Controllable Akhmediev breather and Kuznetsov-Ma soliton trains in PT-symmetric coupled waveguides.
Dai, Chaoqing; Wang, Yueyue; Zhang, Xiaofei
2014-12-01
The PT-symmetric and PT-antisymmetric Akhmediev breather (AB) and Kuznetsov-Ma (KM) soliton train solutions of a (2+1)-dimensional variable-coefficient coupled nonlinear Schrödinger equation in PT-symmetric coupled waveguides with gain and loss are derived via the Darboux transformation method. From these analytical solutions, we investigate the controllable behaviors of AB and KM soliton trains in a diffraction decreasing system with exponential profile. By adjusting the relation between the maximum Zm of effective propagation distance and the peak locations Zi of AB and KM soliton trains, we can control the restraint, maintenance and postpone excitations of AB and KM soliton trains.
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Amore, Paolo, E-mail: paolo.amore@gmail.com [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima (Mexico); Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar [INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina); Garcia, Javier [INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina); Gutierrez, German [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima (Mexico)
2014-04-15
We study both analytically and numerically the spectrum of inhomogeneous strings with PT-symmetric density. We discuss an exactly solvable model of PT-symmetric string which is isospectral to the uniform string; for more general strings, we calculate exactly the sum rules Z(p)≡∑{sub n=1}{sup ∞}1/E{sub n}{sup p}, with p=1,2,… and find explicit expressions which can be used to obtain bounds on the lowest eigenvalue. A detailed numerical calculation is carried out for two non-solvable models depending on a parameter, obtaining precise estimates of the critical values where pair of real eigenvalues become complex. -- Highlights: •PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. •We study PT-symmetric strings with complex density. •They exhibit regions of unbroken PT symmetry. •We calculate the critical parameters at the boundaries of those regions. •There are exact real sum rules for some particular complex densities.
Experimental demonstration of PT-symmetric stripe lasers
Gu, Zhiyuan; Lyu, Quan; Li, Meng; Xiao, Shumin; Song, Qinghai
2015-01-01
Recently, the coexistence of parity-time (PT) symmetric laser and absorber has gained tremendous research attention. While the PT symmetric absorber has been observed in microwave metamaterials, the experimental demonstration of PT symmetric laser is still absent. Here we experimentally study PT-symmetric laser absorber in stripe waveguide. Using the concept of PT symmetry to exploit the light amplification and absorption, PT-symmetric laser absorbers have been successfully obtained. Different from the single-mode PT symmetric lasers, the PT-symmetric stripe lasers have been experimentally confirmed by comparing the relative wavelength positions and mode spacing under different pumping conditions. When the waveguide is half pumped, the mode spacing is doubled and the lasing wavelengths shift to the center of every two initial lasing modes. All these observations are consistent with the theoretical predictions and confirm the PT-symmetry breaking well.
Revisiting the Optical PT-Symmetric Dimer
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José Delfino Huerta Morales
2016-08-01
Full Text Available Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of PT -symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical PT -symmetric dimer, a two-waveguide coupler where the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry-based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar N-waveguide couplers that are the optical realization of the Lorentz group in 2 + 1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of the Ehrenfest theorem.
Revisiting the optical $PT$-symmetric dimer
Morales, J D Huerta; López-Aguayo, S; Rodríguez-Lara, B M
2016-01-01
Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of $\\mathcal{PT}$-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical $\\mathcal{PT}$-symmetric dimer, a two-waveguide coupler were the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar $N$-waveguide couplers that are the optical realization of Lorentz group in 2+1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of Ehrenfest theorem.
Bender, Carl M.
2015-07-01
The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian H = p2 + ix3, which is obviously not Dirac Hermitian, has a positive real discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory. Evidently, the axiom of Dirac Hermiticity is too restrictive. While H = p2 + ix3 is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined parity P (space reflection) and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past few years, some of these properties have been verified in laboratory experiments. A particularly interesting PT-symmetric Hamiltonian is H = p2 - x4, which contains an upside-down potential. This potential is discussed in detail, and it is explained in intuitive as well as in rigorous terms why the energy levels of this potential are real, positive, and discrete. Applications of PT-symmetry in quantum field theory are also discussed.
PT-symmetric phase in kagome photonic lattices
Chern, Gia-Wei; Saxena, Avadh
2015-01-01
Kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Here we propose a complex photonic lattice by placing $\\mathcal{PT}$-symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gai...
PT-symmetric phase in kagome photonic lattices
Chern, Gia-Wei
2015-01-01
Kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Here we propose a complex photonic lattice by placing $\\mathcal{PT}$-symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gain and loss on individual dimers, the system exhibits a $\\mathcal{PT}$-symmetric phase for finite gain/loss parameter up to a critical value. The beam evolution in this complex kagome waveguide array exhibits a novel oscillatory rotation of optical power along the propagation distance. Long-lived local chiral structures originating from the nearly flat bands of the kagome structure are observed when the lattice is subject to a narrow beam excitation.
PT-symmetric phase in kagome-based photonic lattices.
Chern, Gia-Wei; Saxena, Avadh
2015-12-15
The kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Here we propose a complex photonic lattice by placing PT-symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gain and loss on individual dimers, the system exhibits a PT-symmetric phase for finite gain/loss parameter up to a critical value. The beam evolution in this complex kagome waveguide array exhibits a novel oscillatory rotation of optical power along the propagation distance. Long-lived local chiral structures originating from the nearly flat bands of the kagome structure are observed when the lattice is subject to a narrow beam excitation.
Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides
Nixon, Sean
2016-01-01
Many classes of non-parity-time (PT) symmetric waveguides with arbitrary gain and loss distributions still possess all-real linear spectrum or exhibit phase transition. In this article, nonlinear light behaviors in these complex waveguides are probed analytically near a phase transition. Using multi-scale perturbation methods, a nonlinear ordinary differential equation (ODE) is derived for the light's amplitude evolution. This ODE predicts that the first class of these non-PT-symmetric waveguides support continuous families of solitons and robust amplitude-oscillating solutions both above and below phase transition, in close analogy with PT-symmetric systems. For the other classes of waveguides, the light's intensity always amplifies under the effect of nonlinearity even if the waveguide is below phase transition. These analytical predictions are confirmed by direct computations of the full system.
$\\mathcal{PT}$-symmetric microring laser-absorber
Longhi, Stefano
2014-01-01
The lasing and coherent perfect absorption (CPA) properties of $\\mathcal{PT}$-symmetric microrings with mixed index and gain gratings, externally coupled to a bus waveguide, are theoretically investigated. For a complex grating at the $\\mathcal{PT}$ symmetry breaking point, perfect unidirectional (either clockwise or counterclockwise) laser emission can be realized, however the grating does not discriminate longitudinal modes and CPA can not be simultaneously achieved. Above the grating $\\mathcal{PT}$ symmetry breaking point, single mode emission and simultaneous CPA can be obtained, with unbalanced and controllable excitation of clockwise and counterclockwise modes in the ring.
Joglekar, Yogesh N
2010-01-01
We study the properties of a parity- and time-reversal- (PT) symmetric tight-binding chain of size N with position-dependent hopping amplitude. In contrast to the fragile PT-symmetric phase of a chain with constant hopping and imaginary impurity potentials, we show that, under very general conditions, our model is {\\it always} in the PT-symmetric phase. We numerically obtain the energy spectrum and the density of states of such a chain, and show that they are widely tunable. By studying the size-dependence of inverse participation ratios, we show that although the chain is not translationally invariant, most of its eigenstates are extended. Our results indicate that tight-binding models with non-Hermitian PT-symmetric hopping have a robust PT-symmetric phase and rich dynamics.
Engineering wavefront caustics trajectories in ${\\cal PT}$-symmetric lattices
Bender, Nicholas; Kottos, Tsampikos
2015-01-01
We utilize caustic theory in ${\\cal PT}-$symmetric lattices to design focusing and curved beam dynamics. We show that the gain and loss parameter in these systems provides an addition degree of freedom which allows for the design of the same caustics trajectories with different intensity distribution in the individual waveguides. Moreover we can create aberration-free focal points at any paraxial distance $z_f$, with anomalously large focal intensity.
PT-Symmetric Quantum Electrodynamics
Bender, C M; Milton, K A; Shajesh, K V; Bender, Carl M.; Cavero-Pelaez, Ines; Milton, Kimball A.
2005-01-01
The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge $e$ is taken to be imaginary. However, if one also specifies that the potential $A^\\mu$ in such a theory transforms as a pseudovector rather than a vector, then the Hamiltonian becomes PT symmetric. The resulting non-Hermitian theory of electrodynamics is the analog of a spinless quantum field theory in which a pseudoscalar field $\\phi$ has a cubic self-interaction of the form $i\\phi^3$. The Hamiltonian for this cubic scalar field theory has a positive spectrum, and it has recently been demonstrated that the time evolution of this theory is unitary. The proof of unitarity requires the construction of a new operator called C, which is then used to define an inner product with respect to which the Hamiltonian is self-adjoint. In this paper the corresponding C operator for non-Hermitian quantum electrodynamics is constructed perturbatively. This construction demonstrates the unitarity of the theory. Non-Hermit...
Optical waveguide arrays: quantum effects and PT symmetry breaking
Joglekar, Yogesh N; Scott, Derek D; Vemuri, Gautam
2013-01-01
Over the last two decades, advances in fabrication have led to significant progress in creating patterned heterostructures that support either carriers, such as electrons or holes, with specific band structure or electromagnetic waves with a given mode structure and dispersion. In this article, we review the properties of light in coupled optical waveguides that support specific energy spectra, with or without the effects of disorder, that are well-described by a Hermitian tight-binding model. We show that with a judicious choice of the initial wave packet, this system displays the characteristics of a quantum particle, including transverse photonic transport and localization, and that of a classical particle. We extend the analysis to non-Hermitian, parity and time-reversal ($\\mathcal{PT}$) symmetric Hamiltonians which physically represent waveguide arrays with spatially separated, balanced absorption or amplification. We show that coupled waveguides are an ideal candidate to simulate $\\mathcal{PT}$-symmetri...
PT-Symmetric Quantum Field Theory
Milton, K A
2003-01-01
In the context of the PT-symmetric version of quantum electrodynamics, it is argued that the C operator introduced in order to define a unitary inner product has nothing to do with charge conjugation.
Scattering properties of PT-symmetric objects
Miri, Mohammad-Ali; Facao, Margarida; Abouraddy, Ayman F; Bakry, Ahmed; Razvi, Mir A N; Alshahrie, Ahmed; Alù, Andrea; Christodoulides, Demetrios N
2016-01-01
We investigate the scattering response of parity-time (PT) symmetric structures. We show that, due to the local flow of energy between gain and loss regions, such systems can deflect light in unusual ways, as a function of the gain/loss contrast. Such structures are highly anisotropic and their scattering patterns can drastically change as a function of the angle of incidence. In addition, we derive a modified optical theorem for PT-symmetric scattering systems, and discuss its ramifications.
Towards nanoscale multiplexing with parity-time symmetric plasmonic coaxial waveguides
Alaeian, Hadiseh; Jankovic, Vladan; Lawrence, Mark; Dionne, Jennifer A
2016-01-01
We theoretically investigate a nanoscale mode-division multiplexing scheme based on parity-time (PT) symmetric coaxial plasmonic waveguides. Coaxial waveguides support paired degenerate modes corresponding to distinct orbital angular momentum states. PT symmetric inclusions of gain and loss break the degeneracy of the paired modes and create new hybrid modes without orbital angular momentum. This process can be made thresholdless by matching the mode order with the number of gain and loss sections within the coaxial ring. Using both a Hamiltonian formulation and degenerate perturbation theory, we show how the wavevectors and fields evolve with increased loss/gain and derive sufficient conditions for thresholdless transitions. As a multiplexing filter, this PT symmetric coaxial waveguide could help double density rates in on-chip nanophotonic networks.
PT-Symmetric Optomechanically-Induced Transparency
Jing, H; Özdemir, S K; Zhang, J; Lü, X -Y; Peng, B; Yang, L; Nori, F
2014-01-01
Optomechanically-induced transparency (OMIT) and the associated slow-light propagation provide the basis for storing photons in nanofabricated phononic devices. Here we study OMIT in parity-time (PT)-symmetric microresonators with a tunable gain-to-loss ratio. This system features a reversed, non-amplifying transparency: inverted-OMIT. When the gain-to-loss ratio is steered, the system exhibits a transition from the PT-symmetric phase to the broken-PT-symmetric phase. We show that by tuning the pump power at fixed gain-to-loss ratio or the gain-to-loss ratio at fixed pump power, one can switch from slow to fast light and vice versa. Moreover, the presence of PT-phase transition results in the reversal of the pump and gain dependence of transmission rates. These features provide new tools for controlling light propagation using optomechanical devices.
PT -symmetric model of immune response
Bender, Carl M.; Ghatak, Ananya; Gianfreda, Mariagiovanna
2017-01-01
The study of PT -symmetric physical systems began in 1998 as a complex generalization of conventional quantum mechanics, but beginning in 2007 experiments began to be published in which the predicted PT phase transition was clearly observed in classical rather than in quantum-mechanical systems. This paper examines the classical PT phase transition in dynamical-system models that are moderately accurate representations of antigen-antibody systems. A surprising conclusion that can be drawn from these models is that it might be possible treat a serious disease in which the antigen concentration grows out of bounds (and the host dies) by injecting a small dose of a second (different) antigen. In this case a PT -symmetric analysis shows there are two possible favorable outcomes. In the unbroken-PT -symmetric phase the disease becomes chronic and is no longer lethal, while in the appropriate broken-PT -symmetric phase the concentration of lethal antigen goes to zero and the disease is completely cured.
Robust PT-symmetric chain and properties of its Hermitian counterpart
Joglekar, Yogesh N.; Saxena, Avadh
2011-05-01
We study the properties of a parity- and time-reversal- (PT) symmetric tight-binding chain of size N with position-dependent hopping amplitude. In contrast to the fragile PT-symmetric phase of a chain with constant hopping and imaginary impurity potentials, we show that, under very general conditions, our model is always in the PT-symmetric phase. We numerically obtain the energy spectrum and the density of states of such a chain, and show that they are widely tunable. By studying the size dependence of inverse participation ratios, we show that although the chain is not translationally invariant, most of its eigenstates are extended. Our results indicate that tight-binding models with non-Hermitian, PT-symmetric hopping have a robust PT-symmetric phase and rich dynamics which may be explored in coupled waveguides.
PT-symmetric deformations of integrable models.
Fring, Andreas
2013-04-28
We review recent results on new physical models constructed as PT-symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of Calogero-Moser-Sutherland type and nonlinear integrable field equations of Korteweg-de Vries type. The quantum spin chain discussed is related to the first example in the series of the non-unitary models of minimal conformal field theories. For the Calogero-Moser-Sutherland models, we provide three alternative deformations: a complex extension for models related to all types of Coxeter/Weyl groups; models describing the evolution of poles in constrained real-valued field equations of nonlinear integrable systems; and genuine deformations based on antilinearly invariant deformed root systems. Deformations of complex nonlinear integrable field equations of Korteweg-de Vries type are studied with regard to different kinds of PT-symmetrical scenarios. A reduction to simple complex quantum mechanical models currently under discussion is presented.
Nonlinear waves in $\\cal PT$-symmetric systems
Konotop, Vladimir V.; Yang, Jianke; Zezyulin, Dmitry A.
2016-01-01
Recent progress on nonlinear properties of parity-time ($\\cal PT$-) symmetric systems is comprehensively reviewed in this article. $\\cal PT$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\\cal PT$ symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a $\\cal PT$-symmetric system. The nat...
Controlling of blow-up responses by nonlinear PT -symmetric coupling
Karthiga, S.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2017-03-01
We investigate the dynamics of a coupled waveguide system with competing linear and nonlinear loss-gain profiles which can facilitate power saturation. We show the usefulness of the model in achieving unidirectional beam propagation. In this regard, the considered type of coupled waveguide system has two drawbacks: (i) difficulty in achieving perfect isolation of light in a waveguide and (ii) existence of blow-up-type behavior for certain input power situations. We here show a nonlinear PT -symmetric coupling that helps to overcome these two drawbacks. Such a nonlinear coupling has close connection with the phenomenon of stimulated Raman scattering. In particular, we have elucidated the role of this nonlinear coupling using an integrable PT -symmetric situation. In particular, using the integrals of motion, we have reduced this coupled waveguide problem to the problem of dynamics of a particle in a potential. With the latter picture, we have clearly illustrated the role of the considered nonlinear coupling. The above PT -symmetric case corresponds to a limiting form of a general equation describing the phenomenon of stimulated Raman scattering. We also point out the ability to transport light unidirectionally even in this general case.
Invisibility in PT-symmetric complex crystals
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Longhi, Stefano, E-mail: longhi@fisi.polimi.it [Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci 32, I-20133 Milano (Italy)
2011-12-02
Bragg scattering in sinusoidal PT-symmetric complex crystals of finite thickness is theoretically investigated by the derivation of exact analytical expressions for reflection and transmission coefficients in terms of modified Bessel functions of first kind. The analytical results indicate that unidirectional invisibility, recently predicted for such crystals by coupled-mode theory (Z Lin et al 2011 Phys. Rev. Lett. http://dx.doi.org/10.1103/PhysRevLett.106.213901), breaks down for crystals containing a large number of unit cells. In particular, for a given modulation depth in a shallow sinusoidal potential, three regimes are encountered as the crystal thickness is increased. At short lengths the crystal is reflectionless and invisible when probed from one side (unidirectional invisibility), whereas at intermediate lengths the crystal remains reflectionless but not invisible; for longer crystals both unidirectional reflectionless and invisibility properties are broken. (paper)
Electrically tunable coalescence of exceptional points in parity-time symmetric waveguides
Wang, Jin; Wu, Raymond P H; Mok, T C; Fung, Kin Hung
2016-01-01
We demonstrate theoretically the high electric tunability of the emergence and coalescence of exceptional points in PT-symmetric waveguides bounded by imperfect conductive layers. Owing to the competition effect of multimode interaction, multiple exceptional points and PT phase transitions could be attained in such a simple system and, meanwhile, their occurrences are strongly dependent on the boundary conductive layers. When the conductive layers become very thin, it is found that the sideway transmittance and reflectance of the same system can be tuned between zero and one by a small change in carrier density. The results may provide an effective method for fast tuning and modulation of optical signals through electrical gating.
Metrology with PT-Symmetric Cavities: Enhanced Sensitivity near the PT-Phase Transition.
Liu, Zhong-Peng; Zhang, Jing; Özdemir, Şahin Kaya; Peng, Bo; Jing, Hui; Lü, Xin-You; Li, Chun-Wen; Yang, Lan; Nori, Franco; Liu, Yu-Xi
2016-09-09
We propose and analyze a new approach based on parity-time (PT) symmetric microcavities with balanced gain and loss to enhance the performance of cavity-assisted metrology. We identify the conditions under which PT-symmetric microcavities allow us to improve sensitivity beyond what is achievable in loss-only systems. We discuss the application of PT-symmetric microcavities to the detection of mechanical motion, and show that the sensitivity is significantly enhanced near the transition point from unbroken- to broken-PT regimes. Our results open a new direction for PT-symmetric physical systems and it may find use in ultrahigh precision metrology and sensing.
Topological states in partially-PT-symmetric azimuthal potentials
Kartashov, Yaroslav V; Torner, Lluis
2015-01-01
We introduce partially-parity-time-symmetric (pPT-symmetric) azimuthal potentials composed from individual PT-symmetric cells located on a ring, where two azimuthal directions are nonequivalent in a sense that in such potentials excitations carrying topological dislo-cations exhibit different dynamics for different directions of energy circulation in the initial field distribution. Such non-conservative ratchet-like structures support rich families of stable vortex solitons in cubic nonlinear media, whose properties depend on the sign of the topological charge due to the nonequivalence of azimuthal directions. In contrast, oppositely charged vortex solitons remain equivalent in similar fully PT-symmetric potentials. The vortex solitons in the pPT- and PT-symmetric potentials are shown to feature qualitatively different internal current distributions, which are described by different discrete rotation symmetries of the intensity profiles.
Feijoo, David; Konotop, Vladimir V
2016-01-01
We analyze a system of three two-dimensional nonlinear Schr\\"odinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time ($\\mathcal{PT}$) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the $\\mathcal{PT}$-symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and $\\mathcal{PT}$-symmetric cases. Interactions and collisions between the conservative and $\\mathcal{PT}$-symmetric solitons are briefly investigated, as well.
Nonlinear waves in $\\cal PT$-symmetric systems
Konotop, Vladimir V; Zezyulin, Dmitry A
2016-01-01
Recent progress on nonlinear properties of parity-time ($\\cal PT$-) symmetric systems is comprehensively reviewed in this article. $\\cal PT$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\\cal PT$ symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a $\\cal PT$-symmetric system. The natural inclusion of nonlinearity into these $\\cal PT$ systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above $\\cal PT$-symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear $\\cal PT$-symmetric systems arising from various physical disciplines ...
Three-dimensional modes of a symmetric nonlinear plane waveguide
Akhmediev, N. N.; Nabiev, R. F.; Popov, Yu. M.
1989-01-01
The three-dimensional problem of a symmetric nonlinear plane waveguide, which consist of a linear medium layer surrounded by nonlinear media, is investigated. The stationary solution of this problem is a mode whose field is falling to zero at infinity in all directions perpendicular to the propagation direction. The even, odd and assymetrical solutions of the problem are obtained.
A symmetric terahertz graphene-based hybrid plasmonic waveguide
Chen, Ming; Sheng, Pengchi; Sun, Wei; Cai, Jianjin
2016-10-01
A graphene-based hybrid plasmonic waveguide (GHPW) structure, which works on the terahertz frequency and includes two identical cylinder robs symmetrically put on each side of graphene sheet with gaps g, has been proposed and investigated. The present waveguide not only significantly improves the propagation length but also maintains a compact mode area, which is due to the coupling between the dielectric waveguide mode and plasmonic mode. The graphene plasmons particularly differ from plasmons in noble metals of which propagation loss can be tuned by adjusting the Fermi energy level or carrier mobility. With a very good Fermi energy level and carrier mobility, a typical propagation length of 26.7 mm, and mode area of optical field of approximately 4 μm2 at 10 THz are achieved. This waveguide structure shows great promise for designing kinds of functional elements in actively tunable integrated optical devices.
PT-symmetric $\\varphi^4$ theory in d=0 dimensions
Bender, Carl M; Messina, Emanuele
2015-01-01
A detailed study of a PT-symmetric zero-dimensional quartic theory is presented and a comparison between the properties of this theory and those of a conventional quartic theory is given. It is shown that the PT-symmetric quartic theory evades the consequences of the Mermin-Wagner-Coleman theorem regarding the absence of symmetry breaking in d<2 dimensions. Furthermore, the PT-symmetric theory does not satisfy the usual Bogoliubov limit for the construction of the Green's functions because one obtains different results for the $h\\to0^-$ and the $h\\to0^+$ limits.
Phase-coupled optical diode based on PT symmetric system
Gao, Yong-Pan; Cao, Cong; Zhang, Yong; Wang, Tie-Jun; Wang, Chuan
2017-01-01
Here we investigate a phase-coupled parity-time symmetric plasmonic system, and theoretically achieved the all optical on-chip plasmonic diode using the coupled mode theory. The proposed symmetrical system consists of one loss cavity and one gain cavity each coupled with the waveguide, and we find that the controllable amplification of the input field can be achieved by changing the power coupling fraction between the resonators and the waveguide. Moreover, this loss-gain symmetric system could work as a frequency comb filter, and the operation on the device could be controlled by tuning the coupling strength between the two plasmonic cavities by tuning the coupling distance between the cavities and the waveguide.
Zero index metamaterials with PT symmetry in a waveguide system.
Fu, Yangyang; Xu, Yadong; Chen, Huanyang
2016-01-25
Inspired by the concept of parity-time symmetry, we propose a new waveguide system consisting of zero index metamaterials with an air gap. Based on analytical calculations and numerical simulations, we demonstrate that there are two exceptional points in such a system, which can induce unidirectional transparency. However, the introduced air gap could effectively manipulate the property of the waveguide system with PT symmetry. In particular, coherent perfect absorber-laser modes could be excited in PT broken phase, if a specific phase difference in the air gap is obtained. More interestingly, when Fabry-Pérot resonances take place in the air gap, the PT symmetry property will be suppressed, i.e., the value of loss/gain could not affect transmission and reflection of the waveguide. As a result, perfect bidirectional transmission without reflection can occur in the waveguide system.
Efficient microfluidic photocatalysis in a symmetrical metal-cladding waveguide.
Zhu, Shu; Dai, Hailang; Jiang, Bei; Shen, Zhenhua; Chen, Xianfeng
2016-02-14
In this paper, a symmetrical metal-cladding optical waveguide based microfluidic chip with a self-organized and free-standing TiO2 nanotube membrane was utilized to perform efficient photocatalysis. The chip has a microchannel bonded with TiO2 nanotube coated glass. The employment of microfluidic chip for hydrolysis reaction can enable the transfer of mass and photons. Moreover, the incorporation of the double metal-cladding waveguide enhances the light-matter interaction and effectively improves the efficiency of photocatalysis.
Anomalous doublets of states in a PT symmetric quantum model
Znojil, M; Roy, P; Roychoudhury, R; Znojil, Miloslav; Levai, Geza; Roy, Pinaki; Roychoudhury, Rajkumar
2001-01-01
A PT symmetric complexification of a conditionally exactly solvable potential in one dimension leads to a paradox. The set of its normalizable solutions proves larger than one would expect on the basis of its point canonical transformation analysis.
Cliffordized NAC supersymmetry and PT-symmetric Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Toppan, Francesco [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: toppan@cbpf.br
2007-07-01
It is shown that non-anti commutative supersymmetry can be described through a Cliffordization of the superspace fermionic coordinates. A NAC supersymmetric quantum mechanical model is shown to be a PT-symmetric Hamiltonian. (author)
Nonlinear switching and solitons in PT-symmetric photonic systems
Suchkov, Sergey V; Huang, Jiahao; Dmitriev, Sergey V; Lee, Chaohong; Kivshar, Yuri S
2015-01-01
One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested Parity-Time (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT-symmetric photonic systems with an intensity-dependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly-induced PT-symmetry breaking, and all-optical switching. Nonl...
$\\mathcal{PT}$-symmetric mode-locking
Longhi, Stefano
2016-01-01
Parity-time ($\\mathcal{PT}$) symmetry is one of the most important accomplishments in optics over the past decade. Here the concept of $\\mathcal{PT}$ mode-locking of a laser is introduced, in which active phase locking of cavity axial modes is realized by asymmetric mode coupling in a complex time crystal. $\\mathcal{PT}$ mode-locking shows a transition from single to double pulse emission as the $\\mathcal{PT}$ symmetry breaking point is crossed. The transition can show a turbulent behavior, depending on a dimensionless modulation parameter that plays the same role as the Reynolds number in hydrodynamic flows.
Remarks on the PT-pseudo-norm in PT-symmetric quantum mechanics
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Duc Tai Trinh [Department of Mathematics, Teacher Training College of Dalat, 29 Yersin, Dalat (Viet Nam)]|[Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Trieste 34014 (Italy)
2005-04-22
This paper presents an underlying analytical relationship between the PT-pseudo-norm associated with the PT-symmetric Hamiltonian H = p{sup 2} + V(q) and the Stokes multiplier of the differential equation corresponding to this Hamiltonian. We show that the sign alternation of the PT-pseudo-norm, which has been observed as a generic feature of the PT-inner product, is essentially controlled by the derivative of a Stokes multiplier with respect to the eigenparameter.
PT-symmetric quantum electrodynamics and unitarity.
Milton, Kimball A; Abalo, E K; Parashar, Prachi; Pourtolami, Nima; Wagner, J
2013-04-28
More than 15 years ago, a new approach to quantum mechanics was suggested, in which Hermiticity of the Hamiltonian was to be replaced by invariance under a discrete symmetry, the product of parity and time-reversal symmetry, PT. It was shown that, if PT is unbroken, energies were, in fact, positive, and unitarity was satisfied. Since quantum mechanics is quantum field theory in one dimension--time--it was natural to extend this idea to higher-dimensional field theory, and in fact an apparently viable version of PT-invariant quantum electrodynamics (QED) was proposed. However, it has proved difficult to establish that the unitarity of the scattering matrix, for example, the Källén spectral representation for the photon propagator, can be maintained in this theory. This has led to questions of whether, in fact, even quantum mechanical systems are consistent with probability conservation when Green's functions are examined, since the latter have to possess physical requirements of analyticity. The status of PT QED will be reviewed in this paper, as well as the general issue of unitarity.
IS PT -SYMMETRIC QUANTUM THEORY FALSE AS A FUNDAMENTAL THEORY?
Directory of Open Access Journals (Sweden)
Miloslav Znojil
2016-06-01
Full Text Available Yi-Chan Lee et al. claim (cf. Phys. Rev. Lett. 112, 130404 (2014 that the “recent extension of quantum theory to non-Hermitian Hamiltonians” (which is widely known under the nickname of “PT-symmetric quantum theory” is “likely false as a fundamental theory”. By their opinion their results “essentially kill any hope of PT-symmetric quantum theory as a fundamental theory of nature”. In our present text we explain that their toy-model-based considerations are misleading and that they do not imply any similar conclusions.
Nonreciprocal Scattering by PT-symmetric stack of the layers
Shramkova, Oksana
2015-01-01
The nonreciprocal wave propagation in PT-symmetric periodic stack of binary dielectric layers characterised by balances loss and gain is analysed. The main mechanisms and resonant properties of the scattered plane waves are illustrated by the simulation results, and the effects of the periodicity and individual layer parameters on the stack nonreciprocal response are discussed. Gaussian beam dynamics in this type of structure is examined. The beam splitting in PT-symmetric periodic structure is observed. It is demonstrated that for slant beam incidence the break of the symmetry of field distribution takes place.
Stability of solitons in PT-symmetric couplers
Driben, Rodislav
2011-01-01
Families of analytical solutions are found for symmetric and antisymmetric solitons in the dual-core system with the Kerr nonlinearity and PT-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the "supersymmetric" case, with equal coefficients of the gain, loss and inter-core coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching ("management").
On the integrability of PT-symmetric dimers
Pickton, J
2013-01-01
The coupled discrete linear and Kerr nonlinear Schrodinger equations with gain and loss describing transport on dimers with parity-time (PT) symmetric potentials are considered. The model is relevant among others to experiments in optical couplers and proposals on Bose-Einstein condensates in PT symmetric double-well potentials. It is shown that the models are integrable. A pendulum equation with a linear potential and a constant force for the phase-difference between the fields is obtained, which explains the presence of unbounded solutions above a critical threshold parameter.
Anomalies in PT-Symmetric Quantum Field Theory
Milton, K A
2004-01-01
It is shown that a version of PT-symmetric electrodynamics based on an axial-vector current coupling massless fermions to the photon possesses anomalies and so is rendered nonrenormalizable. An alternative theory is proposed based on the conventional vector current constructed from massive Dirac fields, but in which the PT transformation properties of electromagnetic fields are reversed. Such a theory seems to possess many attractive features.
Unidirectional invisibility induced by PT-symmetric periodic structures.
Lin, Zin; Ramezani, Hamidreza; Eichelkraut, Toni; Kottos, Tsampikos; Cao, Hui; Christodoulides, Demetrios N
2011-05-27
Parity-time (PT) symmetric periodic structures, near the spontaneous PT-symmetry breaking point, can act as unidirectional invisible media. In this regime, the reflection from one end is diminished while it is enhanced from the other. Furthermore, the transmission coefficient and phase are indistinguishable from those expected in the absence of a grating. The phenomenon is robust even in the presence of Kerr nonlinearities, and it can also effectively suppress optical bistabilities. © 2011 American Physical Society
Super Bloch Oscillation in a PT symmetric system
Turker, Z
2016-01-01
Wannier-Stark ladder in a PT symmetric system is generally complex that leads to amplified/damped Bloch oscillation. We show that a non-amplified wave packet oscillation with very large amplitude can be realized in a non-Hermitian tight binding lattice if certain conditions are satisfied. We show that pseudo PT symmetry guarantees the reality of the quasi energy spectrum in our system.
PT-Symmetric Quantum Electrodynamics and Unitarity
Milton, Kimball A; Parashar, Prachi; Pourtolami, Nima; Wagner, J
2012-01-01
More than 15 years ago, a new approach to quantum mechanics was suggested, in which Hermiticity of the Hamiltonian was to be replaced by invariance under a discrete symmetry, the product of parity and time-reversal symmetry, $\\mathcal{PT}$. It was shown that if $\\mathcal{PT}$ is unbroken, energies were, in fact, positive, and unitarity was satisifed. Since quantum mechanics is quantum field theory in 1 dimension, time, it was natural to extend this idea to higher-dimensional field theory, and in fact an apparently viable version of $\\mathcal{PT}$-invariant quantum electrodynamics was proposed. However, it has proved difficult to establish that the unitarity of the scattering matrix, for example, the K\\"all\\'en spectral representation for the photon propagator, can be maintained in this theory. This has led to questions of whether, in fact, even quantum mechanical systems are consistent with probability conservation when Green's functions are examined, since the latter have to possess physical requirements of ...
All-optical $\\mathcal{PT}$-symmetric amplitude to phase modulator
Gutiérrez, Oscar Ignacio Zaragoza; Rodríguez-Lara, B M
2015-01-01
We study electromagnetic field propagation through a planar three-waveguide coupler with linear gain and loss, in a configuration that is the optical analog of a quantum $\\mathcal{PT}$-symmetric system, and provide its closed-form analytic propagator. At an specific propagation length, we show that the device provides all-optical amplitude to phase modulation with a $\\pi$ modulation range, if an extra binary phase is allowed in the reference signal, as well as phase to amplitude modulation, with an amplitude modulation range that depends linearly on the gain-to-coupling ratio of the system.
Resonant mode conversion in the waveguides with an unbroken and broken PT-symmetry
Vysloukh, Victor A
2014-01-01
We study resonant mode conversion in the PT-symmetric multimode waveguides, where symmetry breaking manifests itself in sequential destabilization (appearance of the complex eigenvalues) of the pairs of adjacent guided modes. We show that the efficient mode conversion is possible even in the presence of the resonant longitudinal modulation of the complex refractive index. The distinguishing feature of the resonant mode conversion in the PT-symmetric structure is a drastic growth of the width of the resonance curve when the gain/losses coefficient approaches a critical value, at which symmetry breaking occurs. We found that in the system with broken symmetry the resonant coupling between exponentially growing mode with stable higher-order one effectively stabilizes dynamically coupled pair of modes and remarkably diminishes the average rate of the total power growth.
Stability analysis for solitons in PT-symmetric optical lattices
Nixon, Sean; Yang, Jianke
2012-01-01
Stability of solitons in parity-time (PT)-symmetric periodic potentials (optical lattices) is analyzed in both one- and two-dimensional systems. First we show analytically that when the strength of the gain-loss component in the PT lattice rises above a certain threshold (phase-transition point), an infinite number of linear Bloch bands turn complex simultaneously. Second, we show that while stable families of solitons can exist in PT lattices, increasing the gain-loss component has an overall destabilizing effect on soliton propagation. Specifically, when the gain-loss component increases, the parameter range of stable solitons shrinks as new regions of instability appear. Thirdly, we investigate the nonlinear evolution of unstable PT solitons under perturbations, and show that the energy of perturbed solitons can grow unbounded even though the PT lattice is below the phase transition point.
Scattering off PT-symmetric upside-down potentials
Bender, Carl M
2016-01-01
The upside-down $-x^4$, $-x^6$, and $-x^8$ potentials with appropriate PT-symmetric boundary conditions have real, positive, and discrete quantum-mechanical spectra. This paper proposes a straightforward macroscopic quantum-mechanical scattering experiment in which one can observe and measure these bound-state energies directly.
Optical solitons in PT-symmetric nonlinear couplers with gain and loss
Alexeeva, N. V.; Barashenkov, I. V.; Sukhorukov, Andrey A.; Kivshar, Yuri S.
2012-06-01
We study spatial and temporal solitons in the PT symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single combination of the soliton's amplitude and the gain-loss coefficient of the waveguides. The unstable perturbations of the high-frequency soliton break the symmetry between its active and lossy components which results in a blowup of the soliton or a formation of a long-lived breather state. The unstable perturbations of the low-frequency soliton separate its two components in space, thereby blocking the power drainage of the active component and cutting the power supply to the lossy one. Eventually this also leads to the blowup or breathing.
Optical solitons in $\\mathcal{PT}$-symmetric nonlinear couplers with gain and loss
Alexeeva, N V; Sukhorukov, Andrey A; Kivshar, Yuri S
2012-01-01
We study spatial and temporal solitons in the $\\mathcal{PT}$ symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single combination of the soliton's amplitude and the gain/loss coefficient of the waveguides. The unstable perturbations of the high-frequency soliton break the symmetry between its active and lossy components which results in a blowup of the soliton or a formation of a long-lived breather state. The unstable perturbations of the low-frequency soliton separate its two components in space blocking the power drainage of the active component and cutting the power supply to the lossy one. Eventually this also leads to the blowup or breathing.
EXCEPTIONAL POINTS IN OPEN AND PT-SYMMETRIC SYSTEMS
Directory of Open Access Journals (Sweden)
Hichem Eleuch
2014-04-01
Full Text Available Exceptional points (EPs determine the dynamics of open quantum systems and cause also PT symmetry breaking in PT symmetric systems. From a mathematical point of view, this is caused by the fact that the phases of the wavefunctions (eigenfunctions of a non-Hermitian Hamiltonian relative to one another are not rigid when an EP is approached. The system is therefore able to align with the environment to which it is coupled and, consequently, rigorous changes of the system properties may occur. We compare analytically as well as numerically the eigenvalues and eigenfunctions of a 2 × 2 matrix that is characteristic either of open quantum systems at high level density or of PT symmetric optical lattices. In both cases, the results show clearly the influence of the environment on the system in the neighborhood of EPs. Although the systems are very different from one another, the eigenvalues and eigenfunctions indicate the same characteristic features.
PT -symmetric spectral singularity and negative-frequency resonance
Pendharker, Sarang; Guo, Yu; Khosravi, Farhad; Jacob, Zubin
2017-03-01
Vacuum consists of a bath of balanced and symmetric positive- and negative-frequency fluctuations. Media in relative motion or accelerated observers can break this symmetry and preferentially amplify negative-frequency modes as in quantum Cherenkov radiation and Unruh radiation. Here, we show the existence of a universal negative-frequency-momentum mirror symmetry in the relativistic Lorentzian transformation for electromagnetic waves. We show the connection of our discovered symmetry to parity-time (PT ) symmetry in moving media and the resulting spectral singularity in vacuum fluctuation-related effects. We prove that this spectral singularity can occur in the case of two metallic plates in relative motion interacting through positive- and negative-frequency plasmonic fluctuations (negative-frequency resonance). Our work paves the way for understanding the role of PT -symmetric spectral singularities in amplifying fluctuations and motivates the search for PT symmetry in novel photonic systems.
Liu, Jiamin; Liang, Huawei; Zhang, Min; Su, Hong
2014-09-10
We report on the broadband terahertz (THz) transmission within a symmetrical plastic film coated parallel-plate waveguide. We theoretically study the antiresonant reflecting mechanism of the waveguide, and we find that the broadband THz wave can transmit in this waveguide with ultralow loss. The loss of the TM mode in this waveguide can be 4 orders of magnitude lower than the uncoated parallel-plate waveguide. The transmission bandwidth of this waveguide is up to 5.12 THz. We further show the mode field distributions which explain the loss mechanism.
Bounded dynamics in finite PT-symmetric magnetic metamaterials.
Molina, Mario I
2014-03-01
We examine the PT-symmetry-breaking transition for a magnetic metamaterial of a finite extent, modeled as an array of coupled split-ring resonators in the equivalent circuit model approximation. Small-size arrays are solved completely in closed form, while for arrays larger than N=5 results were computed numerically for several gain and loss spatial distributions. In all cases, it is found that the parameter stability window decreases rapidly with the size of the array, until at N=20 approximately it is not possible to support a stable PT-symmetric phase.
PT-symmetric quantum oscillator in an optical cavity
Longhi, Stefano
2016-01-01
The quantum harmonic oscillator with parity-time ($\\mathcal{PT}$) symmetry, obtained from the ordinary (Hermitian) quantum harmonic oscillator by an imaginary displacement of the spatial coordinate, provides an important and exactly-solvable model to investigate non-Hermitian extension of the Ehrenfest theorem. Here it is shown that transverse light dynamics in an optical resonator with off-axis longitudinal pumping can emulate a $\\mathcal{PT}$-symmetric quantum harmonic oscillator, providing an experimentally accessible system to investigate non-Hermitian coherent state propagation.
PT-symmetric ladders with a scattering core
Energy Technology Data Exchange (ETDEWEB)
D' Ambroise, J. [Department of Mathematics, Amherst College, Amherst, MA 01002-5000 (United States); Lepri, S. [CNR – Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del piano 10, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Malomed, B.A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Kevrekidis, P.G. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-9305 (United States)
2014-08-01
We consider a PT-symmetric chain (ladder-shaped) system governed by the discrete nonlinear Schrödinger equation where the cubic nonlinearity is carried solely by two central “rungs” of the ladder. Two branches of scattering solutions for incident plane waves are found. We systematically construct these solutions, analyze their stability, and discuss non-reciprocity of the transmission associated with them. To relate the results to finite-size wavepacket dynamics, we also perform direct simulations of the evolution of the wavepackets, which confirm that the transmission is indeed asymmetric in this nonlinear system with the mutually balanced gain and loss. - Highlights: • We model a PT-symmetric ladder system with cubic nonlinearity on two central rungs. • We examine non-reciprocity and stability of incident plane waves. • Simulations of wavepackets confirm our results.
PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model
Mostafazadeh, A
2004-01-01
We perform a perturbative calculation of the physical observables, in particular pseudo-Hermitian position and momentum operators, the equivalent Hermitian Hamiltonian operator, and the classical Hamiltonian for the PT-symmetric cubic anharmonic oscillator, $ H=p^1/(2m)+\\mu^2x^2/2+i\\epsilon x^3 $. Ignoring terms of order $ \\epsilon^4 $ and higher, we show that this system describes an ordinary quartic anharmonic oscillator with a position-dependent mass and real and positive coupling constants. This observation elucidates the classical origin of the reality and positivity of the energy spectrum. We also discuss the quantum-classical correspondence for this PT-symmetric system, compute the associated conserved probability density, and comment on the issue of factor-ordering in the pseudo-Hermitian canonical quantization of the underlying classical system.
Non-Hermitian supersymmetry and singular PT symmetrized oscillators
Znojil, M
2002-01-01
SUSY partnership between singular potentials often breaks down. Via regularization it can be restored on certain ad hoc subspaces of Hilbert space [Das and Pernice, Nucl. Phys. B 561 (1999) 357]. Within the naturally complexified (so called PT symmetric) quantum mechanics we show how SUSY between strongly singular harmonic oscillators can completely be re-established. Our recipe leads to a new form of the bosonic creation and annihilation operators and proves continuous near the usual regular (i.e., linear harmonic) limit.
Bright solitons in a PT-symmetric chain of dimers
Kirikchi, Omar B; Susanto, Hadi
2016-01-01
We study the existence and stability of fundamental bright discrete solitons in a parity-time (PT)-symmetric coupler composed by a chain of dimers, that is modelled by linearly coupled discrete nonlinear Schrodinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anti-continuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, on the contrary of the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quart...
