution to the Einstein--Klein--Gordon equations.
On some fractional equations with convex-concave and logistic-type nonlinearities
Carboni, Giulia; Mugnai, Dimitri
2017-02-01
We consider existence and multiplicity results for a semilinear problem driven by the square root of the negative Laplacian in presence of a nonlinear term which is the difference of two powers. In the case of convex-concave powers, a precise description of the problem at the threshold value of a given parameter is established through variational methods and truncation techniques.
A variational model for fully non-linear water waves of Boussinesq type
Klopman, Gert; Dingemans, Maarten W.; Groesen, van Brenny; Grue, J.
2005-01-01
Using a variational principle and a parabolic approximation to the vertical structure of the velocity potential, the equations of motion for surface gravity waves over mildly sloping bathymetry are derived. No approximations are made concerning the non-linearity of the waves. The resulting model equ
A double optical solitary wave in a nonlinear Schr(o)dinger-type equation
Institute of Scientific and Technical Information of China (English)
Yin Jiu-Li; Ding Shan-Yu
2013-01-01
A qualitative analysis method to efficiently solve the shallow wave equations is improved,so that a more complicated nonlinear Schr(o)dinger equation can be considered.By using the detailed study,some quite strange optical solitary waves are obtained in which the bright and dark optical solitary waves are allowed to coexist.
Solitons and vortices in nonlinear two-dimensional photonic crystals of the Kronig-Penney type.
Mayteevarunyoo, Thawatchai; Malomed, Boris A; Roeksabutr, Athikom
2011-08-29
Solitons in the model of nonlinear photonic crystals with the transverse structure based on two-dimensional (2D) quadratic- or rhombic-shaped Kronig-Penney (KP) lattices are studied by means of numerical methods. The model can also applies to a Bose-Einstein condensate (BEC) trapped in a superposition of linear and nonlinear 2D periodic potentials. The analysis is chiefly presented for the self-repulsive nonlinearity, which gives rise to several species of stable fundamental gap solitons, dipoles, four-peak complexes, and vortices in two finite bandgaps of the underlying spectrum. Stable solitons with complex shapes are found, in particular, in the second bandgap of the KP lattice with the rhombic structure. The stability of the localized modes is analyzed in terms of eigenvalues of small perturbations, and tested in direct simulations. Depending on the value of the KP's duty cycle (DC, i.e., the ratio of the void's width to the lattice period), an internal stability boundary for the solitons and vortices may exist inside of the first bandgap. Otherwise, the families of the localized modes are entirely stable or unstable in the bandgaps. With the self-attractive nonlinearity, only unstable solitons and vortices are found in the semi-infinite gap.
A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry
DEFF Research Database (Denmark)
Madsen, Per A.; Fuhrman, David R.; Wang, Benlong
2006-01-01
and class II Bragg scattering from an undular sea bottom. The computations are verified against measurements, theoretical solutions and numerical models from the literature. Finally, we make a detailed investigation of nonlinear class III Bragg scattering and results are given for the sub-harmonic and super...
Existence of solutions for nonlinear mixed type integrodifferential equation of second order
Directory of Open Access Journals (Sweden)
Haribhau Laxman Tidke
2010-04-01
Full Text Available In this paper, we investigate the existence of solutions for nonlinear mixed Volterra-Fredholm integrodifferential equation of second order with nonlocal conditions in Banach spaces. Our analysis is based on Leray-Schauder alternative, rely on a priori bounds of solutions and the inequality established by B. G. Pachpatte.
Surface area products for Kerr-Taub-NUT space-time
Pradhan, Parthapratim
2016-08-01
We examine properties of the inner and outer horizon thermodynamics of Taub-NUT (Newman-Unti-Tamburino) and Kerr-Taub-NUT (KTN) black hole (BH) in four-dimensional Lorentzian geometry. We compare and contrasted these properties with the properties of Reissner Nordstrøm (RN) BH and Kerr BH. We focus on “area product”, “entropy product”, “irreducible mass product” of the event horizon and Cauchy horizons. Due to mass dependence, we speculate that these products have no nice quantization feature. Nor do they have any universal property. We further observe that the first law of BH thermodynamics and Smarr-Gibbs-Duhem relations do not hold for Taub-NUT (TN) and KTN BH in Lorentzian regime. The failure of these aforementioned features are due to the presence of the non-trivial NUT charge which makes the space-time be asymptotically non-flat, in contrast with RN BH and Kerr BH. Another reason for the failure is that Lorentzian TN and Lorentzian KTN geometries contain Dirac-Misner-type singularity, which is a manifestation of a non-trivial topological twist of the manifold. The black-hole mass formula and Christodoulou-Ruffini mass formula for TN and KTN BHs are also computed. These thermodynamic product formulae give us further understanding of the nature of inner as well as outer BH entropy at the microscopic level.
Energy Technology Data Exchange (ETDEWEB)
Kengne, Jacques [Laboratoire d' Automatique et Informatique Apliquée (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Bandjoun (Cameroon); Kenmogne, Fabien [Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototype, University of Yaoundé 1, Yaoundé (Cameroon)
2014-12-15
The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by using time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.
Thermodynamics of Magnetised Kerr-Newman Black Holes
Gibbons, G W; Pope, C N
2013-01-01
The thermodynamics of a magnetised Kerr-Newman black hole is studied to all orders in the appended magnetic field $B$. The asymptotic properties of the metric and other fields are dominated by the magnetic flux that extends to infinity along the axis, leading to subtleties in the calculation of conserved quantities such as the angular momentum and the mass. We present a detailed discussion of the implementation of a Wald-type procedure to calculate the angular momentum, showing how ambiguities that are absent in the usual asymptotically-flat case may be resolved by the requirement of gauge invariance. We also present a formalism from which we are able to obtain an expression for the mass of the magnetised black holes. The expressions for the mass and the angular momentum are shown to be compatible with the first law of thermodynamics and a Smarr type relation. Allowing the appended magnetic field $B$ to vary results in an extra term in the first law of the form $-\\mu dB$ where $\\mu$ is interpreted as an induc...
Electromagnetic Quantum Field Theory on Kerr-Newman Black Holes
Casals, Marc
2004-01-01
We study classical and quantum aspects of electromagnetic perturbations on black hole space-times. We develop an elegant formalism introduced by Wald, which sets up the theory of linear perturbations in a Type-D background in a compact and transparent manner. We derive expressions for the electromagnetic potential in terms of the single Newman-Penrose scalar \\phi_0.This enables the formulation of the quantum theory of the electromagnetic field as that of a complex scalar field. We study the separable field equations obeyed by the various Newman-Penrose scalars in the Kerr-Newman background and find, for various limits, the asymptotic behaviour of the radial and angular solutions. We correct and build on a study by Breuer, Ryan and Waller to find a uniformly valid asymptotic behaviour for large frequency of the angular solutions and the eigenvalues. We follow Candelas, Chrzanowski and Howard (CCH) in their canonical quantization of the electromagnetic potential and field. We perform an asymptotic analysis of t...
Ekşioğlu, Yasa; Güven, Kaan
2011-01-01
We propose that a weakly-coupled nonlinear dielectric waveguide -- surface-plasmon system can be formulated as a new type of Josephson junction. Such a system can be realized along a metal - dielectric interface where the dielectric medium hosts a nonlinear waveguide (e.g. fiber) for soliton propagation. We demonstrate that the system is in close analogy to the bosonic Josephson-Junction (BJJ) of atomic condensates at very low temperatures, yet exhibits different dynamical features. In particular, the inherently dynamic coupling parameter between soliton and surface-plasmon generates self-trapped oscillatory states at nonzero fractional populations with zero and $\\pi$ time averaged phase difference. The salient features of the dynamics are presented in the phase space.
Walasik, Wiktor; Renversez, Gilles
2014-01-01
We study the nonlinear waves propagating in metal slot waveguides with a Kerr-type dielectric core. We develop two independent semi-analytical models to describe the properties of such waveguides. Using those models we compute the dispersion curves for the first ten modes of a nonlinear slot waveguide. For symmetric waveguides we find symmetric, antisymmetric, and asymmetric modes which are grouped in two families. In addition, we study the influence of the slot width on the first symmetric and asymmetric modes, and we show that the dispersion curve of the first asymmetric mode is invariant with respect to the slot width for high propagation constant values and we provide analytical approximations of this curve.
Zeng, Nianyin; Wang, Zidong; Li, Yurong; Du, Min; Liu, Xiaohui
2011-07-01
In this paper, a mathematical model for sandwich-type lateral flow immunoassay is developed via short available time series. A nonlinear dynamic stochastic model is considered that consists of the biochemical reaction system equations and the observation equation. After specifying the model structure, we apply the extended Kalman filter (EKF) algorithm for identifying both the states and parameters of the nonlinear state-space model. It is shown that the EKF algorithm can accurately identify the parameters and also predict the system states in the nonlinear dynamic stochastic model through an iterative procedure by using a small number of observations. The identified mathematical model provides a powerful tool for testing the system hypotheses and also for inspecting the effects from various design parameters in both rapid and inexpensive way. Furthermore, by means of the established model, the dynamic changes in the concentration of antigens and antibodies can be predicted, thereby making it possible for us to analyze, optimize, and design the properties of lateral flow immunoassay devices. © 2011 IEEE
Grimsmo, Arne L.; Parkins, Scott
2014-03-01
We consider a generalized version of the Rabi model that includes a nonlinear, dispersive-type atom-field interaction in addition to the usual linear dipole coupling, as well as cavity dissipation. An effective system of this sort arises, for example, in a quantum simulation of the Rabi model based upon Raman transitions in an optical cavity QED setting [A. L. Grimsmo and S. Parkins, Phys. Rev. A 87, 033814 (2013), 10.1103/PhysRevA.87.033814]. For a range of the nonlinear interaction strength about a special value, degeneracies or near degeneracies of the states in the cavity-mode vacuum and single-photon subspaces, in combination with cavity loss, gives rise to an essentially closed cycle of excitations and photon emissions within these subspaces. Consequently, the cavity output field is strongly antibunched, while over this range of nonlinear strengths the atomic population undergoes an abrupt inversion. We develop a quantum-trajectory-based description of the system that models its key properties very well, and use a simple dressed-state picture to explain the novel structure of the cavity fluorescence spectrum. We also present numerical results for a potential realization of the system using a rubidium atom coupled strongly to a high-finesse optical cavity mode.
Orbital resonances in discs around braneworld Kerr black holes
Stuchlik, Zdenek; 10.1007/s10714-008-0709-2
2008-01-01
Rotating black holes in the brany universe of the Randall-Sundrum type are described by the Kerr geometry with a tidal charge b representing the interaction of the brany black hole and the bulk spacetime. For b1 are allowed. We investigate the role of the tidal charge b in the orbital resonance model of QPOs in black hole systems. The orbital Keplerian, the radial and vertical epicyclic frequencies of the equatorial, quasicircular geodetical motion are given and their radial profiles are discussed. The resonant conditions are given in three astrophysically relevant situations: for direct (parametric) resonances, for the relativistic precession model, and for some trapped oscillations of the warped discs, with resonant combinational frequencies. It is shown, how b could influence matching of the observational data indicating the 3:2 frequency ratio observed in GRS 1915+105 microquasar with prediction of the orbital resonance model; limits on allowed range of the black hole parameters a and b are established. T...
Nonlinear plasmonic amplification via dissipative soliton-plasmon resonances
Ferrando, Albert
2017-01-01
In this contribution we introduce a strategy for the compensation of plasmonic losses based on a recently proposed nonlinear mechanism: the resonant interaction between surface plasmon polaritons and spatial solitons propagating in parallel along a metal/dielectric/Kerr structure. This mechanism naturally leads to the generation of a quasiparticle excitation, the so-called soliplasmon resonance. We analyze the role played by the effective nonlinear coupling inherent to this system and how this can be used to provide a mechanism of quasiresonant nonlinear excitation of surface plasmon polaritons. We will pay particular attention to the introduction of asymmetric linear gain in the Kerr medium. The unique combination of nonlinear propagation, nonlinear coupling, and gain give rise to a scenario for the excitation of long-range surface plasmon polaritons with distinguishing characteristics. The connection between plasmonic losses and soliplasmon resonances in the presence of gain will be discussed.
Directory of Open Access Journals (Sweden)
Ching-Hung Lee
2011-01-01
Full Text Available This paper proposes a new type fuzzy neural systems, denoted IT2RFNS-A (interval type-2 recurrent fuzzy neural system with asymmetric membership function, for nonlinear systems identification and control. To enhance the performance and approximation ability, the triangular asymmetric fuzzy membership function (AFMF and TSK-type consequent part are adopted for IT2RFNS-A. The gradient information of the IT2RFNS-A is not easy to obtain due to the asymmetric membership functions and interval valued sets. The corresponding stable learning is derived by simultaneous perturbation stochastic approximation (SPSA algorithm which guarantees the convergence and stability of the closed-loop systems. Simulation and comparison results for the chaotic system identification and the control of Chua's chaotic circuit are shown to illustrate the feasibility and effectiveness of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Yao Yuqin [College of Sciences, Shanghai University, Shanghai 200436 (China)] e-mail: yyqinw@126.com
2005-11-01
In this paper, based on the well-known Sine-Poisson equation, a new Sine-Poisson equation expansion method with constant coefficients or variable coefficients is presented, which can be used to construct more new exact solutions of nonlinear evolution equations in mathematical physics. The KdV-mKdV equation and the typical breaking soliton equation are chosen to illustrate our method such that many types of new exact solutions are obtained, which include exponential solutions, kink-shaped solutions, singular solutions and soliton-like solutions.
Institute of Scientific and Technical Information of China (English)
Gabriele BONANNO; Giovanni MOLICA BISCI; Vicentiu R(A)DULESCU
2013-01-01
Under an appropriate oscillating behavior either at zero or at infinity of the nonlinear data,the existence of a sequence of weak solutions for parametric quasilinear systems of the gradient-type on the Sierpi(n)ski gasket is proved.Moreover,by adopting the same hypotheses on the potential and in presence of suitable small perturbations,the same conclusion is achieved.The approach is based on variational methods and on certain analytic and geometrical properties of the Sierpi(n)ski fractal as,for instance,a compact embedding result due to Fukushima and Shima.
Institute of Scientific and Technical Information of China (English)
Kong Linghua; Wang Jinhuan; Zheng Sining
2012-01-01
This article deals with a nonlocal heat system subject to null Dirichlet boundary conditions,where the coupling nonlocal sources consist of mixed type asymmetric nonlinearities.We at first give the criterion for simultaneous blow-up of solutions,and then establish the uniform blow-up profiles of solutions near the blow-up time.It is observed that not only the simultaneous blow-up rates of the two components u and v are asymmetric,but also the blow-up rates of the same component u (or v) may be in different levels under different dominations.
Based on interval type-2 adaptive fuzzy H∞ tracking controller for SISO time-delay nonlinear systems
Lin, Tsung-Chih; Roopaei, Mehdi
2010-12-01
In this article, based on the adaptive interval type-2 fuzzy logic, by adjusting weights, centers and widths of proposed fuzzy neural network (FNN), the modeling errors can be eliminated for a class of SISO time-delay nonlinear systems. The proposed scheme has the advantage that can guarantee the H∞ tracking performance to attenuate the lumped uncertainties caused by the unmodelled dynamics, the approximation error and the external disturbances. Moreover, the stability analysis of the proposed control scheme will be guaranteed in the sense that all the states and signals are uniformly bounded and arbitrary small attenuation level. The simulation results are demonstrated to show the effectiveness of the advocated design methodology.
DEFF Research Database (Denmark)
Da Ros, Francesco; Sackey, I.; Jazayerifar, M.
2015-01-01
Kerr nonlinearity compensation by optical phase conjugation is demonstrated in a WDM PDM 16-QAM system. Improved received signal quality is reported for both dispersion-compensated and dispersion-uncompensated transmission and a comparison with digital backpropagation is provided....
Nonlinear relativistic and quantum equations with a common type of solution.
Nobre, F D; Rego-Monteiro, M A; Tsallis, C
2011-04-08
Generalizations of the three main equations of quantum physics, namely, the Schrödinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index q, are considered in such a way that the standard linear equations are recovered in the limit q→1. Interestingly, these equations present a common, solitonlike, traveling solution, which is written in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics. In all cases, the well-known Einstein energy-momentum relation is preserved for arbitrary values of q.
Exponential stability of solutions to nonlinear time-delay systems of neutral type
Directory of Open Access Journals (Sweden)
Gennadii V. Demidenko
2016-01-01
Full Text Available We consider a nonlinear time-delay system of neutral equations with constant coefficients in the linear terms $$ \\frac{d}{dt}\\big(y(t + D y(t-\\tau\\big = A y(t + B y(t-\\tau + F(t, y(t, y(t-\\tau, $$ where $$ \\|F(t,u,v\\| \\le q_1\\|u\\|^{1+\\omega_1} + q_2\\|v\\|^{1+\\omega_2}, \\quad q_1, q_2, \\omega_1, \\omega_2 > 0. $$ We obtain estimates characterizing the exponential decay of solutions at infinity and estimates for attraction sets of the zero solution.
Oscillation of solutions to second-order nonlinear differential equations of generalized Euler type
Directory of Open Access Journals (Sweden)
Asadollah Aghajani
2013-08-01
Full Text Available We are concerned with the oscillatory behavior of the solutions of a generalized Euler differential equation where the nonlinearities satisfy smoothness conditions which guarantee the uniqueness of solutions of initial value problems, however, no conditions of sub(super linearity are assumed. Some implicit necessary and sufficient conditions and some explicit sufficient conditions are given for all nontrivial solutions of this equation to be oscillatory or nonoscillatory. Also, it is proved that solutions of the equation are all oscillatory or all nonoscillatory and cannot be both.
Localization in physical systems described by discrete nonlinear Schrodinger-type equations.
Bishop, A R; Kalosakas, G; Rasmussen, K O; Kevrekidis, P G
2003-06-01
Following a short introduction on localized modes in a model system, namely the discrete nonlinear Schrodinger equation, we present explicit results pertaining to three different physical systems described by similar equations. The applications range from the Raman scattering spectra of a complex electronic material through intrinsic localized vibrational modes, to the manifestation of an abrupt and irreversible delocalizing transition of Bose-Einstein condensates trapped in two-dimensional optical lattices, and to the instabilities of localized modes in coupled arrays of optical waveguides.
Makin, V. S.; Pestov, Yu. I.; Makin, R. S.
2017-08-01
A new nonlinear physical model of the formation of ordered structures of a surface topography of a semiconductor by ultrashort pulses of linearly polarized laser radiation has been proposed. The model is based on the formation of the dynamic near-surface waveguide due to the optical Kerr effect, interference with the part of waveguide modes, and the formation of microgratings on the surface, which are oriented by polarization of radiation. The model is confirmed by experimental data.