Discrete solitons in self-defocusing systems with $\\mathcal{PT}$-symmetric defects
Chen, Zhiqiang; Chai, Jinglei; Zhang, Xiangyu; Li, Yongyao; Malomed, Boris A
2015-01-01
We construct families of discrete solitons (DSs) in an array of self-defocusing waveguides with an embedded $\\mathcal{PT}$ (parity-time)-symmetric dimer, which is represented by a pair of waveguides carrying mutually balanced gain and loss. Four types of states attached to the embedded defect are found, namely, staggered and unstaggered bright localized modes and gray or anti-gray DSs. Their existence and stability regions expand with the increase of the strength of the coupling between the dimer-forming sites. The existence of the gray and staggered bright DSs is qualitatively explained by dint of the continuum limit. All the gray and anti-gray DSs are stable (some of them are unstable if the dimer carries the nonlinear $\\mathcal{PT}$ symmetry, represented by balanced nonlinear gain and loss; in that case, the instability does not lead to a blowup, but rather creates oscillatory dynamical states). The boundary between the gray and anti-gray DSs is predicted in an approximate analytical form.
PT-Symmetric Nonlinear Metamaterials and Zero-Dimensional Systems
Tsironis, G P
2013-01-01
A one dimensional, parity-time (${\\cal PT}$)-symmetric magnetic metamaterial comprising split-ring resonators having both gain and loss is investigated. In the linear regime, the transition from the exact to the broken ${\\cal PT}$-phase is determined through the calculation of the eigenfrequency spectrum for two different configurations; the one with equidistant split-rings and the other with the split-rings forming a binary pattern (${\\cal PT}$ dimer chain). The latter system features a two-band, gapped spectrum with its shape determined by the gain/loss coefficient as well as the inter-element coupling. In the presense of nonlinearity, the ${\\cal PT}$ dimer chain with balanced gain and loss supports nonlinear localized modes in the form of novel discrete breathers below the lower branch of the linear spectrum. These breathers, that can be excited from a weak applied magnetic field by frequency chirping, can be subsequently driven solely by the gain for very long times. The effect of a small imbalance betwee...
Electrically Injected Single Transverse-Mode Coupled Waveguide Lasers by Parity-time (PT) Symmetry
Yao, Ruizhe; Podolskiy, Viktor; Guo, Wei
2016-01-01
In this report, we demonstrate the single transverse-mode operation of InAs quantum dot (QD) broad-area coupled waveguide lasers by parity-time (PT) symmetry. A novel waveguide design is adopted by adding gain and loss in the electrically injected coupled waveguide laser cavity. In such counterintuitive waveguide design, the single mode operation is achieved by harnessing notions from PT symmetry breaking and mode selections. By further varying the loss in the coupled waveguides, the coupled waveguide operation in different PT symmetry regions is experimentally demonstrated and agrees well with the numerical models. The demonstration of an electrically pumped single transverse-mode based on PT symmetry breaking paves a way to the next-generation optoelectronic devices and advanced laser science.
Bright Solitons in a PT-Symmetric Chain of Dimers
Directory of Open Access Journals (Sweden)
Omar B. Kirikchi
2016-01-01
Full Text Available We study the existence and stability of fundamental bright discrete solitons in a parity-time- (PT- symmetric coupler composed by a chain of dimers that is modelled by linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anticontinuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, in contrast to the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quartet of complex eigenvalues. In general, the gain-loss term can be considered parasitic as it reduces the stability region of the onsite solitons. Additionally, we analyse the dynamic behaviour of the onsite and intersite solitons when unstable, where typically it is either in the form of travelling solitons or soliton blow-ups.
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.
Uniform Core Field in Symmetrical Planar Waveguides and Circular Fibers with Nonlinear Claddings
Institute of Scientific and Technical Information of China (English)
庞霖; 严瑛白; 金国藩; 邬敏贤; 郭履容; 陈波
2001-01-01
It is known that no uniform electric field profile exists in a planar linear waveguide. The uniform core field can be shown to exist in symmetrical planar waveguides and circular fibers with nonlinear claddings. Theoretical analysis and numerical calculations are carried out to show that when the modal index equals to the core refractive-index, the core field becomes uniform at an appropriate optical power. Analysis for a step-index circular fiber with nonlinear cladding have also shown that the core field becomes uniform under similar conditions. The occurrence of a uniform field in a waveguide core may believe to have promising applications in waveguide, optoelectronic and photonic devices.
Scattering properties of PT- symmetric layered periodic structures
Shramkova, O. V.; Tsironis, G. P.
2016-10-01
The optical properties of PT-symmetric periodic stacks of the layers with balanced loss and gain are examined. We demonstrate that the tunnelling phenomenon in periodic structures is connected with excitation of surface waves at the boundaries separating gain and loss regions within each unit cell and tunnelling conditions for periodic stacks can be reduced to the conditions for one period. Alternatively, it is shown that coherent perfect absorber laser states are mediated by excitation of surface modes localised at all internal boundaries of the structure. The effects of structure parameters, angles, direction of incidence on the resonant phenomena and spontaneous symmetry breaking transition are determined. It is shown that structural periodicity significantly increases the number of resonant phenomena, especially in stacks with high real and imaginary parts of dielectric permittivity of the layers.
Spectral Singularity in confined PT symmetric optical potential
Sinha, Anjana
2013-01-01
We present an analytical study for the scattering amplitudes (Reflection |R| and Transmission |T|), of the periodic PT symmetric optical potential V(x) = W_0 cos^2 x + i W_0 V_0 sin 2x confined within the region 0 0.5) scattering is found to be anomalous (|T|^2, |R|^2 not necessarily \\leq 1). Additionally, in this parameter regime of V_0, one observes infinite number of spectral singularities E_{SS} at different values of V_0. Furthermore, for L = 2n \\pi, the transition point V_0 = 0.5 shows unidirectional invisibility with zero reflection when the beam is incident from the absorptive side (Im[V(x)] 0), transmission being identically unity in both cases.
Jamming anomaly in $\\mathcal{PT}$-symmetric systems
Barashenkov, I V; Konotop, Vladimir V
2016-01-01
The Schr\\"odinger equation with a $\\mathcal{PT}$-symmetric potential is used to model an optical structure consisting of an element with gain coupled to an element with loss. At low gain-loss amplitudes $\\gamma$, raising the amplitude results in the energy flux from the active to the leaky element being boosted. We study the anomalous behaviour occurring for larger $\\gamma$, where the increase of the amplitude produces a drop of the flux across the gain-loss interface. We show that this jamming anomaly is either a precursor of the exceptional point, where two real eigenvalues coalesce and acquire imaginary parts, or precedes the eigenvalue's immersion in the continuous spectrum.
Phase transition in PT symmetric active plasmonic systems
Mattheakis, M; Molina, M I; Tsironis, G P
2015-01-01
Surface plasmon polaritons (SPPs) are coherent electromagnetic surface waves trapped on an insulator-conductor interface. The SPPs decay exponentially along the propagation due to conductor losses, restricting the SPPs propagation length to few microns. Gain materials can be used to counterbalance the aforementioned losses. We provide an exact expression for the gain, in terms of the optical properties of the interface, for which the losses are eliminated. In addition, we show that systems characterized by lossless SPP propagation are related to PT symmetric systems. Furthermore, we derive an analytical critical value of the gain describing a phase transition between lossless and prohibited SPPs propagation. The regime of the aforementioned propagation can be directed by the optical properties of the system under scrutiny. Finally, we perform COMSOL simulations verifying the theoretical findings.
PT-Symmetric Versus Hermitian Formulations of Quantum Mechanics
Bender, C M; Milton, K A; Bender, Carl M.; Chen, Jun-Hua; Milton, Kimball A.
2006-01-01
A non-Hermitian Hamiltonian that has an unbroken PT symmetry can be converted by means of a similarity transformation to a physically equivalent Hermitian Hamiltonian. This raises the following question: In which form of the quantum theory, the non-Hermitian or the Hermitian one, is it easier to perform calculations? This paper compares both forms of a non-Hermitian $ix^3$ quantum-mechanical Hamiltonian and demonstrates that it is much harder to perform calculations in the Hermitian theory because the perturbation series for the Hermitian Hamiltonian is constructed from divergent Feynman graphs. For the Hermitian version of the theory, dimensional continuation is used to regulate the divergent graphs that contribute to the ground-state energy and the one-point Green's function. The results that are obtained are identical to those found much more simply and without divergences in the non-Hermitian PT-symmetric Hamiltonian. The $\\mathcal{O}(g^4)$ contribution to the ground-state energy of the Hermitian version ...
Analytic Results for a PT-symmetric Optical Structure
Jones, H F
2011-01-01
Propagation of light through media with a complex refractive index in which gain and loss are engineered to be $PT$ symmetric has many remarkable features. In particular the usual unitarity relations are not satisfied, so that the reflection coefficients can be greater than one, and in general are not the same for left or right incidence. Within the class of optical potentials of the form $v(x)=v_1\\cos(2\\beta x)+iv_2\\sin(2\\beta x)$ the case $v_2=v_1$ is of particular interest, as it lies on the boundary of $PT$-symmetry breaking. It has been shown in a recent paper by Lin et al. that in this case one has the property of "unidirectional invisibility", while for propagation in the other direction there is a greatly enhanced reflection coefficient proportional to $L^2$, where $L$ is the length of the medium in the direction of propagation. For this potential we show how analytic expressions can be obtained for the various transmission and reflection coefficients, which are expressed in a very succinct form in te...
${\\mathcal{PT}}$ symmetry breaking in photonic waveguides with competing gain rates
Kalozoumis, P A; Diakonos, F K; Schmelcher, P
2016-01-01
We consider a discrete $\\mathcal{PT}$ symmetric quadrimer optical structure with two competing gain parameters. The existence of the additional loss/gain rate has a major impact on the phase diagram of the system leading to multiple transitions, not only between the unbroken and a broken phase, but also between broken phases with distinct light propagation properties. The $\\mathcal{PT}$-unbroken phase is shown to be characterized by the vanishing of a symmetry-adapted nonlocal current ${Q}$, whose site-average behaves as a natural order parameter across the spontaneous symmetry breaking transition. Utilizing the quadrimer as a unit cell of a uniform lattice, we investigate how the corresponding band structure and the attendant beam dynamics in large waveguide arrays are affected by the existence of the second loss/gain parameter. The enriched band structure landscape yields the possibility to control the propagation length of a beam before divergence when the system resides in the broken $\\mathcal{PT}$ phase.
Tailoring Spectral Properties of Binary PT-Symmetric Gratings by Duty-Cycle Methods
DEFF Research Database (Denmark)
Lupu, Anatole T.; Benisty, Henri; Lavrinenko, Andrei
2016-01-01
We explore the frequency selective functionalities of a nonuniform PT-symmetric Bragg grating with modulated complex index profile. We start by assessing the possibility to achieve an efficient apodization of the PT-symmetric Bragg grating spectral response by using direct adaptations of the conv...
Scarcity of real discrete eigenvalues in non-analytic complex $\\mathcal{PT}$-symmetric potentials
Indian Academy of Sciences (India)
Zafar Ahmed
2009-08-01
We find that a non-differentiability occurring whether in real or imaginary part of a complex $\\mathcal{PT}$-symmetric potential causes a scarcity of the real discrete eigenvalues despite the real part alone possessing an infinite spectrum. We demonstrate this by perturbing the real potentials 2 and || by imaginary $\\mathcal{PT}$ -symmetric potentials || and , respectively.
Sublattice signatures of transitions in a $\\mathcal{PT}$-symmetric dimer lattice
Harter, Andrew K
2016-01-01
Lattice models with non-hermitian, parity and time-reversal ($\\mathcal{PT}$) symmetric Hamiltonians, realized most readily in coupled optical systems, have been intensely studied in the past few years. A $\\mathcal{PT}$-symmetric dimer lattice consists of dimers with intra-dimer coupling $\
Quantum mechanics of $PT$ and non-$PT$ -symmetric potentials in three dimensions
Indian Academy of Sciences (India)
BHARDWAJ S B; SINGH RAM MEHAR; MISHRA S C
2016-07-01
With a view of exploring new vistas with regard to the nature of complex eigenspectra of a non-Hermitian Hamiltonian, the quasi-exact solutions of the Schrödinger equation are investigated for a shifted harmonic potential under the framework of extended complex phase-space approach. Analyticity property ofthe eigenfunction alone is found sufficient to throw light on the nature of the eigenvalues and eigenfunctions of a system. Explicit expressions of eigenvalues and eigenfunctions for the ground state as well as excited state including their $PT$-symmetric version are worked out.
Silicon waveguide filter based on cladding modulated anti-symmetric long-period grating.
Liu, Qing; Gu, Zhonghua; Kee, Jack Sheng; Park, Mi Kyoung
2014-12-01
In this paper, we demonstrate an optical filter using cladding modulated anti-symmetric long-period grating in a two-mode silicon waveguide. The filter consists of a two-mode waveguide connected with an input and output single-mode waveguide through two linear tapers. The anti-symmetric grating is formed by placing two periodic arrays of silicon squares offset by half of a grating pitch along the two-mode waveguide. Light coupling occurs between two co-propagating modes at the coupling wavelength through the grating and results in a rejection band at the output. The grating pitch, coupling coefficient, transmission spectrum and 3-dB bandwidth of the grating are investigated with the coupled-mode theory. By using a cladding modulated grating, the grating coupling strength can be controlled over a wide range by the two-mode waveguide width or separation distance between the grating and waveguide. Band-rejection filters are experimentally demonstrated in 1-μm, 0.8-μm and 0.7-μm wide two-mode silicon waveguides and rejection bands with different bandwidths and maximal attenuation contrasts larger than 15 dB (~97% coupling efficiency) have been achieved.
Longhi, Stefano
2017-01-01
We consider wave transport phenomena in a PT -symmetric extension of the periodically kicked quantum rotator model and reveal that dynamical localization assists the unbroken PT phase. In the delocalized (quantum resonance) regime, PT symmetry is always in the broken phase and ratchet acceleration arises as a signature of unidirectional non-Hermitian transport. An optical implementation of the periodically kicked PT -symmetric Hamiltonian, based on transverse beam propagation in a passive optical resonator with combined phase and loss gratings, is suggested to visualize acceleration modes in fractional Talbot cavities.
Spectral singularity in confined PT symmetric optical potential
Energy Technology Data Exchange (ETDEWEB)
Sinha, Anjana [Department of Instrumentation Science, Jadavpur University, Kolkata - 700 032 (India); Roychoudhury, R. [Department of Mathematics, Bethune College, Kolkata - 700 006, India and Advanced Centre for Nonlinear and Complex Phenomena, 1175 Survey Park, Kolkata - 700075 (India)
2013-11-15
We present an analytical study for the scattering amplitudes (Reflection ‖R‖ and Transmission ‖T‖), of the periodic PT symmetric optical potential V(x)=W{sub 0}cos{sup 2}x+iV{sub 0}sin2x confined within the region 0 ⩽x⩽L, embedded in a homogeneous medium having uniform potential W{sub 0}. The confining length L is considered to be some integral multiple of the period π. We give some new and interesting results. Scattering is observed to be normal (‖T‖{sup 2}⩽ 1, ‖R‖{sup 2}⩽ 1) for V{sub 0}⩽ 0.5, when the above potential can be mapped to a Hermitian potential by a similarity transformation. Beyond this point (V{sub 0} > 0.5) scattering is found to be anomalous (‖T‖{sup 2}, ‖R‖{sup 2} not necessarily ⩽1). Additionally, in this parameter regime of V{sub 0}, one observes infinite number of spectral singularities E{sub SS} at different values of V{sub 0}. Furthermore, for L= 2nπ, the transition point V{sub 0}= 0.5 shows unidirectional invisibility with zero reflection when the beam is incident from the absorptive side (Im[V(x)] < 0) but with finite reflection when the beam is incident from the emissive side (Im[V(x)] > 0), transmission being identically unity in both cases. Finally, the scattering coefficients ‖R‖{sup 2} and ‖T‖{sup 2} always obey the generalized unitarity relation : ‖T|{sup 2}−1|=√(|R{sub R}|{sup 2}|R{sub L}|{sup 2}), where subscripts R and L stand for right and left incidence, respectively.
Symmetric Reverse-Coupling Waveguide Orthomode Transducer for the 3-mm Band
Navarrini, Alessandro; Nesti, Renzo
2009-01-01
We describe the design, construction, and performance of a waveguide orthomode transducer (OMT) for the 3-mm band (84-116 GHz). The OMT is based on a symmetric backward coupling structure and has a square waveguide input port (2.54 mm times 2.54 mm) and two single-mode waveguide outputs: a standard WR10 rectangular waveguide (2.54 mm times 1.27 mm), and an oval waveguide with full-radius corners. The reverse coupling structure is located in the common square waveguide arm and splits one polarization signal in two opposite rectangular waveguide sidearms using broadband -3-dB .E-plane branch-line hybrid couplers. The device was optimized using a commercial 3-D electromagnetic simulator. The OMT consists of two mechanical blocks fabricated in split- block configuration using conventional CNC milling machine. From 84 to 116 GHz, the measured input reflection coefficient was less than -17 dB, the cross polarization was less than -30 dB, the isolation between the outputs was greater than 50 dB, and the insertion loss was less than 0.35 dB at room temperature for both polarization channels. The device is suitable for scaling to higher frequency.
Complex {PT}-symmetric extensions of the nonlinear ultra-short light pulse model
Yan, Zhenya
2012-11-01
The short pulse equation u_{xt}=u+\\frac{1}{2}(u^2u_x)_x is PT symmetric, which arises in nonlinear optics for the ultra-short pulse case. We present a family of new complex PT-symmetric extensions of the short pulse equation, i[(iu_x)^{\\sigma }]_t=au+bu^m+ic[u^n(iu_x)^{\\epsilon }]_x \\,\\, (\\sigma ,\\, \\epsilon ,\\,a,\\,b,\\,c,\\,m,\\,n \\in {R}), based on the complex PT-symmetric extension principle. Some properties of these equations with some chosen parameters are studied including the Hamiltonian structures and exact solutions such as solitary wave solutions, doubly periodic wave solutions and compacton solutions. Our results may be useful to understand complex PT-symmetric nonlinear physical models. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Compactons in $\\mathcal{PT}$-symmetric generalized Korteweg–de Vries equations
Indian Academy of Sciences (India)
Carl M Bender; Fred Cooper; Avinash Khare; Bogdan Mihaila; Avadh Saxena
2009-08-01
This paper considers the $\\mathcal{PT}$-symmetric extensions of the equations examined by Cooper, Shepard and Sodano. From the scaling properties of the $\\mathcal{PT}$-symmetric equations a general theorem relating the energy, momentum and velocity of any solitary-wave solution of the generalized KdV equation is derived. We also discuss the stability of the compacton solution as a function of the parameters affecting the nonlinearities.
Symmetrical waveguide devices fabricated by direct UV writing
DEFF Research Database (Denmark)
Færch, Kjartan Ullitz; Svalgaard, Mikael
2002-01-01
Power splitters and directional couplers fabricated by direct UV writing in index matched silica-on-silicon samples can suffer from an asymmetrical device performance, even though the UV writing is carried out in a symmetrical fashion. This effect originates from a reduced photosensitivity...... in the vicinity of previous exposed areas. The imbalance can be counteracted by an appropriate reduction of the applied scan velocity in areas, where a previous scan has been carried out nearby...
Nonlinear plasmonic dispersion and coupling analysis in the symmetric graphene sheets waveguide
Jiang, Xiangqian; Yuan, Haiming; Sun, Xiudong
2016-12-01
We study the nonlinear dispersion and coupling properties of the graphene-bounded dielectric slab waveguide at near-THz/THz frequency range, and then reveal the mechanism of symmetry breaking in nonlinear graphene waveguide. We analyze the influence of field intensity and chemical potential on dispersion relation, and find that the nonlinearity of graphene affects strongly the dispersion relation. As the chemical potential decreases, the dispersion properties change significantly. Antisymmetric and asymmetric branches disappear and only symmetric one remains. A nonlinear coupled mode theory is established to describe the dispersion relations and its variation, which agrees with the numerical results well. Using the nonlinear couple model we reveal the reason of occurrence of asymmetric mode in the nonlinear waveguide.
Floquet control of the gain and loss in a PT-symmetric optical coupler
Wu, Yi; Zhu, Bo; Hu, Shu-Fang; Zhou, Zheng; Zhong, Hong-Hua
2017-02-01
Controlling the balanced gain and loss in a PT-symmetric system is a rather challenging task. Utilizing Floquet theory, we explore the constructive role of periodic modulation in controlling the gain and loss of a PT-symmetric optical coupler. It is found that the gain and loss of the system can be manipulated by applying a periodic modulation. Further, such an original non-Hermitian system can even be modulated into an effective Hermitian system derived by the high-frequency Floquet method. Therefore, compared with other PT symmetry control schemes, our protocol can modulate the unbroken PT-symmetric range to a wider parameter region. Our results provide a promising approach for controlling the gain and loss of a realistic system.
Tunable polarization beam splitting based on a symmetrical metal-cladding waveguide structure.
Wang, Yi; Cao, Zhuangqi; Li, Honggen; Shen, Qishun; Yuan, Wen; Xiao, Pingping
2009-08-03
Electrical tuning of polarization beam splitting is demonstrated in the structure of symmetrical metal-cladding waveguide by introducing optically nonlinear material into both the coupling prism and the guiding layer. Due to the anisotropy of the coupling material, different excitation conditions for TE and TM modes are obtained, which results in polarization-dependent reflections and transmissions. And the splitting effect of the two orthogonally polarized beams can be manipulated through an electrical modulation of the guiding layer properties.
A Temperature Sensor Based on a Symmetrical Metal-Cladding Optical Waveguide
Institute of Scientific and Technical Information of China (English)
ZHOU Guo-Rui; FENG Guo-Ying; ZHANG Yi; MA Zi; WANG Jian-Jun
2012-01-01
A compact temperature sensor based on a symmetrical metal-cladding optical waveguide using free-space coupling is proposed and demonstrated theoretically and experimentally. The symmetrical Au-cladding optical waveguide is based on a thin LiNbO3 slab sandwiched between two metal films, which serve as the coupling layer and reflecting panel, respectively. The sensitivity of this sensor of 9.08×10-2 deg/℃, 6.6 ×10-2 deg/℃ and 4.8 × 10-2 deg/℃ corresponding to 3238-order, 3237-order and 3236-order modes, respectively, are obtained. Higher resolution is predicted with a larger linear expansion coefficient material and a higher resolution θ/2θ goniometer.%A compact temperature sensor based on a symmetrical metal-cladding optical waveguide using free-space coupling is proposed and demonstrated theoretically and experimentally.The symmetrical Au-cladding optical waveguide is based on a thin LiNbO3 slab sandwiched between two metal films,which serve as the coupling layer and reflecting panel,respectively.The sensitivity of this sensor of 9.08 × 10-2 deg/℃,6.6 × 10-2 deg/℃ and 4.8 × 10-2 deg/℃ corresponding to 3238-order,3237-order and 3236-order modes,respectively,are obtained.Higher resolution is predicted with a larger linear expansion coefficient material and a higher resolution θ/2θ goniometer.
Light propagation through a PT-symmetric photonic-crystal.
Konotop, Vladimir V; Mantsyzov, Boris I
2016-11-14
Light propagation through a finite-width periodically modulated layer obeying parity-time (PT) symmetry is considered. We consider the configuration when the resonant conditions of mode coupling by the grating are satisfied. It is shown that the dependence of the transmission and reflection coefficients on the slab width has resonant character featuring strong amplification of reflected and transmitted waves with negative angles. The dependence of the scattering data on the gain-and-loss intensity also feature strong resonances near the PT-symmetry breaking point, when the slab strongly amplifies waves reflected and transmitted with negative angles, provided the incident wave has a positive angle of incidence.
From $\\mathcal{PT}$ -symmetric quantum mechanics to conformal field theory
Indian Academy of Sciences (India)
Patrick Dorey; Clare Dunning; Roberto Tateo
2009-08-01
One of the simplest examples of a $\\mathcal{PT}$-symmetric quantum system is the scaling Yang–Lee model, a quantum field theory with cubic interaction and purely imaginary coupling. We give a historical review of some facts about this model in ≤ 2 dimensions, from its original definition in connection with phase transitions in the Ising model and its relevance to polymer physics, to the role it has played in studies of integrable quantum field theory and $\\mathcal{PT}$-symmetric quantum mechanics. We also discuss some more general results on $\\mathcal{PT}$-symmetric quantum mechanics and the ODE/IM correspondence, and mention applications to magnetic systems and cold atom physics.
Controlling electric, magnetic, and chiral dipolar emission with PT-symmetric potentials
Energy Technology Data Exchange (ETDEWEB)
Alaeian, Hadiseh; Dionne, Jennifer A.
2015-06-01
We investigate the effect of parity-time (PT) symmetric optical potentials on the radiation of achiral and chiral dipole sources. Two properties unique to PT-symmetric potentials are observed. First, the dipole can be tuned to behave as a strong optical emitter or absorber based on the non-Hermiticity parameter and the dipole location. Second, exceptional points give rise to new system resonances that lead to orders-of-magnitude enhancements in the dipolar emitted or absorbed power. Utilizing these properties, we show that enantiomers of chiral molecules near PT-symmetric metamaterials exhibit a 4.5-fold difference in their emitted power and decay rate. The results of this work could enable new atom-cavity interactions for quantum optics, as well as all-optical enantioselective separation.
Compactons in PT-symmetric generalized Korteweg-de Vries equations
Energy Technology Data Exchange (ETDEWEB)
Saxena, Avadh B [Los Alamos National Laboratory; Mihaila, Bogdan [Los Alamos National Laboratory; Bender, Carl M [WASHINGTON UNIV; Cooper, Fred [SANTA FE INSTITUTE; Khare, Avinash [INSTITUTE OF PHYSICS
2008-01-01
In an earlier paper Cooper, Shepard, and Sodano introduced a generalized KdV equation that can exhibit the kinds of compacton solitary waves that were first seen in equations studied by Rosenau and Hyman. This paper considers the PT-symmetric extensions of the equations examined by Cooper, Shepard, and Sodano. From the scaling properties of the PT-symmetric equations a general theorem relating the energy, momentum, and velocity of any solitary-wave solution of the generalized KdV equation is derived, and it is shown that the velocity of the solitons is determined by their amplitude, width, and momentum.
Compactons in PT-symmetric generalized Korteweg-de Vries equations
Energy Technology Data Exchange (ETDEWEB)
Saxena, Avadh B [Los Alamos National Laboratory; Mihaila, Bogdan [Los Alamos National Laboratory; Bender, Carl M [WASHINGTON UNIV; Cooper, Fred [SANTA FE INSTITUTE; Khare, Avinash [INSTITUTE OF PHYSICS
2008-01-01
In an earlier paper Cooper, Shepard, and Sodano introduced a generalized KdV equation that can exhibit the kinds of compacton solitary waves that were first seen in equations studied by Rosenau and Hyman. This paper considers the PT-symmetric extensions of the equations examined by Cooper, Shepard, and Sodano. From the scaling properties of the PT-symmetric equations a general theorem relating the energy, momentum, and velocity of any solitary-wave solution of the generalized KdV equation is derived, and it is shown that the velocity of the solitons is determined by their amplitude, width, and momentum.
Anomalous Light Scattering by Topological PT-symmetric Particle Arrays
Ling, C. W.; Choi, Ka Hei; Mok, T. C.; Zhang, Zhao-Qing; Fung, Kin Hung
2016-12-01
Robust topological edge modes may evolve into complex-frequency modes when a physical system becomes non-Hermitian. We show that, while having negligible forward optical extinction cross section, a conjugate pair of such complex topological edge modes in a non-Hermitian -symmetric system can give rise to an anomalous sideway scattering when they are simultaneously excited by a plane wave. We propose a realization of such scattering state in a linear array of subwavelength resonators coated with gain media. The prediction is based on an analytical two-band model and verified by rigorous numerical simulation using multiple-multipole scattering theory. The result suggests an extreme situation where leakage of classical information is unnoticeable to the transmitter and the receiver when such a -symmetric unit is inserted into the communication channel.
Design of Symmetrical Beam Triple-Aperture Waveguide Antenna for Primary Feed of Reflector
Directory of Open Access Journals (Sweden)
Kanawat Nuangwongsa
2016-01-01
Full Text Available This research presents a triple-aperture waveguide antenna as the primary feed of parabolic reflectors. The proposed antenna is able to rectify the asymmetry and also achieve a symmetrical unidirectional beam through the application of two parasitic coupling apertures. The design of the antenna is that of a rectangular waveguide (radiating aperture vertically jointed to the two coupling apertures of the same measurement widthwise (i.e., one stacked on top and the other underneath to achieve the symmetrical beam. The rectangular waveguide is 97.60 mm and 46.80 mm in width (a and height (b, respectively, to propagate the WLAN frequency band of 2.412–2.484 GHz. Simulations were carried out to determine the optimal antenna parameters and an antenna prototype was subsequently fabricated and tested. The simulated beamwidths in the E- and H-planes at -3 dB were equally 67° (i.e., 67° for both the E- and H-planes and at -10 dB also equally 137°, while the measured results at -3 dB were equally 65° and at -10 dB equally 135°. The simulation and measured results are thus in good agreement. The simulated and measured antenna gains are, respectively, 8.25 dBi and 9.17 dBi. The findings validate the applicability of the antenna as the prime feed for rotationally symmetric parabolic reflectors.
Chen, Yijing; Ho, Seng-Tiong; Krishnamurthy, Vivek
2013-12-20
All-optical switching operation based on manipulation of absorption in a three-waveguide directional coupler is theoretically investigated. The proposed structure consists of one absorptive central waveguide and two identical passive side waveguides. Optically induced absorption change in the central waveguide effectively controls the coupling of light between the two side waveguides, leading to optical switching action. The proposed architecture alleviates the fabrication challenges and waveguide index matching conditions that limit previous demonstrations of similar switching schemes based on a two-waveguide directional coupler. The proposed device accommodates large modal index difference between absorptive and passive waveguides without compromising the switching extinction ratio.
Dynamics of higher-order solitons in regular and PT-symmetric nonlinear couplers
Driben, R
2012-01-01
Dynamics of symmetric and antisymmetric 2-solitons and 3-solitons is studied in the model of the nonlinear dual-core coupler and its PT-symmetric version. Regions of the convergence of the injected perturbed symmetric and antisymmetric N-solitons into symmetric and asymmetric quasi-solitons are found. In the PT-symmetric system, with the balanced gain and loss acting in the two cores, borders of the stability against the blowup are identified. Notably, in all the cases the stability regions are larger for antisymmetric 2-soliton inputs than for their symmetric counterparts, on the contrary to previously known results for fundamental solitons (N=1). Dynamical regimes (switching) are also studied for the 2-soliton injected into a single core of the coupler. In particular, a region of splitting of the input into a pair of symmetric solitons is found, which is explained as a manifestation of the resonance between the vibrations of the 2-soliton and oscillations of energy between the two cores in the coupler.
A saccharides sensor developed by symmetrical optical waveguide-based surface plasmon resonance
Ang Li; Zhouyi Guo; Qing Peng; Chan Du; Xida Han; Le Liu; Jun Guo; Yonghong He; Yanhong Ji
2015-01-01
We proposed a new saccharides sensor developed by symmetrical optical waveguide (SOW)-based surface plasmon resonance (SPR). This unique MgF2/Au/MgF2/Analyte film structure results in longer surface plasmon wave (SPW) propagation lengths and depths, leading to an increment of resolution. In this paper, we managed to decorate the dielectric interface (MgF2 layer) by depositing a thin polydopamine film as surface-adherent that provides a platform for secondary reactions with the probe molecule....
PT-symmetric dimer of coupled nonlinear oscillators
Indian Academy of Sciences (India)
Avinash Khare
2015-11-01
We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry, i.e., one of them has gain and the other an equal and opposite amount of loss. We first discuss various symmetries of the model. We show that both the linear system as well as a special case of the nonlinear system can be derived from a Hamiltonian, whose structure is similar to the Pais–Uhlenbeck Hamiltonian. Exact solutions are obtained in a few special cases. We show that the system is a superintegrable system within the rotating wave approximation (RWA). We also obtain several exact solutions of these RWA equations. Further, we point out a novel superposition in the context of periodic solutions in terms of Jacobi elliptic functions that we obtain in this problem. Finally, we briefly mention numerical results about the stability of some of the solutions.
PT-symmetric coupler with a coupling defect: soliton interaction with exceptional point
Bludov, Yuli V; Huang, Guoxiang; Konotop, Vladimir V
2014-01-01
We study interaction of a soliton in a parity-time (PT) symmetric coupler which has local perturbation of the coupling constant. Such a defect does not change the PT-symmetry of the system, but locally can achieve the exceptional point. We found that the symmetric solitons after interaction with the defect either transform into breathers or blow up. The dynamics of anti-symmetric solitons is more complex, showing domains of successive broadening of the beam and of the beam splitting in two outwards propagating solitons, in addition to the single breather generation and blow up. All the effects are preserved when the coupling strength in the center of the defect deviates from the exceptional point. If the coupling is strong enough the only observable outcome of the soliton-defect interaction is the generation of the breather.
Green's Function of a General PT-Symmetric Non-Hermitian Non-central Potential
Mourya, Brijesh Kumar
2016-01-01
We study the path integral solution of a system of particle moving in certain class of PT symmetric non-Hermitian and non-central potential. The Hamil- tonian of the system is converted to a separable Hamiltonian of Liouville type in parabolic coordinates and is further mapped into a Hamiltonian corresponding to two 2-dimensional simple harmonic oscillators (SHOs). Thus the explicit Green's functions for a general non-central PT symmetric non hermitian potential are cal- culated in terms of that of 2d SHOs. The entire spectrum for this three dimensional system is shown to be always real leading to the fact that the system remains in unbroken PT phase all the time.
Non-Hermitian Neutrino Oscillations in Matter with PT Symmetric Hamiltonians
Ohlsson, Tommy
2015-01-01
We introduce and develop a novel approach to extend the ordinary two-flavor neutrino oscillation formalism in matter using a non-Hermitian PT symmetric effective Hamiltonian. The condition of PT symmetry is weaker and less mathematical than that of Hermicity, but more physical, and such an extension of the formalism can give rise to sub-leading effects in neutrino flavor transitions similar to the effects by so-called non-standard neutrino interactions. We derive the necessary conditions for the spectrum of the effective Hamiltonian to be real as well as the mappings between the fundamental and effective parameters including the corresponding two-flavor neutrino transition probability. We find that the effective leptonic mixing must always be maximal and that the real spectrum of the effective Hamiltonian will depend on all new fundamental parameters introduced in the non-Hermitian PT symmetric extension of the usual neutrino oscillation formalism.
A selection rule for transitions in PT-symmetric quantum theory
Mead, Lawrence R
2016-01-01
Carl Bender and collaborators have developed a quantum theory governed by Hamiltonians that are PT-symmetric rather than Hermitian. To implement this theory, the inner product was redefined to guarantee positive norms of eigenstates of the Hamiltonian. In the general case, which includes arbitrary time-dependence in the Hamiltonian, a modification of the Schrodinger equation is necessary as shown by Gong and Wang to conserve probability. In this paper, we derive the following selection rule: transitions induced by time dependence in a PT-symmetric Hamiltonian cannot occur between normalized states of differing PT-norm. We show three examples of this selection rule in action: two matrix models and one in the continuum.
Three-dimensional topological solitons in PT-symmetric optical lattices
Kartashov, Yaroslav V; Huang, Guoxiang; Torner, Lluis
2016-01-01
We address the properties of fully three-dimensional solitons in complex parity-time (PT)-symmetric periodic lattices with focusing Kerr nonlinearity, and uncover that such lattices can stabilize both, fundamental and vortex-carrying soliton states. The imaginary part of the lattice induces internal currents in the solitons that strongly affect their domains of existence and stability. The domain of stability for fundamental solitons can extend nearly up to the PT-symmetry breaking point, where the linear lattice spectrum becomes complex. Vortex solitons feature spatially asymmetric profiles in the PT-symmetric lattices, but they are found to still exist as stable states within narrow regions. Our results provide the first example of continuous families of stable three-dimensional propagating solitons supported by complex potentials.
On PT-Symmetric Periodic Potential, Quark Confinement, and Other Impossible Pursuits
Directory of Open Access Journals (Sweden)
Christianto V.
2009-01-01
Full Text Available As we know, it has been quite common nowadays for particle physicists to think of six impossible things before breakfast, just like what their cosmology fellows used to do. In the present paper, we discuss a number of those impossible things, including PT-symmetric periodic potential, its link with condensed matter nuclear science, and possible neat link with Quark confinement theory. In recent years, the PT-symmetry and its related periodic potential have gained considerable interests among physicists. We begin with a review of some results from a preceding paper discussing derivation of PT-symmetric periodic potential from biquaternion Klein-Gordon equation and proceed further with the remaining issues. Further observation is of course recommended in order to refute or verify this proposition.
Ge, Li
2016-01-01
The scattering matrix $S$ obeys the unitary relation $S^\\dagger S=1$ in a Hermitian system and the symmetry property ${\\cal PT}S{\\cal PT}=S^{-1}$ in a Parity-Time (${\\cal PT}$) symmetric system. Here we report a different symmetry relation of the $S$ matrix in a one-dimensional heterostructure, which is given by the amplitude ratio of the incident waves in the scattering eigenstates. It originates from the optical reciprocity and holds independent of the Hermiticity or $\\cal PT$ symmetry of the system. Using this symmetry relation, we probe a quasi-transition that is reminiscent of the spontaneous symmetry breaking of a $\\cal PT$-symmetric $S$ matrix, now with unbalanced gain and loss and even in the absence of gain. We show that the additional symmetry relation provides a clear evidence of an exceptional point, even when all other signatures of the $\\cal PT$ symmetry breaking are completely erased. We also discuss the existence of a final exceptional point in this correspondence, which is attributed to asymm...
From particle in a box to PT -symmetric systems via isospectral deformation
Cherian, Philip; Panigrahi, P K
2011-01-01
A family of PT -symmetric complex potentials are obtained which is isospectral to free particle in an infinite complex box in one dimension (1-D). These are generalizations to the cosec2(x) potential, isospectral to particle in a real infinite box. In the complex plane, the infinite box is extended parallel to the real axis having a real width, which is found to be an integral multiple of a constant quantum factor, arising due to boundary conditions necessary for maintaining the PT -symmetry of the superpartner. As the spectra of the particle in a box is still real, it necessarily picks out the unbroken PT -sector of its superpartner, thereby invoking a close relation between PT -symmetry and SUSY for this case.
The Horizons of Observability in PT-symmetric Four-site Quantum Lattices
Directory of Open Access Journals (Sweden)
M. Znojil
2011-01-01
Full Text Available One of the key merits of PT-symmetric (i.e., parity times time reversal symmetric quantum Hamiltonians H lies in the existence of a horizon of the stability of the system. Mathematically speaking, this horizon is formed by the boundary of the domain D(H ⊂ RD of the (real coupling strengths for which the spectrum of energies is real and non-degenerate, i.e., in principle, observable. It is shown here that even in the elementary circular four-site quantum lattices with D = 2 or D = 3 the domain of hidden Hermiticity D(H proves multiply connected, i.e., topologically nontrivial.
Controlling electric, magnetic, and chiral dipolar emission with PT-symmetric potentials
Alaeian, Hadiseh
2014-01-01
We investigate the effect of parity-time (PT)-symmetric optical potentials on the radiation of achiral and chiral emitters. Mode coalescence and the appearance of exceptional points lead to orders-of-magnitude enhancements in the emitted dipole power. Further, the emitter can be tuned to behave as a strong optical source or absorber based on the non-Hermiticity parameter. Chiral enantiomers radiating near PT metamaterials exhibit a 4.5-fold difference in their decay rate. The results of this work could enable new atom-cavity interactions for quantum optics, as well as all- optical enantio-specific separation.
Nonlinear localized modes in PT-symmetric Rosen-Morse potential well
Midya, Bikashkali
2013-01-01
We report the existence and properties of localized modes described by nonlinear Schroedinger equation with complex PT-symmetric Rosen-Morse potential well. Exact analytical expressions of the localized modes are found in both one dimensional and two-dimensional geometry with self-focusing and self-defocusing Kerr nonlinearity. Linear stability analysis reveals that these localized modes are unstable for all real values of the potential parameters although corresponding linear Schroedinger eigenvalue problem possesses unbroken PT-symmetry. This result has been verified by the direct numerical simulation of the governing equation. The transverse power flow density associated with these localized modes has also been examined.
Anomalous Light Scattering by Topological ${\\mathcal{PT}}$-symmetric Particle Arrays
Ling, C W; Mok, T C; Zhang, Z Q; Fung, Kin Hung
2016-01-01
Robust topological edge modes may evolve into complex-frequency modes when a physical system becomes non-Hermitian. We show that, while having negligible forward optical extinction cross section, a conjugate pair of such complex topological edge modes in a non-Hermitian $\\mathcal{PT}$-symmetric system can give rise to an anomalous sideway scattering when they are simultaneously excited by a plane wave. We propose a realization of such scattering state in a linear array of subwavelength resonators coated with gain media. The prediction is based on an analytical two-band model and verified by rigorous numerical simulation using multiple-multipole scattering theory. The result suggests an extreme situation where leakage of classical information is unnoticeable to the transmitter and the receiver when such a $\\mathcal{PT}$-symmetric unit is inserted into the communication channel.
Eigenvalue spectra of a $\\mathcal{PT}$ -symmetric coupled quartic potential in two dimensions
Indian Academy of Sciences (India)
Fakir Chand; Savita; S C Mishra
2010-10-01
The Schrödinger equation was solved for a generalized $\\mathcal{PT}$-symmetric quartic potential in two dimensions. It was found that, under a suitable ansatz for the wave function, the system possessed real and discrete energy eigenvalues. Analytic expressions for the energy eigenvalues and the eigenfunctions for the first four states were obtained. Some constraining relations among the wave function parameters rendered the problem quasi-solvable.
Various scattering properties of a new PT-symmetric non-Hermitian potential
Energy Technology Data Exchange (ETDEWEB)
Ghatak, Ananya, E-mail: gananya04@gmail.com [Department of Physics, Banaras Hindu University, Varanasi-221005 (India); Mandal, Raka Dona Ray, E-mail: rakad.ray@gmail.com [Department of Physics, Rajghat Besant School, Varanasi-221001 (India); Mandal, Bhabani Prasad, E-mail: bhabani.mandal@gmail.com [Department of Physics, Banaras Hindu University, Varanasi-221005 (India)
2013-09-15
We complexify a 1-d potential V(x)=V{sub 0}cosh{sup 2}μ(tanh[(x−μd)/d]+tanh(μ)){sup 2} which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters (μ,d) becomes imaginary. For the case of μ→iμ, we have an entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this potential becomes invisible from the left (or right) at certain discrete energies. The penetrating states in the other case (d→id) are always reciprocal even though it is PT-invariant and no spectral singularity (SS) is present in this case. The presence of MSS and reflectionlessness is also discussed for the free states in the later case. -- Highlights: •Existence of multiple spectral singularities (MSS) in PT-symmetric non-Hermitian system is shown. •Reciprocity is restored at discrete positive energies even for parity non-invariant complex system. •Co-existence of MSS with deep energy minima of transitivity is obtained. •Possibilities of both unidirectional and bidirectional invisibility are explored for a non-Hermitian system. •Penetrating states are shown to be reciprocal for all energies for PT-symmetric system.
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase transition point
Nixon, Sean; Yang, Jianke
2012-01-01
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase-transition point are analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of novel phenomena known to exist in this envelope equation are shown to also exist in the full equation including wave blowup, periodic bound states and solitary wave solutions.
Modulation theory in PT-Symmetric Magnetic Metamaterial Arrays in the continuum limit
Wang, Danhua
2013-01-01
We present results on the dynamics of split-ring dimers having both gain and loss in one dimensional nonlinear parity-time- (PT-)symmetric magnetic metamaterials. For the longwave (continuum) limit approximation and in the weakly nonlinear limit, we show analytic results on the existence of gap soliton solutions and on symmetry breaking phenomenon at a critical value of the gain/loss term.