Light-shift-induced photonic nonlinearities
Energy Technology Data Exchange (ETDEWEB)
Brandao, F G S L; Hartmann, M J; Plenio, M B [Institute for Mathematical Sciences, Imperial College London, 53 Exhibition Road, SW7 2PE (United Kingdom)], E-mail: fernando@brandao@imperial.ac.uk
2008-04-15
We propose a new method to produce self- and cross-Kerr photonic nonlinearities, using light-induced Stark shifts due to the interaction of a cavity mode with atoms. The proposed experimental set-up is simpler than in previous approaches, while the strength of the nonlinearity obtained with a single atom is the same as in the setting based on electromagnetically induced transparency. Furthermore our scheme can be applied to engineer effective photonic nonlinear interactions whose strength increases with the number of atoms coupled to the cavity mode, leading to photon-photon interactions several orders of magnitude larger than previously considered possible.
Kerr-Newman black holes with scalar hair
Delgado, Jorge F. M.; Herdeiro, Carlos A. R.; Radu, Eugen; Rúnarsson, Helgi
2016-10-01
We construct electrically charged Kerr black holes (BHs) with scalar hair. Firstly, we take an uncharged scalar field, interacting with the electromagnetic field only indirectly, via the background metric. The corresponding family of solutions, dubbed Kerr-Newman BHs with ungauged scalar hair, reduces to (a sub-family of) Kerr-Newman BHs in the limit of vanishing scalar hair and to uncharged rotating boson stars in the limit of vanishing horizon. It adds one extra parameter to the uncharged solutions: the total electric charge. This leading electromagnetic multipole moment is unaffected by the scalar hair and can be computed by using Gauss's law on any closed 2-surface surrounding (a spatial section of) the event horizon. By contrast, the first sub-leading electromagnetic multipole - the magnetic dipole moment -, gets suppressed by the scalar hair, such that the gyromagnetic ratio is always smaller than the Kerr-Newman value (g = 2). Secondly, we consider a gauged scalar field and obtain a family of Kerr-Newman BHs with gauged scalar hair. The electrically charged scalar field now stores a part of the total electric charge, which can only be computed by applying Gauss' law at spatial infinity and introduces a new solitonic limit - electrically charged rotating boson stars. In both cases, we analyze some physical properties of the solutions.
Electrically charged Kerr black holes with scalar hair
Delgado, Jorge F M; Radu, Eugen; Runarsson, Helgi
2016-01-01
We construct electrically charged Kerr black holes (BHs) with scalar hair. Firstly, we take an uncharged scalar field, interacting with the electromagnetic field only indirectly, via the background metric. The corresponding family of solutions, dubbed Kerr-Newman BHs with ungauged scalar hair, reduces to (a sub-family of) Kerr-Newman BHs in the limit of vanishing scalar hair and to uncharged rotating boson stars in the limit of vanishing horizon. It adds one extra parameter to the uncharged solutions: the total electric charge. This leading electromagnetic multipole moment is unaffected by the scalar hair and can be computed by using Gauss's law on any closed 2-surface surrounding (a spatial section of) the event horizon. By contrast, the first sub-leading electromagnetic multipole -- the magnetic dipole moment --, gets suppressed by the scalar hair, such that the gyromagnetic ratio is always smaller than the Kerr-Newman value ($g=2$). Secondly, we consider a gauged scalar field and obtain a family of Kerr-Ne...
High-resolution fully vectorial scanning Kerr magnetometer.
Flajšman, Lukáš; Urbánek, Michal; Křižáková, Viola; Vaňatka, Marek; Turčan, Igor; Šikola, Tomáš
2016-05-01
We report on the development of a high-resolution scanning magnetometer, which fully exploits the vectorial nature of the magneto-optical Kerr effect. The three-dimensional nature of magnetization is at the basis of many micromagnetic phenomena and from these data, we can fully characterize magnetization processes of nanostructures in static and dynamic regimes. Our scanning Kerr magnetometer uses a high numerical aperture microscope objective where the incident light beam can be deterministically deviated from the objective symmetry axis, therefore, both in-plane (via the longitudinal Kerr effect) and out-of-plane (via the polar Kerr effect) components of the magnetization vector may be detected. These components are then separated by exploiting the symmetries of the polar and longitudinal Kerr effects. From four consecutive measurements, we are able to directly obtain the three orthogonal components of the magnetization vector with a resolution of 600 nm. Performance of the apparatus is demonstrated by a measurement of 3D magnetization vector maps showing out-of-plane domains and in-plane domain walls in an yttrium-iron-garnet film and on a study of magnetization reversal in a 4-μm-wide magnetic disk.
Shadows of Kerr Black Holes with Scalar Hair.
Cunha, Pedro V P; Herdeiro, Carlos A R; Radu, Eugen; Rúnarsson, Helgi F
2015-11-20
Using backwards ray tracing, we study the shadows of Kerr black holes with scalar hair (KBHSH). KBHSH interpolate continuously between Kerr BHs and boson stars (BSs), so we start by investigating the lensing of light due to BSs. Moving from the weak to the strong gravity region, BSs-which by themselves have no shadows-are classified, according to the lensing produced, as (i) noncompact, which yield not multiple images, (ii) compact, which produce an increasing number of Einstein rings and multiple images of the whole celestial sphere, and (iii) ultracompact, which possess light rings, yielding an infinite number of images with (we conjecture) a self-similar structure. The shadows of KBHSH, for Kerr-like horizons and noncompact BS-like hair, are analogous to, but distinguishable from, those of comparable Kerr BHs. But for non-Kerr-like horizons and ultracompact BS-like hair, the shadows of KBHSH are drastically different: novel shapes arise, sizes are considerably smaller, and multiple shadows of a single BH become possible. Thus, KBHSH provide quantitatively and qualitatively new templates for ongoing (and future) very large baseline interferometry observations of BH shadows, such as those of the Event Horizon Telescope.
Shadows of Kerr black holes with scalar hair
Cunha, Pedro V P; Radu, Eugen; Runarsson, Helgi F
2015-01-01
Using backwards ray tracing, we study the shadows of Kerr black holes with scalar hair (KBHsSH). KBHsSH interpolate continuously between Kerr BHs and boson stars (BSs), so we start by investigating the lensing of light due to BSs. Moving from the weak to the strong gravity region, BSs - which by themselves have no shadows - are classified, according to the lensing produced, as: $(i)$ non-compact, which yield no multiple images; $(ii)$ compact, which produce an increasing number of Einstein rings and multiple images of the whole celestial sphere; $(iii)$ ultra-compact, which possess light rings, yielding an infinite number of images with (we conjecture) a self-similar structure. The shadows of KBHsSH, for Kerr-like horizons and non-compact BS-like hair, are analogous to, but distinguishable from, those of comparable Kerr BHs. But for non-Kerr-like horizons and ultra-compact BS-like hair, the shadows of KBHsSH are drastically different: novel shapes arise, sizes are considerably smaller and multiple shadows of ...
Nonlinear Methods to Assess Changes in Heart Rate Variability in Type 2 Diabetic Patients
Energy Technology Data Exchange (ETDEWEB)
Bhaskar, Roy, E-mail: imbhaskarall@gmail.com [Indian Institute of Technology (India); University of Connecticut, Farmington, CT (United States); Ghatak, Sobhendu [Indian Institute of Technology (India)
2013-10-15
Heart rate variability (HRV) is an important indicator of autonomic modulation of cardiovascular function. Diabetes can alter cardiac autonomic modulation by damaging afferent inputs, thereby increasing the risk of cardiovascular disease. We applied nonlinear analytical methods to identify parameters associated with HRV that are indicative of changes in autonomic modulation of heart function in diabetic patients. We analyzed differences in HRV patterns between diabetic and age-matched healthy control subjects using nonlinear methods. Lagged Poincaré plot, autocorrelation, and detrended fluctuation analysis were applied to analyze HRV in electrocardiography (ECG) recordings. Lagged Poincare plot analysis revealed significant changes in some parameters, suggestive of decreased parasympathetic modulation. The detrended fluctuation exponent derived from long-term fitting was higher than the short-term one in the diabetic population, which was also consistent with decreased parasympathetic input. The autocorrelation function of the deviation of inter-beat intervals exhibited a highly correlated pattern in the diabetic group compared with the control group. The HRV pattern significantly differs between diabetic patients and healthy subjects. All three statistical methods employed in the study may prove useful to detect the onset and extent of autonomic neuropathy in diabetic patients.
Energy Technology Data Exchange (ETDEWEB)
Anthony L. Crawford
2012-08-01
Natural movements and force feedback are important elements in using teleoperated equipment if complex and speedy manipulation tasks are to be accomplished in remote and/or hazardous environments, such as hot cells, glove boxes, decommissioning, explosives disarmament, and space to name a few. In order to achieve this end the research presented in this paper has developed an admittance type exoskeleton like multi-fingered haptic hand user interface that secures the user’s palm and provides 3-dimensional force feedback to the user’s fingertips. Atypical to conventional haptic hand user interfaces that limit themselves to integrating the human hand’s characteristics just into the system’s mechanical design this system also perpetuates that inspiration into the designed user interface’s controller. This is achieved by manifesting the property differences of manipulation and grasping activities as they pertain to the human hand into a nonlinear master-slave force relationship. The results presented in this paper show that the admittance-type system has sufficient bandwidth that it appears nearly transparent to the user when the user is in free motion and when the system is subjected to a manipulation task, increased performance is achieved using the nonlinear force relationship compared to the traditional linear scaling techniques implemented in the vast majority of systems.
Robust bound states in the continuum in Kerr microcavity embedded in photonic crystal waveguide
Bulgakov, Evgeny N
2014-01-01
We present a two-dimensional photonic crystal design with a microcavity of four defect dielectric rods with eigenfrequencies residing in the propagating band of directional waveguide. In the linear case for tuning of material parameters of defect rods the nonrobust bound state in the continuum (BSC) might occur. The BSC is a result of full destructive interference of resonant monopole and quadrupole modes with the same parity. % to trap light interior of the microcavity. A robust BSC arises in a self-adaptive way without necessity to tune the parameters of the microcavity with the Kerr effect. Lack of the superposition principle in nonlinear systems gives rise to coupling of the BSC with injecting light. That forms a peculiar shape of isolated transmittance resonance around BSC frequency. We show if injecting light is switched off the BSC storages light that opens a way for light accumulation.
Mohammadzadeh, Ardashir; Ghaemi, Sehraneh
2015-09-01
This paper proposes a novel approach for training of proposed recurrent hierarchical interval type-2 fuzzy neural networks (RHT2FNN) based on the square-root cubature Kalman filters (SCKF). The SCKF algorithm is used to adjust the premise part of the type-2 FNN and the weights of defuzzification and the feedback weights. The recurrence property in the proposed network is the output feeding of each membership function to itself. The proposed RHT2FNN is employed in the sliding mode control scheme for the synchronization of chaotic systems. Unknown functions in the sliding mode control approach are estimated by RHT2FNN. Another application of the proposed RHT2FNN is the identification of dynamic nonlinear systems. The effectiveness of the proposed network and its learning algorithm is verified by several simulation examples. Furthermore, the universal approximation of RHT2FNNs is also shown.
Energy extraction from Kerr black holes by rigidly rotating strings
Kinoshita, Shunichiro; Tanabe, Kentaro
2016-01-01
In this paper, we show that a rigidly rotating string can extract the rotational energy from a rotating black hole. We consider Nambu-Goto strings stationary with respect to a co-rotating Killing vector with an uniform angular velocity $\\omega$ in the Kerr spacetime. We show that a necessary condition of the energy-extraction process is that an effective horizon on the string worldsheet, which corresponds to the inner light surface, is inside the ergosphere of the Kerr black hole and the angular velocity $\\omega$ is less than that of the black hole $\\Omega_\\mathrm{h}$. Furthermore, we discuss global configurations of such strings in both of a slow-rotation limit and the extremal Kerr case.
Schwarzschild and Kerr Solutions of Einstein's Field Equation -- an introduction
Heinicke, Christian; .,
2015-01-01
Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(-Droste) solution, and into one specific stationary axially symmetric solution, the Kerr solution. The Schwarzschild solution is unique and its metric can be interpreted as the exterior gravitational field of a spherically symmetric mass. The Kerr solution is only unique if the multipole moments of its mass and its angular momentum take on prescribed values. Its metric can be interpreted as the exterior gravitational field of a suitably rotating mass distribution. Both solutions describe objects exhibiting an event horizon, a frontier of no return. The corresponding notion of a black hole is explained to some extent. Eventually, we present some generalizations of the Kerr solution.
Modes of the Kerr geometry with purely imaginary frequencies
Cook, Gregory B
2016-01-01
In this paper, we examine the behavior of modes of the Kerr geometry when the mode's frequency is purely imaginary. We demonstrate that quasinormal modes must be polynomial in nature if their frequency is purely imaginary, and present a method for computing such modes. The nature of these modes, however, is not always easy to determine. Some of the polynomial modes we compute are quasinormal modes. However, some are simultaneously quasinormal modes and total transmission modes, while others fail to satisfy the requisite boundary conditions for either. This analysis is, in part, an extension of the results known for Schwarzschild black holes, but clarifies misconceptions for the behavior of modes when the black hole has angular momentum. We also show that the algebraically special modes of Kerr with m=0 have an additional branch of solutions not seen before in the literature. All of these results are in precise agreement with new numerical solutions for sequences of gravitational quasinormal modes of Kerr. How...
The General Kerr-de Sitter Metrics in All Dimensions
Gibbons, G W; Page, D N; Pope, C N
2005-01-01
We give the general Kerr-de Sitter metric in arbitrary spacetime dimension D, with the maximal number [(D-1)/2] of independent rotation parameters. We obtain the metric in Kerr-Schild form, where it is written as the sum of a de Sitter metric plus the square of a null geodesic vector, and in generalised Boyer-Lindquist coordinates. The Kerr-Schild form is simpler for verifying that the Einstein equations are satisfied, and we have explicitly checked our results for all dimensions D \\le 11. We discuss the global structure of the metrics, and obtain formulae for the surface gravities and areas of the event horizons. We also obtain the Euclideanised solutions, and we construct complete non-singular compact Einstein spaces on associated S^{D-2} bundles over S^2.
Chaos and dynamics of spinning particles in Kerr spacetime
Han, Wen-Biao
2010-01-01
We study chaos dynamics of spinning particles in Kerr spacetime of rotating black holes use the Papapetrou equations by numerical integration. Because of spin, this system exists many chaos solutions, and exhibits some exceptional dynamic character. We investigate the relations between the orbits chaos and the spin magnitude S, pericenter, polar angle and Kerr rotation parameter a by means of a kind of brand new Fast Lyapulov Indicator (FLI) which is defined in general relativity. The classical definition of Lyapulov exponent (LE) perhaps fails in curve spacetime. And we emphasize that the Poincar\\'e sections cannot be used to detect chaos for this case. Via calculations, some new interesting conclusions are found: though chaos is easier to emerge with bigger S, but not always depends on S monotonically; the Kerr parameter a has a contrary action on the chaos occurrence. Furthermore, the spin of particles can destroy the symmetry of the orbits about the equatorial plane. And for some special initial condition...
Pollicott, M
2002-01-01
In this paper we analyze a variant of the famous Schelling segregation model in economics as a dynamical system. This model exhibits, what appears to be, a new clustering mechanism. In particular, we explain why the limiting behavior of the non-locally determined lattice system exhibits a number of pronounced geometric characteristics. Part of our analysis uses a geometrically defined Lyapunov function which we show is essentially the total Laplacian for the associated graph Laplacian. The limit states are minimizers of a natural non-linear, non-homogeneous variational problem for the Laplacian, which can also be interpreted as ground state configurations for the lattice gas whose Hamiltonian essentially coincides with our Lyapunov function. Thus we use dynamics to explicitly solve this problem for which there is no known analytic solution. We prove an isoperimetric characterization of the global minimizers on the torus which enables us to explicitly obtain the global minimizers for the graph variational prob...
Motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime and analytical solutions
Cebeci, Hakan; Özdemir, Nülifer; Şentorun, Seçil
2016-05-01
In this work, we study the motion of charged test particles in Kerr-Newman-Taub-NUT spacetime. We analyze the angular and the radial parts of the orbit equations and examine the possible orbit types. We also investigate the spherical orbits and their stabilities. Furthermore, we obtain the analytical solutions of the equations of motion and express them in terms of Jacobian and Weierstrass elliptic functions. Finally, we discuss the observables of the bound motion and calculate the perihelion shift and Lense-Thirring effect for the bound orbits.
Motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime and analytical solutions
Cebeci, Hakan; Şentorun, Seçil
2015-01-01
In this work, we study the motion of charged test particles in Kerr-Newman-Taub-NUT spacetime. We analyze the angular and the radial parts of the orbit equations and examine the possible orbit types. We also investigate the spherical orbits and their stabilities. Furthermore, we obtain the analytical solutions of the equations of motion and express them in terms of Jacobian and Weierstrass elliptic functions. Finally, we discuss the observables of the bound motion and calculate the perihelion shift and Lense-Thirring effect for three dimensional bound orbits.
2010-04-16
... Bureau of Indian Affairs Final Environmental Impact Statement for Drought Management Planning at the Kerr... Management Planning at the Kerr Hydroelectric Project, Flathead Lake, Montana, is now available for public review and comment. DATES: The BIA will issue a final decision on drought management planning at the Kerr...
Self-guiding light in layered nonlinear media
DEFF Research Database (Denmark)
Bergé, L.; Mezentsev, V. K.; Juul Rasmussen, Jens;
2000-01-01
We study the propagation of intense optical beams in layered Kerr media. With appropriate shapes, beams with a power close to the self-focusing threshold are shown to propagate over long distances as quasistationary waveguides in cubic media supporting a periodic nonlinear refractive index. (C...
Uncertainty relation and black hole entropy of Kerr spacetime
Institute of Scientific and Technical Information of China (English)
Hu Shuang-Qi; Zhao Ren
2005-01-01
The properties of thermal radiation are discussed by using a new equation of state density, which is motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of Kerr black hole. When the new equation of state density is utilized to investigate the entropy of a Bosonic field and Fermionic field outside the horizon of a static Kerr black hole, the divergence appearing in the brick wall model is removed, without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.
Cosmic Censorship Conjecture in Kerr-Sen Black Hole
Gwak, Bogeun
2016-01-01
The validity of cosmic censorship conjecture for the Kerr-Sen black hole, which is a solution to the low-energy effective field theory for four-dimensional heterotic string theory, is investigated using charged particle absorption. When the black hole absorbs the particle, its charges are changed due to the conserved quantities of the particle. Changes in the black hole are constrained to the equation for the motion of the particle and are consistent with the laws of thermodynamics. Particle absorption increases the mass of the extremal Kerr-Sen black hole to more than its charges, so the black hole cannot be overcharged. Therefore, cosmic censorship conjecture is valid.
Instability of the extreme Kerr-Newman black-holes
Reiris, M.
2013-01-01
Using black-hole inequalities and the increase of the horizon's areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme Reissner-Nordstrom black-hole that, (by contradiction), cannot decay in time into any extreme Kerr-Newman black-hole. This proves the expectation that the family of extreme Kerr-Newman black-holes is unstable. It remains of course to be seen whether the whole family of charged black-holes, including those extre...
Hawking radiation from magnetized Kerr-Newman black hole
Rizwan, Muhammad; Saifullah, K.