Ultraslow-light effects in symmetric and asymmetric waveguide structures with moon-like scatterers
Wan, Yong; Ge, Xiao-Hui; Xu, Sheng; Guo, Yue; Yuan, Feng
2017-02-01
Ultraslow-light effects in two-dimensional hexagonal-lattice coupled waveguide with moon-like scatterers were theoretically studied using the plane-wave expansion method. For symmetric structures, simulations showed that slow light with high group index can be achieved by shifting the scatterers and adjusting the radius of moon-like scatterers. The maximum group index was over 8:0 × 104. For asymmetric structures, simulations showed that slow light with flat band and high group index can be obtained by shifting the scatterers, adjusting the radius of moon-like scatterers, and rotating the scatterers. The maximum group index was over 5:7 × 105 with a "saddle-like" relationship between the frequency and group index.
A saccharides sensor developed by symmetrical optical waveguide-based surface plasmon resonance
Directory of Open Access Journals (Sweden)
Ang Li
2015-03-01
Full Text Available We proposed a new saccharides sensor developed by symmetrical optical waveguide (SOW-based surface plasmon resonance (SPR. This unique MgF2/Au/MgF2/Analyte film structure results in longer surface plasmon wave (SPW propagation lengths and depths, leading to an increment of resolution. In this paper, we managed to decorate the dielectric interface (MgF2 layer by depositing a thin polydopamine film as surface-adherent that provides a platform for secondary reactions with the probe molecule. 3-Aminophenylboronic acid (3-PBA is chosen to be the saccharides sense probe molecule in the present work. The aqueous humor of Diabetes and Cataract patient whose blood glucose level is normal are analyzed and the results demonstrated that this sensor shows great potential in monitoring the blood sugar and can be adapted in the field of biological monitoring in the future.
Hardhienata, Hendradi
2012-01-01
Two dimensional (2D) photonic crystals are well known for its ability to manipulate the propagation of electromagnetic wave inside the crystal. 1D and 2D photonic crystals are relatively easier to fabricate than 3D because the former work in the microwave and far infrared regions whereas the later work in the visible region and requires smaller lattice constants. In this paper, simulation for a modified 2D PC with two symmetric waveguide channels where a defect is located inside one of the channel is performed. The simulation results show that optical switching is possible by modifying the refractive index of the defect. If more than one structure is applied this feature can potentially be applied to produce a cascade optical switch.
Classical irregular blocks, Hill's equation and PT-symmetric periodic complex potentials
Piatek, Marcin; Pietrykowski, Artur R.
2016-07-01
The Schrödinger eigenvalue problems for the Whittaker-Hill potential {Q}_2(x) = 1/2{h}^2 cos 4x + 4hμ cos 2x and the periodic complex potential {Q}_1(x)=1/4{h}^2{e}^{-} 4ix} + 2{h}^2 cos 2x are studied using their realizations in two-dimensional conformal field theory (2dCFT). It is shown that for the weak coupling (small) h ∈ ℝ and non-integer Floquet parameter ν ∉ ℤ spectra of hamiltonians ℋi = - d2/d x 2 + Q i( x), i = 1, 2 and corresponding two linearly independent eigenfunctions are given by the classical limit of the "single flavor" and "two flavors" ( N f = 1 , 2) irregular conformal blocks. It is known that complex nonhermitian hamiltonians which are PT-symmetric (= invariant under simultaneous parity P and time reversal T transformations) can have real eigenvalues. The hamiltonian ℋ1 is PT-symmetric for h, x ∈ ℝ. It is found that ℋ1 has a real spectrum in the weak coupling region for ν ∈ ℝ ℤ. This fact in an elementary way follows from a definition of the N f = 1 classical irregular block. Thus, ℋ1 can serve as yet another new model for testing postulates of PT-symmetric quantum mechanics.
Longhi, Stefano
2016-01-01
We consider wave transport phenomena in a $\\mathcal{PT}$-symmetric extension of the periodically-kicked quantum rotator model and reveal that dynamical localization assists the unbroken $\\mathcal{PT}$ phase. In the delocalized (quantum resonance) regime, $\\mathcal{PT}$ symmetry is always in the broken phase and ratchet acceleration arises as a signature of unidirectional non-Hermitian transport. An optical implementation of the periodically-kicked $\\mathcal{PT}$-symmetric Hamiltonian, based on transverse beam propagation in a passive optical resonator with combined phase and loss gratings, is suggested to visualize acceleration modes in fractional Talbot cavities.
Nonlinear modal interactions in parity-time (${\\cal PT}$) symmetric lasers
Ge, Li
2016-01-01
Parity-time ($\\cal PT$) symmetric lasers have attracted considerable attention lately due to their promising applications and intriguing properties, such as free spectral range doubling and single-mode lasing. In this work we discuss nonlinear modal interactions in these laser systems under steady state conditions, and we demonstrate that several gain clamping scenarios can occur for lasing operation in the $\\cal PT$-symmetric and $\\cal PT$-broken phases. In particular, we show that, depending on the system's design and the external pump profile, its operation in the nonlinear regime falls into two different categories: in one the system is frozen in the $\\cal PT$ phase space as the applied gain increases, while in the other the system is pulled towards its exceptional point. These features are first illustrated by a coupled mode formalism and later verified by employing the Steady-state Ab-initio Laser Theory (SALT). Our findings shine light on the robustness of single-mode operation in these lasers against ...
Indian Academy of Sciences (India)
E Caliceti; S Graffi
2009-08-01
We generalize some recently established criteria for the reality and non-reality of the spectrum of some classes of $\\mathcal{PT}$-symmetric Schrödinger operators. The criteria include cases of discrete spectra and continuous ones.
Light propagation in periodically modulated complex waveguides
Nixon, Sean
2014-01-01
Light propagation in optical waveguides with periodically modulated index of refraction and alternating gain and loss are investigated for linear and nonlinear systems. Based on a multiscale perturbation analysis, it is shown that for many non-parity-time ($\\mathcal{PT}$) symmetric waveguides, their linear spectrum is partially complex, thus light exponentially grows or decays upon propagation, and this growth or delay is not altered by nonlinearity. However, several classes of non-$\\mathcal{PT}$-symmetric waveguides are also identified to possess all-real linear spectrum. In the nonlinear regime longitudinally periodic and transversely quasi-localized modes are found for $\\mathcal{PT}$-symmetric waveguides both above and below phase transition. These nonlinear modes are stable under evolution and can develop from initially weak initial conditions.
Non-Hermitian neutrino oscillations in matter with PT symmetric Hamiltonians
Ohlsson, Tommy
2016-03-01
We introduce and develop a novel approach to extend the ordinary two-flavor neutrino oscillation formalism in matter using a non-Hermitian PT symmetric effective Hamiltonian. The condition of PT symmetry is weaker and less mathematical than that of hermicity, but more physical, and such an extension of the formalism can give rise to sub-leading effects in neutrino flavor transitions similar to the effects by so-called non-standard neutrino interactions. We derive the necessary conditions for the spectrum of the effective Hamiltonian to be real as well as the mappings between the fundamental and effective parameters. We find that the real spectrum of the effective Hamiltonian will depend on all new fundamental parameters introduced in the non-Hermitian PT symmetric extension of the usual neutrino oscillation formalism and that either i) the spectrum is exact and the effective leptonic mixing must always be maximal or ii) the spectrum is approximate and all new fundamental parameters must be small.
Non-reciprocal mu-near-zero mode in PT-symmetric magnetic domains
Wang, Jin; Ling, Chi Wai; Chan, C T; Fung, Kin Hung
2014-01-01
We find that a new type of non-reciprocal modes exist at an interface between two \\emph{parity-time} ($\\mathcal{PT}$) symmetric magnetic domains (MDs) near the frequency of zero effective permeability. The new mode is non-propagating and purely magnetic when the two MDs are semi-infinite while it becomes propagating in the finite case. In particular, two pronounced nonreciprocal responses could be observed via the excitation of this mode: one-way optical tunneling for oblique incidence and unidirectional beam shift at normal incidence. When the two MDs system becomes finite in size, it is found that perfect-transmission mode could be achieved if $\\mathcal{PT}$-symmetry is maintained. The unique properties of such an unusual mode are investigated by analytical modal calculation as well as numerical simulations. The results suggest a new approach to the design of compact optical isolator.
Nonreciprocal μ -near-zero mode in PT -symmetric magnetic domains
Wang, Jin; Dong, Hui Yuan; Ling, Chi Wai; Chan, C. T.; Fung, Kin Hung
2015-06-01
We find that a new type of nonreciprocal modes exists at an interface between two parity-time- (PT -) symmetric magnetic domains (MDs) near the frequency of zero effective permeability. This mode is nonpropagating and purely magnetic when the two MDs are semi-infinite, while it becomes propagating in the finite case. In particular, two pronounced nonreciprocal responses could be observed via the excitation of this mode: one-way optical tunneling for oblique incidence and unidirectional beam shift at normal incidence. When the two MDs system becomes finite in size, it is found that perfect-transmission mode could be achieved if PT symmetry is maintained. The unique properties of such an unusual mode are investigated by analytical modal calculation as well as numerical simulations. The results suggest a different approach to the design of compact optical isolator.
Kartashov, Yaroslav V; Konotop, Vladimir V; Torner, Lluis
2016-01-01
We address the propagation of light beams in longitudinally modulated PT-symmetric lattices, built as arrays of couplers with periodically varying separation between their channels, and show a number of possibilities for efficient diffraction control available in such non-conservative structures. The dynamics of light in such lattices crucially depends on the ratio of the switching length for the straight segments of each coupler and the longitudinal lattice period. Depending on the longitudinal period, one can achieve either beam rectification, when the input light propagates at a fixed angle across the structure without diffractive broadening, or dynamic localization, when the initial intensity distribution is periodically restored after each longitudinal period. Importantly, the transition between these two different propagation regimes can be achieved by tuning only gain and losses acting in the system, provided that the PT-symmetry remains unbroken. The impact of Kerr nonlinearity is also discussed.
PT-symmetric microring lasers: Self-adapting broadband mode-selective resonators
Hodaei, Hossein; Heinrich, Matthias; Christodoulides, Demetrios N; Khajavikhan, Mercedeh
2014-01-01
We demonstrate experimentally that stable single longitudinal mode operation can be readily achieved in PT-symmetric arrangements of coupled microring resonators. Whereas any active resonator is in principle capable of displaying single-wavelength operation, selective breaking of PT-symmetry can be utilized to systematically enhance the maximum achievable gain of this mode, even if a large number of competing longitudinal or transverse resonator modes fall within the amplification bandwidth of the inhomogeneously broadened active medium. This concept is robust with respect to fabrication tolerances, and its mode selectivity is established without the need for additional components or specifically designed filters. Our results may pave the way for a new generation of versatile cavities lasing at a desired longitudinal resonance. Along these lines, traditionally highly multi-moded microring resonator configurations can be fashioned to suppress all but one longitudinal mode.
Solitons in PT-symmetric periodic systems with the logarithmically saturable nonlinearity
Zhan, Kaiyun; Tian, Hao; Li, Xin; Xu, Xianfeng; Jiao, Zhiyong; Jia, Yulei
2016-09-01
We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain.
Zero width resonance (spectral singularity) in a complex PT-symmetric potential
Ahmed, Zafar
2009-01-01
We show that the complex PT-Symmetric potential, $V(x)=-V_1 {sech}^2x + iV_2 {sech}x ~\\tanh x, $, entails a single zero-width resonance (spectral singularity) when $V_1+|V_2|=4n^2+4n+{3\\over 4}(n=1,2,3.., |V_2|>|V_1|+ {{sgn}(V_1) \\over 4})$ and the positive resonant energy is given as $E_*={1 \\over 4}[|V_2|-(1/4+V_1)]$.
Kulishov, Mykola; Kress, Bernard
2015-01-01
We study the diffraction produced by a slab of purely reflective PT-symmetric volume Bragg grating that combines modulations of refractive index and gain/loss of the same periodicity with a quarter-period shift between them. Such a complex grating has a directional coupling between the different diffraction orders, which allows us to find an analytic solution for the first three orders of the full Maxwell equations without resorting to the paraxial approximation. This is important, because only with the full equations can the boundary conditions, allowing for the reflections, be properly implemented. Using our solution we analyze unidirectional invisibility of such a grating in a wide variety of configurations.
Families of particles with different masses in PT-symmetric quantum field theory.
Bender, Carl M; Klevansky, S P
2010-07-16
An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the Dyson-Schwinger equations derived from a Lagrangian can have many different but equally valid solutions. Nonunique solutions to the Dyson-Schwinger equations arise when the functional integral for the Green's functions of the quantum field theory converges in different pairs of Stokes' wedges in complex-field space, and the solutions are physically viable if the pairs of Stokes' wedges are PT symmetric.
Floquet Topological Phases Driven by $\\mathcal{PT}$ Symmetric Nonunitary Time Evolution
Kim, Dakyeong; Kawakami, Norio; Obuse, Hideaki
2016-01-01
We study Floquet topological phases driven by $\\mathcal{PT}$ symmetric nonunitary time evolution in one dimension, based on an experimental setup of discrete-time quantum walks. We develop, for nonunitary time-evolution operators, a procedure to calculate topological invariants for Floquet topological phases and find that the bulk-edge correspondence gives correct predictions of the emergent edge states. These edge states make exponential growth of wavefunction amplitudes at specific positions with time controllable. Hereby, we propose that these phenomena inherent in open quantum systems are feasibly observed by present experiments of quantum walks in both classical and quantum regimes.
P T -Symmetric Coupled-Resonator Waveguide Based on Buried Heterostructure Nanocavities
Takata, Kenta; Notomi, Masaya
2017-05-01
We propose and theoretically study a parity-time (P T )-symmetric photonic-crystal coupled-resonator optical waveguide (CROW) based on buried heterostructure nanocavities which has potential scalability and controllability. We analytically reveal its spectral transport properties with a tight-binding model and show the possibility of the wide-range control of its group velocity using the P T phase transition. While the group velocity at the P T phase-transition point diverges, the group-velocity dispersion converges. A numerical estimation of the system response to temporal pulse inputs shows that the pulse broadening is not severe in a device of hundreds of micrometers in size. Furthermore, a longer pulse duration results in a higher upper limit of the pulse peak velocity, which can be, in principle, superluminal. We next perform numerical simulations on the considered photonic-crystal slab structures with the finite-element method, and we successfully observe P T phase transitions. In the simulated parameter range, gain and loss coefficients of the order of 100 cm-1 meet the condition for the maximum group-velocity coefficient in the context of the tight-binding approach. A 9.3-fold increase in the group velocity at 1502 nm is obtained in a three-dimensional device by switching between the conventional and P T -symmetric CROWs. Meanwhile, we also encounter band smoothing around the phase transition, which hampers the group-velocity divergence. Our simulation result indicates that it arises from interfering evanescent waves decaying out of the device structure, and we discuss ways to suppress this effect.
Yu, Tianyi; Li, Honggen; Cao, Zhuangqi; Wang, Yi; Shen, Qishun; He, Ying
2008-05-01
An oscillating wave displacement sensor based on the enhanced Goos-Hänchen (G-H) effect in a symmetrical metal-cladding optical waveguide is proposed. Since the detected signal is irrelevant to the power fluctuation of the incident light and the magnitude of the G-H shift is enhanced to hundreds of micrometers, a 40 pm resolution is demonstrated in our experiment without employing any complicated optical equipment and servo techniques.
Generation of families of spectra in PT-symmetric quantum mechanics and scalar bosonic field theory.
Schmidt, Steffen; Klevansky, S P
2013-04-28
This paper explains the systematics of the generation of families of spectra for the -symmetric quantum-mechanical Hamiltonians H=p(2)+x(2)(ix)(ε), H=p(2)+(x(2))(δ) and H=p(2)-(x(2))(μ). In addition, it contrasts the results obtained with those found for a bosonic scalar field theory, in particular in one dimension, highlighting the similarities to and differences from the quantum-mechanical case. It is shown that the number of families of spectra can be deduced from the number of non-contiguous pairs of Stokes wedges that display PT symmetry. To do so, simple arguments that use the Wentzel-Kramers-Brillouin approximation are used, and these imply that the eigenvalues are real. However, definitive results are in most cases presently only obtainable numerically, and not all eigenvalues in each family may be real. Within the approximations used, it is illustrated that the difference between the quantum-mechanical and the field-theoretical cases lies in the number of accessible regions in which the eigenfunctions decay exponentially. This paper reviews and implements well-known techniques in complex analysis and PT-symmetric quantum theory.
Non-Hermitian ${\\cal PT}$-symmetric relativistic quantum theory in an intensive magnetic field
Rodionov, V N
2016-01-01
We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of physical parameters. This condition not only guarantees the reality of the eigenvalues of Hamiltonian operators, but also implies the preservation of the probabilities of the considered quantum processes. However as it was shown relatively recently (Bender, Boettcher 1998), Hermiticity is a sufficient but it is not a necessary condition. It turned out that among non-Hermitian Hamiltonians it is possible to allocate a number of such which have real energy spectra and can ensure the development of systems over time with preserving unitarity. This type of Hamiltonians includes so-called parity-time (${\\cal PT}$) symmetric models which is already used in various fields of modern physics. The most developed in this respect are models, which used in the field of ${\\cal PT}$-symmetric op...
A possible method for non-Hermitian and Non-PT-symmetric Hamiltonian systems.
Li, Jun-Qing; Miao, Yan-Gang; Xue, Zhao
2014-01-01
A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator η+ and defining the annihilation and creation operators to be η+ -pseudo-Hermitian adjoint to each other. The operator η+ represents the η+ -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator η+ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-PT-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution) are found not to be altered by the noncommutativity.
A possible method for non-Hermitian and Non-PT-symmetric Hamiltonian systems.
Directory of Open Access Journals (Sweden)
Jun-Qing Li
Full Text Available A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator η+ and defining the annihilation and creation operators to be η+ -pseudo-Hermitian adjoint to each other. The operator η+ represents the η+ -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator η+ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-PT-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution are found not to be altered by the noncommutativity.
Transverse waveguide mode suppression for Pt-electrode SAW resonators on quartz and LGS.
Meulendyk, Bennett J; Pereira da Cunha, Mauricio
2011-12-01
SAW resonators on ST-X quartz and langasite (LGS) [0°, 144°, 24°] are currently being used for hydrogen fluoride (HF) vapor sensing and high-temperature sensing, respectively. For these applications, the use of Pt-based electrodes allows the resonators to withstand the targeted harsh environments. This work reveals that for Pt-electrode resonators with conventional short-circuit gratings on the aforementioned quartz and LGS orientations, acoustic energy leaks from the grating region to the bus bars, thus degrading the resonator response. To resolve this problem, this paper proposes and implements open-circuit gratings for resonators fabricated with these substrate/metal combinations. The open-circuit gratings guide the acoustic energy within the grating region, resulting in greater quality factors and reduced losses in the resonator response. In addition, scalar potential theory is utilized in this work to identify transverse waveguide modes in the responses of open-circuit grating resonators on quartz and LGS. A transverse waveguide mode dispersion relation was derived to extend the scalar potential theory to account for asymmetry in the slowness curve around the propagation direction. This is the case for several commonly used LGS orientations, in particular LGS [0°, 144°, 24°]. Finally, this work addresses spurious transverse mode mitigation by scaling both the transducer's grating aperture and electrode overlap width. Open circuit grating resonators with appropriately scaled transducer designs were fabricated and tested, resulting in a 71% increase in quality factor and a spurious mode rejection of over 26 dBc for Pt-electrode devices on ST-X quartz. This progress directly translates into better frequency resolution and increased dynamic range for HF vapor sensors and high-temperature SAW devices.
Four-wave mixing in a parity-time (PT)-symmetric coupler.
Wasak, T; Szańkowski, P; Konotop, V V; Trippenbach, M
2015-11-15
Parity-time (PT) symmetry allows for implementing controllable matching conditions for the four-wave mixing in 1D coupled waveguides. Different types of the process involving energy transition between slow and fast modes are established. In the case of defocusing Kerr media, the degenerated four-wave mixing is studied in detail. It is shown that unbroken PT symmetry supports the process existing in the conservative limit and, at the same time, originates new types of matching conditions, which cannot exist in the conservative system. In the former case, a slow beam splits into two fast beams, with nearly conserved total power, while in the latter case, one slow beam and one fast beam are generated. In the last process, the energy of the input primary slow beam is not changed and growth of the energy of the generated slow beam varies due to gain and loss of the medium. The appreciable generation of the fifth mode, i.e., the effect of the secondary resonant interactions, is observed.
Singular Mapping for a $PT$-Symmetric Sinusoidal Optical Lattice at the Symmetry-Breaking Threshold
Jones, H F
2014-01-01
A popular $PT$-symmetric optical potential (variation of the refractive index) that supports a variety of interesting and unusual phenomena is the imaginary exponential, the limiting case of the potential $V_0[\\cos(2\\pi x/a)+i\\lambda\\sin(2\\pi x/a)]$ as $\\lambda \\to 1$, the symmetry-breaking point. For $\\lambda<1$, when the spectrum is entirely real, there is a well-known mapping by a similarity transformation to an equivalent Hermitian potential. However, as $\\lambda \\to 1$, the spectrum, while remaining real, contains Jordan blocks in which eigenvalues and the corresponding eigenfunctions coincide. In this limit the similarity transformation becomes singular. Nonetheless, we show that the mapping from the original potential to its Hermitian counterpart can still be implemented; however, the inverse mapping breaks down. We also illuminate the role of Jordan associated functions in the original problem, showing that they map onto eigenfunctions in the associated Hermitian problem.
Nonlinear wave dynamics near phase transition in $\\mathcal{PT}$-symmetric localized potentials
Nixon, Sean
2015-01-01
Nonlinear wave propagation in parity-time ($\\mathcal{PT}$) symmetric localized potentials is investigated analytically near a phase-transition point where a pair of real eigenvalues of the potential coalesce and bifurcate into the complex plane. Necessary conditions for phase transition to occur are derived based on a generalization of the Krein signature. Using multi-scale perturbation analysis, a reduced nonlinear ODE model is derived for the amplitude of localized solutions near phase transition. Above phase transition, this ODE model predicts a family of stable solitons not bifurcating from linear (infinitesimal) modes under a certain sign of nonlinearity. In addition, it predicts periodically-oscillating nonlinear modes away from solitons. Under the opposite sign of nonlinearity, it predicts unbounded growth of solutions. Below phase transition, solution dynamics is predicted as well. All analytical results are compared to direct computations of the full system and good agreement is observed.
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Energy Technology Data Exchange (ETDEWEB)
Midya, Bikashkali, E-mail: bikash.midya@gmail.com [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India); Roychoudhury, Rajkumar, E-mail: rroychoudhury123@gmail.com [Advanced Center for Nonlinear and Complex Phenomena, Kolkata 700075 (India)
2014-02-15
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expression of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effects of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined. -- Highlights: • Existence of localized modes is investigated in PT-symmetric complex potentials. • Exact analytical expression of the localized modes is obtained. • Effect of gain/loss profile on the stability of these localized modes is discussed. • Localized modes in 2D and associated transverse power-flow density are also examined.
Observation of Bloch oscillations in complex PT-symmetric photonic lattices.
Wimmer, Martin; Miri, Mohammed-Ali; Christodoulides, Demetrios; Peschel, Ulf
2015-12-07
Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals exhibit unusual properties like secondary emissions and resonant restoration of PT symmetry. In addition, we present a versatile method for reconstructing the real and imaginary components of the band structure by directly monitoring the light evolution during a cycle of these oscillations.
STABILITY OF BOSE-EINSTEIN CONDENSATES IN A PT-SYMMETRIC DOUBLE-δ POTENTIAL CLOSE TO BRANCH POINTS
Directory of Open Access Journals (Sweden)
Andreas Löhle
2014-04-01
Full Text Available A Bose-Einstein condensate trapped in a double-well potential, where atoms are incoupled to one side and extracted from the other, can in the mean-field limit be described by the nonlinear Gross-Pitaevskii equation (GPE with a PT symmetric external potential. If the strength of the in- and outcoupling is increased two PT broken states bifurcate from the PT symmetric ground state. At this bifurcation point a stability change of the ground state is expected. However, it is observed that this stability change does not occur exactly at the bifurcation but at a slightly different strength of the in-/outcoupling effect. We investigate a Bose-Einstein condensate in a PT symmetric double-δ potential and calculate the stationary states. The ground state’s stability is analysed by means of the Bogoliubov-de Gennes equations and it is shown that the difference in the strength of the in-/outcoupling between the bifurcation and the stability change can be completely explained by the norm-dependency of the nonlinear term in the Gross-Pitaevskii equation.
Modulational instability in a PT-symmetric vector nonlinear Schrödinger system
Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.
2016-12-01
A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.
Perturbation Theory for PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold
Jones, H F
2011-01-01
The $PT$ symmetric potential $V_0[\\cos(2\\pi x/a)+i\\lambda\\sin(2\\pi x/a)]$ has a completely real spectrum for $\\lambda\\le 1$, and begins to develop complex eigenvalues for $\\lambda>1$. At the symmetry-breaking threshold $\\lambda=1$ some of the eigenvectors become degenerate, giving rise to a Jordan-block structure for each degenerate eigenvector. In general this is expected to give rise to a secular growth in the amplitude of the wave. However, it has been shown in a recent paper by Longhi, by numerical simulation and by the use of perturbation theory, that for an initial wave packet this growth is suppressed, giving instead a constant maximum amplitude. We revisit this problem by developing the perturbation theory further. We verify that the results found by Longhi persist to second order, and with different input wave packets we are able to see the seeds in perturbation theory of the phenomenon of birefringence first discovered by El-Ganainy et al.
Propagation properties for five-layer symmetric slab waveguides including left-handed materials
Institute of Scientific and Technical Information of China (English)
SHEN Lu-fa; WANG Zi-hua; LI Su-ping
2008-01-01
In this paper,we discussed a slab wave-guide of five layers,The core is a left-handed material,but the claddings are righthanded materials.A dispersion equation of TE modes is obtained by using Maxwell's equations,and some new dispersion characteristics are obtained based on the equation.
Ge, Li
2016-01-01
The CPA-laser is a coexisting state of coherent perfect absorption and lasing that was proposed in parity-time ($\\cal PT$) symmetric photonic systems. In this work we show that the spectral signature of a CPA-laser displayed by the singular value spectrum of the scattering matrix ($S$) can be orders of magnitude wider than that displayed by the eigenvalue spectrum of $S$. Since the former reflects how strongly light can be absorbed or amplified and the latter announces the spontaneous symmetry breaking of $S$, these contrasting spectral signatures indicate that near perfect absorption and extremely strong amplification can be achieved even in the $\\cal PT$-symmetric phase of $S$, which is known for and defined by its flux-conserving eigenstates. We also show that these contrasting spectral signatures are accompanied by strikingly different sensitivities to disorder and imperfection, suggesting that the eigenvalue spectrum is potentially suitable for sensing and the singular value spectrum for robust switching...
TE Magnetostatic Surface Waves in Symmetric Dielectric Negative Permittivity Material Waveguide
Directory of Open Access Journals (Sweden)
A. I. Ass'ad
2009-01-01
Full Text Available Nonlinear magnetostatic surface wave in a slab waveguide structure has been investigated. The design consisted of dielectric film between two thick nonlinear nonmagnetic negative permittivity material (NPM layers. A dispersion relation for TE nonlinear Magnetostatic surface waves (NMSSWs has been derived into the proposed structure and has been numerically investigated. Effective refractive index decreases with thickness and frequency increase have been found. Effective refractive index decrease with optical nonlinearity increase and switching to negative values of effective refractive index at a certain value of optical nonlinearity have been found. This meant that the structure behaved like a left-handed material over certain range. We found that the power flow was changing by changing the operating frequency, the dielectric film thickness, and the optical nonlinearity. Also, the effective refractive index and power flow attained constant values over certain values of dielectric constant values.
Indian Academy of Sciences (India)
Fakir Chand; S C Mishra; Ram Mehar Singh
2009-08-01
We investigate the quasi-exact solutions of an analogous Schrödinger wave equation for two-dimensional non-Hermitian complex Hamiltonian systems within the framework of an extended complex phase space characterized by = 1 + 3, = 2 + 4, = 1 + 3, = 2 + 4. Explicit expressions for the energy eigenvalues and eigenfunctions for ground and first excited states of a two-dimensional $\\mathcal{PT}$-symmetric sextic potential and some of its variants are obtained. The eigenvalue spectra are found to be real within some parametric domains.
Hang, Chao; Gabadadze, Gregory; Huang, Guoxiang
2017-02-01
We present a physical setup for realizing all-real-spectrum optical potentials with arbitrary gain-and-loss distributions in a coherent medium consisting of a cold three-level atomic gas driven by control and probe laser fields. We show that by the interference of Raman resonances and the Stark shift induced by a far-detuned laser field, tunable, non-parity-time (non-PT )-symmetric optical potentials with all-real spectra proposed recently by Nixon and Yang [Phys. Rev. A 93, 031802(R) (2016), 10.1103/PhysRevA.93.031802] can be actualized physically. We also show that when the real parts of the non-PT -symmetric optical potentials are tuned cross certain thresholds, phase transitions—where the eigenspectrum of the system changes from all real to complex—may occur and hence the stability of the probe-field propagation is altered. Our scheme can also be extended to high dimensions and to a nonlinear propagation regime, where stable optical solitons with power of the order of nano-Watts may be generated in the system.
Stabilizing and destabilizing perturbations of PT-symmetric indefinitely damped systems.
Kirillov, O N
2013-04-28
Eigenvalues of a potential dynamical system with damping forces that are described by an indefinite real symmetric matrix can behave as those of a Hamiltonian system when gain and loss are in a perfect balance. This happens when the indefinitely damped system obeys parity-time ( ) symmetry. How do pure imaginary eigenvalues of a stable -symmetric indefinitely damped system behave when variation in the damping and potential forces destroys the symmetry? We establish that it is essentially the tangent cone to the stability domain at the exceptional point corresponding to the Whitney umbrella singularity on the stability boundary that manages transfer of instability between modes.
Rodionov, V N
2013-01-01
The modified Dirac equations for the massive particles with the replacement of the physical mass $m$ with the help of the relation $m\\rightarrow m_1+ \\gamma_5 m_2$ are investigated. It is shown that for a fermion theory with a $\\gamma_5$-mass term, the limiting of the mass specter by the value $ m_{max}= {m_1}^2/2m_2$ takes place. In this case the different regions of the unbroken $\\cal PT$ symmetry may be expressed by means of the restriction of the physical mass $m\\leq m_{max}$. It should be noted that in the approach which was developed by C.Bender et al. for the $\\cal PT$-symmetric version of the massive Thirring model with $\\gamma_5$-mass term, the region of the unbroken $\\cal PT$-symmetry was found in the form $m_1\\geq m_2$ \\cite{ft12}. However on the basis of the mass limitation $m\\leq m_{max}$ we obtain that the domain $m_1\\geq m_2$ consists of two different parametric sectors: i) $0\\leq m_2 \\leq m_1/\\sqrt{2}$ -this values of mass parameters $m_1,m_2$ correspond to the traditional particles for which ...
Directory of Open Access Journals (Sweden)
Holger Cartarius
2013-01-01
Full Text Available We investigate the Gross-Pitaevskii equation for a Bose-Einstein condensate in a PT symmetric double-well potential by means of the time-dependent variational principle and numerically exact solutions. A one-dimensional and a fully three-dimensional setup are used. Stationary states are determined and the propagation of wave function is investigated using the time-dependent Gross-Pitaevskii equation. Due to the nonlinearity of the Gross-Pitaevskii equation the potential dependson the wave function and its solutions decide whether or not the Hamiltonian itself is PT symmetric. Stationary solutions with real energy eigenvalues fulfilling exact PT symmetry are found as well as PT broken eigenstates with complex energies. The latter describe decaying or growing probability amplitudes and are not true stationary solutions of the time-dependent Gross-Pitaevskii equation. However, they still provide qualitative information about the time evolution of the wave functions.
Observation of Bloch oscillations in complex PT-symmetric photonic lattices
Wimmer, Martin; Christodoulides, Demetrios; Peschel, Ulf
2016-01-01
Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals ...
Particles versus fields in $\\mathcal{PT}$-symmetrically deformed integrable systems
Indian Academy of Sciences (India)
Andreas Fring
2009-08-01
We review some recent results on how $\\mathcal{PT}$ symmetry, that is a simultaneous time-reversal and parity transformation, can be used to construct new integrable models. Some complex valued multi-particle systems, such as deformations of the Calogero–Moser– Sutherland models, are shown to arise naturally from real valued field equations of non-linear integrable systems. Deformations of complex non-linear integrable field equations, some of them even allowing for compacton solutions, are also investigated. The integrabilty of various systems is established by means of the Painlevé test.
One- and two-dimensional solitons in PT-symmetric systems emulating the spin-orbit coupling
Sakaguchi, Hidetsugu
2016-01-01
We introduce a two-dimensional (2D) system, which can be implemented in dual-core planar optical couplers with the Kerr nonlinearity in its cores, making it possible to blend effects of the PT symmetry, represented by the balanced linear gain and loss in the two cores, and spin-orbit coupling (SOC), emulated by a spatially biased coupling between the cores. Families of 1D and 2D solitons and their stability boundaries are identified. In the 1D setting, the addition of the SOC terms leads, at first, to shrinkage of the stability area for PT-symmetric solitons, which is followed by its rapid expansion. 2D solitons have their stability region too, in spite of the simultaneous action of two major destabilizing factors, viz., the collapse driven by the Kerr nonlinearity, and a trend towards spontaneous breakup of the gain-loss balance. In the limit of the SOC terms dominating over the intrinsic diffraction, the 1D system gives rise to a new model for gap solitons, which admits exact analytical solutions.
Haldar, Raktim; Mishra, V.; Dutt, Avik; Varshney, Shailendra K.
2016-10-01
In this work, we propose novel schemes to design on-chip ultra-compact optical directional couplers (DC) and broadband polarization beam splitters (PBS) based on off-centered and asymmetric dielectric slot waveguides, respectively. Slot dimensions and positions are optimized to achieve maximum coupling coefficients between two symmetric and non-symmetric slotted Si wire waveguides through overlap integral method. We observe >88% of enhancement in the coupling coefficients when the size-optimized slots are placed in optimal positions, with respect to the same waveguides with no slot. When the waveguides are parallel, in that case, a coupling length as short as 1.73 μm is accomplished for TM mode with the off-centered and optimized slots. This scheme enables us to design optical DC with very small footprint, L c ∼ 0.9 μm in the presence of S-bends. We also report a compact (L c ∼ 1.1 μm) on-chip broadband PBS with hybrid slots. Extinction ratios of 13 dB and 22.3 dB are realized with very low insertion loss (0.055 dB and 0.008 dB) for TM and TE modes at 1.55 μm, respectively. The designed PBS exhibits a bandwidth of 78 nm for the TM mode (C-and partial L-bands) and >100 nm for the TE mode (S + C + L wavelength bands). Such on-chip devices can be used to design compact photonic interconnects and quantum information processing units efficiently. We have also investigated the fabrication tolerances of the proposed devices and described the fabrication steps to realize such hybrid devices. Our results are in good agreement with 3D FDTD simulations.
Nonlinear wave dynamics near phase transition in PT-symmetric localized potentials
Nixon, Sean; Yang, Jianke
2016-09-01
Nonlinear wave propagation in parity-time symmetric localized potentials is investigated analytically near a phase-transition point where a pair of real eigenvalues of the potential coalesce and bifurcate into the complex plane. Necessary conditions for a phase transition to occur are derived based on a generalization of the Krein signature. Using the multi-scale perturbation analysis, a reduced nonlinear ordinary differential equation (ODE) is derived for the amplitude of localized solutions near phase transition. Above the phase transition, this ODE predicts a family of stable solitons not bifurcating from linear (infinitesimal) modes under a certain sign of nonlinearity. In addition, it predicts periodically-oscillating nonlinear modes away from solitons. Under the opposite sign of nonlinearity, it predicts unbounded growth of solutions. Below the phase transition, solution dynamics is predicted as well. All analytical results are compared to direct computations of the full system and good agreement is observed.
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Midya, Bikashkali
2014-01-01
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expressions of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effect of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined.
Asymmetric soliton mobility in competing linear-nonlinear PT-symmetric lattices
Kartashov, Yaroslav V; Torner, Lluis
2016-01-01
We address the transverse mobility of spatial solitons in competing parity-time-symmetric linear and nonlinear lattices. The competition between out-of-phase linear and nonlinear lattices results in a drastic mobility enhancement within a range of soliton energies. We show that within such range, the addition of even a small imaginary part in the linear potential makes soliton mobility strongly asymmetric. The minimal phase tilt required for setting solitons into radiationless motion across the lattice in the direction opposite to that of the internal current drops to nearly zero, while the minimal phase tilt required for motion in the opposite direction notably increases. For a given initial phase tilt, the velocity of soliton motion grows with an increase of the balanced gain/losses. In this regime of enhanced mobility, tilted solitons can efficiently drag other solitons that were initially at rest, to form moving soliton pairs.
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.
Ams, Martin; Marshall, G. D.; Spence, D. J.; Withford, M. J.
2005-07-01
We report both theoretical and experimental results of a slit beam shaping configuration for fabricating photonic waveguides by use of femtosecond laser pulses. Most importantly we show the method supports focusing objectives with a long depth of field and allows the direct-writing of microstructures with circular cross-sections whilst employing a perpendicular writing scheme. We applied this technique to write low loss (0.39 dB/cm), single mode waveguides in phosphate glass.
PT-symmetry and kagome lattices (Conference Presentation)
Saxena, Avadh; Chern, Gia-Wei
2016-09-01
We consider a complex photonic lattice by placing PT-symmetric dimers at the Kagome lattice points. This lattice is a two-dimensional network of corner-sharing triangles. Each dimer represents a pair of strongly coupled waveguides. The frustrated coupling between waveguide modes results in a dispersionless flat band comprising spatially localized modes. For a balanced arrangement of gain and loss on each dimer, up to a critical value of the gain/loss parameter the system exhibits a PT-symmetric phase. The beam evolution in the waveguide array leads to an oscillatory rotation of the optical power. We observe local chiral structures with a narrow beam excitation. We also study nonlinearity and disorder in this set up.
Dirichlet spectra of the paradigm model of complex PT-symmetric potential: V(x) = -(ix) N
Ahmed, Zafar; Kumar, Sachin; Sharma, Dhruv
2017-08-01
So far the spectra En(N) of the paradigm model of complex PT(Parity-Time)-symmetric potential VBB(x , N) = -(ix) N is known to be analytically continued for N > 4. Consequently, the well known eigenvalues of the Hermitian cases (N = 6 , 10) cannot be recovered. Here, we illustrate Kato's theorem that even if a Hamiltonian H(λ) is an analytic function of a real parameter λ, its eigenvalues En(λ) may not be analytic at finite number of Isolated Points (IPs). In this light, we present the Dirichlet spectra En(N) of VBB(x , N) for 2 ≤ N < 12 using the numerical integration of Schrödinger equation with ψ(x = ± ∞) = 0 and the diagonalization of H =p2 / 2 μ +VBB(x , N) in the harmonic oscillator basis. We show that these real discrete spectra are consistent with the most simple two-turning point CWKB (C refers to complex turning points) method provided we choose the maximal turning points (MxTP) [ - a + ib , a + ib , a , b ∈ R] such that | a | is the largest for a given energy among all (multiple) turning points. We find that En(N) are continuous function of N but non-analytic (their first derivative is discontinuous) at IPs N = 4 , 8; where the Dirichlet spectrum is null (as VBB becomes a Hermitian flat-top potential barrier). At N = 6 and 10, VBB(x , N) becomes a Hermitian well and we recover its well known eigenvalues.
Nie, Yiyou; Li, Yuanhua; Wu, Zhijing; Wang, Xianping; Yuan, Wen; Sang, Minghuang
2014-04-21
We present a novel and simple optical structure, i.e., the symmetrical metal-cladding waveguide, in which a polymer layer is added into the guiding layer, for sensitive detection of chemical vapor by using the enhanced Goos-Hänchen (GH) shift (nearly a millimeter scale). Owing to the high sensitivity of the excited ultrahigh-order modes, the vapor-induced effect (swelling effect and refractive index change) in the polymer layer will lead to a dramatic variation of the GH shift. The detected GH shift signal is irrelevant to the power fluctuation of the incident light. The detection limit of 9.5 ppm for toluene and 28.5 ppm for benzene has been achieved.
Mostafazadeh, Ali
2016-01-01
Among the interesting outcomes of the study of the physical applications of spectral singularities in PT-symmetric optical systems is the discovery of CPA-lasers. These are devices that act both as a threshold laser and a coherent perfect absorber (CPA) for the same values of their physical parameters. Unlike a homogeneous slab that is made to act as a CPA, a slab CPA-laser would absorb the incident waves coming from the left and right of the device provided that they have appropriate intensity and phase contrasts. We provide a comprehensive study of one of the simplest experimentally accessible examples of a CPA-laser, namely a PT-symmetric optical slab system consisting of a balanced pair of adjacent or separated gain and loss components. In particular, we give a closed form expression describing the spectral singularities of the system which correspond to its CPA-laser configurations. We determine the intensity and phase contrasts for the TE and TM waves that are emitted (absorbed) whenever the slab acts a...
Energy Technology Data Exchange (ETDEWEB)
Neilson, Jeffrey M.
2017-07-25
A cylindrical waveguide with a mode converter transforms a whispering gallery mode from a gyrotron cylindrical waveguide with a helical cut launch edge to a quasi-Gaussian beam suitable for conveyance through a corrugated waveguide. This quasi-Gaussian beam is radiated away from the waveguide using a spiral cut launch edge, which is in close proximity to a first mode converting reflector. The first mode converting reflector is coupled to a second mode converting reflector which provides an output free-space HE11 mode wave suitable for direct coupling into a corrugated waveguide. The radiated beam produced at the output of the second mode converting reflector is substantially circular.
Progress in planar optical waveguides
Wang, Xianping; Cao, Zhuangqi
2016-01-01
This book provides a comprehensive description of various slab waveguide structures ranged from graded-index waveguide to symmetrical metal-cladding waveguide. In this book, the transfer Matrix method is developed and applied to analyze the simplest case and the complex generalizations. A novel symmetrical metal-cladding waveguide structure is proposed and systematically investigated for several issues of interest, such as biochemical sensing, Goos-Hänchen shift and the slow light effect, etc. Besides, this book summarizes the authors’ research works on waveguides over the last decade. The readers who are familiar with basic optics theory may find this book easy to read and rather inspiring.
Mostafazadeh, Ali; Sarısaman, Mustafa
2016-12-01
Among the interesting outcomes of the study of the physical applications of spectral singularities in PT-symmetric optical systems is the discovery of CPA-lasers. These are devices that act both as a threshold laser and a coherent perfect absorber (CPA) for the same values of their physical parameters. Unlike a homogeneous slab that is made to act as a CPA, a slab CPA-laser would absorb the incident waves coming from the left and right of the device provided that they have appropriate intensity and phase contrasts. We provide a comprehensive study of one of the simplest experimentally accessible examples of a CPA-laser, namely a PT-symmetric optical slab system consisting of a balanced pair of adjacent or separated gain and loss components. In particular, we give a closed form expression describing the spectral singularities of the system which correspond to its CPA-laser configurations. We determine the intensity and phase contrasts for the TE and TM waves that are emitted (absorbed) whenever the slab acts as a laser (CPA). We also investigate the behavior of the time-averaged energy density and Poynting vector for these waves. This is necessary for determining the optimal values of the physical parameters of the system that make it act as a CPA-laser. These turn out to correspond to situations where the separation distance s between the gain and loss layers is an odd multiple of a characteristic length scale s0. A curious by-product of our study is that, except for the cases where s is an even integer multiple of s0, there is a critical angle of polarization beyond which the energy of the waves emitted from the lossy layer can be larger than the energy of those emitted from the gain layer.
Znojil, Miloslav
2017-07-01
The phenomenon of the birth of an isolated quantum bound state at the lower edge of the continuum is studied for a particle moving along a discrete real line of coordinates x ∈Z . The motion is controlled by a weakly nonlocal 2 J -parametric external potential V which is non-Hermitian but P T symmetric. The model is found exactly solvable. The bound states are interpreted as Sturmians. Their closed-form definitions are presented and discussed up to J =7 .