2016-12-01
Hawking radiation of charged scalar and Dirac particles from the event horizon of magnetized Kerr-Newman black holes is studied using the Hamilton-Jacobi method and WKB approximation. This is done by calculating tunneling probabilities of these particles from the horizons of magnetized black holes. This method yields the Hawking temperature of magnetized Kerr-Newman black holes as well. It is interesting to note that while the tunneling probabilities depend upon the background magnetic field, the Hawking temperature is not affected by magnetization.
Uncertainty relation and black hole entropy of Kerr spacetime
Hu, Shuang-Qi; Zhao, Ren
2005-07-01
The properties of thermal radiation are discussed by using a new equation of state density, which is motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of Kerr black hole. When the new equation of state density is utilized to investigate the entropy of a Bosonic field and Fermionic field outside the horizon of a static Kerr black hole, the divergence appearing in the brick wall model is removed, without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.
Note on a new parametrization for testing the Kerr metric
Energy Technology Data Exchange (ETDEWEB)
Ghasemi-Nodehi, M. [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Bambi, Cosimo [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Eberhard-Karls Universitaet Tuebingen, Theoretical Astrophysics, Tuebingen (Germany)
2016-05-15
We propose a new parametrization for testing the Kerr nature of astrophysical black hole candidates. The common approaches focus on the attempt to constrain possible deviations from the Kerr solution described by new terms in the metric. Here we adopt a different perspective. The mass and the spin of a black hole make the spacetime curved and we want to check whether they do it with the strength predicted by general relativity. As an example, we apply our parametrization to the black hole shadow, an observation that may be possible in a not too distant future. (orig.)
Odyssey: Ray tracing and radiative transfer in Kerr spacetime
Pu, Hung-Yi; Yun, Kiyun; Younsi, Ziri; Yoon, Suk-Jin
2016-01-01
Odyssey is a GPU-based General Relativistic Radiative Transfer (GRRT) code for computing images and/or spectra in Kerr metric describing the spacetime around a rotating black hole. Odyssey is implemented in CUDA C/C++. For flexibility, the namespace structure in C++ is used for different tasks; the two default tasks presented in the source code are the redshift of a Keplerian disk and the image of a Keplerian rotating shell at 340GHz. Odyssey_Edu, an educational software package for visualizing the ray trajectories in the Kerr spacetime that uses Odyssey, is also available.
Regularization of Kerr-NUT spacetimes and their thermodynamical quantities
Nashed, G G L
2015-01-01
In the context of the teleparallel equivalent of general relativity (TEGR) theory, continues calculations of the total energy and momentum for Kerr-NUT spacetimes using three different methods, the gravitational energy-momentum, the Riemannian connection 1-form, ${\\widetilde{\\Gamma}_\\alpha}^\\beta$ and the Euclidean continuation method, have been achieved. Many local Lorentz transformations, that play the role of regularizing tool, are given to get the commonly known form of energy and momentum. We calculate the thermodynamic quantities of Kerr-NUT spacetime. We also investigate the first law of thermodynamics and quantum statistical relation.
Entropy of Kerr-de Sitter black hole
Li, Huai-Fan; Ma, Meng-Sen; Zhang, Li-Chun; Zhao, Ren
2017-07-01
Based on the consideration that the black hole horizon and the cosmological horizon of Kerr-de Sitter black hole are not independent of each other, we conjecture the total entropy of the system should have an extra term contributed from the correlations between the two horizons, except for the sum of the two horizon entropies. By employing globally effective first law and effective thermodynamic quantities, we obtain the corrected total entropy and find that the region of stable state for Kerr-de Sitter is related to the angular velocity parameter a, i.e., the region of stable state becomes bigger as the rotating parameters a is increases.
The road towards nonlinear magneto-plasmonics
Zheng, Wei; Liu, Xiao; Lüpke, Günter; Hanbicki, Aubrey T.; Jonker, Berend T.
2016-10-01
Nonlinear magneto-plasmonics (NMP) describes systems where nonlinear optics, magnetics and plasmonics are all involved. NMP can be referred to as interdisciplinary studies at the intersection of Nonlinear Plasmonics (NP), Magneto- Plasmonics (MP), and nanoscience. In NMP systems, nanostructures are the bases, Surface Plasmons (SPs) work as catalyst due to strong field enhancement effects, and the nonlinear magneto-optical Kerr effect (nonlinear MOKE) plays an important role as a characterization method. Many new effects were discovered recently, which include enhanced magnetization-induced harmonic generation, controlled and enhanced magnetic contrast, magneto-chiral effect, correlation between giant magnetroresistance (GMR) and nonlinear MOKE, etc. We review the structures, experiments, findings, and the applications of NMP.
ASYMPTOTIC STABILITY OF A CLASS OF NONLINEAR NEUTRAL-TYPE SYSTEMS
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
By Lyapunov functional method, sufficient conditions for the asymptotic stability of a class of neutral-type systems are discussed in this paper. This work extends some results on the stability of neutral-type systems in the previous papers. Several numerical examples are listed in the end of this paper to confirm our results.
Hu, Kun; Peng, C. K.; Huang, Norden E.; Wu, Zhaohua; Lipsitz, Lewis A.; Cavallerano, Jerry; Novak, Vera
2008-04-01
Cerebral autoregulation is an important mechanism that involves dilatation and constriction in arterioles to maintain relatively stable cerebral blood flow in response to changes of systemic blood pressure. Traditional assessments of autoregulation focus on the changes of cerebral blood flow velocity in response to large blood pressure fluctuations induced by interventions. This approach is not feasible for patients with impaired autoregulation or cardiovascular regulation. Here we propose a newly developed technique-the multimodal pressure-flow (MMPF) analysis, which assesses autoregulation by quantifying nonlinear phase interactions between spontaneous oscillations in blood pressure and flow velocity during resting conditions. We show that cerebral autoregulation in healthy subjects can be characterized by specific phase shifts between spontaneous blood pressure and flow velocity oscillations, and the phase shifts are significantly reduced in diabetic subjects. Smaller phase shifts between oscillations in the two variables indicate more passive dependence of blood flow velocity on blood pressure, thus suggesting impaired cerebral autoregulation. Moreover, the reduction of the phase shifts in diabetes is observed not only in previously-recognized effective region of cerebral autoregulation (type 2 diabetes mellitus alters cerebral blood flow regulation over a wide frequency range and that this alteration can be reliably assessed from spontaneous oscillations in blood pressure and blood flow velocity during resting conditions. We also show that the MMPF method has better performance than traditional approaches based on Fourier transform, and is more suitable for the quantification of nonlinear phase interactions between nonstationary biological signals such as blood pressure and blood flow.
Nonlinear optics with stationary pulses of light
Andre, A.; Bajcsy, M.; Zibrov, A. S.; Lukin, M. D.
2004-01-01
We show that the recently demonstrated technique for generating stationary pulses of light [Nature {\\bf 426}, 638 (2003)] can be extended to localize optical pulses in all three spatial dimensions in a resonant atomic medium. This method can be used to dramatically enhance the nonlinear interaction between weak optical pulses. In particular, we show that an efficient Kerr-like interaction between two pulses can be implemented as a sequence of several purely linear optical processes. The resul...
Time-periodic Solution to a Nonlinear Parabolic Type Equation of Higher Order
Institute of Scientific and Technical Information of China (English)
Yan-ping Wang; You-lin Zhang
2008-01-01
In this paper, the existence and uniqueness of time-periodic generalized solutions and time-periodic classical solutions to a class of parabolic type equation of higher order are proved by Gaierkin method.
Institute of Scientific and Technical Information of China (English)
Liu YANG; Zongmin QIAO
2012-01-01
In this paper,the existence and multiplicity of positive solutions for Robin type boundary value problem of differential equation involving the Riemann-Liouville fractional order derivative are established.
Directory of Open Access Journals (Sweden)
Chung-Ta Li
2014-01-01
Full Text Available We propose a species-based hybrid of the electromagnetism-like mechanism (EM and back-propagation algorithms (SEMBP for an interval type-2 fuzzy neural system with asymmetric membership functions (AIT2FNS design. The interval type-2 asymmetric fuzzy membership functions (IT2 AFMFs and the TSK-type consequent part are adopted to implement the network structure in AIT2FNS. In addition, the type reduction procedure is integrated into an adaptive network structure to reduce computational complexity. Hence, the AIT2FNS can enhance the approximation accuracy effectively by using less fuzzy rules. The AIT2FNS is trained by the SEMBP algorithm, which contains the steps of uniform initialization, species determination, local search, total force calculation, movement, and evaluation. It combines the advantages of EM and back-propagation (BP algorithms to attain a faster convergence and a lower computational complexity. The proposed SEMBP algorithm adopts the uniform method (which evenly scatters solution agents over the feasible solution region and the species technique to improve the algorithm’s ability to find the global optimum. Finally, two illustrative examples of nonlinear systems control are presented to demonstrate the performance and the effectiveness of the proposed AIT2FNS with the SEMBP algorithm.
Mohammad A. Assareh; Behrouz Asgarian
2008-01-01
The operation for offshore oil has become an important issue in the recent years. Offshore platforms are some of those structures which are built to withstand environmental and accidental loads during oil exploitation operation. One of the most usual types of these platforms is the Jacket Type Offshore Platform (JTOP) which can be divided into three important parts, which are Deck, Jacket and piles. In order to increase the safety, particular attention should be paid to ea...
Indian Academy of Sciences (India)
M Mohjoei; M M Golshan; H Safari
2013-05-01
In this paper the time evolution of von Neumann entropy, as a measure of entanglement between V-type three-level atoms and the union of a two-mode field, is studied. The atom–field interaction is assumed to occur in a Kerr-type medium with an intensity-dependent coupling. Introducing a Casmir operator whose eigenvalues, , give total excitations in the system and commutes with the governing Hamiltonian, it is concluded that the latter is block-diagonal with ever growing dimensions. As we shall show, however, each block consists of two 2 × 2 blocks while all the others, ( −1) in number, are 3 × 3. We then proceed to analytically calculate the time-evolution operator which is also block-diagonal, each block with the same properties as that of the Hamiltonian. Our calculations show that, as expected, the atom–field entanglement oscillates which, depending upon the initial state, exhibits the phenomenon of collapse revivals. It is further shown that collapse revivals occur whenever both 2 × 2 blocks are involved in the time evolution of the system. Properties of such behaviour in the entanglement are also discussed in detail.
Amalgamation of interacting light beamlets in Kerr-type media
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Rasmussen, Kim; Berge, L;
1997-01-01
The interaction of optical filaments in bulk self-focusing media is investigated theoretically and numerically. The nature of this interaction is shown to vary with the incident individual powers and relative phases of the beamlets. By means of virial arguments supported by numerical results it i...
On the origin of heavy-tail statistics in equations of the Nonlinear Schrödinger type
Energy Technology Data Exchange (ETDEWEB)
Onorato, Miguel, E-mail: miguel.onorato@gmail.com [Dipartimento di Fisica, Università degli Studi di Torino, 10125 Torino (Italy); Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Torino, 10125 Torino (Italy); Proment, Davide [School of Mathematics, University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ (United Kingdom); El, Gennady [Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU (United Kingdom); Randoux, Stephane; Suret, Pierre [Laboratoire de Physique des Lasers, Atomes et Molecules, Université de Lille, UMR-CNRS 8523 (France)
2016-09-16
We study the formation of extreme events in incoherent systems described by the Nonlinear Schrödinger type of equations. We consider an exact identity that relates the evolution of the normalized fourth-order moment of the probability density function of the wave envelope to the rate of change of the width of the Fourier spectrum of the wave field. We show that, given an initial condition characterized by some distribution of the wave envelope, an increase of the spectral bandwidth in the focusing/defocusing regime leads to an increase/decrease of the probability of formation of rogue waves. Extensive numerical simulations in 1D+1 and 2D+1 are also performed to confirm the results.
Directory of Open Access Journals (Sweden)
P. S. Hiremath
2008-01-01
recognition in the framework of symbolic data analysis. Classical KDA extracts features, which are single-valued in nature to represent face images. These single-valued variables may not be able to capture variation of each feature in all the images of same subject; this leads to loss of information. The symbolic KDA algorithm extracts most discriminating nonlinear interval-type features which optimally discriminate among the classes represented in the training set. The proposed method has been successfully tested for face recognition using two databases, ORL database and Yale face database. The effectiveness of the proposed method is shown in terms of comparative performance against popular face recognition methods such as kernel Eigenface method and kernel Fisherface method. Experimental results show that symbolic KDA yields improved recognition rate.
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.
Collapse of Incoherent Light Beams in Inertial Bulk Kerr Media
DEFF Research Database (Denmark)
Bang, Ole; Edmundson, Darran; Królikowski, Wieslaw
1999-01-01
We use the coherent density function theory to show that partially coherent beams are unstable and may collapse in inertial bulk Kerr media. The threshold power for collapse, and its dependence on the degree of coherence, is found analytically and checked-numerically. The internal dynamics of the...
Rebound Effect in the Kerr-Newman-Kasuya Field
Institute of Scientific and Technical Information of China (English)
HE Tang-Mei; WANG Yong-Jiu
2005-01-01
@@ It is shown that the repulsive gravitational action of electric charge and magnetic charge make it possible that the neutral particles moving in the Kerr-Newman-Kasuya field stop and rebound at the surface of r = r0 =(e2 + q2)/(2m). The phenomenon of dragging of inertial frames is analysed.
Astrophysical imaging of Kerr black holes with scalar hair
Vincent, F H; Herdeiro, C; Radu, E
2016-01-01
We address the astrophysical imaging of a family of deformed Kerr black holes (BHs). These are stationary, asymptotically flat black hole (BH) spacetimes, that are solutions of General Relativity minimally coupled to a massive, complex scalar field: Kerr BHs with scalar hair (KBHsSH). Such BHs bifurcate from the vacuum Kerr solution and can be regarded as a horizon within a rotating boson star. In a recent letter, it was shown that KBHsSH can exhibit very distinct shadows from the ones of their vacuum counterparts. The setup therein, however, considered the light source to be a celestial sphere sufficiently far away from the BH. Here, we analyse KBHsSH surrounded by an emitting torus of matter, simulating a more realistic astrophysical environment, and study the corresponding lensing of light as seen by a very far away observer, to appropriately model ground-based observations of Sgr A*. We find that the differences in imaging between KBHsSH and comparable vacuum Kerr BHs remain, albeit less dramatic than tho...
Microscopics of extremal Kerr from spinning M5 branes
Compère, G.; Song, W.; Virmani, A.
2010-01-01
We show that the spinning magnetic one-brane in minimal five-dimensional supergravity admits a decoupling limit that interpolates smoothly between a self-dual null orbifold of AdS_3 x S^2 and the near-horizon limit of the extremal Kerr black hole times a circle. We use this interpolating solution to
Microscopics of extremal Kerr from spinning M5 branes
Compère, G.; Song, W.; Virmani, A.
2011-01-01
We show that the spinning magnetic one-brane in minimal five-dimensional supergravity admits a decoupling limit that interpolates smoothly between a self-dual null orbifold of AdS3 × S 2 and the near-horizon limit of the extremal Kerr black hole times a circle. We use this interpolating solution to
Classification of kink type solutions to the extended derivative nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Wyller, J.; Fla, T.; Juul Rasmussen, J.
1998-01-01
The Raman Extended Derivative Non Linear Schrodinger (R-EDNLS) equation which models single mode propagation in optical fibers, is shown to possess travelling and stationary kink envelope solutions of monotonic and oscillatory type. These structures have been called optical shocks in analogy...... with hydrodynamical shocks or optical double layers in analogy with electrostatic double layers in plasma physics. Hydrodynamical equations for the action density and local wave number are derived and shock wave solutions of the Rankine-Hugionot type are constructed. They are consistent with the kink structures when...
Chen, Hong; Huang, Xuanqi; Fu, Houqiang; Lu, Zhijian; Zhang, Xiaodong; Montes, Jossue A.; Zhao, Yuji
2017-05-01
We report the basic nonlinear optical properties, namely, two-photon absorption coefficient ( β ), three-photon absorption coefficient ( γ ), and Kerr nonlinear refractive index ( n kerr), of GaN crystals in polar c-plane, nonpolar m-plane, and semipolar ( 20 21 ¯ ) plane orientations. A typical Z-scan technique was used for the measurement with a femtosecond Ti:S laser from wavelengths of 724 nm to 840 nm. For the two-photon absorption coefficient ( β ), similar values were obtained for polar, nonpolar, and semipolar samples, which are characterized to be ˜0.90 cm/GW at 724 nm and ˜0.65 cm/GW at 730 nm for all the three samples. For the Kerr nonlinear refractive index ( n kerr), self-focusing features were observed in this work, which is different from previous reports where self-defocusing features were observed on GaN in the visible and near-UV spectral regions. At 724 nm, n kerr was measured to be ˜2.5 0 × 10 - 14 cm 2 / W for all three samples. Three-photon absorption coefficients ( γ ) were also determined, which were found to be consistent with previous reports. This study provides valuable information on the basic nonlinear optical properties of III-nitride semiconductors, which are vital for a wide range of applications such as integrated photonics and quantum photonics.
Contrast structures for a quasilinear Sobolev-type equation with unbalanced nonlinearity
Bykov, A. A.; Nefedov, N. N.; Sharlo, A. S.
2014-08-01
The existence of a solution to a generalized Kolmogorov-Petrovskii-Piskunov equation is proved and its asymptotic expansion of the internal transition layer type is constructed. The convergence of the asymptotics is proved by applying the asymptotic comparison principle developed for a new class of problems.
Energy Technology Data Exchange (ETDEWEB)
Liang, Peixin; Chai, Feng [State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001 (China); Department of Electrical Engineering, Harbin Institute of Technology, Harbin 150001 (China); Bi, Yunlong [Department of Electrical Engineering, Harbin Institute of Technology, Harbin 150001 (China); Pei, Yulong, E-mail: peiyulong1@163.com [Department of Electrical Engineering, Harbin Institute of Technology, Harbin 150001 (China); Cheng, Shukang [State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001 (China); Department of Electrical Engineering, Harbin Institute of Technology, Harbin 150001 (China)
2016-11-01
Based on subdomain model, this paper presents an analytical method for predicting the no-load magnetic field distribution, back-EMF and torque in general spoke-type motors with magnetic bridges. Taking into account the saturation and nonlinearity of magnetic material, the magnetic bridges are equivalent to fan-shaped saturation regions. For getting standard boundary conditions, a lumped parameter magnetic circuit model and iterative method are employed to calculate the permeability. The final field domain is divided into five types of simple subdomains. Based on the method of separation of variables, the analytical expression of each subdomain is derived. The analytical results of the magnetic field distribution, Back-EMF and torque are verified by finite element method, which confirms the validity of the proposed model for facilitating the motor design and optimization. - Highlights: • The no-load magnetic field of poke-type motors is firstly calculated by analytical method. • The magnetic circuit model and iterative method are employed to calculate the permeability. • The analytical expression of each subdomain is derived.. • The proposed method can effectively reduce the predesign stages duration.