Nguyen, Ba Phi
2016-01-01
We study numerically the transport and localization properties of waves in ordered and disordered ladder-shaped lattices with local $\\mathcal{PT}$ symmetry. Using a transfer matrix method, we calculate the transmittance and the reflectance for the individual channels and the Lyapunov exponent for the whole system. In the absence of disorder, we find that when the gain/loss parameter $\\rho$ is smaller than the interchain coupling parameter $t_{v}$, the transmittance and the reflectance are periodic functions of the system size, whereas when $\\rho$ is larger than $t_{v}$, the transmittance is found to be an exponentially-decaying function while the reflectance attains a saturation value in the thermodynamic limit. For a fixed system size, there appear perfect transmission resonances in each individual channel at several values of the gain/loss strength smaller than $t_{v}$. A singular behavior of the transmittance is also found to appear at various values of $\\rho$ for a given system size. When disorder is inse...
PT-symmetry breaking with divergent potentials: lattice and continuum cases
Joglekar, Yogesh N; Saxena, Avadh
2014-01-01
We investigate the parity- and time-reversal ($\\mathcal{PT}$)-symmetry breaking in lattice models in the presence of long-ranged, non-hermitian, $\\mathcal{PT}$-symmetric potentials that remain finite or become divergent in the continuum limit. By scaling analysis of the fragile $\\mathcal{PT}$ threshold for an open finite lattice, we show that continuum loss-gain potentials $V_\\alpha(x)\\propto i |x|^\\alpha \\mathrm{sign}(x)$ have a positive $\\mathcal{PT}$-breaking threshold for $\\alpha>-2$, and a zero threshold for $\\alpha\\leq -2$. When $\\alpha<0$ localized states with complex (conjugate) energies in the continuum energy-band occur at higher loss-gain strengths. We investigate the signatures of $\\mathcal{PT}$-symmetry breaking in coupled waveguides, and show that the emergence of localized states dramatically shortens the relevant time-scale in the $\\mathcal{PT}$-symmetry broken region.
Directory of Open Access Journals (Sweden)
Daniel Haag
2014-04-01
Full Text Available We consider the linear and nonlinear Schrödinger equation for a Bose-Einstein condensate in a harmonic trap with PT-symmetric double-delta function loss and gain terms. We verify that the conditions for the applicability of a recent proposition by Mityagin and Siegl on singular perturbations of harmonic oscillator type self-adjoint operators are fulfilled. In both the linear and nonlinear case we calculate numerically the shifts of the unperturbed levels with quantum numbers n of up to 89 in dependence on the strength of the non-Hermiticity and compare with rigorous estimates derived by those authors. We confirm that the predicted 1/n1/2 estimate provides a valid upper bound on the shrink rate of the numerical eigenvalues. Moreover, we find that a more recent estimate of log(n/n3/2 is in excellent agreement with the numerical results. With nonlinearity the shrink rates are found to be smaller than without nonlinearity, and the rigorous estimates, derived only for the linear case, are no longer applicable.
Xiao, Pingping; Wang, Xianping; Sun, Jingjing; Huang, Meizhen; Chen, Xianfeng; Cao, Zhuangqi
2012-06-18
A new scheme is proposed to measure the electro-optical (EO) and converse-piezoelectric (CPE) coefficients of the PMN-PT ceramics simultaneously, in which the PMN-PT ceramics acts as the guiding layer of a symmetrical metal-cladding waveguide. As the applied electric field exerts on the waveguide, the effective refractive index (RI) (or synchronous angle) can be effectively tuned from a selected mode to another adjacent mode owing to the high sensitivity and the small spacing of the ultra-high order modes. Subsequently, a correlation between EO and CPE coefficients is established. With this correlation and the measurement of the effective RI change to the applied voltage, the quadratic EO and CPE coefficients of PMN-PT ceramics are obtained simultaneously. The obtained results are further checked by fitting the variations of effective RI to a quadratic function. Our measurement method can be extended to a wide range of other materials.
Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
Peng, Bo; Lei, Fuchuan; Monifi, Faraz; Gianfreda, Mariagiovanna; Long, Gui Lu; Fan, Shanhui; Nori, Franco; Bender, Carl M; Yang, Lan
2013-01-01
Optical systems combining balanced loss and gain profiles provide a unique platform to implement classical analogues of quantum systems described by non-Hermitian parity-time- (PT-) symmetric Hamiltonians and to originate new synthetic materials with novel properties. To date, experimental works on PT-symmetric optical systems have been limited to waveguides in which resonances do not play a role. Here we report the first demonstration of PT-symmetry breaking in optical resonator systems by using two directly coupled on-chip optical whispering-gallery-mode (WGM) microtoroid silica resonators. Gain in one of the resonators is provided by optically pumping Erbium (Er3+) ions embedded in the silica matrix; the other resonator exhibits passive loss. The coupling strength between the resonators is adjusted by using nanopositioning stages to tune their distance. We have observed reciprocal behavior of the PT-symmetric system in the linear regime, as well as a transition to nonreciprocity in the PT symmetry-breaking...
Nonlinearity-induced PT-symmetry without material gain
Miri, Mohammad-Ali; Alù, Andrea
2016-06-01
Parity-time symmetry has raised a great deal of attention in optics in recent years, yet its application has been so far hindered by the stringent requirements on coherent gain balanced with loss. In this paper, we show that the conditions to enable parity and time symmetry can be simultaneously satisfied for a pair of modes with mixed frequencies interacting in a nonlinear medium, without requiring the presence of material gain. First, we consider a guided wave structure with second order nonlinearity and we derive the PT-symmetric Hamiltonian that governs the interaction of two waves of mixed frequencies when accompanied by a high intensity pump beam at the sum frequency. We also extend the results to an array of coupled nonlinear waveguide channels. It is shown that the evolution dynamics of the low-frequency waves is associated with a periodic PT-symmetric lattice while the phase of the pump beams can be utilized as a control parameter to modify the gain and loss distribution, thus realizing different PT lattices by design. Our results suggest that nonlinear wave mixing processes can form a rich platform to realize PT-symmetric Hamiltonians of arbitrary dimensions in optical systems, without requiring material gain.
PT Symmetry as a Generalization of Hermiticity
Wang, Qing-hai; Zhang, Jie-hong
2010-01-01
The Hilbert space in PT-symmetric quantum mechanics is formulated as a linear vector space with a dynamic weight function in the inner product. The most general PT-symmetric matrix Hamiltonians are constructed for 2*2 and 3*3 cases. In the former case, the PT-symmetric Hamiltonian represents the most general matrix Hamiltonian with a real spectrum. In both cases, the Hermitian matrix is shown to be a special case of PT-symmetric matrices. This finding confirms and strengthens the early belief that the PT-symmetric quantum mechanics is a generalization of the conventional Hermitian quantum mechanics.
Othman, Mohamed A K
2016-01-01
We present a transmission line theory of exceptional points of degeneracy (EPD) in coupled-mode guiding structures, i.e., a theory that illustrates the characteristics of coupled electromagnetic modes under a special dispersion degeneracy condition, yet unexplored in the contest of gain and loss. We demonstrate the concept of Parity-Time ($\\cal{PT}$)-symmetry in coupled uniform waveguides with balanced and symmetric gain and loss and how this condition is associated with a second order EPD. We show that by introducing gain into naturally lossy structures provides for the conditions whereby exceptional points of non-Hermitian degeneracies can be manifested, such as in $\\cal{PT}$- symmetric structures. Furthermore, we also demonstrate that $\\cal{PT}$- symmetry, despite being the method often suggested for obtaining non-Hermitian degeneracies at optical frequencies, is not a necessary condition and indeed we show that EPD can be obtained with broken topological symmetry in uniform TLs. Operating near such specia...
Chen, Yong; Yan, Zhenya; Mihalache, Dumitru; Malomed, Boris A
2017-04-28
Since the parity-time-([Formula: see text]-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with [Formula: see text]-symmetric potentials have been investigated. However, previous studies of [Formula: see text]-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized [Formula: see text]-symmetric Scarf-II potentials. The broken linear [Formula: see text] symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than [Formula: see text]-symmetric ones, but feature similar properties. Our results may suggest new experiments for [Formula: see text]-symmetric nonlinear waves in nonlinear nonuniform optical media.
MOSTAFAZADEH, Ali
2013-01-01
PHYSICAL REVIEW A 87, 012103 (2013) Invisibility and PT symmetry Ali Mostafazadeh* Department of Mathematics, Koc¸ University, Sarıyer 34450, Istanbul, Turkey (Received 9 July 2012; published 3 January 2013) For a general complex scattering potential defined on a real line, we show that the equations governing invisibility of the potential are invariant under the combined action of parity and time-reversal (PT ) transformation. We determine the PT -symmetric as well as no...
Optimal geometry of nonlinear silicon slot waveguides accounting for the effect of waveguide losses.
Ong, Jun Rong; Chen, Valerian H
2015-12-28
The optimal geometry of silicon-organic hybrid slot waveguides is investigated in the context of the efficiency of four-wave mixing (FWM), a χ(3) nonlinear optical process. We study the effect of slot and waveguide widths, as well as waveguide asymmetry on the two-photon absorption (TPA) figure of merit and the roughness scattering loss. The optimal waveguide core width is shown to be 220nm (symmetric) with a slot width of 120nm, at a fixed waveguide height of 220nm. We also show that state-of-the-art slot waveguides can outperform rib waveguides, especially at high powers, due to the high TPA figure-of-merit.
de Zutter, D.; Lagasse, P.; Buus, J.; Young, T. P.; Dillon, B. M.
1989-10-01
In order to compare various modeling techniques for the eigenmode analysis of integrated optical waveguides, twelve different methods are applied to the analysis of two typical III-V rib waveguides. Both a single and a coupled waveguide case are considered. Results focus on the effective refractive index value for the lowest order TE-mode in the case of the single waveguide, and on the coupling length between the lowest order symmetric and antisymmetric TE-modes of the coupled waveguides.
Bender, Carl M; DeKieviet, Maarten; Klevansky, S P
2013-04-28
PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics.
Znojil, M
2002-01-01
A re-formulated, non-Hermitian version of the Witten's supersymmetric quantum mechanics is presented. Its use of pseudo-Hermitian (so called PT symmetric) Hamiltonians is reviewed and illustrated via several forms of an innovated supersymmetric partnership between strongly singular ("spiked") harmonic oscillators.
Suppression of crosstalk in coupled plasmonic waveguides
Kuznetsov, E V; Zyablovsky, A A; Vinogradov, A P; Lisyansky, A A
2016-01-01
We demonstrate the suppression of crosstalk between two dielectric nanowaveguides by placing an auxiliary linear waveguide between loaded waveguides spaced by one wavelength. The total cross-sectional dimension of the system containing two transmission lines is less than two microns that is hundred times smaller than a cross-section of a system made of dielectric fiber. The propagating modes in these waveguides are the sum and the difference of symmetric and antisymmetric modes of the coupled system. Crosstalk is suppressed by matching the wavenumbers of these modes. The analytically obtained results are confirmed by numerical simulation.
Reciprocity and the scattering matrix of waveguide modes
Svendsen, Guro K; Skaar, Johannes
2013-01-01
The implications of the Lorentz reciprocity theorem for a scatterer connected to waveguides with arbitrary modes, including degenerate, evanescent, and complex modes, are discussed. In general it turns out that a matrix $CS$ is symmetric, where $C$ is the matrix of generalized orthogonality coefficients, and $S$ is the scattering matrix. Examples are given, including a scatterer surrounded by waveguides or free space, and discontinuities of waveguides.
Wave-guided optical waveguides
DEFF Research Database (Denmark)
Palima, Darwin; Bañas, Andrew Rafael; Vizsnyiczai, George
2012-01-01
This work primarily aims to fabricate and use two photon polymerization (2PP) microstructures capable of being optically manipulated into any arbitrary orientation. We have integrated optical waveguides into the structures and therefore have freestanding waveguides, which can be positioned anywhe...... bridge the diffraction barrier. This structure-mediated paradigm may be carried forward to open new possibilities for exploiting beams from far-field optics down to the subwavelength domain....
Magnetosonic Waveguide Model of Solar Wind Flow Tubes
Indian Academy of Sciences (India)
A. K. Srivastava; B. N. Dwivedi
2006-06-01
We consider solar wind flow tubes as a magnetosonic wave-guide. Assuming a symmetric expansion in edges of slab-modelled wave-guide, we study the propagation characteristics of magnetosonic wave in the solar wind flow tubes. We present the preliminary results and discuss their implications.
Baum, Brian; Dionne, Jennifer; Alaeian, Hadiseh; Jankovic, Vladan; Lawrence, Mark
2016-09-01
Metasurfaces offer exotic optical properties, which often originate from carefully designed material geometries. With locked geometries, these metasurfaces are difficult or impossible to change post-fabrication. Here, we theoretically explore a nano-scale coaxial structure capable of adjustably manipulating the polarization, phase, and spatial distribution of light through the introduction of parity-time (PT) symmetric perturbations. Coaxial waveguides possess degenerate modes, corresponding to different orbital angular momentum (OAM) states. The degeneracy of OAM modes can be lifted through the introduction of any non-zero amount of gain and loss into the structure in a way that matches the azimuthal periodicity of the degenerate mode pair. New hybrid complex conjugate modes are created which lose their pure OAM nature and are either amplifying or lossy. We confirm this behavior using both a Hamiltonian formulation and degenerate perturbation theory, and propose this selective excitation and absorption scheme as a new method of filtering for mode division multiplexing in on-chip nanophotonic systems. In addition to the creation of new hybrid modes, we show that these PT-symmetric perturbations in coaxial apertures are capable of converting incident circularly polarized light into linearly polarized light with unity efficiency. Further, due to the localization of field intensity within the gain sections, it is possible to rotate linear polarization and induce up to a pi-phase shift. We describe how our PT-symmetric coaxial aperture could function as a reconfigurable meta-atom for phase, amplitude, and polarization controlled meta-surfaces, and discuss routes toward unity-efficiency, reconfigurable holography.
Energy losses at junctions of single-mode slab waveguides with truncated parabolic profiles
Kalosha, V. P.; Khapaliuk, A. P.
1984-01-01
The Marcuse method is used to calculate radiative losses of the fundamental H-mode at the junction of two symmetric slab optical waveguides with truncated parabolic profiles of the refreactive index. Exact expressions for the fields of the principal directrix and radiative H-modes of the waveguides are used. An analysis is made of the dependence of the loss coefficient on differences in values of thicknesses, refractive indices in the centers of the waveguide layers, and inhomogeneity parameters of the waveguides.
Vasiljević, Gorazd
2014-01-01
This BSc thesis deals with certain topics from graph theory. When we talk about studying graphs, we usually mean studying their structure and their structural properties. By doing that, we are often interested in automorphisms of a graph (symmetries), which are permutations of its vertex set, preserving adjacency. There exist graphs, which are symmetric enough, so that automorhism group acts transitively on their vertex set. This means that for any pair of vertices of the graph, there is an a...
Ultrafast laser fabrication of Bragg waveguides in chalcogenide glass.
McMillen, Ben; Li, Mingshan; Huang, Sheng; Zhang, Botao; Chen, Kevin P
2014-06-15
Bragg waveguides are fundamental components in photonic integrated circuits and are particularly interesting for mid-IR applications in high index, highly nonlinear materials. In this work, we present Bragg waveguides fabricated in bulk chalcogenide glass using an ultrafast laser. Waveguides with near circularly symmetric cross sections and low propagation loss are obtained through spatial and temporal beam shaping. Using a single-pass technique, the waveguide and Bragg structure are formed at the same time. First through sixth order gratings with strengths of up to 25 dB are realized, and performance is evaluated based on the modulation duty cycle of the writing beam.
Topologically protected bound states in photonic parity-time-symmetric crystals.
Weimann, S; Kremer, M; Plotnik, Y; Lumer, Y; Nolte, S; Makris, K G; Segev, M; Rechtsman, M C; Szameit, A
2017-04-01
Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.
Accessing the exceptional points of parity-time symmetric acoustics
Shi, Chengzhi; Dubois, Marc; Chen, Yun; Cheng, Lei; Ramezani, Hamidreza; Wang, Yuan; Zhang, Xiang
2016-03-01
Parity-time (PT) symmetric systems experience phase transition between PT exact and broken phases at exceptional point. These PT phase transitions contribute significantly to the design of single mode lasers, coherent perfect absorbers, isolators, and diodes. However, such exceptional points are extremely difficult to access in practice because of the dispersive behaviour of most loss and gain materials required in PT symmetric systems. Here we introduce a method to systematically tame these exceptional points and control PT phases. Our experimental demonstration hinges on an active acoustic element that realizes a complex-valued potential and simultaneously controls the multiple interference in the structure. The manipulation of exceptional points offers new routes to broaden applications for PT symmetric physics in acoustics, optics, microwaves and electronics, which are essential for sensing, communication and imaging.
PT-Symmetry Quantum Electrodynamics--PTQED
Milton, Kimball A; Parashar, Prachi; Shajesh, K V; Wagner, Jef
2007-01-01
The construction of $\\mathcal{PT}$-symmetric quantum electrodynamics is reviewed. In particular, the massless version of the theory in 1+1 dimensions (the Schwinger model) is solved. Difficulties with unitarity of the $S$-matrix are discussed.
Simulations of the spontaneous emission of a quantum dot near a gap plasmon waveguide
Energy Technology Data Exchange (ETDEWEB)
Perera, Chamanei S., E-mail: cp.hettiarachchige@qut.edu.au; Vernon, Kristy C.; Mcleod, Angus [Plasmonic Device Group, Queensland University of Technology, GPO box 2434, Brisbane, Queensland (Australia)
2014-02-07
In this paper, we modeled a quantum dot at near proximity to a gap plasmon waveguide to study the quantum dot-plasmon interactions. Assuming that the waveguide is single mode, this paper is concerned about the dependence of spontaneous emission rate of the quantum dot on waveguide dimensions such as width and height. We compare coupling efficiency of a gap waveguide with symmetric configuration and asymmetric configuration illustrating that symmetric waveguide has a better coupling efficiency to the quantum dot. We also demonstrate that optimally placed quantum dot near a symmetric waveguide with 50 nm × 50 nm cross section can capture 80% of the spontaneous emission into a guided plasmon mode.
Long-range hybrid wedge plasmonic waveguide.
Zhang, Zhonglai; Wang, Jian
2014-11-03
We design a novel long-range hybrid wedge plasmonic (LRHWP) waveguide composed of two identical dielectric nanowires symmetrically placed on two opposed wedges of a diamond shaped metal wire. With strong coupling between the dielectric nanowire mode and long-range surface plasmon polariton (SPP) mode, both deep subwavelength mode confinement and low propagation loss are achieved. On one hand, when compared to the previous long-range hybrid SPP waveguide, LRHWP waveguide can achieve smaller mode size with similar propagation length; on the other hand, when compared to the previous hybrid wedge SPP waveguide, LRHWP waveguide can provide an order of magnitude longer propagation length with similar level of mode confinement. The designed LRHWP waveguide also features an overall advantage of one-order improvement of Figure of Merit. We further evaluate in detail the impacts of possible practical fabrication imperfections on the mode properties. The obtained results of mode properties show that the proposed LRHWP waveguide with an optimized wedge tip angle of 140 degree is fairly tolerant to practical fabrication errors in geometry parameters such as misalignment in the horizontal direction, asymmetry in the vertical direction, variation of wedge tip angle, tilt or rotation of metal wire, and variation of wedge tip curvature radius.
Nonlinear optical localization in embedded chalcogenide waveguide arrays
Directory of Open Access Journals (Sweden)
Mingshan Li
2014-05-01
Full Text Available We report the nonlinear optical localization in an embedded waveguide array fabricated in chalcogenide glass. The array, which consists of seven waveguides with circularly symmetric cross sections, is realized by ultrafast laser writing. Light propagation in the chalcogenide waveguide array is studied with near infrared laser pulses centered at 1040 nm. The peak intensity required for nonlinear localization for the 1-cm long waveguide array was 35.1 GW/cm2, using 10-nJ pulses with 300-fs pulse width, which is 70 times lower than that reported in fused silica waveguide arrays and with over 7 times shorter interaction distance. Results reported in this paper demonstrated that ultrafast laser writing is a viable tool to produce 3D all-optical switching waveguide circuits in chalcogenide glass.
Institute of Scientific and Technical Information of China (English)
冉茂武; 曹庄琪; 陈险峰; 陈凡
2011-01-01
根据对称金属包覆电光波导中本征损耗与古斯-亨兴(Goos- H(a)nchen)位移的理论公式,导出了古斯-亨兴位移与作用于波导两侧电压的二次关系公式.用622 μm厚度的四方相铌镁酸铅-钛酸铅(PMN-PT)透明电光陶瓷片作为导波层制备了对称金属包覆波导,测量了古斯-亨兴位移与作用于波导两侧电压的关系曲线,计算了所用透明电光陶瓷片的二次电光系数.实验结果与理论分析一致.%The Goos-Hanchen shift at both sides of the waveguide is conducted, which gives rise to a quadric-curve relation between Goos-Hanchen shift and the applied voltage, based on the theoretical analysis of the intrinsic loss in a symmetrical metal-cladding electro-optic waveguide. A symmetrical metal-cladding waveguide is fabricated with a 622 pan-thick Pb(Mg1/3 Nb2/3 O3 )-PbTiO3 (PMN-PT) transparent ceramic which serves as the guiding layer of the waveguide. Measurements of the relation between Goos-Hanchen shift and the applied voltage are carried out and the quadratic electro-optic coefficient of the PMN-PT ceramic is obtained. Experimental results are agreed well with the numerical simulations.
Chen, Yong; Yan, Zhenya
2017-01-01
The effect of derivative nonlinearity and parity-time-symmetric (PT -symmetric) potentials on the wave propagation dynamics is explored in the derivative nonlinear Schrödinger equation, where the physically interesting Scarf-II and harmonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken and broken linear PT -symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT -symmetric phases are broken. The semielastic interactions between particular bright solitons and exotic incident waves are illustrated such that we find that particular nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT -symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT -symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT -symmetric phase.
Polymers in Waveguide Packaging
Institute of Scientific and Technical Information of China (English)
Zhiyi Zhang; G. Z.Xiao; Jiaren Liu; C. P. Grover
2003-01-01
Polymers were successfully used in the packaging of waveguide-based photonic components in the area of fiber-to-waveguide coupling, waveguide die attachment, strain relief, and waveguide encapsulation. The application results of these polymers were described in this paper.
Directory of Open Access Journals (Sweden)
Ayryan E.A.
2016-01-01
Full Text Available A local variation in the thickness of the waveguide layer of integrated optics waveguide causes a local decrease of phase velocity, and hence bending of rays and of the wave front. The relationship of the waveguide layer thickness profile h (y, z with the distribution of the effective refractive index of the waveguide β (y, z is described in terms of a particular model of waveguide solutions of the Maxwell equations. In the model of comparison waveguides the support of the thickness irregularity of the waveguide layer Δh coincides with the support of inhomogeneity of the effective refractive index Δβ. A more adequate but more cumbersome model of the adiabatic waveguide modes allows them to mismatch supp Δh ⊃ supp Δβ. In this paper, we solve the problem of the Δh reconstruction on the base of given Δβ of the thin film generalized waveguide Luneburg lens in a model of adiabatic waveguide modes. The solution is found in the form of a linear combination of Gaussian exponential functions and in the form of a cubic spline for the cylindrically symmetric Δh (r and in the form of a cubic spline for Δβ (r.
Low-loss single-mode integrated waveguides in soda-lime glass
Dyakonov, I. V.; Kalinkin, A. A.; Saygin, M. Yu.; Abroskin, A. G.; Radchenko, I. V.; Straupe, S. S.; Kulik, S. P.
2016-09-01
Low-loss single-mode optical waveguide fabrication process in extra-white soda-lime glass is demonstrated. Waveguiding structures are formed in bulk substrates employing femtosecond laser writing technology. The combination of a slit beam shaping method and a multiscan fabrication process enables writing of waveguides with a well-defined symmetric cross-sectional profile. Fabricated waveguides exhibit 0.86 dB/cm propagation loss for 800-nm wavelength. Bending loss in the waveguides is addressed experimentally and compared with a model for radiation loss.
Low-loss single-mode integrated waveguides in soda-lime glass
Kalinkin, Alexander; Abroskin, Andrey; Radchenko, Igor; Straupe, Stanislav; Kulik, Sergei
2016-01-01
Low-loss single-mode optical waveguide fabrication process in extra-white soda-lime glass is demonstrated. Waveguiding structures are formed in bulk substrates employing femtosecond laser writing technology. The combination of a slit beam-shaping method and a multiscan fabrication process enables printing of waveguides with a well-defined symmetric cross-section profile. Fabricated waveguides exhibit 0.86 dB/cm propagation loss for 800~nm wavelength. Bending loss in the waveguides are addressed experimentally and compared with a model for radiation loss.
Kim, Sang-Il; Seo, Min-Su; Choi, Yeon Suk; Park, Seung-Young
2017-01-01
Magnetic field (H) sweeping direction dependences of the mixed voltage Vmix induced by the inverse-spin Hall effect(ISHE) and spin-rectified effect (SRE) in a CoFeB (5 nm)/Pt (10 nm) bilayer structure are investigated using the ferromagnetic resonance in the TE mode cavities and coplanar waveguide methods. Conventionally, the magnitude of ISHE voltage VISH (symmetric) excluding the SRE (antisymmetric component) was unavoidably separated from the fitting curve of Vmix (a sum of a symmetric and an antisymmetric part) for one direction of H-source. By studying the ratio of the two voltage parts with the bi-directional H sweeping, the optimized VISH (no SRE condition) value which also include a well-defined spin Hall angle can be obtained via the linear response relation of ISHE and SRE components.
Exner, Pavel
2015-01-01
This monograph explains the theory of quantum waveguides, that is, dynamics of quantum particles confined to regions in the form of tubes, layers, networks, etc. The focus is on relations between the confinement geometry on the one hand and the spectral and scattering properties of the corresponding quantum Hamiltonians on the other. Perturbations of such operators, in particular, by external fields are also considered. The volume provides a unique summary of twenty five years of research activity in this area and indicates ways in which the theory can develop further. The book is fairly self-contained. While it requires some broader mathematical physics background, all the basic concepts are properly explained and proofs of most theorems are given in detail, so there is no need for additional sources. Without a parallel in the literature, the monograph by Exner and Kovarik guides the reader through this new and exciting field.
Compact waveguide circular polarizer
Tantawi, Sami G.
2016-08-16
A multi-port waveguide is provided having a rectangular waveguide that includes a Y-shape structure with first top arm having a first rectangular waveguide port, a second top arm with second rectangular waveguide port, and a base arm with a third rectangular waveguide port for supporting a TE.sub.10 mode and a TE.sub.20 mode, where the end of the third rectangular waveguide port includes rounded edges that are parallel to a z-axis of the waveguide, a circular waveguide having a circular waveguide port for supporting a left hand and a right hand circular polarization TE.sub.11 mode and is coupled to a base arm broad wall, and a matching feature disposed on the base arm broad wall opposite of the circular waveguide for terminating the third rectangular waveguide port, where the first rectangular waveguide port, the second rectangular waveguide port and the circular waveguide port are capable of supporting 4-modes of operation.
Fabrication of plasmonic waveguides for device applications
DEFF Research Database (Denmark)
Boltasseva, Alexandra; Leosson, Kristjan; Rosenzveig, Tiberiu
2007-01-01
We report on experimental realization of different metal-insulator geometries that are used as plasmonic waveguides guiding electromagnetic radiation along metal-dielectric interfaces via excitation of surface plasmon polaritons (SPPs). Three configurations are considered: metal strips, symmetric...... based on metal V-grooves that offer subwavelength confinement are also considered. We focus on recent advances in manufacturing of nanostructured metal strips and metal V-grooves using combined UV, electron-beam and nanoimprint lithography....
Chen, B. C. J.; Hartop, R. W.
1981-04-01
An improved system is described for cooling high power waveguides by the use of cooling ducts extending along the waveguide, which minimizes hot spots at the flanges where waveguide sections are connected together. The cooling duct extends along substantially the full length of the waveguide section, and each flange at the end of the section has a through hole with an inner end connected to the duct and an opposite end that can be aligned with a flange hole in another waveguide section. Earth flange is formed with a drainage groove in its face, between the through hole and the waveguide conduit to prevent leakage of cooling fluid into the waveguide. The ducts have narrowed sections immediately adjacent to the flanges to provide room for the installation of fasteners closely around the waveguide channel.
Microfabricated Waveguide Atom Traps.
Energy Technology Data Exchange (ETDEWEB)
Jau, Yuan-Yu
2017-09-01
A nano - scale , microfabricated waveguide structure can in - principle be used to trap atoms in well - defined locations and enable strong photon - atom interactions . A neutral - atom platf orm based on this microfabrication technology will be pre - aligned , which is especially important for quantum - control applications. At present, there is still no reported demonstration of evanescent - field atom trapping using a microfabricated waveguide structure. We described the capabilities established by our team for future development of the waveguide atom - trapping technology at SNL and report our studies to overcome the technical challenges of loading cold atoms into the waveguide atom traps, efficient and broadband optical coupling to a waveguide, and the waveguide material for high - power optical transmission. From the atomic - physics and the waveguide modeling, w e have shown that a square nano - waveguide can be utilized t o achieve better atomic spin squeezing than using a nanofiber for first time.
Taming the Exceptional Points of Parity-Time Symmetric Acoustics
Dubois, Marc; Shi, Chengzhi; Chen, Yun; Cheng, Lei; Ramezani, Hamidreza; Wang, Yuan; Zhang, Xiang
Parity-time (PT) symmetric concept and development lead to a wide range of applications including coherent perfect absorbers, single mode lasers, unidirectional cloaking and sensing, and optical isolators. These new applications and devices emerge from the existence of a phase transition in PT symmetric complex-valued potential obtained by balancing gain and loss materials. However, the systematic extension of such devices is adjourned by the key challenge in the management of the complex scattering process within the structure in order to engineer PT phase and exceptional points. Here, based on active acoustic elements, we experimentally demonstrate the simultaneous control of complex-valued potentials and multiple interference inside the structure at any given frequency. This method broadens the scope of applications for PT symmetric devices in many fields including optics, microwaves, electronics, which are crucial for sensing, imaging, cloaking, lasing, absorbing, etc.
Cavity-photon-switched coherent transient transport in a double quantum waveguide
Energy Technology Data Exchange (ETDEWEB)
Abdullah, Nzar Rauf, E-mail: nra1@hi.is; Gudmundsson, Vidar, E-mail: vidar@raunvis.hi.is [Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik (Iceland); Tang, Chi-Shung [Department of Mechanical Engineering, National United University, 1, Lienda, 36003 Miaoli, Taiwan (China); Manolescu, Andrei [School of Science and Engineering, Reykjavik University, Menntavegur 1, IS-101 Reykjavik (Iceland)
2014-12-21
We study a cavity-photon-switched coherent electron transport in a symmetric double quantum waveguide. The waveguide system is weakly connected to two electron reservoirs, but strongly coupled to a single quantized photon cavity mode. A coupling window is placed between the waveguides to allow electron interference or inter-waveguide transport. The transient electron transport in the system is investigated using a quantum master equation. We present a cavity-photon tunable semiconductor quantum waveguide implementation of an inverter quantum gate, in which the output of the waveguide system may be selected via the selection of an appropriate photon number or “photon frequency” of the cavity. In addition, the importance of the photon polarization in the cavity, that is, either parallel or perpendicular to the direction of electron propagation in the waveguide system is demonstrated.
Institute of Scientific and Technical Information of China (English)
罗雪雪; 陈家璧; 胡金兵; 梁斌明; 蒋强
2015-01-01
Symmetrical metal-cladding waveguide (SMCW) is a kind of new waveguide construction, and it consists of a planar glass slab sandwiched in two metal films with different thicknesses. The metal in this structure is usually a noble metal, such as Au, Ag and Cu etc. One of the characteristics of the glass is the sub-millimeter thickness, which is useful for exciting the ultrahigh order mode. Since the SMCW structure was proposed, it has received much attention from the researchers for its excellent characteristics of free-space coupling technique and ultrahigh order mode excitation. This free-space coupling technology has a higher sensitivity compared with the end-face coupling, prism coupling and grating coupling techniques. The ultrahigh order mode is very sensitive to the incident light wavelength, the thickness of guiding layer and the refractive index, but not sensitive to polarization. Based on the thermal-optical effect and thermal expansion effect of metal film and guiding layer materials, we research the temperature property of the SMCW structure. Researching methods include simulation analysis and experimental demonstration. First, we calculate the relation of the thickness and dielectric property of metal films, and the thickness and refractive index of the guiding layer with the temperature. Results show that these four factors are nearly proportional to the temperature difference. Then, we simulate the relationship of the reflectivity of the SMCW structure with those four factors by means of single-factor investigation under spectral and angular interrogation mode of operation, and find that the temperature-dependence of thickness of the guiding layer makes the chief contribution to the waveguide function of SMCW. Meanwhile, we analyze the sensitivity of the sensors based on SMCW structure, and the result shows that the sensitivity of this kind of sensor can be up to 21.89 pm/K (spectral mode) and 1.449 × 10−3 rad/K (angular mode). Finally, we
Symmetric Powers of Symmetric Bilinear Forms
Institute of Scientific and Technical Information of China (English)
Se(a)n McGarraghy
2005-01-01
We study symmetric powers of classes of symmetric bilinear forms in the Witt-Grothendieck ring of a field of characteristic not equal to 2, and derive their basic properties and compute their classical invariants. We relate these to earlier results on exterior powers of such forms.
PT symmetry breaking in the presence of random, periodic, long-range hopping
Harter, Andrew K.; Onanga, Franck Assogba; Joglekar, Yogesh N.
2016-09-01
Over the past five years, open systems with balanced gain and loss have been investigated for extraordinary properties that are not shared by their closed counterparts. Non-Hermitian, Parity-Time (PT ) symmetric Hamiltonians faithfully model such systems. Such a Hamiltonian typically consists of a reflection-symmetric, Hermitian, nearest-neighbor hopping profile and a PT-symmetric, non-Hermitian, gain and loss potential, and has a robust PT -symmetric phase. Here we investigate the robustness of this phase in the presence of long-range hopping disorder that is not PT-symmetric, but is periodic. We find that the PT-symmetric phase remains robust in the presence of such disorder, and characterize the configurations where that happens. Our results are found using a tight-binding model, and we validate our predictions through the beam-propagation method.
Surface plasmon enhancement of spontaneous emission in graphene waveguides
Cuevas, Mauro
2016-01-01
This work analyzes the spontaneous emission of a single emitter placed near the graphene waveguide formed by two parallel graphene monolayers, with an insulator spacer layer. In this case, the eigenmodes supported by the structure, such as surface plasmon and wave guided modes, provide decay channels for the electric dipole placed close to the waveguide. We calculated the contribution to the decay rate of symmetric and antisymmetric eigenmodes as a function of frequency and the orientation of the emitter. Our results show that the modi?cation of the spontaneous emission due to excitation of guided modes is much lower than the corresponding decays through the excitation of symmetric and antisymmetric surface plasmons, for which, the spontaneous emission is dramatically enhanced. As a consequence of the high con?nement of surface plasmons in the graphene waveguide, we found that the decay rate of the emitter with vertical orientation (with respect to graphene sheets) is twice the corresponding decay of the same...
Tsai, Wan-Shao; Liu, Yen-Huang; Barkman, Ondrej; Prajzler, Vaclav; Stanek, Stanislav; Nekvindova, Pavla
2015-01-01
Two-step field-assisted ion-exchanged waveguides have been fabricated on a glass substrate. The concentration profiles of the exchanged ions were measured with electron microprobe. The waveguides were characterized under scanning electron microscope and optical microscope for the investigation of burying structures. Guiding mode patterns were characterized with near-field measurement, where symmetric profiles were observed for the burying-type waveguide. The refractive index profiles were also measured with a modified end-fire coupling method. The relation between ion concentration profiles and index profiles were compared for the waveguides with different fabrication process.
Jiang, Haiyong
2016-04-11
We present an automatic algorithm for symmetrizing facade layouts. Our method symmetrizes a given facade layout while minimally modifying the original layout. Based on the principles of symmetry in urban design, we formulate the problem of facade layout symmetrization as an optimization problem. Our system further enhances the regularity of the final layout by redistributing and aligning boxes in the layout. We demonstrate that the proposed solution can generate symmetric facade layouts efficiently. © 2015 IEEE.
Symmetrization of Facade Layouts
Jiang, Haiyong
2016-02-26
We present an automatic approach for symmetrizing urban facade layouts. Our method can generate a symmetric layout through minimally modifying the original input layout. Based on the principles of symmetry in urban design, we formulate facade layout symmetrization as an optimization problem. Our method further enhances the regularity of the final layout by redistributing and aligning elements in the layout. We demonstrate that the proposed solution can effectively generate symmetric facade layouts.
Chambler, A F; Chapman-Sheath, P J; Pearse, M F; Hollingdale, J
1997-10-01
Chronic recurrent multifocal osteomyelitis is often confused with symmetrical Brodie's abscess as it has a similar pathogenesis. We report an otherwise healthy 17-year-old boy presenting with a true symmetrical Brodie's abscess. We conclude that a symmetrical Brodie's abscess presenting in an otherwise healthy patient is a separate clinical condition with a different management protocol.
Multimode waveguide based directional coupler
Ahmed, Rajib; Rifat, Ahmmed A.; Sabouri, Aydin; Al-Qattan, Bader; Essa, Khamis; Butt, Haider
2016-07-01
The Silicon-on-Insulator (SOI) based platform overcomes limitations of the previous copper and fiber based technologies. Due to its high index difference, SOI waveguide (WG) and directional couplers (DC) are widely used for high speed optical networks and hybrid Electro-Optical inter-connections; TE00-TE01, TE00-TE00 and TM00-TM00 SOI direction couplers are designed with symmetrical and asymmetrical configurations to couple with TE00, TE01 and TM00 in a multi-mode semi-triangular ring-resonator configuration which will be applicable for multi-analyte sensing. Couplers are designed with effective index method and their structural parameters are optimized with consideration to coupler length, wavelength and polarization dependence. Lastly, performance of the couplers are analyzed in terms of cross-talk, mode overlap factor, coupling length and coupling efficiency.
Launching transverse-electric Localized Waves from a circular waveguide
Salem, Mohamed
2011-07-01
Axially symmetric transverse electric (TE) modes of a circular waveguide section are used to synthesize the vector TE Localized Wave (LW) field at the open end of the waveguide section. The necessary excitation coefficients of these modes are obtained by the method of matching, taking advantage of the modal power orthogonality relations. The necessary excitation of modes provided by a number of coaxial loop antennas inserted inside the waveguide section. The antennas currents are computed from the solution of the waveguide excitation inverse problem. The accuracy of the synthesized wave field (compared to the mathematical model) and the power efficiency of the generation technique are evaluated in order to practically realize a launcher for LWs in the microwave regime. © 2011 IEEE.
Graphene antidot lattice waveguides
DEFF Research Database (Denmark)
Pedersen, Jesper Goor; Gunst, Tue; Markussen, Troels
2012-01-01
We introduce graphene antidot lattice waveguides: nanostructured graphene where a region of pristine graphene is sandwiched between regions of graphene antidot lattices. The band gaps in the surrounding antidot lattices enable localized states to emerge in the central waveguide region. We model...... the waveguides via a position-dependent mass term in the Dirac approximation of graphene and arrive at analytical results for the dispersion relation and spinor eigenstates of the localized waveguide modes. To include atomistic details we also use a tight-binding model, which is in excellent agreement...... with the analytical results. The waveguides resemble graphene nanoribbons, but without the particular properties of ribbons that emerge due to the details of the edge. We show that electrons can be guided through kinks without additional resistance and that transport through the waveguides is robust against...
Waveguide arrangements based on adiabatic elimination
Energy Technology Data Exchange (ETDEWEB)
Suchowski, Haim; Mrejen, Michael; Wu, Chihhui; Zhang, Xiang
2016-09-13
This disclosure provides systems, methods, and apparatus related to nanophotonics. In one aspect, an arrangement of waveguides includes a substrate and three waveguides. Each of the three waveguides may be a linear waveguide. A second waveguide is positioned between a first waveguide and a third waveguide. The dimensions and positions of the first, the second, and the third waveguides are specified to substantially eliminate coupling between the first waveguide and the third waveguide over a distance of about 1 millimeter to 2 millimeters along lengths of the first waveguide, the second waveguide, and the third waveguide.
Canteaut, Anne; Videau, Marion
2005-01-01
http://www.ieee.org/; We present an extensive study of symmetric Boolean functions, especially of their cryptographic properties. Our main result establishes the link between the periodicity of the simplified value vector of a symmetric Boolean function and its degree. Besides the reduction of the amount of memory required for representing a symmetric function, this property has some consequences from a cryptographic point of view. For instance, it leads to a new general bound on the order of...
DÍaz, R.; Rivas, M.
2010-01-01
In order to study Boolean algebras in the category of vector spaces we introduce a prop whose algebras in set are Boolean algebras. A probabilistic logical interpretation for linear Boolean algebras is provided. An advantage of defining Boolean algebras in the linear category is that we are able to study its symmetric powers. We give explicit formulae for products in symmetric and cyclic Boolean algebras of various dimensions and formulate symmetric forms of the inclusion-exclusion principle.
Pollnau, Markus; Orlovic, V.A.; Pachenko, V.; Scherbakov, I.A.
2007-01-01
Our recent results on planar and channel waveguide fabrication and lasers in the dielectric oxide materials Ti:sapphire and rare-earth-ion-doped potassium yttrium double tungstate (KYW) are reviewed. We have employed waveguide fabrication methods such as liquid phase epitaxy and reactive ion etching
A double-strip plasmonic waveguide coupled to an electrically driven nanowire LED.
No, You-Shin; Choi, Jae-Hyuck; Ee, Ho-Seok; Hwang, Min-Soo; Jeong, Kwang-Yong; Lee, Eun-Khwang; Seo, Min-Kyo; Kwon, Soon-Hong; Park, Hong-Gyu
2013-02-13
We demonstrate the efficient integration of an electrically driven nanowire (NW) light source with a double-strip plasmonic waveguide. A top-down-fabricated GaAs NW light-emitting diode (LED) is placed between two straight gold strip waveguides with the gap distance decreasing to 30 nm at the end of the waveguide and operated by current injection through the p-contact electrode acting as a plasmonic waveguide. Measurements of polarization-resolved images and spectra show that the light emission from the NW LED was coupled to a plasmonic waveguide mode, propagated through the waveguide, and was focused onto a subwavelength-sized spot of surface plasmon polaritons at the tapered end of the waveguide. Numerical simulation agreed well with these experimental results, confirming that a symmetric plasmonic waveguide mode was excited on the top surface of the waveguide. Our demonstration of a plasmonic waveguide coupled to an electrically driven NW LED represents important progress toward further miniaturization and practical implementation of ultracompact photonic integrated circuits.
Exact equivalent straight waveguide model for bent and twisted waveguides
DEFF Research Database (Denmark)
Shyroki, Dzmitry
2008-01-01
Exact equivalent straight waveguide representation is given for a waveguide of arbitrary curvature and torsion. No assumptions regarding refractive index contrast, isotropy of materials, or particular morphology in the waveguide cross section are made. This enables rigorous full-vector modeling o...... of in-plane curved or helically wound waveguides with use of available simulators for straight waveguides without the restrictions of the known approximate equivalent-index formulas....
Strip Waveguide Directional Coupling Modulator with Equivalent Refractive Index
Institute of Scientific and Technical Information of China (English)
LI Hong-tao; HE Dui-yan
2004-01-01
The equivalent refractive index(ERI) method is employed to analyze the function of the strip waveguide directional coupling modulator(SWM). Through deducing the diagnostic equation of the Exmn mode of the four-layer media film waveguide equivalent to the SWM,the transmission constant of the symmetrical mode of the positive phase and negative one and the coupling length of powerful transference are obtained. The veracity of ERI is validated with the example of Ex11 basal mode under the condition of comparing the three results of ERI,EIM and Marcatili.
Phase radiation characteristics of an open-ended circular waveguide
DEFF Research Database (Denmark)
Shishkova, Anna; Pivnenko, Sergey; Kim, Oleksiy S.
2007-01-01
General analytical expressions are derived for the far-field amplitude and phase radiation patterns of an open-ended circular waveguide (OE-CWG) regardless of its radius or the operation frequency for the dominant and symmetric higher-order excitation modes. The derivation is based on the rigorous...... solution to the problem of diffraction at an open end of a waveguide proposed by Weinstein. The near-field amplitude and phase patterns of an OE-CWG are then calculated using the spherical wave expansion technique. The measurement of the radiation pattern of an OE-CWG was carried out to verify the validity...
PT Symmetry in Classical and Quantum Statistical Mechanics
Meisinger, Peter N
2012-01-01
PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside of the conventional equilibrium statistical mechanics of Hermitian systems. PT-symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviors than Hermitian systems, displaying sinusoidally-modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with PT symmetry include Z(N) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbor Ising (ANNNI) model. Quantum many-body problems with a non-zero chemical potential have a natural PT-symmetric representation related to the sign problem. Two-dimensional QCD with heavy quarks at non-zero chemical potential can be solved by diagona...
Pseudo-Hermitian Hamiltonians Generating Waveguide Mode Evolution
Chen, Penghua
2016-01-01
We study the properties of Hamiltonians defined as the generators of transfer matrices in quasi- one-dimensional waveguides. For single- or multi-mode waveguides obeying flux conservation and time-reversal invariance, the Hamiltonians defined in this way are non-Hermitian, but satisfy sym- metry properties that have previously been identified in the literature as "pseudo Hermiticity" and "spectral anti-PT symmetry". We show how simple one-channel and two-channel models exhibit symmetry-breaking transitions between real, imaginary, and complex eigenvalue pairs.
Inverse Symmetric Inflationary Attractors
Odintsov, S D
2016-01-01
We present a class of inflationary potentials which are invariant under a special symmetry, which depends on the parameters of the models. As we show, in certain limiting cases, the inverse symmetric potentials are qualitatively similar to the $\\alpha$-attractors models, since the resulting observational indices are identical. However, there are some quantitative differences which we discuss in some detail. As we show, some inverse symmetric models always yield results compatible with observations, but this strongly depends on the asymptotic form of the potential at large $e$-folding numbers. In fact when the limiting functional form is identical to the one corresponding to the $\\alpha$-attractors models, the compatibility with the observations is guaranteed. Also we find the relation of the inverse symmetric models with the Starobinsky model and we highlight the differences. In addition, an alternative inverse symmetric model is studied and as we show, not all the inverse symmetric models are viable. Moreove...
Symmetric cryptographic protocols
Ramkumar, Mahalingam
2014-01-01
This book focuses on protocols and constructions that make good use of symmetric pseudo random functions (PRF) like block ciphers and hash functions - the building blocks for symmetric cryptography. Readers will benefit from detailed discussion of several strategies for utilizing symmetric PRFs. Coverage includes various key distribution strategies for unicast, broadcast and multicast security, and strategies for constructing efficient digests of dynamic databases using binary hash trees. • Provides detailed coverage of symmetric key protocols • Describes various applications of symmetric building blocks • Includes strategies for constructing compact and efficient digests of dynamic databases
PT phase transition in multidimensional quantum systems
Bender, Carl M
2012-01-01
Non-Hermitian PT-symmetric quantum-mechanical Hamiltonians generally exhibit a phase transition that separates two parametric regions, (i) a region of unbroken PT symmetry in which the eigenvalues are all real, and (ii) a region of broken PT symmetry in which some of the eigenvalues are complex. This transition has recently been observed experimentally in a variety of physical systems. Until now, theoretical studies of the PT phase transition have generally been limited to one-dimensional models. Here, four nontrivial coupled PT-symmetric Hamiltonians, $H=p^2/2+x^2/2+q^2/2+y^2/2+igx^2y$, $H=p^2/2+x^2/2+q^2/2+y^2+igx^2y$, $H=p^2/2+x^2/2+q^2/2+y^2/2+r^2/2+z^2/2+igxyz$, and $H=p^2/2+x^2/2+q^2/2+y^2+r^2/2+3z^2/2+igxyz$ are examined. Based on extensive numerical studies, this paper conjectures that all four models exhibit a phase transition. The transitions are found to occur at $g\\approx 0.1$, $g\\approx 0.04$, $g\\approx 0.1$, and $g\\approx 0.05$. These results suggest that the PT phase transition is a robust phen...
A waveguide orthomode transducer for 385-500 GHz
Groppi, Christopher; Navarrini, Alessandro; Chattopadhyay, Goutam
2010-07-01
We describe the design, construction, and performance of a waveguide Orthomode Transducer (OMT) for the 385-500 GHz band. The OMT is based on a symmetric backward coupling structure with a square waveguide input (0.56x0.56 mm2) and two single-mode waveguide outputs: a standard WR2.2 waveguide (0.56x0.28 mm2) and an oval waveguide with full-radius corners. The OMT is rescaled from a lower frequency design that was developed for the 3 mm band; it was optimized using a commercial 3D electromagnetic simulator. The OMT consists of two mechanical blocks in split-block configuration, fabricated using a CNC micromilling machine. A first prototype copper alloy OMT employing standard UG387 flanges at all ports was fabricated and tested. From 385 to 500 GHz the measured input reflection coefficient was less than -10 dB, the isolation between the outputs was less than -25 dB, the cross polarization was less than -10 dB, and the transmission was ~-2 dB at room temperature for both polarization channels. The effects of misalignment errors in the OMT performance were studied using electromagnetic simulation. A second OMT version utilizing custom made mini-flanges and much shorter waveguides was designed and will be tested soon. This novel OMT is more tolerant to misalignment errors of the block halves and is expected to have much improved performance over the first prototype.
Optical waveguide enhanced photovoltaics.
Rühle, Sven; Greenwald, Shlomit; Koren, Elad; Zaban, Arie
2008-12-22
Enhanced light to electric power conversion efficiency of photovoltaic cells with a low absorbance was achieved using waveguide integration. We present a proof of concept using a very thin dye-sensitized solar cell which absorbed only a small fraction of the light at normal incidence. The glass substrate in conjunction with the solar cells reflecting back contact formed a planar waveguide, which lead to more than four times higher conversion efficiency compared to conventional illumination at normal incidence. This illumination concept leads to a new type of multi-junction PV systems based on enforced spectral splitting along the waveguide.
Weber, Markus; Boehm, Florian; Fischer, Peter; Kraus, Marion; Tashima, Toshiyuki; Liebermeister, Lars; Altpeter, Philipp; Weinfurter, Harald
2016-01-01
We experimentally demonstrate the propagation of long-range surface plasmon-polaritons in a nobel metal stripe waveguide at an optical wavelength of 780 nm. To minimize propagation damping the lithographically structured waveguide is produced from a thin gold stripe embedded in a dielectric polymer. Our waveguide geometry supports a symmetric fundamental and anti-symmetric first order mode. For the fundamental mode we measure a propagation loss of $(6.12^{+0.66} _{-0.54})$ dB/mm, in good agreement with numerical simulations using a vectorial eigenmode solver. Our results are a promising starting point for coupling fluorescence of individual solid state quantum emitters to integrated plasmonic waveguide structures.
Giant Transverse Optical Forces in Nanoscale Slot Waveguides of Hyperbolic Metamaterials
He, Yingran; Gao, Jie; Yang, Xiaodong
2015-01-01
Here we demonstrate that giant transverse optical forces can be generated in nanoscale slot waveguides of hyperbolic metamaterials, with more than two orders of magnitude stronger compared to the force created in conventional silicon slot waveguides, due to the nanoscale optical field enhancement and the extreme optical energy compression within the air slot region. Both numerical simulation and analytical treatment are carried out to study the dependence of the optical forces on the waveguide geometries and the metamaterial permittivity tensors, including the attractive optical forces for the symmetric modes and the repulsive optical forces for the anti-symmetric modes. The significantly enhanced transverse optical forces result from the strong optical mode coupling strength between two metamaterial waveguides, which can be explained with an explicit relation derived from the coupled mode theory. Moreover, the calculation on realistic metal-dielectric multilayer structures indicates that the predicted giant ...
Engineering chiral light--matter interaction in photonic crystal waveguides with slow light
Mahmoodian, Sahand; Söllner, Immo; Stobbe, Søren; Lodahl, Peter
2016-01-01
We design photonic crystal waveguides with efficient chiral light--matter interfaces that can be integrated with solid-state quantum emitters. By using glide-plane-symmetric waveguides, we show that chiral light-matter interaction can exist even in the presence of slow light with slow-down factors of up to $100$ and therefore the light--matter interaction exhibits both strong Purcell enhancement and chirality. This allows for near-unity directional $\\beta$-factors for a range of emitter positions and frequencies. Additionally, we design an efficient mode adapter to couple light from a standard nanobeam waveguide to the glide-plane symmetric photonic crystal waveguide. Our work sets the stage for performing future experiments on a solid-state platform.
Ultrafast laser fabrication of low-loss waveguides in chalcogenide glass with 0.65 dB/cm loss.
McMillen, Ben; Zhang, Botao; Chen, Kevin P; Benayas, Antonio; Jaque, Daniel
2012-05-01
This Letter reports on the fabrication of low-loss waveguides in gallium-lanthanum-sulfide chalcogenide glasses using an ultrafast laser. Spatial beam shaping and temporal pulse width tuning were used to optimize the guided mode profiles and optical loss of laser-written waveguides. Highly symmetric single-mode waveguides guiding at 1560 nm with a loss of 0.65 dB/cm were fabricated using 1.5 ps laser pulses. This Letter suggests a pathway to produce high quality optical waveguides in substrates with strong nonlinearity using the ultrafast laser direct writing technique.
Planar waveguide with left-handed material guiding film for refractometry applications
2013-01-01
A symmetric 3-layer slab waveguide with a left-handed material as a guiding layer is examined analytically for cover refractive index detection. The TM mode dispersion relation of the proposed waveguide is investigated. The sensitivity of the proposed sensor to changes in the cover refractive index and the power flowing within each layer are presented. Some unusual features are found; for example, the sensitivity of the proposed sensor is negative. Moreover, the sensitivity improvem...
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J.
1977-08-01
Causally symmetric spacetimes are spacetimes with J/sup +/(S) isometric to J/sup -/(S) for some set S. We discuss certain properties of these spacetimes, showing for example that, if S is a maximal Cauchy surface with matter everywhere on S, then the spacetime has singularities in both J/sup +/(S) and J/sup -/(S). We also consider totally vicious spacetimes, a class of causally symmetric spacetimes for which I/sup +/(p) =I/sup -/(p) = M for any point p in M. Two different notions of stability in general relativity are discussed, using various types of causally symmetric spacetimes as starting points for perturbations.
Symmetrization and Applications
Kesavan, S
2006-01-01
The study of isoperimetric inequalities involves a fascinating interplay of analysis, geometry and the theory of partial differential equations. Several conjectures have been made and while many have been resolved, a large number still remain open.One of the principal tools in the study of isoperimetric problems, especially when spherical symmetry is involved, is Schwarz symmetrization, which is also known as the spherically symmetric and decreasing rearrangement of functions. The aim of this book is to give an introduction to the theory of Schwarz symmetrization and study some of its applicat
Omnidirectional optical waveguide
Bora, Mihail; Bond, Tiziana C.
2016-08-02
In one embodiment, a system includes a scintillator material; a detector coupled to the scintillator material; and an omnidirectional waveguide coupled to the scintillator material, the omnidirectional waveguide comprising: a plurality of first layers comprising one or more materials having a refractive index in a first range; and a plurality of second layers comprising one or more materials having a refractive index in a second range, the second range being lower than the first range, a plurality of interfaces being defined between alternating ones of the first and second layers. In another embodiment, a method includes depositing alternating layers of a material having a relatively high refractive index and a material having a relatively low refractive index on a substrate to form an omnidirectional waveguide; and coupling the omnidirectional waveguide to at least one surface of a scintillator material.
Jahani, Saman
2014-01-01
Recently, we introduced a paradigm shift in light confinement strategy and introduced a class of extreme skin depth (e-skid) photonic structures (S. Jahani and Z. Jacob, "Transparent sub-diffraction optics: nanoscale light confinement without metal," Optica 1, 96-100 (2014)). Here, we analytically establish that figures of merit related to light confinement in dielectric waveguides are fundamentally tied to the skin depth of waves in the cladding. We contrast the propagation characteristics of the fundamental mode of e-skid waveguides and conventional waveguides to show that the decay constant in the cladding is dramatically larger in e-skid waveguides, which is the origin of sub-diffraction confinement. Finally, we propose an approach to verify the reduced skin depth in experiment using the decrease in the Goos-H\\"anchen phase shift.
Nanoscale waveguiding methods.
Wang, Chia-Jean; Lin, Lih Y
2007-05-01
While 32 nm lithography technology is on the horizon for integrated circuit (IC) fabrication, matching the pace for miniaturization with optics has been hampered by the diffraction limit. However, development of nanoscale components and guiding methods is burgeoning through advances in fabrication techniques and materials processing. As waveguiding presents the fundamental issue and cornerstone for ultra-high density photonic ICs, we examine the current state of methods in the field. Namely, plasmonic, metal slot and negative dielectric based waveguides as well as a few sub-micrometer techniques such as nanoribbons, high-index contrast and photonic crystals waveguides are investigated in terms of construction, transmission, and limitations. Furthermore, we discuss in detail quantum dot (QD) arrays as a gain-enabled and flexible means to transmit energy through straight paths and sharp bends. Modeling, fabrication and test results are provided and show that the QD waveguide may be effective as an alternate means to transfer light on sub-diffraction dimensions.
Dunajewski, Adam; Dusza, Jacek J.; Rosado Muñoz, Alfredo
2014-11-01
The article presents a proposal for the description of human gait as a periodic and symmetric process. Firstly, the data for researches was obtained in the Laboratory of Group SATI in the School of Engineering of University of Valencia. Then, the periodical model - Mean Double Step (MDS) was made. Finally, on the basis of MDS, the symmetrical models - Left Mean Double Step and Right Mean Double Step (LMDS and RMDS) could be created. The method of various functional extensions was used. Symmetrical gait models can be used to calculate the coefficients of asymmetry at any time or phase of the gait. In this way it is possible to create asymmetry, function which better describes human gait dysfunction. The paper also describes an algorithm for calculating symmetric models, and shows exemplary results based on the experimental data.
Linear Amplification of Optical Signal in Coupled Photonic Crystal Waveguides
Jandieri, Vakhtang
2015-01-01
We introduce a weakly coupled photonic crystal waveguide as a promising and realistic model for all-optical amplification. A symmetric pillar type coupled photonic crystal waveguide consisting of dielectric rods periodically distributed in a free space is proposed as all-optical amplifier. Using the unique features of the photonic crystals to control and guide the light, we have properly chosen the frequency at which only one mode (odd mode) becomes the propagating mode in the coupled photonic crystal waveguide, whereas another mode (even mode) is completely reflected from the guiding structure. Under this condition, the all-optical amplification is fully realized. The amplification coefficient for the continuous signal and the Gaussian pulse is calculated.
Some properties of the circular waveguide with azimuthally magnetized ferrite
Ivanov, Kamen P.; Georgiev, Georgi N.
1990-05-01
A comprehensive analysis of normal rotationally symmetric TE modes in a circular waveguide, filled with ferrite, magnetized azimuthally to remanence by a coaxial switching conductor of finite radius, is presented. The characteristic equation of the structure, derived in terms of Kummer and Tricomi confluent hypergeometric functions of complex parameter and variable, is solved numerically, using specially compiled tables of wave functions. Families of theoretically calculated nonreciprocal phase characteristics of the gyrotropic waveguide are shown in normalized form for the two latched states of remanent magnetization, a variety of ferrite parameters, and different values of switching conductor to waveguide radius ratio. The influence of structure geometry and parameters of anisotropic ferrite on normalized differential phase shift and cutoff frequency spectrum of the TE01 mode is discussed.
Analysis of EM scattering in Waveguide Filter using Neural Network
Directory of Open Access Journals (Sweden)
Manidipa Nath
2012-03-01
Full Text Available This paper discusses the application of Neural Network (NN technique in the modeling of a typical electromagnetic (EM field scattering problem in a waveguide filter structure [1]. The structure underconsideration is a rectangular waveguide with four dielectric circular rod inserted symmetrically. The Neural Network takes into consideration the geometrical and material parameters of the EM model of the structure and the reflection coefficient values for different frequencies in the frequency band of interest. The Neural Network is trained off line using training data sets generated by the image theory. The work is to find out an acceptable Neural Network model of the waveguide structure having four dielectric post, verification using Method of moment by simulation and the corresponding filter structure practically implemented in hardware for verification.
Lobanov, Valery E; Kartashov, Yaroslav V
2010-01-01
We consider evolution of multichannel excitations in longitudinally modulated waveguide arrays where refractive index either oscillates out-of-phase in all neighboring waveguides or when it is modulated in phase in several central waveguides surrounded by out-of-phase oscillating neighbors. Both types of modulations allow resonant inhibition of light tunneling, but only the modulation of latter type conserves the internal structure of multichannel excitations. We show that parameter regions where light tunneling inhibition is possible depend on the symmetry and structure of multichannel excitations. Antisymmetric multichannel excitations are more robust than their symmetric counterparts and experience nonlinearity-induced delocalization at higher amplitudes.
Metal strips and wires as plasmonic waveguides for integrated-optics components
DEFF Research Database (Denmark)
Boltasseva, Alexandra; Leosson, Kristjan; Bozhevolnyi, Sergey I.
2007-01-01
Propagation of long-range surface plasmon polaritons in different waveguide components based on nm-thin and ¿m-wide metal strips and symmetrical sub-wavelength metal nanowires embedded in a uniform dielectric is experimentally studied at telecom wavelengths.......Propagation of long-range surface plasmon polaritons in different waveguide components based on nm-thin and ¿m-wide metal strips and symmetrical sub-wavelength metal nanowires embedded in a uniform dielectric is experimentally studied at telecom wavelengths....
Twofold Transition in PT-symmetric Coupled Oscillators
2013-12-26
2Dipartimento di Matematica e Fisica Ennio De Giorgi, Università del Salento and I. N. F. N. Sezione di Lecce, Via Arnesano, I-73100 Lecce, Italy...supermode, as shown in Fig. 6, instead of two pairs of real frequencies. B. Unbalanced loss and gain Let us consider the general case (2) in which μ = ν...correspond to the eigenfunctions ψm,n(x,y). The eigenfunctions have the general form ψm,n(x,y) = e−(2axy+bx2+cy2)/2Pm,n(x,y), (12) where b = c∗ = 2(a
Dichromatic nonlinear eigenmodes in slab waveguide with chi(2) nonlinearity.
Darmanyan, S A; Nevière, M
2001-03-01
The existence of purely nonlinear eigenmodes in a waveguiding structure composed of a slab with quadratic nonlinearity surrounded by (non)linear claddings is reported. Modes having bright and dark solitonlike shapes and consisting of two mutually locked harmonics are identified. Asymmetrical modes are shown to exist in symmetrical environments. Constraints for the existence of the modes are derived in terms of parameters of guiding structure materials.
Waveguide Studies for Fiber Optics and Optical Signal Processing Applications.
1980-04-01
a written policy governing the release of the copyright appearing on pages 66- 68 , which gives full permission to reproduce same. This report has been...symmetric and asymmetric, again requiring the same propagation vector in each waveguide. 5-7 These losses were calculated from equations of Marcuse ... Marcuse in microbend loss calculations of slab guides with a parabolic index profile . This reduc- tion of radiation loss at small periodicities of
Gap Surface Plasmon Waveguide Analysis
DEFF Research Database (Denmark)
Nielsen, Michael Grøndahl; Bozhevolnyi, Sergey I.
2014-01-01
Plasmonic waveguides supporting gap surface plasmons (GSPs) localized in a dielectric spacer between metal films are investigated numerically and the waveguiding properties at telecommunication wavelengths are presented. Especially, we emphasize that the mode confinement can advantageously...
Experimental Demonstration of Luneburg Waveguides
Directory of Open Access Journals (Sweden)
Vera N. Smolyaninova
2015-04-01
Full Text Available Transformation optics gives rise to numerous unusual optical devices, such as novel metamaterial lenses and invisibility cloaks. Very recently, Mattheakis et al. (Luneburg lens waveguide networks. J. Opt. 2012, 14, 114006 have suggested theoretical design of an optical waveguide, based on a network of Luneburg lenses, which may be useful in sensing and nonlinear optics applications. Here, we report the first experimental realization of such Luneburg waveguides. We have studied wavelength and polarization dependent performance of the waveguides.
Nanoporous polymer liquid core waveguides
DEFF Research Database (Denmark)
Gopalakrishnan, Nimi; Christiansen, Mads Brøkner; Ndoni, Sokol
2010-01-01
We demonstrate liquid core waveguides defined by UV to enable selective water infiltration in nanoporous polymers, creating an effective refractive index shift Δn=0.13. The mode confinement and propagation loss in these waveguides are presented.......We demonstrate liquid core waveguides defined by UV to enable selective water infiltration in nanoporous polymers, creating an effective refractive index shift Δn=0.13. The mode confinement and propagation loss in these waveguides are presented....
DESIGN OF INTEGRATING WAVEGUIDE BIOSENSOR
The Integrating Waveguide Biosensor allows for rapid and sensitive detection of pathogenic agents, cells and proteins via immunoassay or PCR products. The analytes are captured on the surface of the waveguide and then tagged with fluorescent labels. The waveguides are illuminated by excitation light...
N>=2 symmetric superpolynomials
Alarie-Vézina, L; Mathieu, P
2015-01-01
The theory of symmetric functions has been extended to the case where each variable is paired with an anticommuting one. The resulting expressions, dubbed superpolynomials, provide the natural N=1 supersymmetric version of the classical bases of symmetric functions. Here we consider the case where two independent anticommuting variables are attached to each ordinary variable. The N=2 super-version of the monomial, elementary, homogeneous symmetric functions, as well as the power sums, are then constructed systematically (using an exterior-differential formalism for the multiplicative bases), these functions being now indexed by a novel type of superpartitions. Moreover, the scalar product of power sums turns out to have a natural N=2 generalization which preserves the duality between the monomial and homogeneous bases. All these results are then generalized to an arbitrary value of N. Finally, for N=2, the scalar product and the homogenous functions are shown to have a one-parameter deformation, a result that...
Counting with symmetric functions
Mendes, Anthony
2015-01-01
This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enu...
Symmetric tensor decomposition
Brachat, Jerome; Mourrain, Bernard; Tsigaridas, Elias
2009-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables of total degree d as a sum of powers of linear forms (Waring's problem), incidence properties on secant varieties of the Veronese Variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester's approach from the dual point of view. Exploiting this duality, we propose necessary and sufficient conditions for the existence of such a decomposition of a given rank, using the properties of Hankel (and quasi-Hankel) matrices, derived from multivariate polynomials and normal form computations. This leads to the resolution of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on th...
Multiparty Symmetric Sum Types
DEFF Research Database (Denmark)
Nielsen, Lasse; Yoshida, Nobuko; Honda, Kohei
2010-01-01
This paper introduces a new theory of multiparty session types based on symmetric sum types, by which we can type non-deterministic orchestration choice behaviours. While the original branching type in session types can represent a choice made by a single participant and accepted by others...... determining how the session proceeds, the symmetric sum type represents a choice made by agreement among all the participants of a session. Such behaviour can be found in many practical systems, including collaborative workflow in healthcare systems for clinical practice guidelines (CPGs). Processes...... with the symmetric sums can be embedded into the original branching types using conductor processes. We show that this type-driven embedding preserves typability, satisfies semantic soundness and completeness, and meets the encodability criteria adapted to the typed setting. The theory leads to an efficient...
Active Photonic Crystal Waveguides
DEFF Research Database (Denmark)
Ek, Sara
This thesis deals with the fabrication and characterization of active photonic crystal waveguides, realized in III-V semiconductor material with embedded active layers. The platform offering active photonic crystal waveguides has many potential applications. One of these is a compact photonic...... crystal semiconductor optical amplier. As a step towards such a component, photonic crystal waveguides with a single quantum well, 10 quantum wells and three layers of quantum dots are fabricated and characterized. An experimental study of the amplied spontaneous emission and a implied transmission...... are presented in this thesis. A variation of photonic crystal design parameters are used leading to a spectral shift of the dispersion, it is veried that the observed effects shift accordingly. An enhancement of the amplified spontaneous emission was observed close to the band edge, where light is slowed down...
Progressive symmetric erythrokeratoderma
Directory of Open Access Journals (Sweden)
Gharpuray Mohan
1990-01-01
Full Text Available Four patients had symmetrically distributed hyperkeratotic plaques on the trunk and extremities; The lesions in all of them had appeared during infancy, and after a brief period of progression, had remained static, All of them had no family history of similar skin lesions. They responded well to topical applications of 6% salicylic acid in 50% propylene glycol. Unusual features in these cases of progressive symmetric erythrokeratoderma were the sparing of palms and soles, involvement of the trunk and absence of erythema.
Waveguide apparatuses and methods
Spencer, James E.
2016-05-10
Optical fiber waveguides and related approaches are implemented to facilitate communication. As may be implemented in accordance with one or more embodiments, a waveguide has a substrate including a lattice structure having a plurality of lattice regions with a dielectric constant that is different than that of the substrate, a defect in the lattice, and one or more deviations from the lattice. The defect acts with trapped transverse modes (e.g., magnetic and/or electric modes) and facilitates wave propagation along a longitudinal direction while confining the wave transversely. The deviation(s) from the lattice produces additional modes and/or coupling effects.
Waveguides for walking droplets
Filoux, Boris; Schlagheck, Peter; Vandewalle, Nicolas
2015-01-01
When gently placing a droplet onto a vertically vibrated bath, a drop can bounce permanently. Upon increasing the forcing acceleration, the droplet is propelled by the wave it generates and becomes a walker with a well defined speed. We investigate the confinement of a walker in different rectangular cavities, used as waveguides for the Faraday waves emitted by successive droplet bounces. By studying the walker velocities, we discover that 1d confinement is optimal for narrow channels. We also propose an analogy with waveguide models based on the observation of the Faraday instability within the channels.
Actively coupled optical waveguides
Alexeeva, N. V.; Barashenkov, I. V.; Rayanov, K.; Flach, S.
2014-01-01
We consider light propagation through a pair of nonlinear optical waveguides with absorption, placed in a medium with power gain. The active medium boosts the in-phase component of the overlapping evanescent fields of the guides, while the nonlinearity of the guides couples it to the damped out-of-phase component creating a feedback loop. As a result, the structure exhibits stable stationary and oscillatory regimes in a wide range of gain-loss ratios. We show that the pair of actively coupled (AC) waveguides can act as a stationary or integrate-and-fire comparator sensitive to tiny differences in their input powers.
Metamaterial Loadings for Waveguide Miniaturization
Odabasi, H
2013-01-01
We show that a rectangular metallic waveguide loaded with metamaterial elements consisting of electric-field coupled (ELC) resonators placed at the side walls can operate well below the cutoff frequency of the respective unloaded waveguide. The dispersion diagrams indicate that propagating modes in ELC-loaded waveguides are of forward-type for both TE and TM modes. We also study the dispersion diagram and transmission characteristics of rectangular metallic waveguides simultaneously loaded with ELCs and split ring resonators (SRRs). Such doubly-loaded waveguides can support both forward wave and backward waves, and provide independent control of the propagation characteristics for the respective modes.
Symmetric Spaces in Supergravity
Ferrara, Sergio
2008-01-01
We exploit the relation among irreducible Riemannian globally symmetric spaces (IRGS) and supergravity theories in 3, 4 and 5 space-time dimensions. IRGS appear as scalar manifolds of the theories, as well as moduli spaces of the various classes of solutions to the classical extremal black hole Attractor Equations. Relations with Jordan algebras of degree three and four are also outlined.
Distributed Searchable Symmetric Encryption
Bösch, Christoph; Peter, Andreas; Leenders, Bram; Lim, Hoon Wei; Tang, Qiang; Wang, Huaxiong; Hartel, Pieter; Jonker, Willem
2014-01-01
Searchable Symmetric Encryption (SSE) allows a client to store encrypted data on a storage provider in such a way, that the client is able to search and retrieve the data selectively without the storage provider learning the contents of the data or the words being searched for. Practical SSE schemes
PT Symmetry and QCD: Finite Temperature and Density
Directory of Open Access Journals (Sweden)
Michael C. Ogilvie
2009-04-01
Full Text Available The relevance of PT symmetry to quantum chromodynamics (QCD, the gauge theory of the strong interactions, is explored in the context of finite temperature and density. Two significant problems in QCD are studied: the sign problem of finite-density QCD, and the problem of confinement. It is proven that the effective action for heavy quarks at finite density is PT-symmetric. For the case of 1+1 dimensions, the PT-symmetric Hamiltonian, although not Hermitian, has real eigenvalues for a range of values of the chemical potential μ, solving the sign problem for this model. The effective action for heavy quarks is part of a potentially large class of generalized sine-Gordon models which are non-Hermitian but are PT-symmetric. Generalized sine-Gordon models also occur naturally in gauge theories in which magnetic monopoles lead to confinement. We explore gauge theories where monopoles cause confinement at arbitrarily high temperatures. Several different classes of monopole gases exist, with each class leading to different string tension scaling laws. For one class of monopole gas models, the PT-symmetric affine Toda field theory emerges naturally as the effective theory. This in turn leads to sine-law scaling for string tensions, a behavior consistent with lattice simulations.
PT symmetry in classical and quantum statistical mechanics.
Meisinger, Peter N; Ogilvie, Michael C
2013-04-28
PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside the conventional equilibrium statistical mechanics of Hermitian systems. PT-symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviours than Hermitian systems, displaying sinusoidally modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with PT-symmetry include Z(N) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbour Ising model. Quantum many-body problems with a non-zero chemical potential have a natural PT-symmetric representation related to the sign problem. Two-dimensional quantum chromodynamics with heavy quarks at non-zero chemical potential can be solved by diagonalizing an appropriate PT-symmetric Hamiltonian.
Gratings in polymeric waveguides
Mishakov, G.; Sokolov, V.; Kocabas, A.; Aydinli, A.
2007-04-01
Laser-induced formation of polymer Bragg grating filters for Dense Wavelength Division Multiplexing (DWDM) applications is discussed. Acrylate monomers halogenated with both fluorine and chlorine, which possess absorption losses less than 0.25 dB/cm and wide choice of refractive indices (from 1.3 to 1.5) in the 1.5 μm telecom wavelength region were used. The monomers are highly intermixable thus permitting to adjust the refractive index of the composition within +/-0.0001. Moreover they are photocurable under UV exposure and exhibit high contrast in polymerization. These properties make halogenated acrylates very promising for fabricating polymeric waveguides and photonic circuits. Single-mode polymer waveguides were fabricated on silicon wafers using resistless contact lithography. Submicron index gratings have been written in polymer waveguides using holographic exposure with He-Cd laser beam (325 nm) through a phase mask. Both uniform and apodized gratings have been fabricated. The gratings are stable and are not erased by uniform UV exposure. The waveguide gratings possess narrowband reflection spectra in the 1.5 μm wavelength region of 0.4 nm width, nearly rectangular shape of the stopband and reflectivity R > 99%. The fabricated Bragg grating filters can be used for multiplexing/demultiplexing optical signals in high-speed DWDM optical fiber networks.
DEFF Research Database (Denmark)
2013-01-01
A waveguide resonator comprising a number of side walls defining a cavity enclosed by said sidewalls defining the cavity; and two or more conductive plates extending into the cavity, each conductive plate having a first side and a second side opposite the first side, and wherein the conductive...
Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo; Shapiro, Jeffrey H.
2003-01-01
We calculate the communication capacity of a broadband electromagnetic waveguide as a function of its spatial dimensions and input power. We analyze the two cases in which either all the available modes or only a single directional mode are employed. The results are compared with those for the free space bosonic channel.
Directory of Open Access Journals (Sweden)
Wang Chia-Jean
2007-01-01
Full Text Available AbstractWhile 32 nm lithography technology is on the horizon for integrated circuit (IC fabrication, matching the pace for miniaturization with optics has been hampered by the diffraction limit. However, development of nanoscale components and guiding methods is burgeoning through advances in fabrication techniques and materials processing. As waveguiding presents the fundamental issue and cornerstone for ultra-high density photonic ICs, we examine the current state of methods in the field. Namely, plasmonic, metal slot and negative dielectric based waveguides as well as a few sub-micrometer techniques such as nanoribbons, high-index contrast and photonic crystals waveguides are investigated in terms of construction, transmission, and limitations. Furthermore, we discuss in detail quantum dot (QD arrays as a gain-enabled and flexible means to transmit energy through straight paths and sharp bends. Modeling, fabrication and test results are provided and show that the QD waveguide may be effective as an alternate means to transfer light on sub-diffraction dimensions.
Fluitman, J.; Popma, Th.
1986-01-01
An overview of the field of optical waveguide sensors is presented. Some emphasis is laid on the development of a single scheme under which the diversity of sensor principles can be arranged. First three types of sensors are distinguished: intrinsic, extrinsic and active. Next, two steps are disting
Control of Power in Parity-Time -Symmetric Lattices
Kozlov, Maksim
2015-01-01
We investigate wave transport properties of Parity-Time (PT) symmetric lattices that are periodically modulated along the direction of propagation. We demonstrate that in the regime of unbroken PT-symmetry the system Floquet-Bloch modes may interfere constructively leading to either controlled oscillations or linear power absorption and amplification occurring exactly at the phase transition point. The differential power response is effected by the overlap of the gain and loss system distribution with wave intensity pattern that is formed through Rabi oscillations engaging the coupled Floquet-Bloch modes.
Chen, Fan; Cao, Zhuangqi; Shen, Qishun; Deng, Xiaoxu; Duan, Biming; Yuan, Wen; Sang, Minghuang; Wang, Shengqian
2005-12-12
An improved scheme for displacement measurement using the ultrahigh-order guided modes in a symmetrical metal-cladding optical waveguide is proposed. Based on this idea together with the lock-in amplification technique, a sensor with a stable displacement resolution of 3.3 pm is experimentally demonstrated without any complicated servo system.
The realization of an integrated Mach-Zehnder waveguide immunosensor in silicon technology
Schipper, E.F.; Brugman, A.M.; Lechuga, L.M.; Kooyman, R.P.H.; Greve, J.; Dominguez, C.
1997-01-01
We describe the realization of a symmetric integrated channel waveguide Mach-Zehnder sensor which uses the evanescent field to detect small refractive-index changes (¿nmin ¿ 1 × 10¿4) near the guiding-layer surface. This guiding layer consists of ridge structures with a height of 3 nm and a width of
Locally parity-time-symmetric and globally parity-symmetric systems
Ahmed, W. W.; Herrero, R.; Botey, M.; Staliunas, K.
2016-11-01
We introduce a class of systems holding parity-time (PT ) symmetry locally, whereas being globally P symmetric. The potential, U =U (|r |) , fulfills PT symmetry with respect to periodically distributed points r0:U (| r0+r |) =U*(| r0-r |) being r0≠0 . We show that such systems hold unusual properties arising from the merging of the two different symmetries, leading to a strong field localization and enhancement at the double-symmetry center, r =0 , when the coupling of outward to inward propagating waves is favored. We explore such general potentials in one and two dimensions, which could have actual realizations combining gain-loss and index modulations in nanophotonic structures. In particular, we show how to render a broad aperture vertical-cavity surface-emitting laser into a bright and narrow beam source, as a direct application.
Generating functions for symmetric and shifted symmetric functions
Jing, Naihuan; Rozhkovskaya, Natasha
2016-01-01
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to treat various families of symmetric functions and their shifted analogues.
Generating functions for symmetric and shifted symmetric functions
Jing, Naihuan; Rozhkovskaya, Natasha
2016-01-01
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to treat various families of symmetric functions and their shifted analogues.
Experimental investigation of plasmofluidic waveguides
Energy Technology Data Exchange (ETDEWEB)
Ku, Bonwoo; Kwon, Min-Suk, E-mail: mskwon@unist.ac.kr [School of Electrical and Computer Engineering, UNIST, 50 UNIST-gil, Eonyang-eup, Ulju-gun, Ulsan 689-798 (Korea, Republic of); Shin, Jin-Soo [Department of Electrical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701 (Korea, Republic of)
2015-11-16
Plasmofluidic waveguides are based on guiding light which is strongly confined in fluid with the assistance of a surface plasmon polariton. To realize plasmofluidic waveguides, metal-insulator-silicon-insulator-metal (MISIM) waveguides, which are hybrid plasmonic waveguides fabricated using standard complementary metal-oxide-semiconductor technology, are employed. The insulator of the MISIM waveguide is removed to form 30-nm-wide channels, and they are filled with fluid. The plasmofluidic waveguide has a subwavelength-scale mode area since its mode is strongly confined in the fluid. The waveguides are experimentally characterized for different fluids. When the refractive index of the fluid is 1.440, the plasmofluidic waveguide with 190-nm-wide silicon has propagation loss of 0.46 dB/μm; the coupling loss between it and an ordinary silicon photonic waveguide is 1.79 dB. The propagation and coupling losses may be reduced if a few fabrication-induced imperfections are removed. The plasmofluidic waveguide may pave the way to a dynamically phase-tunable ultracompact device.
EQUIFOCAL HYPERSURFACES IN SYMMETRIC SPACES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This note investigates the multiplicity problem of principal curvatures of equifocal hyper surfaces in simply connected rank 1 symmetric spaces. Using Clifford representation theory, and the author also constructs infinitely many equifocal hypersurfaces in the symmetric spaces.
Homogenous finitary symmetric groups
Directory of Open Access Journals (Sweden)
Otto. H. Kegel
2015-03-01
Full Text Available We characterize strictly diagonal type of embeddings of finitary symmetric groups in terms of cardinality and the characteristic. Namely, we prove the following. Let kappa be an infinite cardinal. If G=underseti=1stackrelinftybigcupG i , where G i =FSym(kappan i , (H=underseti=1stackrelinftybigcupH i , where H i =Alt(kappan i , is a group of strictly diagonal type and xi=(p 1 ,p 2 ,ldots is an infinite sequence of primes, then G is isomorphic to the homogenous finitary symmetric group FSym(kappa(xi (H is isomorphic to the homogenous alternating group Alt(kappa(xi , where n 0 =1,n i =p 1 p 2 ldotsp i .
Chen, Yan; Feng, Huijuan; Ma, Jiayao; Peng, Rui; You, Zhong
2016-06-01
The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.
Symmetric Extended Ockham Algebras
Institute of Scientific and Technical Information of China (English)
T.S. Blyth; Jie Fang
2003-01-01
The variety eO of extended Ockham algebras consists of those algealgebra with an additional endomorphism k such that the unary operations f and k commute. Here, we consider the cO-algebras which have a property of symmetry. We show that there are thirty two non-isomorphic subdirectly irreducible symmetric extended MS-algebras and give a complete description of them.2000 Mathematics Subject Classification: 06D15, 06D30
Symmetrization Selection Rules, 1
Page, P R
1996-01-01
We introduce a category of strong and electromagnetic interaction selection rules for the two-body connected decay and production of exotic J^{PC} = 0^{+-}, 1^{-+}, 2^{+-}, 3^{-+}, ... hybrid and four-quark mesons. The rules arise from symmetrization in states in addition to Bose symmetry and CP invariance. Examples include various decays to \\eta'\\eta, \\eta\\pi, \\eta'\\pi and four-quark interpretations of a 1^{-+} signal.
Symmetrization Selection Rules, 2
Page, P R
1996-01-01
We introduce strong interaction selection rules for the two-body decay and production of hybrid and conventional mesons coupling to two S-wave hybrid or conventional mesons. The rules arise from symmetrization in states in the limit of non-relativistically moving quarks. The conditions under which hybrid coupling to S-wave states is suppressed are determined by the rules, and the nature of their breaking is indicated.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Haibin; Eaton, Shane M; Li, Jianzhao; Herman, Peter R [The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, 10 King' s College Road, Toronto, ON, M5S 3G4 (Canada)
2007-04-15
During high repetition rate (>200 kHz) ultrafast laser waveguide writing, visible heat modified zones surrounding the formed waveguide occur as a result of heat accumulation. The radii of the heat-modified zones increase with the laser net fluence, and were found to correlate with the formation of low-loss and cylindrically symmetric optical waveguides. A numerical thermal model based on the finite difference method is applied here to account for cumulative heating and diffusion effects. The model successfully shows that heat propagation and accumulation accurately predict the radius of the 'heat modified' zones observed in borosilicate glass waveguides formed across a wide range of laser exposure conditions. Such modelling promises better control of thermal effects for optimizing the fabrication and performance of three-dimensional optical devices in transparent materials.
Lu, Jiahui; Wang, Guanghui
2016-11-01
We explore the dispersion properties and optical gradient forces from mutual coupling of surface plasmon polariton (SPP) modes at two interfaces of nanoscale plasmonic waveguides with hyperbolic metamaterial cladding. With Maxwell’s equations and Maxwell stress tensor, we calculate and compare the dispersion relation and optical gradient force for symmetric and antisymmetric SPP modes in two kinds of nanoscale plasmonic waveguides. The numerical results show that the optical gradient force between two coupled hyperbolic metamaterial waveguides can be engineered flexibly by adjusting the waveguide structure parameters. Importantly, an alternative way to boost the optical gradient force is provided through engineering the hyperbolic metamaterial cladding of suitable orientation. These special optical properties will open the door for potential optomechanical applications, such as optical tweezers and actuators. Project supported by the National Natural Science Foundation of China (Grant No. 11474106) and the Natural Science Foundation of Guangdong Province, China (Grant No. 2016A030313439).
Design of non-reciprocal acoustic waveguides by indirect interband transitions
Ishikawa, Atsushi; Tsuruta, Kenji
2017-07-01
We numerically demonstrate a non-reciprocal acoustic waveguide by utilizing the indirect interband transition between two guided modes. The waveguide, consisting of a water core sandwiched between parallel steel plates, is designed to support symmetric and asymmetric guided modes with different frequencies and wavevectors. Dynamic mode conversion is then achieved by applying spatio-temporal density modulation in the core of the waveguide to induce both frequency and wavevector shifts of the incident guided wave. Numerical simulations prove that the phase matching condition is satisfied only for the forward propagation, not for the backward one, thus realizing the non-reciprocal acoustic waveguide. Our approach based on a linear dynamic system may achieve wide-band tunable operation with a low-energy consumption, paving the way toward the sophisticated acoustic diode applications.
Optical Intensity Modulation in an LiNbO3 Slab-Coupled Waveguide
Directory of Open Access Journals (Sweden)
Yalin Lu
2008-01-01
Full Text Available Optical intensity modulation has been demonstrated through switching the optical beam between the main core waveguide and a closely attached leaky slab waveguide by applying a low-voltage electrical field. Theory for simulating such an LiNbO3 slab-coupled waveguide structure was suggested, and the result indicates the possibility of making the spatial guiding mode large, circular and symmetric, which further allows the potential to significantly reduce the coupling losses with adjacent lasers and optical networks. Optical intensity modulation using electro-optic effect was experimentally demonstrated in a 5 cm long waveguide fabricated by using a procedure of soft proton exchange and then an overgrowth of thin LN film on top of a c-cut LiNbO3 wafer.
PT; Pro-time; Anticoagulant-prothrombin time; Clotting time: protime; INR; International normalized ratio ... PT is measured in seconds. Most of the time, results are given as what is called INR ( ...