An Improved Ishikawa-type Iteration for Nonlinear Quase-Contraction Mappings%非线性拟压缩映射的改进Ishikawa型迭代
Institute of Scientific and Technical Information of China (English)
田有先
2001-01-01
在凸度量空间内，引入了非线性拟压缩映射序列和改进的Ishikawa型迭代序列，证明了改进的Ishikawa型迭代序列收敛于非线性拟压缩映射序列的唯一公共不动点。%The notion of nonlinear qusi-contraction mappings squence and improved Ishikawa-type iteration are introduced in convex matric space.The result that the improved lshikawa-type iteration sequence converges to unique common fixed point of nonlinear quasi-contraction-mappings sequence is also given.
Model reduction of cavity nonlinear optics for photonic logic: a quasi-principal components approach
Shi, Zhan; Nurdin, Hendra I.
2016-11-01
Kerr nonlinear cavities displaying optical thresholding have been proposed for the realization of ultra-low power photonic logic gates. In the ultra-low photon number regime, corresponding to energy levels in the attojoule scale, quantum input-output models become important to study the effect of unavoidable quantum fluctuations on the performance of such logic gates. However, being a quantum anharmonic oscillator, a Kerr-cavity has an infinite dimensional Hilbert space spanned by the Fock states of the oscillator. This poses a challenge to simulate and analyze photonic logic gates and circuits composed of multiple Kerr nonlinearities. For simulation, the Hilbert of the oscillator is typically truncated to the span of only a finite number of Fock states. This paper develops a quasi-principal components approach to identify important subspaces of a Kerr-cavity Hilbert space and exploits it to construct an approximate reduced model of the Kerr-cavity on a smaller Hilbert space. Using this approach, we find a reduced dimension model with a Hilbert space dimension of 15 that can closely match the magnitudes of the mean transmitted and reflected output fields of a conventional truncated Fock state model of dimension 75, when driven by an input coherent field that switches between two levels. For the same input, the reduced model also closely matches the magnitudes of the mean output fields of Kerr-cavity-based AND and NOT gates and a NAND latch obtained from simulation of the full 75 dimension model.
DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Hesthaven, Jan; Bingham, Harry B.
2008-01-01
We present a high-order nodal Discontinuous Galerkin Finite Element Method (DG-FEM) solution based on a set of highly accurate Boussinesq-type equations for solving general water-wave problems in complex geometries. A nodal DG-FEM is used for the spatial discretization to solve the Boussinesq equ...... and absorbed in the interior of the computational domain using a flexible relaxation technique applied on the free surface variables....
Peleg, Avner; Tran, Thinh P
2015-01-01
We study stabilization and destabilization of propagating soliton sequences in broadband fiber optics systems with $N$ frequency channels, taking into account second-order dispersion, Kerr nonlinearity, delayed Raman response, and linear gain-loss. We employ a propagation model consisting of a system of $N$ coupled nonlinear Schr\\"odinger (NLS) equations and a reduced $N$-dimensional predator-prey model for amplitude dynamics. Numerical simulations with the coupled-NLS model with $2 \\le N \\le 4$ show stable oscillatory dynamics of soliton amplitudes at short-to-intermediate distances, in agreement with predictions of the predator-prey model. Furthermore, the main destabilizing mechanism at long distances is due to generation of radiative sidebands, where the sidebands for a given channel form at the frequencies of solitons in the neighboring channels. This destabilizing process can be partially mitigated by employing frequency dependent linear gain-loss. Moreover, significant enhancement of transmission stabi...
Feshbach Resonances in Kerr Frequency Combs
Matsko, Andrey B
2014-01-01
We show that both the power and repetition rate of a frequency comb generated in a nonlinear ring resonator, pumped with continuous wave (cw) coherent light, are modulated. The modulation is brought about by the interaction of the cw background with optical pulses excited in the resonator, and occurs in resonators with nonzero high-order chromatic dispersion and wavelength-dependent quality factor. The modulation frequency corresponds to the detuning of the pump frequency from the eigenfrequency of the pumped mode in the resonator.
Solookinejad, G.
2016-09-01
In this study, the linear and nonlinear susceptibility of a single-layer graphene nanostructure driven by a weak probe light and an elliptical polarized coupling field is discussed theoretically. The Landau levels of graphene can be separated in infrared or terahertz regions under the strong magnetic field. Therefore, by using the density matrix formalism in quantum optic, the linear and nonlinear susceptibility of the medium can be derived. It is demonstrated that by adjusting the elliptical parameter, one can manipulate the linear and nonlinear absorption as well as Kerr nonlinearity of the medium. It is realized that the enhanced Kerr nonlinearity can be possible with zero linear absorption and nonlinear amplification at some values of elliptical parameter. Our results may be having potential applications in quantum information science based on Nano scales devices.
Energy Technology Data Exchange (ETDEWEB)
Solookinejad, G., E-mail: ghsolooki@gmail.com
2016-09-15
In this study, the linear and nonlinear susceptibility of a single-layer graphene nanostructure driven by a weak probe light and an elliptical polarized coupling field is discussed theoretically. The Landau levels of graphene can be separated in infrared or terahertz regions under the strong magnetic field. Therefore, by using the density matrix formalism in quantum optic, the linear and nonlinear susceptibility of the medium can be derived. It is demonstrated that by adjusting the elliptical parameter, one can manipulate the linear and nonlinear absorption as well as Kerr nonlinearity of the medium. It is realized that the enhanced Kerr nonlinearity can be possible with zero linear absorption and nonlinear amplification at some values of elliptical parameter. Our results may be having potential applications in quantum information science based on Nano scales devices.
Elementary Superconductivity in Nonlinear Electrodynamics Coupled to Gravity
Dymnikova, Irina
2015-01-01
Source-free equations of nonlinear electrodynamics minimally coupled to gravity admit regular axially symmetric asymptotically Kerr-Newman solutions which describe charged rotating black holes and electromagnetic spinning solitons (lumps). Asymptotic analysis of solutions shows, for both black holes and solitons, the existence of de Sitter vacuum interior which has the properties of a perfect conductor and ideal diamagnetic and displays superconducting behaviour which can be responsible for practically unlimited life time of an object. Superconducting current flows on the equatorial ring replacing the Kerr ring singularity of the Kerr-Newman geometry. Interior de Sitter vacuum supplies the electron with the finite positive electromagnetic mass related the interior de Sitter vacuum of the electroweak scale and to breaking of space-time symmetry, which allows to explain the mass-square differences for neutrino and the appearance of the minimal length scale in the annihilation reaction $e^{+}e^{-}\\rightarrow\\gam...
Derivation of an Applied Nonlinear Schroedinger Equation.
Energy Technology Data Exchange (ETDEWEB)
Pitts, Todd Alan; Laine, Mark Richard; Schwarz, Jens; Rambo, Patrick K.; Karelitz, David B.
2015-01-01
We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release
Localized modes in nonlinear photonic kagome nanoribbons
Energy Technology Data Exchange (ETDEWEB)
Molina, Mario I., E-mail: mmolina@uchile.cl [Departamento de Física, MSI – Nucleus for Advanced Optics, and Center for Optics and Photonics (CEFOP), Facultad de Ciencias, Universidad de Chile, Santiago (Chile)
2012-10-01
We examine localization of light in nonlinear (Kerr) kagome lattices in the shape of narrow strips of varying width. For the narrowest ribbon, the band structure features a flat band leading to linear dynamical trapping of an initially localized excitation. We also find a geometry-induced bistability of the nonlinear modes as the width of the strip is changed. A crossover from one to two dimensions localization behavior is observed as the width is increased, attaining two-dimensional behavior for relatively narrow ribbons.
Derivation of an applied nonlinear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Pitts, Todd Alan [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Laine, Mark Richard [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Schwarz, Jens [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Rambo, Patrick K. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Karelitz, David B. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
2015-01-01
We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release
Multi-bi- and tri-stability using nonlinear plasmonic Fano resonators
Amin, Muhammad
2013-09-01
A plasmonic Fano resonator embedding Kerr nonlinearity is used to achieve multi-bi- and tri-stability. Fano resonance is obtained by inducing higher-order plasmon modes on metallic surfaces via geometrical symmetry breaking. The presence of the multiple higher order plasmon modes provides the means for producing multi-bi- or tri-stability in the response of the resonator when it is loaded with a material with Kerr nonlinearity. The multi-stability in the response of the proposed resonator enables its use in three-state all optical memory and switching applications. © 2013 IEEE.
Evaluation of the capacity of communication lines with nonlinear finite memory
Shapiro, E. G.; Shapiro, D. A.
2016-12-01
We propose a method for calculating the capacity of a finite-memory channel up to the square of the nonlinear memory parameter. A comparison with a regular Gaussian model is performed, in which the Kerr nonlinearity is considered as an additional Gaussian noise. The estimate by the regular Gaussian model is shown to yield a greater capacity as compared with the estimate obtained by the nonlinear memory model. The optimal signal powers, providing the maximum mutual information, are found to be equal.
Carrillo-Delgado, C.; Torres-Torres, D.; Trejo-Valdez, M.; Rebollo, N. R.; Hernández-Gómez, L. H.; Torres-Torres, C.
2015-08-01
Experimental and numerical results about the propagation of optical signals in a bidirectional two-wave mixing system with Au nanocomposites and carbon nanotubes are presented. Au nanoparticles embedded in a TiO2 thin solid film were prepared by a sol-gel processing route; while carbon nanotubes were obtained by a thermal decomposition approach. A thin film conformed by carbon nanotubes was put on top of the Au nanocomposites for the nonlinear optical measurements. A two-wave mixing experiment was conducted to distinguish the direction of propagation of a probe-beam through the exploration of an induced birefringence and two-photon absorption. The third-order nonlinear optical response of the sample was evaluated by considering discrete groups of energy numerically modeled by the beam propagation method. Remarkable differences exhibited by the propagation and counter-propagation of a polarized probe beam were identified by nanosecond pulses at 532 nm wavelength. By employing a 405 nm wavelength as a probe beam, we were able to change the behavior of the direction of maximum Kerr transmittance in a particular geometry of a non-degenerated multi-wave system. It can be contemplated that the influence of distinctive near- and off-resonant excitations of the samples seems to be useful to control a selective one-way transmittance with potential applications for developing all-optical systems.