Efficient Cartesian-grid-based modeling of rotationally symmetric bodies
DEFF Research Database (Denmark)
Shyroki, Dzmitry
2007-01-01
Axially symmetric waveguides, resonators, and scatterers of arbitrary cross section and anisotropy in the cross section can be modeled rigorously with use of 2-D Cartesian-grid based codes by means of mere redefinition of material permittivity and permeability profiles. The method is illustrated...... by the frequencydomain simulations of resonant modes in a circular-cylinder cavity with perfectly conducting walls, a shielded uniaxial anisotropic dielectric cylinder, and an open dielectric sphere for which, after proper implementation of the perfectly matched layer boundary conditions, the radiation quality factor...
Symmetric reconfigurable capacity assignment in a bidirectional DWDM access network.
Ortega, Beatriz; Mora, José; Puerto, Gustavo; Capmany, José
2007-12-10
This paper presents a novel architecture for DWDM bidirectional access networks providing symmetric dynamic capacity allocation for both downlink and uplink signals. A foldback arrayed waveguide grating incorporating an optical switch enables the experimental demonstration of flexible assignment of multiservice capacity. Different analog and digital services, such as CATV, 10 GHz-tone, 155Mb/s PRBS and UMTS signals have been transmitted in order to successfully test the system performance under different scenarios of total capacity distribution from the Central Station to different Base Stations with two reconfigurable extra channels for each down and upstream direction.
Surface plasmon enhancement of spontaneous emission in graphene waveguides
Cuevas, Mauro
2016-10-01
This work analyzes the spontaneous emission of a single emitter placed near the graphene waveguide formed by two parallel graphene monolayers, with an insulator spacer layer. In this case, the eigenmodes supported by the structure, such as surface plasmon and wave guided modes, provide decay channels for the electric dipole placed close to the waveguide. We calculated the contribution to the decay rate of symmetric and antisymmetric eigenmodes as a function of frequency and the orientation of the emitter. Our results show that the modification of the spontaneous emission due to excitation of guided modes is much lower than the corresponding decays through the excitation of symmetric and antisymmetric surface plasmons, for which, the spontaneous emission is dramatically enhanced. As a consequence of the high confinement of surface plasmons in the graphene waveguide, we found that the decay rate of the emitter with vertical orientation (with respect to graphene sheets) is twice the corresponding decay of the same emitter with parallel orientation in the whole frequency range where surface plasmon modes exist. Differently from metallo-dielectric structures, where structural parameters determine the range and magnitude of this emission, our work shows that, by dynamically tuning the chemical potential of graphene, the spectral region where the decay rate is enhanced can be chosen over a wide range.
Phonon waveguides for electromechanical circuits
Hatanaka, D.; Mahboob, I.; Onomitsu, K.; Yamaguchi, H.
2014-07-01
Nanoelectromechanical systems (NEMS), utilizing localized mechanical vibrations, have found application in sensors, signal processors and in the study of macroscopic quantum mechanics. The integration of multiple mechanical elements via electrical or optical means remains a challenge in the realization of NEMS circuits. Here, we develop a phonon waveguide using a one-dimensional array of suspended membranes that offers purely mechanical means to integrate isolated NEMS resonators. We demonstrate that the phonon waveguide can support and guide mechanical vibrations and that the periodic membrane arrangement also creates a phonon bandgap that enables control of the phonon propagation velocity. Furthermore, embedding a phonon cavity into the phonon waveguide allows mobile mechanical vibrations to be dynamically switched or transferred from the waveguide to the cavity, thereby illustrating the viability of waveguide-resonator coupling. These highly functional traits of the phonon waveguide architecture exhibit all the components necessary to permit the realization of all-phononic NEMS circuits.
Waveguide submillimeter mixers
Goldsmith, Paul F.; Erickson, Neal R.
1986-01-01
A waveguide Schottky barrier diode mixer, which in preliminary tests has yielded a single sideband receiver noise temperature of 4300 K at 692 GHz, when cooled to 77 K is presented. Further refinements and operation at 20 K should produce a significant improvement in performance. From a system point of view, the very high efficiency of the radiation pattern produced by the conical feedhorn with cylindrical corrector mirror enhances the effective sensitivity by a factor of 1.5 to 2 compared to open-structure corner-reflector systems. A second-harmonic mixer for 557 GHz, also in the fundamental mode rectangular waveguide was developed. When combined with a frequency-tripled Gunn oscillator, this makes an extremely compact and lightweight submillimeter radiometer.
Miniaturized dielectric waveguide filters
Sandhu, Muhammad Y.; Hunter, Ian C.
2016-10-01
Design techniques for a new class of integrated monolithic high-permittivity ceramic waveguide filters are presented. These filters enable a size reduction of 50% compared to air-filled transverse electromagnetic filters with the same unloaded Q-factor. Designs for Chebyshev and asymmetric generalised Chebyshev filter and a diplexer are presented with experimental results for an 1800 MHz Chebyshev filter and a 1700 MHz generalised Chebyshev filter showing excellent agreement with theory.
Spontaneous breakdown of $\\mathcal{PT}$ symmetry in the complex Coulomb potential
Indian Academy of Sciences (India)
G Lévai
2009-08-01
The $\\mathcal{PT}$ symmetry of the Coulomb potential and its solutions are studied along trajectories satisfying the $\\mathcal{PT}$ symmetry requirement. It is shown that with appropriate normalization constant the general solutions can be chosen $\\mathcal{PT}$ -symmetric if the parameter that corresponds to angular momentum in the Hermitian case is real. $\\mathcal{PT}$ symmetry is spontaneously broken, however, for complex values of the form $L = − \\dfrac{1}{2} + i$. In this case the potential remains $\\mathcal{PT}$ -symmetric, while the two independent solutions are transformed to each other by the $\\mathcal{PT}$ operation and at the same time, the two series of discrete energy eigenvalues turn into each other’s complex conjugate.
Cup Cylindrical Waveguide Antenna
Acosta, Roberto J.; Darby, William G.; Kory, Carol L.; Lambert, Kevin M.; Breen, Daniel P.
2008-01-01
The cup cylindrical waveguide antenna (CCWA) is a short backfire microwave antenna capable of simultaneously supporting the transmission or reception of two distinct signals having opposite circular polarizations. Short backfire antennas are widely used in mobile/satellite communications, tracking, telemetry, and wireless local area networks because of their compactness and excellent radiation characteristics. A typical prior short backfire antenna contains a half-wavelength dipole excitation element for linear polarization or crossed half-wavelength dipole elements for circular polarization. In order to achieve simultaneous dual circular polarization, it would be necessary to integrate, into the antenna feed structure, a network of hybrid components, which would introduce significant losses. The CCWA embodies an alternate approach that entails relatively low losses and affords the additional advantage of compactness. The CCWA includes a circular cylindrical cup, a circular disk subreflector, and a circular waveguide that serves as the excitation element. The components that make it possible to obtain simultaneous dual circular polarization are integrated into the circular waveguide. These components are a sixpost polarizer and an orthomode transducer (OMT) with two orthogonal coaxial ports. The overall length of the OMT and polarizer (for the nominal middle design frequency of 2.25 GHz) is about 11 in. (approximately equal to 28 cm), whereas the length of a commercially available OMT and polarizer for the same frequency is about 32 in. (approximately equal to 81 cm).
Anisotropic and nonlinear optical waveguides
Someda, CG
1992-01-01
Dielectric optical waveguides have been investigated for more than two decades. In the last ten years they have had the unique position of being simultaneously the backbone of a very practical and fully developed technology, as well as an extremely exciting area of basic, forefront research. Existing waveguides can be divided into two sets: one consisting of waveguides which are already in practical use, and the second of those which are still at the laboratory stage of their evolution. This book is divided into two separate parts: the first dealing with anisotropic waveguides, an
Waveguide mutually pumped phase conjugators
James, S. W.; Youden, K.E.; Jeffrey, P. M.; EASON, R. W.; Chandler, P.J.; Zhang, L.; Townsend, P.D.
1993-01-01
The operation of the Bridge Mutually Pumped Phase Conjugator is reported in a planar waveguide structure in photorefractive BaTiO3. The waveguide was fabricated by the technique of ion implantation. using 1.5 MeV H+ at a dose of 10^16 ions/cm^2. An order of magnitude decrease in response time is observed in the waveguide as compared to typical values obtained in bulk crystals, probably resulting from a combination of the optical confinement within the waveguide, and possibly modification of t...
Dual-side backward coupler waveguide orthomode transducer for the 3 mm band
Navarrini, Alessandro; Nesti, Renzo
2008-07-01
We describe the design, construction, and characterization results of a waveguide Orthomode Transducer (OMT) for the 3 mm band (84-116 GHz.) The OMT is based on a symmetric backward coupling structure and has a square waveguide input port (2.54 mm × 2.54 mm) and two single-mode waveguide outputs: a standard WR10 rectangular waveguide (2.54 mm × 1.27 mm,) and an oval waveguide with full-radius corners. The reverse coupling structure is located in the common square waveguide arm and splits one polarization signal in two opposite rectangular waveguide sidearms using broadband -3 dB E-plane branch-line hybrid couplers. The device was optimized using a commercial 3D electromagnetic simulator. The OMT consists of two mechanical blocks fabricated in split-block configuration using conventional CNC milling machine. From 84 to 116 GHz the measured input reflection coefficient was less than -17 dB, the isolation between the outputs was less than -50 dB, the cross polarization was less than -30 dB, and the transmission was larger than -0.35 dB at room temperature for both polarization channels. The device is suitable for scaling to higher frequency.
Yang, Jianke
2016-01-01
Stability of soliton families in one-dimensional nonlinear Schroedinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of parameter values both below and above phase transition. In addition, a pseudo-Hamiltonian-Hopf bifurcation is revealed, where pairs of purely-imaginary eigenvalues in the linear-stability spectra of solitons collide and bifurcate off the imaginary axis, creating oscillatory instability, which resembles Hamiltonian-Hopf bifurcations of solitons in Hamiltonian systems even though the present system is dissipative and non-Hamiltonian. The most important numerical finding is that, eigenvalues of linear-stability operators of these solitons appear in quartets $(\\lambda, -\\lambda, \\lambda^*, -\\lambda^*)$, similar to conservative systems and PT-symmetric systems. This quartet eigenvalue symmetry is very surprising for non-PT-symmetric systems, and it has far-reaching consequences ...
Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of total degree d as a sum of powers of linear forms (Waring’s problem), incidence properties on secant varieties of the Veronese variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester’s approach from the dual point of view...
Symmetrically Constrained Compositions
Beck, Matthias; Lee, Sunyoung; Savage, Carla D
2009-01-01
Given integers $a_1, a_2, ..., a_n$, with $a_1 + a_2 + ... + a_n \\geq 1$, a symmetrically constrained composition $\\lambda_1 + lambda_2 + ... + lambda_n = M$ of $M$ into $n$ nonnegative parts is one that satisfies each of the the $n!$ constraints ${\\sum_{i=1}^n a_i \\lambda_{\\pi(i)} \\geq 0 : \\pi \\in S_n}$. We show how to compute the generating function of these compositions, combining methods from partition theory, permutation statistics, and lattice-point enumeration.
Low crosstalk Arrayed Waveguide Grating with Cascaded Waveguide Grating Filter
Energy Technology Data Exchange (ETDEWEB)
Deng Yang; Liu Yuan; Gao Dingshan, E-mail: dsgao@mail.hust.edu.cn [Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074 (China)
2011-02-01
We propose a highly compact and low crosstalk arrayed waveguide grating (AWG) with cascaded waveguide grating (CWGF). The side lobes of the silicon nanowire AWG, which are normally introduced by fabrication errors, can be effectively suppressed by the CWGF. And the crosstalk can be improved about 15dB.
Nonlinear behaviors of parity-time-symmetric lasers
Yang, Jianke
2016-01-01
We propose a time-dependent partial differential equation model to investigate the dynamical behavior of the parity-time (PT) symmetric laser during the nonlinear stage of its operation. This model incorporates physical effects such as the refractive index distribution, dispersion, material loss, nonlinear gain saturation and self-phase modulation. We show that when the loss is weak, multiple stable steady states and time-periodic states of light exist above the lasing threshold, rendering the laser multi-mode. However, when the loss is strong, only a single stable steady state of broken PT symmetry exists for a wide range of the gain amplitude, rendering the laser single-mode. These results reveal the important role the loss plays in maintaining the single-mode operation of PT lasers.
Oscillating Guided Modes in Graphene-Based Asymmetric Waveguides
Institute of Scientific and Technical Information of China (English)
PENG Ping; ZHANG Peng; LIU Jian-Ke; CAO Zhen-Zhou; LI Guan-Qiang
2012-01-01
We investigate the guided modes in monolayer graphene-based waveguides with asymmetric quantum well structure induced by unequal dc voltages. The dispersion relation for the guided modes is obtained analytically, the structures of the guided modes are discussed under three distinct cases. For the cases of the classical motion and the Klein tunneling, the asymmetric structure does not influence the mode structures dramatically compared with that in the symmetric waveguide. But for the mixing case of the former two, the mode structures and the motion characteristics for the electron and the hole exhibit different behaviors at same condition. The results may be helpful for the practical application of graphene-based quantum devices.
Realization of Tapered Waveguide by Stretching the Rod Waveguide
Institute of Scientific and Technical Information of China (English)
XIA Ke-yu; YU Rong-jin; MENG Hua-mao
2004-01-01
By stretching the rod waveguide with different velocities in opposite directions,the tapered waveguide can be fabricated.In condition of taking no account of volume expansion caused by heating and under the assumptions of volume conservation,the rod waveguide can be stretched freely in the heated region without being stretched outside of the heated region. A model,which shows the relation of the transition shape and the two factors,that is the ratio of two velocity and the heated region length,is presented for the shape of the taper transition through mathematic deduction.Based on this model,a desired tapered waveguide can be fabricated.The tapered waveguide are widely used for fabricating tapered fiber couplers and sensors.In addition,the conclusion can be used for fabricating fused fiber coupler.
Holographic Spherically Symmetric Metrics
Petri, Michael
The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.
Sirsi, Swarnamala; Hegde, Subramanya
2011-01-01
Quantum computation on qubits can be carried out by an operation generated by a Hamiltonian such as application of a pulse as in NMR, NQR. Quantum circuits form an integral part of quan- tum computation. We investigate the nonlocal operations generated by a given Hamiltonian. We construct and study the properties of perfect entanglers, that is, the two-qubit operations that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power. Our work addresses the problem of analyzing the quantum evolution in the special case of two qubit symmetric states. Such a symmetric space can be considered to be spanned by the angular momentum states {|j = 1,m>;m = +1, 0,-1}. Our technique relies on the decomposition of a Hamiltonian in terms of newly defined Hermitian operators Mk's (k= 0.....8) which are constructed out of angular momentum operators Jx, Jy, Jz. These operators constitute a linearly independent set of traceless matrices (except for M0). Further...
Directory of Open Access Journals (Sweden)
Giuseppe Di Maio
2008-04-01
Full Text Available The subject of hyperspace topologies on closed or closed and compact subsets of a topological space X began in the early part of the last century with the discoveries of Hausdorff metric and Vietoris hit-and-miss topology. In course of time, several hyperspace topologies were discovered either for solving some problems in Applied or Pure Mathematics or as natural generalizations of the existing ones. Each hyperspace topology can be split into a lower and an upper part. In the upper part the original set inclusion of Vietoris was generalized to proximal set inclusion. Then the topologization of the Wijsman topology led to the upper Bombay topology which involves two proximities. In all these developments the lower topology, involving intersection of finitely many open sets, was generalized to locally finite families but intersection was left unchanged. Recently the authors studied symmetric proximal topology in which proximity was used for the first time in the lower part replacing intersection with its generalization: nearness. In this paper we use two proximities also in the lower part and we obtain the lower Bombay hypertopology. Consequently, a new hypertopology arises in a natural way: the symmetric Bombay topology which is the join of a lower and an upper Bombay topology.
The Symmetricity of Normal Modes in Symmetric Complexes
Song, Guang
2016-01-01
In this work, we look at the symmetry of normal modes in symmetric structures, particularly structures with cyclic symmetry. We show that normal modes of symmetric structures have different levels of symmetry, or symmetricity. One novel theoretical result of this work is that, for a ring structure with $m$ subunits, the symmetricity of the normal modes falls into $m$ groups of equal size, with normal modes in each group having the same symmetricity. The normal modes in each group can be computed separately, using a much smaller amount of memory and time (up to $m^3$ less), thus making it applicable to larger complexes. We show that normal modes with perfect symmetry or anti-symmetry have no degeneracy while the rest of the modes have a degeneracy of two. We show also how symmetry in normal modes correlates with symmetry in structure. While a broken symmetry in structure generally leads to a loss of symmetricity in symmetric normal modes, the symmetricity of some symmetric normal modes is preserved even when s...
Hollow waveguide cavity ringdown spectroscopy
Dreyer, Chris (Inventor); Mungas, Greg S. (Inventor)
2012-01-01
Laser light is confined in a hollow waveguide between two highly reflective mirrors. This waveguide cavity is used to conduct Cavity Ringdown Absorption Spectroscopy of loss mechanisms in the cavity including absorption or scattering by gases, liquid, solids, and/or optical elements.
RT-Symmetric Laplace Operators on Star Graphs: Real Spectrum and Self-Adjointness
Directory of Open Access Journals (Sweden)
Maria Astudillo
2015-01-01
Full Text Available How ideas of PT-symmetric quantum mechanics can be applied to quantum graphs is analyzed, in particular to the star graph. The class of rotationally symmetric vertex conditions is analyzed. It is shown that all such conditions can effectively be described by circulant matrices: real in the case of odd number of edges and complex having particular block structure in the even case. Spectral properties of the corresponding operators are discussed.
Actively coupled optical waveguides
Alexeeva, N. V.; Barashenkov, I. V.; Rayanov, K.; Flach, S.
2013-01-01
We consider light propagation through a pair of nonlinear optical waveguides with absorption, placed in a medium with power gain. The active medium boosts the in-phase component of the overlapping evanescent fields of the guides, while the nonlinearity of the guides couples it to the damped out-of-phase component creating a feedback loop. As a result, the structure exhibits stable stationary and oscillatory regimes in a wide range of gain-loss ratios. We show that the pair of actively-coupled...
Plane symmetric cosmological models
Yadav, Anil Kumar; Ray, Saibal; Mallick, A
2016-01-01
In this work, we perform the Lie symmetry analysis on the Einstein-Maxwell field equations in plane symmetric spacetime. Here Lie point symmetries and optimal system of one dimensional subalgebras are determined. The similarity reductions and exact solutions are obtained in connection to the evolution of universe. The present study deals with the electromagnetic energy of inhomogeneous universe where $F_{12}$ is the non-vanishing component of electromagnetic field tensor. To get a deterministic solution, it is assumed that the free gravitational field is Petrov type-II non-degenerate. The electromagnetic field tensor $F_{12}$ is found to be positive and increasing function of time. As a special case, to validate the solution set, we discuss some physical and geometric properties of a specific sub-model.
Institute of Scientific and Technical Information of China (English)
傅育熙
1998-01-01
An alternative presentation of the π－calculus is given.This version of the π-calculus is symmetric in the sense that communications are symmetric and there is no difference between input and output prefixes.The point of the symmetric π-calculus is that it has no abstract names.The set of closed names is therefore homogeneous.The π－calculus can be fully embedded into the symmetric π-calculus.The symmetry changes the emphasis of the communication mechanism of the π-calculus and opens up possibility for further variations.
Band gaps and cavity modes in dual phononic and photonic strip waveguides
Directory of Open Access Journals (Sweden)
Y. Pennec
2011-12-01
Full Text Available We discuss theoretically the simultaneous existence of phoxonic, i.e., dual phononic and photonic, band gaps in a periodic silicon strip waveguide. The unit-cell of this one-dimensional waveguide contains a hole in the middle and two symmetric stubs on the sides. Indeed, stubs and holes are respectively favorable for creating a phononic and a photonic band gap. Appropriate geometrical parameters allow us to obtain a complete phononic gap together with a photonic gap of a given polarization and symmetry. The insertion of a cavity inside the perfect structure provides simultaneous confinement of acoustic and optical waves suitable to enhance the phonon-photon interaction.
Near-field characterization of plasmonic waveguides
DEFF Research Database (Denmark)
Zenin, Volodymyr
2014-01-01
This PhD thesis presents investigation of plasmonic waveguides and waveguiding components by means of scanning near-field optical microscopy characterizations, far-field optical observations, and numerical simulations. The plasmonic waveguiding attracts huge interest due to several reasons: 1...... simply by changing geometric parameters of the waveguide, keeping in mind the trade-off between confinement and propagation losses. A broad variety of plasmonic waveguides and waveguide components, including antennas for coupling the light in/out of the waveguide, requires correspondent characterization...
Dupuis, Alexandre
In this thesis we have explored a wide variety of dielectric waveguides that rely on many different waveguiding mechanisms to guide THz (far-infrared) radiation. We have explored both theoretically and experimentally a large number of waveguide designs with the aim of reducing propagation and bending losses. The different waveguides can be classified into two fundamentally different strategies for reducing the propagation loss: small-core single-mode evanescent-field fibers or large hollow-core multi-mode tubes. Our focus was first set on exploring the small-core evanescent-field fiber strategy for reducing propagation losses. Following initial theoretical work in our group, much effort was spent on the fabrication and measurement of evanescent porous subwavelength diameter plastic fibers, in an attempt to further reduce the propagation losses. The fabrication of such fibers is a challenge and many novel techniques were devised to enable fiber drawing without hole collapse. The first method sealed the holes of an assembly of polymer tubes and lead to fibers of relatively low porosity (˜25% air within the core) due to reduction in hole size during fiber drawing. The second method was a novel sacrificial polymer technique whereby drawing a completely solid fiber prevented any hole collapse and the subsequent dissolution of the sacrificial polymer revealed the holes in the fiber. The third method was a combination of preform casting using glass molds and drawing with pressurized air within the holes. This led to fibers of record porosity (86% air). The measurement of these porous fibers began with a collaboration with a group from the university of Sherbrooke. At the time, the only available detector was a frequency integrating liquid-helium-cooled bolometer (powermeter). A novel directional coupler method for measuring the losses of subwavelength fibers was developed whereby an evanescent coupler is formed by bringing a probe fiber in proximity to the sample fiber
Representation of Fuzzy Symmetric Relations
1986-03-19
Std Z39-18 REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. Valverde Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda...REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. "Valverde* Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda. Diagonal, 649
Parallel Symmetric Eigenvalue Problem Solvers
2015-05-01
Plemmons G. Golub and A. Sameh. High-speed computing : scientific appli- cations and algorithm design. University of Illinois Press, Champaign, Illinois , 1988...16. SECURITY CLASSIFICATION OF: Sparse symmetric eigenvalue problems arise in many computational science and engineering applications such as...Eigenvalue Problem Solvers Report Title Sparse symmetric eigenvalue problems arise in many computational science and engineering applications such as
Propagation properties of a modified surface plasmonic waveguide with an arc slot
Institute of Scientific and Technical Information of China (English)
Xue Wen-Rui; Guo Ya-Nan; Zhang Wen-Mei
2009-01-01
We introduce a modified surface plasmonic waveguide with an arc slot. The dependences of distribution of energy flux density, effective index, propagation length and mode area of the symmetric mode supported by this waveguide on geometrical parameters and working wavelength are analysed by using the finite-difference frequency-domain (FDFD)method. Results show that the energy flux density distributes mainly in four corners which are formed by two arcs, and the closer to the corners it is, the stronger the energy flux density will be. The effective index, the propagation length and the mode area are influenced by geometrical parameters, including the width, the thickness and the arc radius of the surface plasmonic waveguide, as well as the working wavelength. It has been shown that the surface plasmonic waveguide with an arc slot has better propagation properties than the surface plasmonic waveguide with a straight slot.This work may be helpful for applying the slot surface plasmonic waveguide to integrated photonics.
Grating-Coupled Waveguide Cloaking
Institute of Scientific and Technical Information of China (English)
WANG Jia-Fu; QU Shao-Bo; XU Zhuo; MA Hua; WANG Cong-Min; XIA Song; WANG Xin-Hua; ZHOU Hang
2012-01-01
Based on the concept of a grating-coupled waveguide (GCW),a new strategy for realizing EM cloaking is presented.Using metallic grating,incident waves are firstly coupled into the effective waveguide and then decoupled into free space behind,enabling EM waves to pass around the obstacle.Phase compensation in the waveguide keeps the wave-front shape behind the obstacle unchanged.Circular,rectangular and triangular cloaks are presented to verify the robustness of the GCW cloaking.Electric field animations and radar cross section (RCS)comparisons convincingly demonstrate the cloaking effect.
Hollow waveguide for urology treatment
Jelínková, H.; Němec, M.; Koranda, P.; Pokorný, J.; Kőhler, O.; Drlík, P.; Miyagi, M.; Iwai, K.; Matsuura, Y.
2010-02-01
The aim of our work was the application of the special sealed hollow waveguide system for the urology treatment - In our experimental study we have compared the effects of Ho:YAG (wavelength 2100 nm) and Er:YAG (wavelength 2940 nm) laser radiation both on human urinary stones (or compressed plaster samples which serve as a model) fragmentation and soft ureter tissue incision in vitro. Cyclic Olefin Polymer - coated silver (COP/Ag) hollow glass waveguides with inner and outer diameters 700 and 850 μm, respectively, were used for the experiment. To prevent any liquid to diminish and stop the transmission, the waveguide termination was utilized.
Exceptional contours and band structure design in parity-time symmetric photonic crystals
Cerjan, Alexander; Fan, Shanhui
2016-01-01
We investigate the properties of multidimensional parity-time symmetric periodic systems whose non-Hermitian periodicity is an integer multiple of the underlying Hermitian system's periodicity. This creates a natural set of degeneracies which can undergo thresholdless $\\mathcal{PT}$ transitions. We derive a $\\mathbf{k} \\cdot \\mathbf{p}$ perturbation theory suited to the continuous eigenvalues of such systems in terms of the modes of the underlying Hermitian system. In photonic crystals, such thresholdless $\\mathcal{PT}$ transitions are shown to yield significant control over the band structure of the system, and can result in all-angle supercollimation, a $\\mathcal{PT}$-superprism effect, and unidirectional behavior.
Exceptional Contours and Band Structure Design in Parity-Time Symmetric Photonic Crystals.
Cerjan, Alexander; Raman, Aaswath; Fan, Shanhui
2016-05-20
We investigate the properties of two-dimensional parity-time symmetric periodic systems whose non-Hermitian periodicity is an integer multiple of the underlying Hermitian system's periodicity. This creates a natural set of degeneracies that can undergo thresholdless PT transitions. We derive a k·p perturbation theory suited to the continuous eigenvalues of such systems in terms of the modes of the underlying Hermitian system. In photonic crystals, such thresholdless PT transitions are shown to yield significant control over the band structure of the system, and can result in all-angle supercollimation, a PT-superprism effect, and unidirectional behavior.
Institute of Scientific and Technical Information of China (English)
冉茂武; 陈险峰; 曹庄琪
2011-01-01
Ultrahigh-order guide modes are excited by employing the free-space coupling technique in a symmetrical metal-cladding optical waveguide fabricated with a submillimeter-scale transparent PMN-PT ceramics. The voltage-dependent variation of the reflectivity of the light intensity is obtained according to the shift of the attenuated total reflection (ATR) resonance dip and the quadratic electro-optic coefficient of the transparent PMN-PT ceramics is then calculated.%以亚毫米尺度的铌镁酸铅-钛酸铅(PMN-PT)透明陶瓷片为导波层制备了对称金属包覆波导,并利用自由空间耦合技术激发了波导中的超高阶导模.根据衰减全反射(ATR)峰的移动,得到了在波导两侧所施加电压与光强反射率的关系,从而计算了PMN-PT透明陶瓷片的二次电光系数.
Complete power concentration into a single waveguide in large-scale waveguide array lenses.
Catrysse, Peter B; Liu, Victor; Fan, Shanhui
2014-10-16
Waveguide array lenses are waveguide arrays that focus light incident on all waveguides at the input side into a small number of waveguides at the output side. Ideal waveguide array lenses provide complete (100%) power concentration of incident light into a single waveguide. While of great interest for several applications, ideal waveguide array lenses have not been demonstrated for practical arrays with large numbers of waveguides. The only waveguide arrays that have sufficient degrees of freedom to allow for the design of an ideal waveguide array lens are those where both the propagation constants of the individual waveguides and the coupling constants between the waveguides vary as a function of space. Here, we use state-of-the-art numerical methods to demonstrate complete power transfer into a single waveguide for waveguide array lenses with large numbers of waveguides. We verify this capability for more than a thousand waveguides using a spatial coupled mode theory. We hereby extend the state-of-art by more than two orders of magnitude. We also demonstrate for the first time a physical design for an ideal waveguide array lens. The design is based on an aperiodic metallic waveguide array and focuses ~100% of the incident light into a deep-subwavelength focal spot.
Diamond nanobeam waveguide optomechanics
Khanaliloo, Behzad; Hryciw, Aaron C; Lake, David P; Kaviani, Hamidreza; Barclay, Paul E
2015-01-01
Optomechanical devices sensitively transduce and actuate motion of nanomechanical structures using light, and are central to many recent fundamental studies and technological advances. Single--crystal diamond promises to improve the performance of optomechanical devices, while also providing opportunities to interface nanomechanics with diamond color center spins and related quantum technologies. Here we demonstrate measurement of diamond nanobeam resonators with a sensitivity of 9.5 fm/Hz^0.5 and bandwidth >120 nm through dissipative waveguide--optomechanical coupling. Nanobeams are fabricated from bulk single--crystal diamond using a scalable quasi--isotropic oxygen plasma undercut etching process, and support mechanical resonances with quality factor of 2.5 x 10^5 at room temperature, and 7.2 x 10^5 in cryogenic conditions (5K). Mechanical self--oscillations, resulting from interplay between optomechanical coupling and the photothermal response of nanobeams in a buckled state, are observed with amplitude e...
Snyder, Allan W
1983-01-01
This text is intended to provide an in-depth, self-contained, treatment of optical waveguide theory. We have attempted to emphasize the underlying physical processes, stressing conceptual aspects, and have developed the mathematical analysis to parallel the physical intuition. We also provide comprehensive supplementary sections both to augment any deficiencies in mathematical background and to provide a self-consistent and rigorous mathematical approach. To assist in. understanding, each chapter con centrates principally on a single idea and is therefore comparatively short. Furthermore, over 150 problems with complete solutions are given to demonstrate applications of the theory. Accordingly, through simplicity of approach and numerous examples, this book is accessible to undergraduates. Many fundamental topics are presented here for the first time, but, more importantly, the material is brought together to give a unified treatment of basic ideas using the simplest approach possible. To achieve such a goa...
Slow Light in Metamaterial Waveguides
Lavoie, Benjamin R
2013-01-01
Metamaterials, which are materials engineered to possess novel optical properties, have been increasingly studied. The ability to fabricate metamaterials has sparked an interest in determining possible applications. We investigate using a metamaterial for boundary engineering in waveguides. A metamaterial-clad cylindrical waveguide is used to provide confinement for an optical signal, thereby increasing the local electromagnetic energy density. We show that metamaterial-clad waveguides have unique optical properties, including new modes, which we call hybrid modes. These modes have properties of both ordinary guided modes and surface plasmon-polariton modes. We show that for certain metamaterial parameters, the surface plasmon-polariton modes of a metamaterial-clad waveguide have less propagation loss than those of a metal-clad guide with the same permittivity. This low-loss mode is exploited for all-optical control of weak fields. Embedding three-level {\\Lambda} atoms in the dielectric core of a metamaterial...
Quantum mechanical description of waveguides
Institute of Scientific and Technical Information of China (English)
Wang Zhi-Yong; Xiong Cai-Dong; He Bing
2008-01-01
Applying the spinor representation of the electromagnetic field,this paper present a quantum-mechanical description of waveguides.As an example of application,a potential qubit generated by photon tunnelling is discussed.
Perfect imaging with geodesic waveguides
Miñano, Juan C.; Benítez, Pablo; González, Juan C.
2010-12-01
Transformation optics is used to prove that a spherical waveguide filled with an isotropic material with radial refractive index n=1/r has radially polarized modes (i.e. the electric field is only radial) with the same perfect focusing properties as the Maxwell fish-eye (MFE) lens. An approximate version of that device, comprising a thin waveguide with a homogeneous core, paves the way to experimentally attaining perfect imaging in the MFE lens.
Multiscaffold DNA Origami Nanoparticle Waveguides
2013-01-01
DNA origami templated self-assembly has shown its potential in creating rationally designed nanophotonic devices in a parallel and repeatable manner. In this investigation, we employ a multiscaffold DNA origami approach to fabricate linear waveguides of 10 nm diameter gold nanoparticles. This approach provides independent control over nanoparticle separation and spatial arrangement. The waveguides were characterized using atomic force microscopy and far-field polarization spectroscopy. This work provides a path toward large-scale plasmonic circuitry. PMID:23841957
Attenuation in Superconducting Circular Waveguides
Directory of Open Access Journals (Sweden)
K. H. Yeap
2016-09-01
Full Text Available We present an analysis on wave propagation in superconducting circular waveguides. In order to account for the presence of quasiparticles in the intragap states of a superconductor, we employ the characteristic equation derived from the extended Mattis-Bardeen theory to compute the values of the complex conductivity. To calculate the attenuation in a circular waveguide, the tangential fields at the boundary of the wall are first matched with the electrical properties (which includes the complex conductivity of the wall material. The matching of fields with the electrical properties results in a set of transcendental equations which is able to accurately describe the propagation constant of the fields. Our results show that although the attenuation in the superconducting waveguide above cutoff (but below the gap frequency is finite, it is considerably lower than that in a normal waveguide. Above the gap frequency, however, the attenuation in the superconducting waveguide increases sharply. The attenuation eventually surpasses that in a normal waveguide. As frequency increases above the gap frequency, Cooper pairs break into quasiparticles. Hence, we attribute the sharp rise in attenuation to the increase in random collision of the quasiparticles with the lattice structure.
Bulgakov, Evgeny; Pichugin, Konstantin; Sadreev, Almas
2013-10-01
We show that two nonlinear resonant cavities aligned between two parallel waveguides can support self-induced bound states in the continuum (BSCs). These BSCs are symmetrical relative to an inversion of the waveguides and to inversion of the transport axis. Due to this BSCs can drop an incident wave from one waveguide to another with very high efficiency. We show also that the frequency of the efficient channel dropping can be tuned by injecting power. All these results are in good agreement with numerical solutions of the Maxwell equations in a two-dimensional photonic crystal of GaAs rods holding two parallel waveguides and two defects made of a Kerr medium.
MINIMIZATION PROBLEM FOR SYMMETRIC ORTHOGONAL ANTI-SYMMETRIC MATRICES
Institute of Scientific and Technical Information of China (English)
Yuan Lei; Anping Liao; Lei Zhang
2007-01-01
By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution (X), which is both a least-squares symmetric orthogonal anti-symmetric solution of the matrix equation ATXA ＝ B and a best approximation to a given matrix X*.Moreover, a numerical algorithm for finding this optimal approximate solution is described in detail, and a numerical example is presented to show the validity of our algorithm.
Spaleniak, Izabela; Jovanovic, Nemanja; Williams, Robert J; Lawrence, Jon S; Ireland, Michael J; Withford, Michael J
2013-01-01
The first demonstration of narrowband spectral filtering of multimode light on a 3D integrated photonic chip using photonic lanterns and waveguide Bragg gratings is reported. The photonic lanterns with multi-notch waveguide Bragg gratings were fabricated using the femtosecond direct-write technique in boro-aluminosilicate glass (Corning, Eagle 2000). Transmission dips of up to 5 dB were measured in both photonic lanterns and reference single-mode waveguides with 10.4-mm-long gratings. The result demonstrates efficient and symmetrical performance of each of the gratings in the photonic lantern. Such devices will be beneficial to space-division multiplexed communication systems as well as for units for astronomical instrumentation for suppression of the atmospheric telluric emission from OH lines.
Development of Traveling Wave Actuators Using Waveguides of Different Geometrical Forms
Directory of Open Access Journals (Sweden)
Ramutis Bansevicius
2016-01-01
Full Text Available The paper covers the research and development of piezoelectric traveling wave actuators using different types of the waveguides. The introduced piezoelectric actuators can be characterized by specific areas of application, different resolution, and torque. All presented actuators are ultrasonic resonant devices and they were developed to increase amplitudes of the traveling wave oscillations of the contact surface. Three different waveguides are introduced, that is, symmetrical, asymmetrical, and cone type waveguide. A piezoelectric ring with the sectioned electrodes is used to excite traveling wave oscillations for all actuators. Operating principle, electrode pattern, and excitation regimes of piezoelectric actuators are described. A numerical modelling of the actuators was performed to validate the operating principle and to calculate trajectories of the contact points motion. Prototype actuators were made and experimental study was performed. The results of numerical and experimental analysis are discussed.
Metal-slotted hybrid optical waveguides for PCB-compatible optical interconnection.
Kim, Jin Tae; Ju, Jung Jin; Park, Suntak
2012-04-23
For development of electro-optical printed circuit board (PCB) systems, PCB-compatible metal-slotted hybrid optical waveguide was proposed and its optical characteristics are investigated at a wavelength of 1.31 μm. To confine light in a metallic multilayered structure, a metal film with a wide trench is inserted at the center of a dielectric medium that is sandwiched between metal films of infinite width. A circularly symmetric spot of the guided mode was measured at the center of the metal-slotted optical waveguide, which is a good agreement with the theoretical prediction by using the finite-element method. The measured propagation loss is about 1.5 dB/cm. Successful transmission of 2.5 Gbps optical signal without any distortion of the eye diagram confirms that the proposed hybrid optical waveguide holds a potential transmission line for the PCB-compatible optical interconnection.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zhengren, E-mail: zhrenzhang@126.com [School of Science, Chongqing Jiaotong University, Chongqing 400074 (China); Zhang, Liwei [School of Physics and Chemistry, Henan Polytechnic University, Jiaozuo 454000 (China); Yin, Pengfei; Han, Xiangyu [School of Science, Chongqing Jiaotong University, Chongqing 400074 (China)
2014-08-01
We investigate theoretically the generation process of coupled resonator-induced transparency (CRIT) in surface plasmon polariton gap waveguide system containing two side-coupled cavities, which locate at a symmetric position. The CRIT is original from the destructive interference of the two detuned cavities. In contrast with the existing electromagnetically induced transparency (EIT) schemes, the occurrence of the CRIT is caused by the two radiative cavities in waveguide, instead of interference between a dark cavity and radiative cavity. This behavior mimics the quantum interference between two direct excitation pathways in a three-level V-type atom. The transmission lineshape can be tuned between an EIT-like resonant peak and a Lorentzian-like resonant dip by tailoring the detuning of the two cavities. Moreover, we also find that the transparency peak moves to high frequency with a line shift and its Q factor decreases with the increase of coupling distance between the cavities and waveguide.
Controlling Single-Photon Transport along an Optical Waveguide by using a Three-Level Atom
Institute of Scientific and Technical Information of China (English)
TIAN Wei; CHEN Bin; XU Wei-Dong
2012-01-01
We theoretically investigate the single-photon transport properties in an optical waveguide embedded with a V-type three-level atom (VTLA) based on symmetric and asymmetric couplings between the photon and the VTLA.Our numerical results show that the transmission spectrum of the incident photon can be well controlled by virtue of both symmetric and asymmetric coupling interactions.A multifrequency photon attenuator is realized by controlling the asymmetric coupling interactions.Furthermore,the influences of dissipation of the VTLA for the realistic physical system on single-photon transport properties are also analyzed.
Controllable scattering of photons in a one-dimensional resonator waveguide
Sun, C. P.; Zhou, L.; Gong, Z. R.; Liu, Y. X.; Nori, F.
2009-03-01
We analyze the coherent transport of a single photon, which propagates in a one-dimensional coupled-resonator waveguide and is scattered by a controllable two-level system located inside one of the resonators of this waveguide. Our approach, which uses discrete coordinates, unifies low and high energy effective theories for single-photon scattering. We show that the controllable two-level system can behave as a quantum switch for the coherent transport of a single photon. This study may inspire new electro-optical single-photon quantum devices. We also suggest an experimental setup based on superconducting transmission line resonators and qubits. [4pt] L. Zhou, Z.R. Gong, Y.X. Liu, C.P. Sun, F. Nori, Controllable scattering of photons in a 1D resonator waveguide, Phys. Rev. Lett. 101, 100501 (2008). URL: http://link.aps.org/abstract/PRL/v101/e100501
Cascaded-focus laser writing of low-loss waveguides in polymers.
Pätzold, Welm M; Reinhardt, Carsten; Demircan, Ayhan; Morgner, Uwe
2016-03-15
Waveguide writing in poly (methyl methacrylate) (PMMA) with femtosecond laser radiation is presented. An adequate refractive index change is induced in the border area below the irradiated focal volume. It supports an almost symmetric fundamental mode with propagation losses down to 0.5 dB/cm, the lowest losses observed so far in this class of materials. The writing process with a cascaded focus is demonstrated to be highly reliable over a large parameter range.
Vawter, G. Allen
2008-02-26
A self-electrooptic effect device ("SEED") is integrated with waveguide interconnects through the use of vertical directional couplers. Light initially propagating in the interconnect waveguide is vertically coupled to the active waveguide layer of the SEED and, if the SEED is in the transparent state, the light is coupled back to the interconnect waveguide.
Miniaturized Waveguide Fourier Transform Spectrometer Project
National Aeronautics and Space Administration — To characterize the IR optical properties of the metal-coated hollow waveguide ensemble; configure the Hollow Waveguide FTS (HWFTS) chip in such a way that we...
Writing Waveguide in LN With fs Laser
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
We investigated the waveguide formation in Lithium Niobate with Femtosecond laser pulse writing directly. The output optical field through waveguide has been observed and refractive-index change was characterized by using grating method.
Antiferromagentic resonance detected by direct current voltages in MnF{sub 2}/Pt bilayers
Energy Technology Data Exchange (ETDEWEB)
Ross, Philipp, E-mail: philipp.ross.13@ucl.ac.uk [Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Garching (Germany); Schreier, Michael, E-mail: michael.schreier@wmi.badw.de; Lotze, Johannes [Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Garching (Germany); Physik-Department, Technische Universität München, Garching (Germany); Huebl, Hans; Goennenwein, Sebastian T. B. [Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Garching (Germany); Nanosystems Initiative Munich, Munich (Germany); Gross, Rudolf [Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Garching (Germany); Physik-Department, Technische Universität München, Garching (Germany); Nanosystems Initiative Munich, Munich (Germany)
2015-12-21
We performed coplanar waveguide-based broadband ferromagnetic resonance experiments on the antiferromagnetic insulator MnF{sub 2}, while simultaneously recording the DC voltage arising in a thin platinum film deposited onto the MnF{sub 2}. The antiferromagnetic resonance is clearly reflected in both the transmission through the waveguide as well as the DC voltage in the Pt strip. The DC voltage remains largely unaffected by field reversal and thus presumably stems from microwave rectification and/or heating effects. However, we identify a small magnetic field orientation dependent contribution, compatible with antiferromagnetic spin pumping theory.
Loop coupled resonator optical waveguides.
Song, Junfeng; Luo, Lian-Wee; Luo, Xianshu; Zhou, Haifeng; Tu, Xiaoguang; Jia, Lianxi; Fang, Qing; Lo, Guo-Qiang
2014-10-06
We propose a novel coupled resonator optical waveguide (CROW) structure that is made up of a waveguide loop. We theoretically investigate the forbidden band and conduction band conditions in an infinite periodic lattice. We also discuss the reflection- and transmission- spectra, group delay in finite periodic structures. Light has a larger group delay at the band edge in a periodic structure. The flat band pass filter and flat-top group delay can be realized in a non-periodic structure. Scattering matrix method is used to calculate the effects of waveguide loss on the optical characteristics of these structures. We also introduce a tunable coupling loop waveguide to compensate for the fabrication variations since the coupling coefficient of the directional coupler in the loop waveguide is a critical factor in determining the characteristics of a loop CROW. The loop CROW structure is suitable for a wide range of applications such as band pass filters, high Q microcavity, and optical buffers and so on.
Pseudo-Hermitian Systems with PT-Symmetry: Degeneracy and Krein Space
Choutri, B.; Cherbal, O.; Ighezou, F. Z.; Drir, M.
2017-02-01
We show in the present paper that pseudo-Hermitian Hamiltonian systems with even PT-symmetry (P2=1,T2=1) admit a degeneracy structure. This kind of degeneracy is expected traditionally in the odd PT-symmetric systems (P2=1,T2=-1) which is appropriate to the fermions (Scolarici and Solombrino, Phys. Lett. A 303, 239 2002; Jones-Smith and Mathur, Phys. Rev. A 82, 042101 2010). We establish that the pseudo-Hermitian Hamiltonians with even PT-symmetry admit a degeneracy structure if the operator PT anticommutes with the metric operator η σ which is necessarily indefinite. We also show that the Krein space formulation of the Hilbert space is the convenient framework for the implementation of unbroken PT-symmetry. These general results are illustrated with great details for four-level pseudo-Hermitian Hamiltonian with even PT -symmetry.
Longitudinal Modes along Thin Piezoelectric Waveguides for Liquid Sensing Applications
Directory of Open Access Journals (Sweden)
Cinzia Caliendo
2015-06-01
Full Text Available The propagation of longitudinally polarized acoustic modes along thin piezoelectric plates (BN, ZnO, InN, AlN and GaN is theoretically studied, aiming at the design of high frequency electroacoustic devices suitable for work in liquid environments. The investigation of the acoustic field profile across the plate revealed the presence of longitudinally polarized Lamb modes, travelling at velocities close to that of the longitudinal bulk acoustic wave propagating in the same direction. Such waves are suitable for the implementation of high-frequency, low-loss electroacoustic devices operating in liquid environments. The time-averaged power flow density, the phase velocity and the electroacoustic coupling coefficient K2 dispersion curves were studied, for the first (S0 and four higher order (S1, S2, S3, S4 symmetrical modes for different electrical boundary conditions. Two electroacoustic coupling configurations were investigated, based on interdigitated transducers, with or without a metal floating electrode at the opposite plate surface. Enhanced performances, such as a K2 as high as 8.5% and a phase velocity as high as 16,700 m/s, were demostrated for the ZnO- and BN-based waveguides, as an example. The relative velocity changes, and the inertial and viscous sensitivities of the first symmetric and anti-symmetric mode, S0 and A0, propagating along thin plates bordered by a viscous liquid were derived using the perturbation approach. The present study highlights the feasibility of the piezoelectric waveguides to the development of high-frequency, integrated-circuits compatible electroacoustic devices suitable for working in liquid environment.
Buried ion-exchanged glass waveguides: burial-depth dependence on waveguide width.
Madasamy, P; West, B R; Morrell, M M; Geraghty, D F; Honkanen, S; Peyghambarian, N
2003-07-01
A detailed theoretical and experimental study of the depth dependence of buried ion-exchanged waveguides on waveguide width is reported. Modeling, which includes the effect of nonhomogeneous time-dependent electric field distribution, agrees well with our experiments showing that burial depth increases linearly with waveguide width. These results may be used in the proper design of integrated optical circuits that need waveguides of different widths at different sections, such as arrayed waveguide gratings.
Jet quenching and high-pt azimuthal asymmetry
Lokhtin, Igor P; Vitev, I
2002-01-01
The azimuthal anisotropy of high-pt particle production in non-central heavy ion collisions is among the most promising observables of partonic energy loss in an azimuthally non-symmetric volume of quark-gluon plasma. We discuss the implications of nuclear geometry for the models of partonic energy loss in the context of recent RHIC data and consequences for observation of jet quenching at the LHC.
Plasmonic waveguides cladded by hyperbolic metamaterials
DEFF Research Database (Denmark)
Ishii, Satoshi; Shalaginov, Mikhail Y.; Babicheva, Viktoriia E.
2014-01-01
Strongly anisotropic media with hyperbolic dispersion can be used for claddings of plasmonic waveguides (PWs). In order to analyze the fundamental properties of such waveguides, we analytically study 1D waveguides arranged from a hyperbolic metamaterial (HMM) in a HMM-Insulator-HMM (HIH) structure...
Graphene nano-ribbon waveguides
He, S; He, Y
2013-01-01
Graphene as a one-atom-thick platform for infrared metamaterial plays an important role in optical science and engineering. Here we study the unique properties of some plasmonic waveguides based on graphene nano-ribbon. It is found that a graphene ribbon of finite width leads to the occurrence of coupled edge mode. The single-mode region of a single freestanding graphene ribbon is identified at a fixed frequency of 30 THz. A low-loss waveguide structure, consisting of a graphene layer, a silica buffer layer and silicon substrate is proposed to reduce the propagation loss and obtain a high figure of merit for future integration of waveguide devices. Furthermore, two coupled ribbon configurations, namely, side-side coupling and top-bottom coupling, are investigated. As a device example, a nano-ring cavity of ultra-small size is designed.
TSUNAMI WAVE PROPAGATION ALONG WAVEGUIDES
Directory of Open Access Journals (Sweden)
Andrei G. Marchuk
2009-01-01
Full Text Available This is a study of tsunami wave propagation along the waveguide on a bottom ridge with flat sloping sides, using the wave rays method. During propagation along such waveguide the single tsunami wave transforms into a wave train. The expression for the guiding velocities of the fastest and slowest signals is defined. The tsunami wave behavior above the ocean bottom ridges, which have various model profiles, is investigated numerically with the help of finite difference method. Results of numerical experiments show that the highest waves are detected above a ridge with flat sloping sides. Examples of tsunami propagation along bottom ridges of the Pacific Ocean are presented.
Particle-vortex symmetric liquid
Mulligan, Michael
2016-01-01
We introduce an effective theory with manifest particle-vortex symmetry for disordered thin films undergoing a magnetic field-tuned superconductor-insulator transition. The theory may enable one to access both the critical properties of the strong-disorder limit, which has recently been confirmed [Breznay et al., PNAS 113, 280 (2016)] to exhibit particle-vortex symmetric electrical response, and the metallic phase discovered earlier [Mason and Kapitulnik, Phys. Rev. Lett. 82, 5341 (1999)] in less disordered samples. Within the effective theory, the Cooper-pair and field-induced vortex degrees of freedom are simultaneously incorporated into an electrically-neutral Dirac fermion minimally coupled to an (emergent) Chern-Simons gauge field. A derivation of the theory follows upon mapping the superconductor-insulator transition to the integer quantum Hall plateau transition and the subsequent use of Son's particle-hole symmetric composite Fermi liquid. Remarkably, particle-vortex symmetric response does not requir...
Harmonic analysis on symmetric spaces
Terras, Audrey
This text explores the geometry and analysis of higher rank analogues of the symmetric spaces introduced in volume one. To illuminate both the parallels and differences of the higher rank theory, the space of positive matrices is treated in a manner mirroring that of the upper-half space in volume one. This concrete example furnishes motivation for the general theory of noncompact symmetric spaces, which is outlined in the final chapter. The book emphasizes motivation and comprehensibility, concrete examples and explicit computations (by pen and paper, and by computer), history, and, above all, applications in mathematics, statistics, physics, and engineering. The second edition includes new sections on Donald St. P. Richards’s central limit theorem for O(n)-invariant random variables on the symmetric space of GL(n, R), on random matrix theory, and on advances in the theory of automorphic forms on arithmetic groups.
Two-Dimentional Photonic Crystal Waveguides
DEFF Research Database (Denmark)
Søndergaard, Thomas; Dridi, Kim
1999-01-01
possible a novel class of optical microcavities, whereas line defects make possible a novel class of waveguides. In this paper we will analyze two-dimensional photonic crystal waveguides based on photonic crystals with rods arranged on a triangular and a square lattice using a plane-wave expansion method...... and a finite-difference-time-domain (FDTD) method. Design parameters, i.e. dielectric constants, rod diameter and waveguide width, where these waveguides are single-moded and multi-moded will be given. We will also show our recent results regarding the energy-flow (the Poynting vector) in these waveguides...
Quantum Electrodynamics in Photonic Crystal Waveguides
DEFF Research Database (Denmark)
Nielsen, Henri Thyrrestrup
In this thesis we have performed quantum electrodynamics (QED) experiments in photonic crystal (PhC) waveguides and cavity QED in the Anderson localized regime in disordered PhC waveguides. Decay rate measurements of quantum dots embedded in PhC waveguides has been used to map out the variations...... probability. The Q-factor distributions of Anderson localized modes have been measured in PhC waveguides with articial induced disorder with embedded emitters. The largest Q-factors are found in the sample with the smallest amount of disorder. From a comparison with the waveguide model the localization length...
Plasmonic waveguides with hyperbolic multilayer cladding
Babicheva, Viktoriia E; Ishii, Satoshi; Boltasseva, Alexandra; Kildishev, Alexander V
2014-01-01
Engineering plasmonic metamaterials with anisotropic optical dispersion enables us to tailor the properties of metamaterial-based waveguides. We investigate plasmonic waveguides with dielectric cores and multilayer metal-dielectric claddings with hyperbolic dispersion. Without using any homogenization, we calculate the resonant eigenmodes of the finite-width cladding layers, and find agreement with the resonant features in the dispersion of the cladded waveguides. We show that at the resonant widths, the propagating modes of the waveguides are coupled to the cladding eigenmodes and hence, are strongly absorbed. By avoiding the resonant widths in the design of the actual waveguides, the strong absorption can be eliminated.
Symmetric autocompensating quantum key distribution
Walton, Zachary D.; Sergienko, Alexander V.; Levitin, Lev B.; Saleh, Bahaa E. A.; Teich, Malvin C.
2004-08-01
We present quantum key distribution schemes which are autocompensating (require no alignment) and symmetric (Alice and Bob receive photons from a central source) for both polarization and time-bin qubits. The primary benefit of the symmetric configuration is that both Alice and Bob may have passive setups (neither Alice nor Bob is required to make active changes for each run of the protocol). We show that both the polarization and the time-bin schemes may be implemented with existing technology. The new schemes are related to previously described schemes by the concept of advanced waves.
The Theory for the Dielectric Slab Waveguide with Complex Refractive Index Applied to GaAs Lasers
DEFF Research Database (Denmark)
Buus, Jens
1977-01-01
In this paper we investigate the homogeneous dielectric slab waveguide in the case of complex dielectric constants. A method for calculating the field distribution in a dielectric waveguide with an arbitrary symmetrical variation in the refractive index is developed, and some of the results...... are presented. The results are applied to the GaAs laser. It is fonud that the guiding mechanism is a combination of gain guiding and index antiguiding. Based on the calculations an explanation of the kinks on the light current characteristics is suggested....
Chen, Zhiquan; Li, Hongjian; He, Zhihui; Xu, Hui; Zheng, Mingfei; Zhao, Mingzhuo
2017-09-01
We numerically and theoretically investigate multiple plasmon-induced transparency (PIT) effects in a multimode-cavity-coupled metal-dielectric-metal (MDM) waveguide system. The introduced multimode coupled-radiating oscillator theory (MC-ROT) gives a clear understanding of multiple PIT effects in the proposed system. Two and three PIT peaks appear in the transmission spectra corresponding to the symmetrical and asymmetrical structures, respectively. Evolution of the PIT peaks can be effectively tuned by adjusting the geometric dimensions and asymmetry of the structure. The ultra-compact plasmonic waveguide structure may have important applications for multichannel filters, optical switches, and other devices in integrated optical circuits.
Compact on-Chip Temperature Sensors Based on Dielectric-Loaded Plasmonic Waveguide-Ring Resonators
Directory of Open Access Journals (Sweden)
Sergey I. Bozhevolnyi
2011-02-01
Full Text Available The application of a waveguide-ring resonator based on dielectric-loaded surface plasmon-polariton waveguides as a temperature sensor is demonstrated in this paper and the influence of temperature change to the transmission through the waveguide-ring resonator system is comprehensively analyzed. The results show that the roundtrip phase change in the ring resonator due to the temperature change is the major reason for the transmission variation. The performance of the temperature sensor is also discussed and it is shown that for a waveguide-ring resonator with the resonator radius around 5 mm and waveguide-ring gap of 500 nm which gives a footprint around 140 µm2, the temperature sensitivity at the order of 10−2 K can be achieved with the input power of 100 mW within the measurement sensitivity limit of a practical optical detector.
Plasmonic Antennas Hybridized with Dielectric Waveguides
Arango, Felipe Bernal; Koenderink, A Femius
2013-01-01
For the purpose of using plasmonics in an integrated scheme where single emitters can be probed efficiently, we experimentally and theoretically study the scattering properties of single nano-rod gold antennas as well as antenna arrays placed on one-dimensional dielectric silicon nitride waveguides. Using real space and Fourier microscopy correlated with waveguide transmission measurements, we quantify the spectral properties, absolute strength and directivity of scattering. The scattering processes can be well understood in the framework of the physics of dipolar objects placed on a planar layered environment with a waveguiding layer. We use the single plasmonic structures on top of the waveguide as dipolar building blocks for new types of antennas where the waveguide enhances the coupling between antenna elements. We report on waveguide hybridized Yagi-Uda antennas which show directionality in out-coupling of guided modes as well as directionality for in-coupling into the waveguide of localized excitations ...
Optical Slot-Waveguide Based Biochemical Sensors
Directory of Open Access Journals (Sweden)
Carlos Angulo Barrios
2009-06-01
Full Text Available Slot-waveguides allow light to be guided and strongly confined inside a nanometer-scale region of low refractive index. Thus stronger light-analyte interaction can be obtained as compared to that achievable by a conventional waveguide, in which the propagating beam is confined to the high-refractive-index core of the waveguide. In addition, slot-waveguides can be fabricated by employing CMOS compatible materials and technology, enabling miniaturization, integration with electronic, photonic and fluidic components in a chip, and mass production. These advantages have made the use of slot-waveguides for highly sensitive biochemical optical integrated sensors an emerging field. In this paper, recent achievements in slot-waveguide based biochemical sensing will be reviewed. These include slot-waveguide ring resonator based refractometric label-free biosensors, label-based optical sensing, and nano-opto-mechanical sensors.
Homogenization analysis of complementary waveguide metamaterials
Landy, Nathan; Hunt, John; Smith, David R.
2013-11-01
We analyze the properties of complementary metamaterials as effective inclusions patterned into the conducting walls of metal waveguide structures. We show that guided wave metamaterials can be homogenized using the same retrieval techniques used for volumetric metamaterials, leading to a description in which a given complementary element is conceptually replaced by a block of material within the waveguide whose effective permittivity and permeability result in equivalent scattering characteristics. The use of effective constitutive parameters for waveguide materials provides an alternative point-of-view for the design of waveguide and microstrip based components, including planar lenses and filters, as well as devices with derived from a bulk material response. In addition to imparting effective constitutive properties to the waveguide, complementary metamaterials also couple energy from waveguide modes into radiation. Thus, complementary waveguide metamaterials can be used to modify and optimize a variety of antenna structures.
Quantum waveguides with corners
Directory of Open Access Journals (Sweden)
Raymond Nicolas
2012-04-01
Full Text Available The simplest modeling of planar quantum waveguides is the Dirichlet eigenproblem for the Laplace operator in unbounded open sets which are uniformly thin in one direction. Here we consider V-shaped guides. Their spectral properties depend essentially on a sole parameter, the opening of the V. The free energy band is a semi-infinite interval bounded from below. As soon as the V is not flat, there are bound states below the free energy band. There are a finite number of them, depending on the opening. This number tends to infinity as the opening tends to 0 (sharply bent V. In this situation, the eigenfunctions concentrate and become self-similar. In contrast, when the opening gets large (almost flat V, the eigenfunctions spread and enjoy a different self-similar structure. We explain all these facts and illustrate them by numerical simulations. La modélisation la plus simple des guides d’ondes quantiques plans est le problème aux valeurs propres pour le laplacien dans des ouverts non bornés qui sont fins dans une direction. Ici nous considérons des guides en forme de V. Leurs propriétés spectrales dépendent essentiellement d’un seul paramètre, l’ouverture du V. La bande d’énergie libre est un intervalle semi-infini borné inférieurement. Dès que le V n’est pas plat, il existe des états liés sous la bande d’énergie libre. Ils sont en nombre fini, fonction de l’ouverture. Ce nombre tend vers l’infini quand l’ouverture tend vers 0 (V très refermé. Dans cette situation, les fonctions propres se concentrent et deviennent auto-similaires. À l’opposé, quand l’ouverture est grande (V très aplati, les fonctions propres s’étalent et jouissent d’une autre structure auto-similaire. Nous expliquons tous ces résultats et les illustrons par des expériences numériques.
Optical waveguides in laser crystals
Pollnau, Markus; Romanyuk, Yaroslav E.
2007-01-01
This article reviews the recent research on different types of planar and channel crystalline optical waveguides, fabrication methods such as liquid phase epitaxy, pulsed laser deposition, thermal bonding, reactive ion or ion beam etching, wet chemical etching, ion in-diffusion, proton exchange, ion
Glass Waveguides for Periodic Poling
DEFF Research Database (Denmark)
Fage-Pedersen, Jacob; Jacobsen, Rune Shim; Kristensen, Martin
2005-01-01
Planar silica-based waveguide devices have been developed for second-harmonic generation by poling with periodic electrodes. We show that detrimental charge transport can occur along interfaces, but with proper choice of fabrication, high-quality devices are obtained....
Dielectric waveguide amplifiers and lasers
Pollnau, Markus
The performance of semiconductor amplifiers and lasers has made them the preferred choice for optical gain on a micro-chip. In the past few years, we have demonstrated that also rare-earth-ion-doped dielectric waveguides show remarkable performance, ranging from a small-signal gain per unit length
Glass Waveguides for Periodic Poling
DEFF Research Database (Denmark)
Fage-Pedersen, Jacob; Jacobsen, Rune Shim; Kristensen, Martin
2005-01-01
Planar silica-based waveguide devices have been developed for second-harmonic generation by poling with periodic electrodes. We show that detrimental charge transport can occur along interfaces, but with proper choice of fabrication, high-quality devices are obtained....
Photonic-crystal waveguide biosensor
DEFF Research Database (Denmark)
Skivesen, Nina; Têtu, Amélie; Kristensen, Martin
2007-01-01
A photonic-crystal waveguide sensor is presented for biosensing. The sensor is applied for refractive index measurements and detection of protein-concentrations. Concentrations around 10 μg/ml (0.15μMolar) are measured with excellent signal to noise ratio, and a broad, dynamic refractive index se...
Coupled-resonator optical waveguides
DEFF Research Database (Denmark)
Raza, Søren; Grgic, Jure; Pedersen, Jesper Goor
2010-01-01
Coupled-resonator optical waveguides hold potential for slow-light propagation of optical pulses. The dispersion properties may adequately be analyzed within the framework of coupled-mode theory. We extend the standard coupled-mode theory for such structures to also include complex-valued paramet...
Parabolic tapers for overmoded waveguides
Doane, J.L.
1983-11-25
A waveguide taper with a parabolic profile, in which the distance along the taper axis varies as the square of the tapered dimension, provides less mode conversion than equal length linear tapers and is easier to fabricate than other non-linear tapers.
Axially Symmetric, Spatially Homothetic Spacetimes
Wagh, S M; Wagh, Sanjay M.; Govinder, Keshlan S.
2002-01-01
We show that the existence of appropriate spatial homothetic Killing vectors is directly related to the separability of the metric functions for axially symmetric spacetimes. The density profile for such spacetimes is (spatially) arbitrary and admits any equation of state for the matter in the spacetime. When used for studying axisymmetric gravitational collapse, such solutions do not result in a locally naked singularity.
Shearfree Spherically Symmetric Fluid Models
Sharif, M
2013-01-01
We try to find some exact analytical models of spherically symmetric spacetime of collapsing fluid under shearfree condition. We consider two types of solutions: one is to impose a condition on the mass function while the other is to restrict the pressure. We obtain totally of five exact models, and some of them satisfy the Darmois conditions.
Particle-vortex symmetric liquid
Mulligan, Michael
2017-01-01
We introduce an effective theory with manifest particle-vortex symmetry for disordered thin films undergoing a magnetic field-tuned superconductor-insulator transition. The theory may enable one to access both the critical properties of the strong-disorder limit, which has recently been confirmed by Breznay et al. [Proc. Natl. Acad. Sci. USA 113, 280 (2016), 10.1073/pnas.1522435113] to exhibit particle-vortex symmetric electrical response, and the nearby metallic phase discovered earlier by Mason and Kapitulnik [Phys. Rev. Lett. 82, 5341 (1999), 10.1103/PhysRevLett.82.5341] in less disordered samples. Within the effective theory, the Cooper-pair and field-induced vortex degrees of freedom are simultaneously incorporated into an electrically neutral Dirac fermion minimally coupled to a (emergent) Chern-Simons gauge field. A derivation of the theory follows upon mapping the superconductor-insulator transition to the integer quantum Hall plateau transition and the subsequent use of Son's particle-hole symmetric composite Fermi liquid. Remarkably, particle-vortex symmetric response does not require the introduction of disorder; rather, it results when the Dirac fermions exhibit vanishing Hall effect. The theory predicts approximately equal (diagonal) thermopower and Nernst signal with a deviation parameterized by the measured electrical Hall response at the symmetric point.
Symmetric relations of finite negativity
Kaltenbaeck, M.; Winkler, H.; Woracek, H.; Forster, KH; Jonas, P; Langer, H
2006-01-01
We construct and investigate a space which is related to a symmetric linear relation S of finite negativity on an almost Pontryagin space. This space is the indefinite generalization of the completion of dom S with respect to (S.,.) for a strictly positive S on a Hilbert space.
Vassiliev Invariants from Symmetric Spaces
DEFF Research Database (Denmark)
Biswas, Indranil; Gammelgaard, Niels Leth
We construct a natural framed weight system on chord diagrams from the curvature tensor of any pseudo-Riemannian symmetric space. These weight systems are of Lie algebra type and realized by the action of the holonomy Lie algebra on a tangent space. Among the Lie algebra weight systems, they are ......, they are exactly characterized by having the symmetries of the Riemann curvature tensor....
Thermophoresis of Axially Symmetric Bodies
2007-11-02
Sweden Abstract. Thermophoresis of axially symmetric bodies is investigated to first order in the Knudsen-mimber, Kn. The study is made in the limit...derived. Asymptotic solutions are studied. INTRODUCTION Thermophoresis as a phenomenon has been known for a long time, and several authors have approached
Axiomatizations of symmetrically weighted solutions
Kleppe, John; Reijnierse, Hans; Sudhölter, P.
2013-01-01
If the excesses of the coalitions in a transferable utility game are weighted, then we show that the arising weighted modifications of the well-known (pre)nucleolus and (pre)kernel satisfy the equal treatment property if and only if the weight system is symmetric in the sense that the weight of a su
Computationally Efficient Searchable Symmetric Encryption
Liesdonk, van Peter; Sedghi, Saeed; Doumen, Jeroen; Hartel, Pieter; Jonker, Willem; Jonker, Willem; Petkovic, Milan
2010-01-01
Searchable encryption is a technique that allows a client to store documents on a server in encrypted form. Stored documents can be retrieved selectively while revealing as little information as possible to the server. In the symmetric searchable encryption domain, the storage and the retrieval are
Symmetrical progressive erythro-keratoderma
Directory of Open Access Journals (Sweden)
Sunil Gupta
1999-01-01
Full Text Available A 13-year-old male child had gradually progressive, bilaterall, symmetrical, erythematous hyperkeratotic plaques over knees, elbows, natal cleft, dorsa of hands and feet with palmoplantar keratoderma. High arched palate, fissured tongue and sternal depression (pectus-excavatum were unusual associations.
A Directly-Written Monolithic Waveguide-Laser Incorporating a DFB Waveguide-Bragg Grating
Marshall, Graham D; Ams, Martin; Piper, James A; Withford, Michael J
2008-01-01
We report the fabrication and performance of the first C-band directly-written monolithic waveguide-laser. The waveguide-laser device was created in an Erbium and Ytterbium doped phosphate glass host and consisted of an optical waveguide that included a distributed feedback Bragg grating structure. The femtosecond laser direct-write technique was used to create both the waveguide and the waveguide-Bragg grating simultaneously and in a single processing step. The waveguide-laser was optically pumped at approximately 980 nm and lased at 1537nm with a bandwidth of less than 4 pm.
Understanding symmetrical components for power system modeling
Das, J C
2017-01-01
This book utilizes symmetrical components for analyzing unbalanced three-phase electrical systems, by applying single-phase analysis tools. The author covers two approaches for studying symmetrical components; the physical approach, avoiding many mathematical matrix algebra equations, and a mathematical approach, using matrix theory. Divided into seven sections, topics include: symmetrical components using matrix methods, fundamental concepts of symmetrical components, symmetrical components –transmission lines and cables, sequence components of rotating equipment and static load, three-phase models of transformers and conductors, unsymmetrical fault calculations, and some limitations of symmetrical components.
Ion-exchanged glass waveguides with low birefringence for a broad range of waveguide widths.
Yliniemi, Sanna; West, Brian R; Honkanen, Seppo
2005-06-01
Optical communications networks require integrated photonic components with negligible polarization dependence, which typically means that the waveguides must feature very low birefringence. Recent studies have shown that waveguides with low birefringence can be obtained, e.g., by use of silica-on-silicon waveguides or buried ion-exchanged glass waveguides. However, many integrated photonic circuits consist of waveguides with varying widths. Therefore low birefringence is consequently required for waveguides having different widths. This is a difficult task for most waveguide fabrication technologies. We present experimental results on waveguide birefringence for buried silver-sodium ion-exchanged glass waveguides. We show that the waveguide birefringence of the order of 10(-6) for waveguide mask opening widths ranging from 2 to 10 microm can be obtained by postprocessing the sample through annealing at an elevated temperature. The measured values are in agreement with the values calculated with our modeling software for ion-exchanged glass waveguides. This unique feature of ion-exchanged waveguides may be of significant importance in a wide variety of integrated photonic circuits requiring polarization-independent operation.
Electromagnetic Scattering at the Waveguide Step between Equilateral Triangular Waveguides
Directory of Open Access Journals (Sweden)
Ana Morán-López
2016-01-01
Full Text Available The analysis of the electromagnetic scattering at discontinuities between equilateral triangular waveguides is studied. The complete electromagnetic solution is derived using analytical closed form expressions for the mode spectrum of the equilateral waveguide. The mathematical formulation of the electromagnetic scattering problem is based on the quasi-analytical Mode-Matching method. This method benefits from the electromagnetic field division into symmetries as well as from the plane wave formulation presented for the expressions involved. The unification of the surface integrals used in the method thanks to the plane wave formulation is revealed, leading to expressions that are very well suited for its implementation in an electromagnetic analysis and design code. The obtained results for some cases of interest (building blocks for microwave components for communication systems are verified using other numerical methods included in a commercial software package, showing the potential of the presented approach based on quasi-analytic expressions.
Invariant currents in lossy acoustic waveguides with complete local symmetry
Kalozoumis, P A; Diakonos, F K; Theocharis, G; Schmelcher, P
2015-01-01
We implement the concept of complete local symmetry in lossy acoustic waveguides. Despite the presence of losses, the existence of a spatially invariant current is shown theoretically and observed experimentally. We demonstrate how this invariant current leads to the generalization of the Bloch and parity theorems for lossy systems defining a mapping of the pressure field between symmetry related spatial domains. Using experimental data we verify this mapping with remarkable accuracy. For the performed experiment we employ a construction technique based on local symmetries which allows the design of setups with prescribed perfect transmission resonances in the lossless case. Our results reveal the fundamental role of symmetries in restricted spatial domains and clearly indicate that completely locally symmetric devices constitute a promising class of setups, regarding the manipulation of wave propagation.
The antipodal sets of compact symmetric spaces
National Research Council Canada - National Science Library
Liu, Xingda; Deng, Shaoqiang
2014-01-01
We study the antipodal set of a point in a compact Riemannian symmetric space. It turns out that we can give an explicit description of the antipodal set of a point in any connected simply connected compact Riemannian symmetric space...
Symmetric normalisation for intuitionistic logic
DEFF Research Database (Denmark)
Guenot, Nicolas; Straßburger, Lutz
2014-01-01
, but using a non-local rewriting. The second system is the symmetric completion of the first, as normally given in deep inference for logics with a DeMorgan duality: all inference rules have duals, as cut is dual to the identity axiom. We prove a generalisation of cut elimination, that we call symmetric...... normalisation, where all rules dual to standard ones are permuted up in the derivation. The result is a decomposition theorem having cut elimination and interpolation as corollaries.......We present two proof systems for implication-only intuitionistic logic in the calculus of structures. The first is a direct adaptation of the standard sequent calculus to the deep inference setting, and we describe a procedure for cut elimination, similar to the one from the sequent calculus...
Institute of Scientific and Technical Information of China (English)
Yuanliang Chu(初元量); Hanyi Zhang(张汉一)
2003-01-01
The dimensions of input waveguide and output waveguide of arrayed waveguide gratings (AWGs) determinethe crosstalk, insertion loss and 1-dB bandwidth. In cascaded optical add/drop multiplexers (OADMs),the value of these parameters will largely affect the power penalty of system. The power penalty ofcascaded OADMs is calculated with different waveguide dimensions of AWGs in this paper. Consideringof wavelength misalignment, an optimization design of AWGs is obtained.
Walasik, Wiktor; Renversez, Gilles
2016-01-01
We describe the results of the two methods we developed to calculate the stationary nonlinear solutions in one-dimensional plasmonic slot waveguides made of a finite-thickness nonlinear dielectric core surrounded by metal regions. These two methods are described in detail in the preceding article [Walasik et al., submitted]. For symmetric waveguides, we provide the nonlinear dispersion curves obtained using the two methods and compare them. We describe the well known low-order modes and the higher-modes that were not described before. All the modes are classified into two families: modes with and without nodes. We also compare nonlinear modes with nodes with the linear modes in similar linear slot waveguides with a homogeneous core. We recover the symmetry breaking Hopf bifurcation of the first symmetric nonlinear mode toward an asymmetric mode and we show that one of the higher modes also exhibits a bifurcation. We study the behavior of the bifurcation of the fundamental mode as a function of the permittivit...
Symmetric two-coordinate photodiode
Directory of Open Access Journals (Sweden)
Dobrovolskiy Yu. G.
2008-12-01
Full Text Available The two-coordinate photodiode is developed and explored on the longitudinal photoeffect, which allows to get the coordinate descriptions symmetric on the steepness and longitudinal resistance great exactness. It was shown, that the best type of the coordinate description is observed in the case of scanning by the optical probe on the central part of the photosensitive element. The ways of improvement of steepness and linear of its coordinate description were analyzed.
Rotationally symmetric viscous gas flows
Weigant, W.; Plotnikov, P. I.
2017-03-01
The Dirichlet boundary value problem for the Navier-Stokes equations of a barotropic viscous compressible fluid is considered. The flow region and the data of the problem are assumed to be invariant under rotations about a fixed axis. The existence of rotationally symmetric weak solutions for all adiabatic exponents from the interval (γ*,∞) with a critical exponent γ* < 4/3 is proved.
Wideband unbalanced waveguide power dividers and combiners
Energy Technology Data Exchange (ETDEWEB)
Halligan, Matthew; McDonald, Jacob Jeremiah; Strassner, II, Bernd H.
2016-05-17
The various technologies presented herein relate to waveguide dividers and waveguide combiners for application in radar systems, wireless communications, etc. Waveguide dividers-combiners can be manufactured in accordance with custom dimensions, as well as in accordance with waveguide standards such that the input and output ports are of a defined dimension and have a common impedance. Various embodiments are presented which can incorporate one or more septum(s), one or more pairs of septums, an iris, an input matching region, a notch located on the input waveguide arm, waveguide arms having stepped transformer regions, etc. The various divider configurations presented herein can be utilized in high fractional bandwidth applications, e.g., a fractional bandwidth of about 30%, and RF applications in the Ka frequency band (e.g., 26.5-40 GHz).
Design Procedure for Compact Folded Waveguide Filters
DEFF Research Database (Denmark)
Dong, Yunfeng; Johansen, Tom Keinicke; Zhurbenko, Vitaliy;
Waveguide filters are widely used in communication systems due to low losses and high power handling capabilities. One drawback of the conventional waveguide filters is their large size, especially for low-frequency and high-order realizations. It has been shown that the footprint of conventional...... waveguide resonators can be reduced to one quarter by folding the electric and magnetic fields inside the cavity (J. S. Hong, Microwave Symposium Digest, 2004, Vol. 1, pp. 213-216). This paper presents a novel systematic procedure for designing compact low-loss bandpass filters by using folded waveguide...... resonators. As a design example, a scaled version of a filter specified for a TETRA (Terrestrial Trunked Radio) system has been considered. The folded waveguide filter is designed to fulfil specific requirements, and the design procedure can be easily applied to other folded waveguide filter designs...
Plasmonic coaxial waveguide-cavity devices.
Mahigir, Amirreza; Dastmalchi, Pouya; Shin, Wonseok; Fan, Shanhui; Veronis, Georgios
2015-08-10
We theoretically investigate three-dimensional plasmonic waveguide-cavity structures, built by side-coupling stub resonators that consist of plasmonic coaxial waveguides of finite length, to a plasmonic coaxial waveguide. The resonators are terminated either in a short or an open circuit. We show that the properties of these waveguide-cavity systems can be accurately described using a single-mode scattering matrix theory. We also show that, with proper choice of their design parameters, three-dimensional plasmonic coaxial waveguide-cavity devices and two-dimensional metal-dielectric-metal devices can have nearly identical transmission spectra. Thus, three-dimensional plasmonic coaxial waveguides offer a platform for practical implementation of two-dimensional metal-dielectric-metal device designs.
Systematic Design of Slow Light Waveguides
DEFF Research Database (Denmark)
Wang, Fengwen
Light can propagate much slower in photonic crystal waveguides and plasmonic waveguides than in vacuum. Slow light propagation in waveguides shows broad prospects in the terabit communication systems. However, it causes severe signal distortions and displays large propagation loss. Moreover...... two different parameterizations. Detailed comparisons show that the bandwidth of slow light propagation can be significantly enhanced by allowing irregular geometries in the waveguides. To mitigate the propagation loss due to scattering in the photonic crystal waveg- uides, an optimization problem...... is formulated to minimize the average propagation loss of the designed modes. The presented approach is employed to design a free-topology slow light waveguide. Numerical result illustrates that slow light propagation in the optimized waveguide displays significantly suppressed propagation loss while keeping...
Long-Period Gratings in Planar Optical Waveguides
Institute of Scientific and Technical Information of China (English)
Kin; Seng; Chiang
2003-01-01
Our progress in the study of long-period gratings (LPGs) in planar optical waveguides is reviewed. In particular, experimental LPGs in glass and polymer waveguides are presented to demonstrate the potential of LPG-based waveguide devices.
Long-Period Gratings in Planar Optical Waveguides
Institute of Scientific and Technical Information of China (English)
Kin Seng Chiang
2003-01-01
Our progress in the study of long-period gratings (LPGs) in planar optical waveguides is reviewed. In particular,experimental LPGs in glass and polymer waveguides are presented to demonstrate the potential of LPG-based waveguide devices.
Multilayer cladding with hyperbolic dispersion for plasmonic waveguides
DEFF Research Database (Denmark)
Babicheva, Viktoriia; Shalaginov, Mikhail Y.; Ishii, Satoshi;
2015-01-01
We study the properties of plasmonic waveguides with a dielectric core and multilayer metal-dielectric claddings that possess hyperbolic dispersion. The waveguides hyperbolic multilayer claddings show better performance in comparison to conventional plasmonic waveguides. © OSA 2015....
Dissipation-Induced Super Scattering and Lasing PT-Spaser
Feng, Simin
2015-01-01
Giant transmission and reflection of a finite bandwidth are shown to occur at the same wavelength when the electromagnetic wave is incident on a periodic array of PT-symmetric dimers embedded in a metallic film. Remarkably, we found that this phenomenon vanishes if the metallic substrate is lossless while keeping other parameters unchanged. When the metafilm is adjusted to the vicinity of a spectral singularity, tuning substrate dissipation to a critical value can lead to supper scattering in stark contrast to what would be expected in conventional systems. The PT-synthetic plasmonic metafilm acts as a lasing PT-spaser, a planar source of coherent radiation. The metallic dissipation provides a mean to couple light out of the dark modes of the PT- spaser. Above a critical gain-loss coupling, the metafilm behaves as a meta-gain medium with the meta-gain atoms made from the PT-plasmonic dimers. This phenomenon implies that super radiation is possible from a cavity having gain elements by tuning the cavity dissip...
DEFF Research Database (Denmark)
Skivesen, Nina
This work concerns planar optical waveguide sensors for biosensing applications, with the focus on deep-probe sensing for micron-scale biological objects like bacteria and whole cells. In the last two decades planar metal-clad waveguides have been brieflyintroduced in the literature applied...... for various biosensing applications, however a thorough study of the sensor configurations has not been presented, but is the main subject of this thesis. Optical sensors are generally well suited for bio-sensing asthey show high sensitivity and give an immediate response for minute changes in the refractive...... index of a sample, due to the high sensitivity of optical bio-sensors detection of non-labeled biological objects can be performed. The majority of opticalsensors presented in the literature and commercially available optical sensors are based on evanescent wave sensing, however most of these sensors...
Reverse-symmetry waveguides: Theory and fabrication
DEFF Research Database (Denmark)
Horvath, R.; Lindvold, Lars René; Larsen, N.B.
2002-01-01
We present an extensive theoretical analysis of reverse-symmetry waveguides with special focus on their potential application as sensor components in aqueous media and demonstrate a novel method for fabrication of such waveguides. The principle of reverse symmetry is based on making the refractiv...... has the advantage of deeper penetration of the evanescent electromagnetic field into the cover medium, theoretically permitting higher sensitivity to analytes compared to traditional waveguide designs. We present calculated sensitivities and probing depths of conventional and reverse...
Talbot Effect in Three Waveguide Arrays
Institute of Scientific and Technical Information of China (English)
LI Zhi; ZHOU Hai-Feng; YANG Jian-Yi; JIANG Xiao-Qing
2008-01-01
By taking the coupling between the non-neighbourhood waveguides into account, the coupling characteristic of three waveguide arrays is analysed. The strong coupling equation of three waveguides is dealt with Laplace transform and LU decomposition. The general field evolution equation is obtained by inversion of the Laplace transform. The results show that the self-imaging conditions (Talbot effect) do not satisfy in general. The theoretical predictions are in good agreement with the BPM simulations.
Two-dimensional Kagome photonic bandgap waveguide
DEFF Research Database (Denmark)
Nielsen, Jens Bo; Søndergaard, Thomas; Libori, Stig E. Barkou;
2000-01-01
The transverse-magnetic photonic-bandgap-guidance properties are investigated for a planar two-dimensional (2-D) Kagome waveguide configuration using a full-vectorial plane-wave-expansion method. Single-moded well-localized low-index guided modes are found. The localization of the optical modes...... is investigated with respect to the width of the 2-D Kagome waveguide, and the number of modes existing for specific frequencies and waveguide widths is mapped out....
Digital Waveguide Adiabatic Passage Part 1: Theory
Vaitkus, Jesse A; Greentree, Andrew D
2016-01-01
Spatial adiabatic passage represents a new way to design integrated photonic devices. In conventional adiabatic passage designs require smoothly varying waveguide separations. Here we show modelling of adiabatic passage devices where the waveguide separation is varied digitally. Despite digitisation, our designs show robustness against variations in the input wavelength and refractive index contrast of the waveguides relative to the cladding. This approach to spatial adiabatic passage opens new design strategies and hence the potential for new photonics devices.
Loveday, Philip W
2007-10-01
A finite-element modeling procedure for computing the frequency response of piezoelectric transducers attached to infinite constant cross-section waveguides, as encountered in guided wave ultrasonic inspection, is presented. Two-dimensional waveguide finite elements are used to model the waveguide. Conventional three-dimensional finite elements are used to model the piezoelectric transducer. The harmonic forced response of the waveguide is used to obtain a dynamic stiffness matrix (complex and frequency dependent), which represents the waveguide in the transducer model. The electrical and mechanical frequency response of the transducer, attached to the waveguide, can then be computed. The forces applied to the waveguide are calculated and are used to determine the amplitude of each mode excited in the waveguide. The method is highly efficient compared to time integration of a conventional finite-element model of a length of waveguide. In addition, the method provides information about each mode that is excited in the waveguide. The method is demonstrated by modeling a sandwich piezoelectric transducer exciting a waveguide of rectangular cross section, although it could be applied to more complex situations. It is expected that the modeling method will be useful during the optimization of piezoelectric transducers for exciting specific wave propagation modes in waveguides.
Optical Waveguide Sensing and Imaging
Bock, Wojtek J; Tanev, Stoyan
2008-01-01
The book explores various aspects of existing and emerging fiber and waveguide optics sensing and imaging technologies including recent advances in nanobiophotonics. The focus is both on fundamental and applied research as well as on applications in civil engineering, biomedical sciences, environment, security and defence. The main goal of the multi-disciplinarry team of Editors was to provide an useful reference of state-of-the-art overviews covering a variety of complementary topics on the interface of engineering and biomedical sciences.
Tantawi, Sami G.; Dolgashev, Valery A.; Yeremian, Anahid D.
2016-03-15
A high-power microwave RF window is provided that includes a cylindrical waveguide, where the cylindrical waveguide includes a ceramic disk concentrically housed in a central region of the cylindrical waveguide, a first rectangular waveguide, where the first rectangular waveguide is connected by a first elliptical joint to a proximal end of the cylindrical waveguide, and a second rectangular waveguide, where the second rectangular waveguide is connected by a second elliptical joint to a distal end of the cylindrical waveguide.
Improved optical planar waveguides for lasers Project
National Aeronautics and Space Administration — Demonstrate efficacy of a novel growth technique for planar waveguides (PWG) Enable PWG laser technology with improved performance, efficiency and manufacturability....
A New Type of Terahertz Waveguides
Institute of Scientific and Technical Information of China (English)
LOU Shu-Qin; GUO Tie-Ying; FANG Hong; LI Hong-Lei; JIAN Shui-Sheng
2006-01-01
A new type of THz waveguides, which employs a solid polyethylene rod as the core and polyethylene tubes in a periodic array of square lattice as the cladding, is proposed. Optical properties of this new THz waveguide, especially in dispersion, confinement loss and single mode property, are investigated in detail with the plane wave expansion method and the beam propagation method. Numerical results demonstrate that the new THz waveguide can reach not only low dispersion but also low confinement loss at single mode propagation. Therefore, the square lattice structure is a better candidate as THz waveguides than the triangular ones.
Microwave gas breakdown in elliptical waveguides
Energy Technology Data Exchange (ETDEWEB)
Koufogiannis, I. D.; Sorolla, E., E-mail: eden.sorolla@epfl.ch; Mattes, M. [École Polytechnique Fédérale de Lausanne, Laboratoire d’Électromagnétisme et d' Acoustique (LEMA), Station 11, CH-1015 Lausanne (Switzerland)
2014-01-15
This paper analyzes the microwave gas discharge within elliptical waveguides excited by the fundamental mode. The Rayleigh-Ritz method has been applied to solve the continuity equation. The eigenvalue problem defined by the breakdown condition has been solved and the effective diffusion length of the elliptical waveguide has been calculated, what is used to find the corona threshold. This paper extends the microwave breakdown model developed for circular waveguides and shows the better corona withstanding capabilities of elliptical waveguides. The corona breakdown electric field threshold obtained with the variational method has been compared with the one calculated with the Finite Elements Method, showing excellent agreement.
Graded-index planar waveguide solar concentrator.
Bouchard, Sébastien; Thibault, Simon
2014-03-01
Planar waveguides are useful to transport, concentrate and distribute light uniformly over large dimensions. Their capacity to collect and gather light efficiently over a large distance is interesting for many applications, like backlighting and solar concentration. For these reasons, the possibility of making them even more efficient could be of considerable interest for the community. The observation of the ray path inside a graded-index (GRIN) fiber inspired the development of a similar technology inside planar waveguides. In this Letter, we show that it has the potential to dramatically increase the efficiency of planar waveguide-based solar concentrators or backlighting using GRIN planar waveguides.