Thermal radiation from optically driven Kerr (χ{sup (3)}) photonic cavities
Energy Technology Data Exchange (ETDEWEB)
Khandekar, Chinmay; Rodriguez, Alejandro W. [Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08540 (United States); Lin, Zin [School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02139 (United States)
2015-04-13
We describe thermal radiation from nonlinear (χ{sup (3)}) photonic cavities coupled to external channels and subject to incident monochromatic light. Our work extends related work on nonlinear mechanical oscillators to the problem of thermal radiation, demonstrating that bistability can enhance thermal radiation by orders of magnitude and result in strong lineshape alternations, including “super-narrow spectral peaks” occurring at the onset of kinetic phase transitions. We show that when the cavities are designed to exhibit perfect linear emissivity (rate matching), such thermally activated transitions can be exploited to dramatically tune the output power and radiative properties of the cavity, leading to a kind of Kerr-mediated thermo-optic effect. Finally, we demonstrate that in certain parameter regimes, the output radiation exhibits Stokes and anti-Stokes side peaks whose relative magnitudes can be altered by tuning the internal temperature of the cavity relative to its surroundings, a consequence of strong correlations and interference between the emitted and reflected radiation.
Noncommutative Nonlinear Supersymmetry
Nishino, H; Nishino, Hitoshi; Rajpoot, Subhash
2002-01-01
We present noncommutative nonlinear supersymmetric theories. The first example is a non-polynomial Akulov-Volkov-type lagrangian with noncommutative nonlinear global supersymmetry in arbitrary space-time dimensions. The second example is the generalization of this lagrangian to Dirac-Born-Infeld lagrangian with nonlinear supersymmetry realized in dimensions D=2,3,4 and 6 (mod 8).
Amini, Saeed K.
2014-06-01
Crystalline pyrazole consists of nonlinear chains of an aromatic molecule. It includes two independent molecules which in turn causes two different types of hydrogen bonds (HBs). These two types of HBs with slight differences in their Nsbnd H⋯N geometries can be considered as interesting ones in the recent studies of cooperativity between different HBs. These HBs are investigated in several pyrazole clusters by electronic structure calculations. Parameters such as structure, binding energy, charge transfer, chemical shielding and electric field gradient (EFG) parameters calculated at the second order Moller-Plesset perturbation (MP2) and density functional (DF) levels of theory. Both the basis set superposition error (BSSE) and zero point vibrational energy (ZPVE) corrections on the cooperativity enhancement were considered. Changes of different properties of clusters against crystal size were investigated by proposed diagrams fitted to a logarithmic function which renders their extrema in the crystal limit. In each cluster, pyrazole molecules for which their parameters are more affected by cooperativity enhancement were explored employing these fitted diagrams. Most calculated energetic and spectroscopic parameters were in good linear correlations with both the structural parameters and charge transfer along HB (q). These correlations in the cases of nuclear magnetic resonance (NMR) and nuclear quadrupolar resonance (NQR) parameters, were explained in the terms of natural charges of bonding (σ(N1sbnd H1)) and antibonding (σ*(N1sbnd H1)) orbitals. Organizing calculated data for mental clusters with similar molecules and HB types produced better regression values in all linear correlations. According to the experimental CQ of N(2) in solid state and zero charge transfer in the gas phase, the value of charge transfer in the crystalline pyrazole and gas phase value of CQ of N(2) were assessed, respectively. Diagrams of the structural parameters against either
The matter-antimatter interpretation of Kerr spacetime
Villata, M
2014-01-01
Repulsive gravity is not very popular in physics. However, one comes across it in at least two main occurrences in general relativity: in the negative-$r$ region of Kerr spacetime, and as the result of the gravitational interaction between matter and antimatter, when the latter is assumed to be CPT-transformed matter. Here we show how these two independent developments of general relativity are perfectly consistent in predicting gravitational repulsion and how the above Kerr negative-$r$ region can be interpreted as the habitat of antimatter. As a consequence, matter particles traveling along vortical geodesics can pass through the throat of a rotating black hole and emerge as antimatter particles (and vice versa). An experimental definitive answer on the gravitational behavior of antimatter is awaited in the next few years.
Spin geometry and conservation laws in the Kerr spacetime
Andersson, Lars; Blue, Pieter
2015-01-01
In this paper we will review some facts, both classical and recent, concerning the geometry and analysis of the Kerr and related black hole spacetimes. This includes the analysis of test fields on these spacetimes. Central to our analysis is the existence of a valence $(2,0)$ Killing spinor, which we use to construct symmetry operators and conserved currents as well as a new energy momentum tensor for the Maxwell test fields on a class of spacetimes containing the Kerr spacetime. We then outline how this new energy momentum tensor can be used to obtain decay estimated for Maxwell test fields. An important motivation for this work is the black hole stability problem, where fields with non-zero spin present interesting new challenges. The main tool in the analysis is the 2-spinor calculus, and for completeness we introduce its main features.
Hidden Conformal Symmetry of the Kerr-Newman Black Hole
Wang, Yong-Qiang
2010-01-01
We investigate the hidden conformal symmetry of the 4-dimensional non-extremal Kerr-Newman (KN) black hole with the idea of the near-region Kerr/CFT Corresponding proposed by Castro, Maloney and Strominger in arXiv:1004.0996[hep-th]. The near-region KN black hole is dual to a 2D CFT with left and right temperatures $T_L=(2 M^2-Q^2)/(4\\pi J)$ and $T_R=\\sqrt{M^4-J^2-M^2Q^2}/(2\\pi J)$. Furthermore, we can reobtain the macroscopic Bekenstein-Hawking entropy of the KN black hole and precisely match the absorption cross section of a near-region scalar field in the KN black hole with the finite-temperature absorbtion cross section for a 2D CFT.
Curved plasma channels: Kerr lens and Airy prism
Kasparian, Jérôme; 10.2971/jeos.2009.09039
2010-01-01
We analytically calculate the transverse energy fluxes that would be respectively induced in high-power Airy beams by the Kerr self-focusing and the Airy profile itself if they were the only active process. In experimental condition representative of laser filamentation experiments of high-power ultrashort laser pulses in air and condensed media, the Kerr lens induces transverse energy fluxes much larger than the Airy "prism" at the main peak. As a consequence, the curved plasma channels in Airy beams are not only a plasma spark on a curved focus, but indeed self-guided filaments, and their curved trajectory appears as a perturbation due to the linear Airy propagation regime.
Observable acceleration of jets by a Kerr black hole
Gariel, J; Wang, Anzhong
2016-01-01
In the framework of a model based on the gravitational field of the Kerr black hole, we turn to analyse the kinematic behaviour of extragalactic jets. We analytically calculate the observable velocities and accelerations along any geodesic. Then, by numerical calculations, we apply our results to a geodesic, typical of the M87 jet, and we probe our results by confrontation to recent observations. A transition from non-relativistic to ultrarelativistic speeds at subparsec scale is highlighted. This transition comes sooner and more abruptly than in models based on magnetic paradigm, which means that we need a weaker magnetic field to explain observed synchrotron radiation. We attribute the ejection phenomenon to the repulsive effect of the gravitomagnetic Kerr field.
Quantization of fermions on Kerr space-time
Casals, Marc; Dolan, Sam R.; Nolan, Brien C.; Ottewill, Adrian C.; Winstanley, Elizabeth
2013-03-01
We study a quantum fermion field on a background nonextremal Kerr black hole. We discuss the definition of the standard black hole quantum states (Boulware, Unruh, and Hartle-Hawking), focussing particularly on the differences between fermionic and bosonic quantum field theory. Since all fermion modes (both particle and antiparticle) have positive norm, there is much greater flexibility in how quantum states are defined compared with the bosonic case. In particular, we are able to define a candidate Boulware-like state, empty at both past and future null infinity, and a candidate Hartle-Hawking-like equilibrium state, representing a thermal bath of fermions surrounding the black hole. Neither of these states have analogues for bosons on a nonextremal Kerr black hole and both have physically attractive regularity properties. We also define a number of other quantum states, numerically compute differences in expectation values of the fermion current and stress-energy tensor between two states, and discuss their physical properties.
Optical limiter based on two-dimensional nonlinear photonic crystals
Belabbas, Amirouche; Lazoul, Mohamed
2016-04-01
The aim behind this work is to investigate the capabilities of nonlinear photonic crystals to achieve ultra-fast optical limiters based on third order nonlinear effects. The purpose is to combine the actions of nonlinear effects with the properties of photonic crystals in order to activate the photonic band according to the magnitude of the nonlinear effects, themselves a function of incident laser power. We are interested in designing an optical limiter based nonlinear photonic crystal operating around 1064 nm and its second harmonic at 532 nm. Indeed, a very powerful solid-state laser that can blind or destroy optical sensors and is widely available and easy to handle. In this work, we perform design and optimization by numerical simulations to determine the better structure for the nonlinear photonic crystal to achieve compact and efficient integrated optical limiter. The approach consists to analyze the band structures in Kerr-nonlinear two-dimensional photonic crystals as a function of the optical intensity. We confirm that these bands are dynamically red-shifted with regard to the bands observed in linear photonic crystals or in the case of weak nonlinear effects. The implemented approach will help to understand such phenomena as intensitydriven optical limiting with Kerr-nonlinear photonic crystals.