Slow light with symmetric gap plasmon guides with finite width metal claddings
Indian Academy of Sciences (India)
S Dutta Gupta
2009-02-01
We study the dispersion relation and the modes of a symmetric gap plasmon guide, where a dielectric planar slab is coated with finite metallic layers on both top and bottom. The finite conductivity of the metal is taken into account. The modes of the structure exhibit significant differences from those of dielectric waveguides with air or metal as the bounding media. Avoided level crossing phenomenon between the plasmon and the guided modes is shown to exist, leading to leaky modes. The structure sandwiched between two high index media is shown to lead to slow light in transmission. The group delay is shown to be larger for higher order modes.
Indian Academy of Sciences (India)
XIE QIONGTAO; YAN LINA; WANG LINMAO; FU JUN
2016-05-01
We investigate both the non-Hermitian parity–time-(PT-)symmetric and Hermitianasymmetric volcano potentials, and present the analytical solution in terms of the confluent Heun function. Under certain special conditions, the confluent Heun function can be terminated as a polynomial, thereby leading to certain exact analytical results. It is found that the non-Hermitian PTsymmetric volcano potentials support the normalizable and non-normalizable reflectionless stateswith real energies. The Hermitian asymmetric volcano potentials allow normalizable reflectionless states with complex energies.
Inkjet printed ferrite-filled rectangular waveguide X-band isolator
Farooqui, Muhammad Fahad
2014-06-01
For the first time, a rectangular waveguide (RWG) isolator realized through inkjet printing on a ferrite substrate is presented. Yttrium iron garnet (YIG) substrate is used for the realization of the ferrite-filled isolator. Contrary to the substrate integrated waveguide (SIW) approach, all four walls of the waveguide have been inkjet printed on the YIG substrate demonstrating the utility of inkjet printing process for realizing non-planar microwave components. The isolation is achieved by applying an anti-symmetrical DC magnetic bias to the ferrite-filled waveguide which then exhibits a unidirectional mode of operation. The isolator is fed by a microstrip to RWG transition and demonstrates an isolation figure-of-merit (IFM) of more than 51 dB in the operating band from 9.95 GHz to 11.73 GHz with a very high peak IFM of 69 dB. The minimum insertion loss in the operating band is 2.73 dB (including losses from the transitions). The isolator measures 33 mm × 8 mm × 0.4 mm. This work introduces an inkjet printed non-planar microwave device which is easy to fabricate showing the ability of inkjet printing for fabricating complex microwave systems. © 2014 IEEE.
Energy Technology Data Exchange (ETDEWEB)
Benayas, A.; Jaque, D. [Universidad Autonoma de Madrid, Departamento de Fisica de Materiales, Madrid (Spain); Silva, W.F.; Jacinto, C. [Universidade Federal de Alagoas, Grupo de Fotonica e Fluidos Complexos, Instituto de Fisica, Maceio, Alagoas (Brazil); Rodenas, A.; Thomsom, R.R.; Psaila, N.D.; Reid, D.T.; Kar, A.K. [Heriot-Watt University, School of Engineering and Physical Sciences, Edinburgh (United Kingdom); Vazquez de Aldana, J. [Universidad de Salamanca, Grupo de Optica, Departamento de Fisica Aplicada, Facultad de Ciencias Fisicas, Salamanca (Spain); Chen, F.; Tan, Y. [Shandong University, School of Physics, Jinan (China); Torchia, G.A. [CONICET-CIC, Centro de Investigaciones Opticas, La Plata (Argentina)
2011-07-15
We report the improvement of ultrafast laser written optical waveguides in Yb:YAG ceramics by tailoring the presence of heat accumulation effects. From a combination of ytterbium micro-luminescence and micro-Raman structural analysis, maps of lattice defects and stress fields have been obtained. We show how laser annealing can strongly reduce the concentration of defects and also reduce compressive stress, leading to an effective 50% reduction in the propagation losses and to more extended and symmetric propagation modes. (orig.)
$\\mathcal{PT}$ symmetry in a fractional Schr\\"odinger equation
Zhang, Yiqi; Belić, Milivoj R; Zhu, Yi; Zhong, Weiping; Zhang, Yanpeng; Christodoulides, Demetrios N; Xiao, Min
2016-01-01
We investigate the fractional Schr\\"odinger equation with a periodic $\\mathcal{PT}$-symmetric potential. In the inverse space, the problem transfers into a first-order nonlocal frequency-delay partial differential equation. We show that at a critical point, the band structure becomes linear and symmetric in the one-dimensional case, which results in a nondiffracting propagation and conical diffraction of input beams. If only one channel in the periodic potential is excited, adjacent channels become uniformly excited along the propagation direction, which can be used to generate laser beams of high power and narrow width. In the two-dimensional case, there appears conical diffraction that depends on the competition between the fractional Laplacian operator and the $\\mathcal{PT}$-symmetric potential. This investigation may find applications in novel on-chip optical devices.
Antisymmetric PT-photonic structures with balanced positive and negative index materials
Ge, Li
2012-01-01
In this Letter we study a new class of synthetic materials in which the refractive index satisfies a special symmetry, n(-x)=-n^*(x), which we term antisymmetric parity-time (APT) systems. Unlike PT-symmetric systems which require balanced gain and loss, i.e. n(-x)=n^*(x), APT systems consist of balanced positive and negative index materials (NIMs). Despite the seemingly PT-symmetric optical potential $V(x)\\equiv n(x)^2\\omega^2/c^2$, such systems are not invariant under combined PT operation due to the discontinuity of the spatial derivative of the wavefunction. We show that APT systems display intriguing properties such as spontaneous phase transition of the scattering matrix, bidirectional invisibility, and a continuous lasing spectrum.
Symmetric products of mixed Hodge modules
Maxim, Laurentiu; Schuermann, Joerg
2010-01-01
Generalizing a theorem of Macdonald, we show a formula for the mixed Hodge structure on the cohomology of the symmetric products of bounded complexes of mixed Hodge modules by showing the existence of the canonical action of the symmetric group on the multiple external self-products of complexes of mixed Hodge modules. We also generalize a theorem of Hirzebruch and Zagier on the signature of the symmetric products of manifolds to the case of the symmetric products of symmetric parings on bounded complexes with constructible cohomology sheaves where the pairing is not assumed to be non-degenerate.
Singular Value Decomposition for Unitary Symmetric Matrix
Institute of Scientific and Technical Information of China (English)
ZOUHongxing; WANGDianjun; DAIQionghai; LIYanda
2003-01-01
A special architecture called unitary sym-metric matrix which embodies orthogonal, Givens, House-holder, permutation, and row (or column) symmetric ma-trices as its special cases, is proposed, and a precise corre-spondence of singular values and singular vectors between the unitary symmetric matrix and its mother matrix is de-rived. As an illustration of potential, it is shown that, for a class of unitary symmetric matrices, the singular value decomposition (SVD) using the mother matrix rather than the unitary symmetric matrix per se can save dramatically the CPU time and memory without loss of any numerical precision.
Fu, Zhongyuan; Zhou, Jian; Huang, Lijun; Sun, Fujun; Tian, Huiping
2016-12-01
We design symmetric-shaft-shape photonic crystal sensor arrays (SSPhCSAs) which can be used in refractive index sensing, and the performance of the structure is investigated. The structure consists of four symmetric-shaft-shape photonic crystal (SSPhC) cavities side-coupled to a W1 photonic crystal (PhC) waveguide. Each cavity has slightly different cavity spacing with different resonant frequency. By using two dimensional finite-difference time-domain (2D-FDTD) method, the simulation result obtained indicates the performance of the sensor arrays. The sensitivities of the four sensor units are 178, 252, 328 and 398 nm/RIU, respectively, with the detection limit of 10-3. The crosstalk lower than 20 dB is obtained.
Wang, Guanghui; Zhang, Weifeng; Lu, Jiahui; Zhao, Huijun
2016-08-01
We analytically study dispersion properties and optical gradient forces of different-order transverse magnetic (TM) modes in two coupled hyperbolic metamaterial waveguides (HMMWs). According to Maxwell's equations, we obtain the dispersion relation of symmetric and antisymmetric modes, and calculate optical gradient forces of different-order modes by using Maxwell stress tensor. Numerical results show that the dispersion properties are dependent on the filling ratio, and the optical gradient forces of high-order TM modes are larger than the fundamental mode when the gap between two HMMWs is very narrow, but they weaken much faster than the case of low-order TM modes with the gap width increasing. In addition, the effects of the dielectric surrounding of waveguides on the coupling effect and optical gradient force are clarified. These properties offer an avenue for various optomechanical applications in optical sensors and actuators.
Directory of Open Access Journals (Sweden)
CHAN DU
2014-01-01
Full Text Available We developed a biosensor that is capable for simultaneous surface plasmon resonance (SPR sensing and hyperspectral fluorescence analysis in this paper. A symmetrical metal-dielectric slab scheme is employed for the excitation of coupled plasmon waveguide resonance (CPWR in the present work. Resonance between surface plasmon mode and the guided waveguide mode generates narrower full width half-maximum of the reflective curves which leads to increased precision for the determination of refractive index over conventional SPR sensors. In addition, CPWR also offers longer surface propagation depths and higher surface electric field strengths that enable the excitation of fluorescence with hyperspectral technique to maintain an appreciable signal-to-noise ratio. The refractive index information obtained from SPR sensing and the chemical properties obtained through hyperspectral fluorescence analysis confirm each other to exclude false-positive or false-negative cases. The sensor provides a comprehensive understanding of the biological events on the sensor chips.
Homentcovschi, Dorel; Miles, Ronald N.
2012-01-01
The paper applies the re-expansion method for analyzing planar discontinuities at the junction of two axi-symmetrical circular waveguides. The normal modes in the two waveguides are expanded at the junction plane into a system of functions accounting for velocity singularities at the corner points. As the new expansion has a high convergence order, only a few terms have to be considered for obtaining the solution of most practical problems. This paper gives the equivalent impedance accounting for nonplanar waves into a plane-wave analysis and also the scattering matrix describing the coupling of arbitrary modes at each side of the discontinuity valid in the case of many propagating modes in both sides of the duct. The last section applies the re-expansion technique to some concentric expansion chambers providing an explicit formula for the transmission loss coefficient. PMID:22352491
Zhang, Qiang; Han, Dezhuan; Qin, Fei Fei; Zhang, Xiao Ming; Yao, Yong
2015-01-01
We propose a multiscale spoof-insulator-spoof (SIS) waveguide by introducing periodic geometry modulation in the wavelength scale to a SIS waveguide made of perfect electric conductor. The MSIS consists of multiple SIS subcells. The dispersion relationship of the fundamental guided mode of the spoof surface plasmon polaritons (SSPPs) is studied analytically within the small gap approximation. It is shown that the multiscale SIS possesses microwave band gap (MBG) due to the Bragg scattering. The "gap maps" in the design parameter space are provided. We demonstrate that the geometry of the subcells can efficiently adjust the effective refraction index of the elementary SIS and therefore further control the width and the position of the MBG. The results are in good agreement with numerical calculations by the finite element method (FEM). For finite-sized MSIS of given geometry in the millimeter scale, FEM calculations show that the first-order symmetric SSPP mode has zero transmission in the MBG within frequency...
Discrete Torsion and Symmetric Products
Dijkgraaf, R
1999-01-01
In this note we point out that a symmetric product orbifold CFT can be twisted by a unique nontrivial two-cocycle of the permutation group. This discrete torsion changes the spins and statistics of corresponding second-quantized string theory making it essentially ``supersymmetric.'' The long strings of even length become fermionic (or ghosts), those of odd length bosonic. The partition function and elliptic genus can be described by a sum over stringy spin structures. The usual cubic interaction vertex is odd and nilpotent, so this construction gives rise to a DLCQ string theory with a leading quartic interaction.
A charged spherically symmetric solution
Indian Academy of Sciences (India)
K Moodley; S D Maharaj; K S Govinder
2003-09-01
We ﬁnd a solution of the Einstein–Maxwell system of ﬁeld equations for a class of accelerating, expanding and shearing spherically symmetric metrics. This solution depends on a particular ansatz for the line element. The radial behaviour of the solution is fully speciﬁed while the temporal behaviour is given in terms of a quadrature. By setting the charge contribution to zero we regain an (uncharged) perfect ﬂuid solution found previously with the equation of state =+ constant, which is a generalisation of a stiff equation of state. Our class of charged shearing solutions is characterised geometrically by a conformal Killing vector.
Spherically symmetric scalar field collapse
Indian Academy of Sciences (India)
Koyel Ganguly; Narayan Banerjee
2013-03-01
It is shown that a scalar field, minimally coupled to gravity, may have collapsing modes even when the energy condition is violated, that is, for ( + 3) < 0. This result may be useful in the investigation of the possible clustering of dark energy. All the examples dealt with have apparent horizons formed before the formation of singularity. The singularities formed are shell focussing in nature. The density of the scalar field distribution is seen to diverge at singularity. The Ricci scalar also diverges at the singularity. The interior spherically symmetric metric is matched with exterior Vaidya metric at the hypersurface and the appropriate junction conditions are obtained.
Immanant Conversion on Symmetric Matrices
Directory of Open Access Journals (Sweden)
Purificação Coelho M.
2014-01-01
Full Text Available Letr Σn(C denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C -> Σn (C satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB = dχ·(Φ(Α + αΦ(Β for all matrices A,В ε Σ„(С and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С.
Observing quantum interference in 3D integrated-photonic symmetric multiports
Crespi, Andrea; Osellame, Roberto; Ramponi, Roberta; Bentivegna, Marco; Flamini, Fulvio; Spagnolo, Nicolò; Viggianiello, Niko; Innocenti, Luca; Mataloni, Paolo; Sciarrino, Fabio
2017-02-01
The investigation of multi-photon quantum interference in symmetric multi-port splitters has both fundamental and applicative interest. Destructive quantum interference in devices with specific symmetry leads to the suppression of a large number of possible output states, generalizing the Hong-Ou-Mandel effect; simple suppression laws have been developed for interferometers implementing the Fourier or the Hadamard transform over the modes. In fact, these enhanced interference features in the output distribution can be used to assess the indistinguishability of single-photon sources, and symmetric interferometers have been envisaged as benchmark or validation devices for Boson-Sampling machines. In this work we devise an innovative approach to implement symmetric multi-mode interferometers that realize the Fourier and Hadamard transform over the optical modes, exploiting integrated waveguide circuits. Our design is based on the optical implementations of the Fast-Fourier and Fast-Hadamard transform algorithms, and exploits a novel three-dimensional layout which is made possible by the unique capabilities of femtosecond laser waveguide writing. We fabricate devices with m = 4 and m = 8 modes and we let two identical photons evolve in the circuit. By characterizing the coincidence output distribution we are able to observe experimentally the known suppression laws for the output states. In particular, we characterize the robustness of this approach to assess the photons' indistinguishability and to rule out alternative non-quantum states of light. The reported results pave the way to the adoption of symmetric multiport interferometers as pivotal tools in the diagnostics and certification of quantum photonic platforms.
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...
Waveguide tapering for beam-width control in a waveguide transducer.
Kwon, Young Eui; Jeon, Hyun Joong; Kim, Hoe Woong; Kim, Yoon Young
2014-03-01
In a waveguide transducer that transmits an ultrasonic wave through a waveguide unit to a test structure, it is most preferred to send a non-dispersive ultrasonic wave of a narrow beam width. However, there is an unresolved conflict between the generation of the non- or less-dispersive wave and the transmission of a narrow-beam wave into a test structure. Among others, the thickness of the waveguide unit in a waveguide transducer is the key variable determining these two conflicting criteria, but the use of a uniformly-thick waveguide of any thickness cannot fulfill the two conflicting criteria simultaneously. In this study, we propose a specially-engineered tapered waveguide unit for the simultaneous satisfaction. An excitation unit is installed at the end of the thin region of the tapered waveguide and generates only the lowest non-dispersive shear-horizontal wave. Then the generated wave propagates through the tapered region of the waveguide unit and reaches the thick region of the waveguide with insignificant mode conversion to higher modes. If the tapered waveguide is used, the surviving lowest mode in the thick region of the waveguide is shown to carry most of the transmitted power and is finally propagated into a test structure. Because the beam size of the propagated wave and the thickness of the contacting waveguide region are inversely related, the thick contacting region of the tapered waveguide ensures narrow beam width. Numerical and experimental investigations were performed to check the effectiveness of the proposed waveguide-tapering approach.
Photonic crystal waveguides in artificial opals
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Kiyan, Roman; Neumeister, Andrei;
2008-01-01
3D photonic crystals based on Si inverted-opals are numerically explored as hosts for effective air-channel waveguides, which can serve as parts of photonic circuits. Two basic shapes of straight waveguides are considered: cylindrical and a chain of spheres. Modelling shows that transmission...
Hyperentangled photon sources in semiconductor waveguides
DEFF Research Database (Denmark)
Kang, Dongpeng; Helt, L. G.; Zhukovsky, Sergei
2014-01-01
We propose and analyze the performance of a technique to generate mode and polarization hyperentangled photons in monolithic semiconductor waveguides using two concurrent type-II spontaneous parametric down-conversion (SPDC) processes. These two SPDC processes are achieved by waveguide engineering...
Sapphire and other dielectric waveguide devices
Pollnau, Markus
2008-01-01
Different fabrication methods have been explored successfully and surface and buried channel waveguide lasers have been demonstrated in Ti:sapphire for the first time. Since the propagation losses of these first-generation waveguides are still rather high, substantial improvement is required in orde
DWDM Devices Based on Planar Waveguide Technologies
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
A review is presented on some of our recent results for designs, simulations and fabrication of several photonic integrated devices, such as arrayed-waveguide gratings (AWGs) and etched diffraction gratings (EDGs), based on planar waveguide technologies. Some novel designs for flat-top AWGs and EDGs with flat-top spectral responses are presented.
Waveguide Prism Based on Porous Silicon
Institute of Scientific and Technical Information of China (English)
JIA Zhen-hong
2004-01-01
The fabrication of the oxidized porous silicon waveguide prism is reported by selectively electrochemical anodisation process. The direction changes of light beams in TE and TM polarization out of this waveguide prism were respectively measured,and the experimental results were analyzed.
Discontinuities during UV writing of waveguides
DEFF Research Database (Denmark)
Svalgaard, Mikael; Harpøth, Anders; Andersen, Marc
2005-01-01
UV writing of waveguides can be hampered by discontinuities where the index change process suddenly shuts down. We show that thermal effects may account for this behaviour.......UV writing of waveguides can be hampered by discontinuities where the index change process suddenly shuts down. We show that thermal effects may account for this behaviour....
Sapphire and other dielectric waveguide devices
Pollnau, Markus
Different fabrication methods have been explored successfully and surface and buried channel waveguide lasers have been demonstrated in Ti:sapphire for the first time. Since the propagation losses of these first-generation waveguides are still rather high, substantial improvement is required in
Bends and splitters in graphene nanoribbon waveguides
DEFF Research Database (Denmark)
Zhu, Xiaolong; Yan, Wei; Mortensen, N. Asger
2013-01-01
We investigate the performance of bends and splitters in graphene nanoribbon waveguides. Although the graphene waveguides are lossy themselves, we show that bends and splitters do not induce any additional loss provided that the nanoribbon width is sub-wavelength. We use transmission line theory...
Silicon waveguides produced by wafer bonding
DEFF Research Database (Denmark)
Poulsen, Mette; Jensen, Flemming; Bunk, Oliver
2005-01-01
X-ray waveguides are successfully produced employing standard silicon technology of UV photolithography and wafer bonding. Contrary to theoretical expectations for similar systems even 100 mu m broad guides of less than 80 nm height do not collapse and can be used as one dimensional waveguides...
Capillary waveguide optrodes for Medical applications
Kieslinger, Dietmar; Weigl, Bernhard H.; Draxler, Sonja; Lippitsch, Max E.
1997-01-01
Glass capillaries with a chemically sensitive coating on the inner surface are used as optical sensors for medical diagnostics. The capillary simultaneously serves as a sample compartment, a sensor element, and an inhomogeneous optical waveguide. Different optical setups have been investigated and compared regarding its waveguiding properties.
Cooling Waveguide Flanges in Microwave Transmitters
Chen, B. C.; Hartop, R. W.
1984-01-01
Flang appendage circulates coolant for conductive heat removal. Flange appendage bore accomodates coolant tube. O-ring surrounds bore; when adjacent waveguide sections are bolted together, continuous conduit is formed for coolant. Pressure release groove in modified flange prevents coolant from entering waveguide should O'ring seal fail.
Infrared nanoantenna couplers for plasmonic slot waveguide
DEFF Research Database (Denmark)
Andryieuski, Andrei; Malureanu, Radu; Lavrinenko, Andrei
A slot plasmonic waveguide is promising solution as a replacement of electrical interconnects in the future optical integrated circuits. In this contribution we consider a set of compact solutions for coupling the infrared light from free space to the plasmonic slot waveguide. We systematically...
Topology optimization of two-dimensional waveguides
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2003-01-01
In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss.......In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss....
Characterization of azo dyes on Pt and Pt/polyaniline/dispersed Pt electrodes
Energy Technology Data Exchange (ETDEWEB)
Molina, J.; Fernandez, J.; Rio, A.I. del; Bonastre, J. [Departamento de Ingenieria Textil y Papelera, EPS de Alcoy, Universitat Politecnica de Valencia, Plaza Ferrandiz y Carbonell s/n, 03801 Alcoy (Spain); Cases, F., E-mail: fjcases@txp.upv.es [Departamento de Ingenieria Textil y Papelera, EPS de Alcoy, Universitat Politecnica de Valencia, Plaza Ferrandiz y Carbonell s/n, 03801 Alcoy (Spain)
2012-06-15
The electrochemical characterization of two organic dyes (amaranth and procion orange MX-2R) has been performed on Pt electrodes and Pt electrodes coated with polyaniline and dispersed Pt. Electrodes with different Pt loads have been synthesized and characterized obtaining that a load of 300 {mu}g cm{sup -2} was the optimum one. Scanning electron microscopy (SEM) and atomic force microscopy (AFM) was employed to observe the distribution and morphology of the Pt nanoparticles. The electroactivity of the electrodes has also been characterized by means of scanning electrochemical microscopy (SECM). The chemical characterization of Pt dispersed Pani coated Pt electrodes (Pt-Pani-Pt) was performed by means of X-ray photoelectron spectroscopy (XPS). The electrochemical characterization of the dyes has been performed by means of cyclic voltammetry. Voltammograms have shown that the presence of the dyes diminishes characteristic Pt oxidation and reduction peaks. However, redox processes due to the dyes, appeared in the voltammograms. The different species responsible of these redox processes were generated in the vicinity of the electrode and were not adsorbed on the electrode surface since after stirring, the different redox processes disappeared. Characterization with different scan rates showed that redox processes of both dyes were controlled by diffusion.
Zhang, Qian; Zhang, Hao Chi; Wu, Han; Cui, Tie Jun
2015-11-10
We propose a hybrid circuit for spoof surface plasmon polaritons (SPPs) and spatial waveguide modes to develop new microwave devices. The hybrid circuit includes a spoof SPP waveguide made of two anti-symmetric corrugated metallic strips and a traditional substrate integrated waveguide (SIW). From dispersion relations, we show that the electromagnetic waves only can propagate through the hybrid circuit when the operating frequency is less than the cut-off frequency of the SPP waveguide and greater than the cut-off frequency of SIW, generating efficient band-pass filters. We demonstrate that the pass band is controllable in a large range by designing the geometrical parameters of SPP waveguide and SIW. Full-wave simulations are provided to show the large adjustability of filters, including ultra wideband and narrowband filters. We fabricate a sample of the new hybrid device in the microwave frequencies, and measurement results have excellent agreements to numerical simulations, demonstrating excellent filtering characteristics such as low loss, high efficiency, and good square ratio. The proposed hybrid circuit gives important potential to accelerate the development of plasmonic integrated functional devices and circuits in both microwave and terahertz frequencies.
Quantum description of electromagnetic fields in waveguides
Kitagawa, Akira
2015-01-01
Using quantum theory, we study the propagation of an optical field in an inhomogeneous dielectric, and apply this scheme to traveling optical fields in a waveguide. We introduce a field-atom interaction Hamiltonian and derive the refractive index using quantum optics. We show that the transmission and reflection of optical fields at an interface between different materials can be described with normalized Fresnel coefficients and that this representation is related to the beam splitter operator. We then study the propagation properties of the optical fields for two types of slab waveguides: step-index and graded-index. The waveguides are divided into multiple layers to represent the spatial dependence of the optical field. We can evaluate the number of photons in an arbitrary volume in the waveguide using this procedure. Using the present method, the quantum properties of weak optical fields in a waveguide are revealed, while coherent states with higher amplitudes reduces to representation of classical wavegu...
Large-bandwidth planar photonic crystal waveguides
DEFF Research Database (Denmark)
Søndergaard, Thomas; Lavrinenko, Andrei
2002-01-01
A general design principle is presented for making finite-height photonic crystal waveguides that support leakage-free guidance of light over large frequency intervals. The large bandwidth waveguides are designed by introducing line defects in photonic crystal slabs, where the material in the lin......-free single-mode guidance is found for a large frequency interval covering 60% of the photonic band-gap.......A general design principle is presented for making finite-height photonic crystal waveguides that support leakage-free guidance of light over large frequency intervals. The large bandwidth waveguides are designed by introducing line defects in photonic crystal slabs, where the material in the line...... defect has appropriate dispersion properties relative to the photonic crystal slab material surrounding the line defect. A three-dimensional theoretical analysis is given for large-bandwidth waveguide designs based on a silicon-air photonic crystal slab suspended in air. In one example, the leakage...
Analysis of waveguiding properties of VCSEL structures
Energy Technology Data Exchange (ETDEWEB)
Erteza, I.A. [Sandia National Labs., Albuquerque, NM (United States). Exploratory Systems Development Center
1996-09-01
In this paper, the authors explore the feasibility of using the distributed Bragg reflector, grown on the substrate for a VCSEL (Vertical Cavity Surface Emitting Laser), to provide waveguiding within the substrate. This waveguiding could serve as an interconnection among VCSELs in an array. Before determining the feasibility of waveguide interconnected VCSELs, two analysis methods are presented and evaluated for their applicability to this problem. The implementations in Mathematica of both these methods are included. Results of the analysis show that waveguiding in VCSEL structures is feasible. Some of the many possible uses of waveguide interconnected VCSELs are also briefly discussed. The tools and analysis presented in this report can be used to evaluate such system concepts and to do detailed design calculations.
On-chip plasmonic waveguide optical waveplate
Gao, Linfei; Huo, Yijie; Zang, Kai; Paik, Seonghyun; Chen, Yusi; Harris, James S.; Zhou, Zhiping
2015-10-01
Polarization manipulation is essential in almost every photonic system ranging from telecommunications to bio-sensing to quantum information. This is traditionally achieved using bulk waveplates. With the developing trend of photonic systems towards integration and miniaturization, the need for an on-chip waveguide type waveplate becomes extremely urgent. However, this is very challenging using conventional dielectric waveguides, which usually require complex 3D geometries to alter the waveguide symmetry and are also difficult to create an arbitrary optical axis. Recently, a waveguide waveplate was realized using femtosecond laser writing, but the device length is in millimeter range. Here, for the first time we propose and experimentally demonstrate an ultracompact, on-chip waveplate using an asymmetric hybrid plasmonic waveguide to create an arbitrary optical axis. The device is only in several microns length and produced in a flexible integratable IC compatible format, thus opening up the potential for integration into a broad range of systems.
Schwarz Methods: To Symmetrize or Not to Symmetrize
Holst, Michael
2010-01-01
A preconditioning theory is presented which establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition and multigrid. It is illustrated why symmetrizing may be a bad idea for linear methods. It is conjectured that enforcing minimal symmetry achieves the best results when combined with conjugate gradient acceleration. Also, it is shown that absence of symmetry in the linear preconditioner is advantageous when the linear method is accelerated by using the Bi-CGstab method. Numerical examples are presented for two test problems which illustrate the theory and conjectures.
Characterization of spin pumping effect in Permalloy/Cu/Pt microfabricated lateral devices
Energy Technology Data Exchange (ETDEWEB)
Yamamoto, Tatsuya, E-mail: tyamamoto@imr.tohoku.ac.jp; Seki, Takeshi; Takanashi, Koki [Institute for Materials Research, Tohoku University, Sendai 980-8577 (Japan); Ono, Shimpei [Central Research Institute of Electric Power Industry, Tokyo 201-8511 (Japan)
2014-05-07
We studied ferromagnetic resonance (FMR) for microfabricated lateral devices consisting of a Permalloy (Py) rectangular element and a Pt nano-element bridged by a Cu wire, which were located on a coplanar waveguide. A change in the resonance linewidth (Δf) was observed in the FMR spectra when the distance between Py and Pt (d) was varied. For devices with d < 400 nm, Δf definitely increased, suggesting the enhancement of the Gilbert damping constant (α). We discussed a possible reason for the this enhancement taking into account the increase in the efficiency of spin pumping into Cu due to the spin absorption of the attached Pt.
Photonic waveguides theory and applications
Boudrioua, Azzedine
2009-01-01
This book presents the principles of non-linear integrated optics. The first objective is to provide the reader with a thorough understanding of integrated optics so that they may be able to develop the theoretical and experimental tools to study and control the linear and non-linear optical properties of waveguides.The potential use of these structures can then be determined in order to realize integrated optical components for light modulation and generation. The theoretical models are accompanied by experimental tools and their setting in order to characterize the studied phenomenon. Th
Ultrafast Laser Fabrication of Bragg Waveguides in GLS Chalcogenide Glass
Directory of Open Access Journals (Sweden)
McMillen Ben
2013-11-01
Full Text Available We present work on the fabrication of Bragg waveguides in gallium-lanthanum-sulfide chalcogenide glass using an ultrafast laser. Waveguides were written with a single pass while modulating the writing beam. The spatial and temporal profile of the writing beam was ontrolled during waveguide fabrication in order to control the shape and size of the waveguide cross-section.
High order mode beam waveguide for technological medium power millimeter wave applications
Energy Technology Data Exchange (ETDEWEB)
Rio, C. del; Gonzalo, R.; Marin, M.; Sorolla, M.; Moebius, A.; Thumm, M. [Universidad Publica de Navarra, Pamplona (Spain)
1995-12-31
The use of medium power millimeter CW gyrotrons (10-30 kW and 30-100 GHz) has several potential applications in advanced materials processing. Since a stochastic field distribution in the applicator is desirable no pencil beam is necessary. Then the possibility to couple the circular symmetric gyrotron output to a higher order free space mode can be considered. Beam waveguides based on iterative reflection of such high order beams on properly disigned mirrors opens the possibility to increase the efficiency and to reduce costs of present compact transmission lines in gyrotron technological systems.
Completely CMOS compatible SiN-waveguide-based fiber coupling structure for Si wire waveguides.
Maegami, Yuriko; Okano, Makoto; Cong, Guangwei; Ohno, Morifumi; Yamada, Koji
2016-07-25
For Si wire waveguides, we designed a highly efficient fiber coupling structure consisting of a Si inverted taper waveguide and a CMOS-compatible thin SiN waveguide with an SiO2 spacer inserted between them. By using a small SiN waveguide with a 310 nm-square core, the optical field can be expanded to correspond to a fiber with a 4.0-μm mode field diameter. A coupled waveguide system with the SiN waveguide and Si taper waveguide can provide low-loss and low-polarization-dependent mode conversion. Both losses in fiber-SiN waveguide coupling and SiN-Si waveguide mode conversion are no more than 1 dB in a wide wavelength bandwidth from 1.36 μm to 1.65 μm. Through a detailed analysis of the effective refractive indices in the coupled waveguide system, we can understand mode conversion accurately and also derive guidelines for reducing the polarization dependence and for shortening device length.
Fine Spectra of Symmetric Toeplitz Operators
Directory of Open Access Journals (Sweden)
Muhammed Altun
2012-01-01
Full Text Available The fine spectra of 2-banded and 3-banded infinite Toeplitz matrices were examined by several authors. The fine spectra of n-banded triangular Toeplitz matrices and tridiagonal symmetric matrices were computed in the following papers: Altun, “On the fine spectra of triangular toeplitz operators” (2011 and Altun, “Fine spectra of tridiagonal symmetric matrices” (2011. Here, we generalize those results to the (2+1-banded symmetric Toeplitz matrix operators for arbitrary positive integer .
Lee, Ja Bin; An, Gwang Guk; Yang, Seung Mo; Hong, Jin Pyo
2014-11-01
We report the structural and magnetic properties of a [Co/Pt] multilayer matrix as a function of Pt thickness. Increasing Pt thickness allows for the formation of a well-aligned fcc (111) CoPt3 structure in a [Co/Pt]n multilayer geometry, where the clear appearance of main (111) peak of CoPt3 measured using the X-ray diffraction patterns was confirmed. High-resolution transmission electron microscopy images, along with the corresponding fast Fourier transform patterns displayed the ordered structure with clear 6-fold symmetric diffraction spots. The c/a lattice constant ratio of 0.949 was calculated by utilizing the XRD and, demonstrating the presence of a well-aligned CoPt3 structure. The Pt thickness-dependent saturation magnetization (M(s)) values for the in- and out-of-plane M-H hysteresis loops obtained by vibrating sample magnetometer measurements showed distinctly opposite trends. The increase in the out-of-plane M(s) value with increasing Pt thickness seems to originate from the enhanced perpendicular orbital moment of the proper CoPt3 structure.
Classification of symmetric toroidal orbifolds
Energy Technology Data Exchange (ETDEWEB)
Fischer, Maximilian; Ratz, Michael; Torrado, Jesus [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-09-15
We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N{>=}1 supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six dimensions. We find in total 520 inequivalent toroidal orbifolds, 162 of them with Abelian point groups such as Z{sub 3}, Z{sub 4}, Z{sub 6}-I etc. and 358 with non-Abelian point groups such as S{sub 3}, D{sub 4}, A{sub 4} etc. We also briefly explore the properties of some orbifolds with Abelian point groups and N=1, i.e. specify the Hodge numbers and comment on the possible mechanisms (local or non-local) of gauge symmetry breaking.
Classification of symmetric toroidal orbifolds
Energy Technology Data Exchange (ETDEWEB)
Fischer, Maximilian; Ratz, Michael; Torrado, Jesus [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-09-15
We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N{>=}1 supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six dimensions. We find in total 520 inequivalent toroidal orbifolds, 162 of them with Abelian point groups such as Z{sub 3}, Z{sub 4}, Z{sub 6}-I etc. and 358 with non-Abelian point groups such as S{sub 3}, D{sub 4}, A{sub 4} etc. We also briefly explore the properties of some orbifolds with Abelian point groups and N=1, i.e. specify the Hodge numbers and comment on the possible mechanisms (local or non-local) of gauge symmetry breaking.
Symmetric functions and Hall polynomials
MacDonald, Ian Grant
1998-01-01
This reissued classic text is the acclaimed second edition of Professor Ian Macdonald's groundbreaking monograph on symmetric functions and Hall polynomials. The first edition was published in 1979, before being significantly expanded into the present edition in 1995. This text is widely regarded as the best source of information on Hall polynomials and what have come to be known as Macdonald polynomials, central to a number of key developments in mathematics and mathematical physics in the 21st century Macdonald polynomials gave rise to the subject of double affine Hecke algebras (or Cherednik algebras) important in representation theory. String theorists use Macdonald polynomials to attack the so-called AGT conjectures. Macdonald polynomials have been recently used to construct knot invariants. They are also a central tool for a theory of integrable stochastic models that have found a number of applications in probability, such as random matrices, directed polymers in random media, driven lattice gases, and...
A Minimally Symmetric Higgs Boson
Low, Ian
2014-01-01
Models addressing the naturalness of a light Higgs boson typically employ symmetries, either bosonic or fermionic, to stabilize the Higgs mass. We consider a setup with the minimal amount of symmetries: four shift symmetries acting on the four components of the Higgs doublet, subject to the constraints of linearly realized SU(2)xU(1) electroweak symmetry. Up to terms that explicitly violate the shift symmetries, the effective lagrangian can be derived, irrespective of the spontaneously broken group G in the ultraviolet, and is universal in all models where the Higgs arises as a pseudo-Nambu-Goldstone boson (PNGB). Very high energy scatterings of vector bosons could provide smoking gun signals of a minimally symmetric Higgs boson.
Undulator radiation in a waveguide
Energy Technology Data Exchange (ETDEWEB)
Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.
2007-03-15
We propose an analytical approach to characterize undulator radiation near resonance, when the presence of the vacuum-pipe considerably affects radiation properties. This is the case of the far-infrared undulator beamline at the Free-electron LASer (FEL) in Hamburg (FLASH), that will be capable of delivering pulses in the TeraHertz (THz) range. This undulator will allow pump-probe experiments where THz pulses are naturally synchronized to the VUV pulse from the FEL, as well as the development of novel electron-beam diagnostics techniques. Since the THz radiation diffraction-size exceeds the vacuum-chamber dimensions, characterization of infrared radiation must be performed accounting for the presence of a waveguide.We developed a theory of undulator radiation in a waveguide based on paraxial and resonance approximation. We solved the field equation with a tensor Green's function technique, and extracted figure of merits describing in a simple way the influence of the vacuum-pipe on the radiation pulse as a function of the problem parameters. Our theory, that makes consistent use of dimensionless analysis, allows treatment and physical understanding of many asymptotes of the parameter space, together with their region of applicability. (orig.)
Computing symmetric colorings of the dihedral group
Zelenyuk, Yuliya
2016-06-01
A symmetry on a group G is a mapping G ∋ x ↦ gx-1 g ∈ G, where g ∈ G. A subset A ⊆ G is symmetric if it is invariant under some symmetry, that is, A = gA-1g. The notion of symmetry has interesting relations to enumerative combinatorics. A coloring is symmetric if χ(gx-1g) = χ(x) for some g ∈ G. We discuss an approach how to compute the number of symmetric r-colorings for any finite group. Using this approach we derive the formula for the number of symmetric r-colorings of the dihedral group D3.
NMR Study of Layered Transition Metal Ditelluride (Ir,Pt)Te2
Magishi, K.; Saito, T.; Koyama, K.; Matsumoto, N.; Nagata, S.
2012-12-01
We report the results of 125Te and 195Pt NMR measurements on (Ir,Pt)Te2 in order to elucidate the characteristic electronic states. For PtTe2, the NMR spectrum exhibits a sharp line, which shows the uniaxially symmetric powder pattern due to the anisotropic Knight shift. The Knight shift is almost independent of temperature and is larger than that for IrTe2. Also, the nuclear spin-lattice relaxation rate 1/T1 of PtTe2 is proportional to the temperature in a wide temperature range, that is, obeys the Korringa relation as expected for simple metallic systems. From the analyses of the Knight shift and 1/T1, it is suggested that the antiferromagnetic correlations slightly exist.
Waveguide-Based Biosensors for Pathogen Detection
Directory of Open Access Journals (Sweden)
Nile Hartman
2009-07-01
Full Text Available Optical phenomena such as fluorescence, phosphorescence, polarization, interference and non-linearity have been extensively used for biosensing applications. Optical waveguides (both planar and fiber-optic are comprised of a material with high permittivity/high refractive index surrounded on all sides by materials with lower refractive indices, such as a substrate and the media to be sensed. This arrangement allows coupled light to propagate through the high refractive index waveguide by total internal reflection and generates an electromagnetic wave—the evanescent field—whose amplitude decreases exponentially as the distance from the surface increases. Excitation of fluorophores within the evanescent wave allows for sensitive detection while minimizing background fluorescence from complex, “dirty” biological samples. In this review, we will describe the basic principles, advantages and disadvantages of planar optical waveguide-based biodetection technologies. This discussion will include already commercialized technologies (e.g., Corning’s EPIC® Ô, SRU Biosystems’ BIND™, Zeptosense®, etc. and new technologies that are under research and development. We will also review differing assay approaches for the detection of various biomolecules, as well as the thin-film coatings that are often required for waveguide functionalization and effective detection. Finally, we will discuss reverse-symmetry waveguides, resonant waveguide grating sensors and metal-clad leaky waveguides as alternative signal transducers in optical biosensing.
Plasmonic antennas hybridized with dielectric waveguides.
Bernal Arango, Felipe; Kwadrin, Andrej; Koenderink, A Femius
2012-11-27
For the purpose of using plasmonics in an integrated scheme where single emitters can be probed efficiently, we experimentally and theoretically study the scattering properties of single nanorod gold antennas as well as antenna arrays placed on one-dimensional dielectric silicon nitride waveguides. Using real space and Fourier microscopy correlated with waveguide transmission measurements, we quantify the spectral properties, absolute strength, and directivity of scattering. The scattering processes can be well understood in the framework of the physics of dipolar objects placed on a planar layered environment with a waveguiding layer. We use the single plasmonic structures on top of the waveguide as dipolar building blocks for new types of antennas where the waveguide enhances the coupling between antenna elements. We report on waveguide hybridized Yagi-Uda antennas which show directionality in out-coupling of guided modes as well as directionality for in-coupling into the waveguide of localized excitations positioned at the feed element. These measurements together with simulations demonstrate that this system is ideal as a platform for plasmon quantum optics schemes as well as for fluorescence lab-on-chip applications.
Nonlinear effect induced in thermally poled glass waveguides
Institute of Scientific and Technical Information of China (English)
REN Yi-tao
2006-01-01
Thermally poled germanium-doped channel waveguides are presented. Multilayer waveguides containing a silicon oxynitride layer were used as charge trapper in this investigation on the effect of the internal field inside the waveguide. Compared to waveguides without the trapping layer, experimental results showed that the induced linear electro-optic (EO) coefficient increases about 20% after poling, suggesting strongly that the internal field is relatively enhanced, and showed it is a promising means for improving nonlinearity by poling in waveguides.
Performance-enhanced superluminescent diode with surface plasmon waveguide.
Ranjbaran, Mehdi; Li, Xun
2009-12-21
Super luminescent Diode (SLD) with a new structure is proposed in which light is guided by surface plasmon waveguide (SPWG) rather than by the conventional dielectric waveguide. This results in a great increase of the spontaneous emission coupling. Other parameters important to the device operation such as the confinement factor, waveguide loss and waveguide facets reflectivities are also considered. It is shown that the new design outperforms the conventional ones using dielectric waveguides in both the output power and optical spectral width.
Birefringence control for ion-exchanged channel glass waveguides.
Ayräs, P; Conti, G N; Honkanen, S; Peyghambarian, N
1998-12-20
We show that at 1.55-mum wavelength the waveguide birefringence of ion-exchanged channel waveguides in glass can be broadly tuned by a potassium and silver double-ion exchange. Two different potassium and silver double-ion-exchange processes are used to make surface waveguides with negligible waveguide birefringence. This process is crucially important in the manufacture of devices for dense wavelength-division multiplexing systems. The dependence of the waveguide birefringence on the channel width is also reported.
Measurement and modeling of dispersive pulse propagation in draw wire waveguides
Madaras, Eric I.; Kohl, Thomas W.; Rogers, Wayne P.
1995-01-01
An analytical model of dispersive pulse propagation in semi-infinite cylinders due to transient axially symmetric end conditions has been experimentally investigated. Specifically, the dispersive propagation of the first axially symmetric longitudinal mode in thin wire waveguides, which have ends in butt contact with longitudinal piezoelectric ultrasonic transducers, is examined. The method allows for prediction of a propagated waveform given a measured source waveform, together with the material properties of the cylinder. Alternatively, the source waveform can be extracted from measurement of the propagated waveform. The material properties required for implementation of the pulse propagation model are determined using guided wave phase velocity measurements. Hard tempered aluminum 1100 and 304 stainless steel wires, with 127, 305, and 406 micron diam., were examined. In general, the drawn wires were found to behave as transversely isotropic media.
Direct UV-writing of waveguides
DEFF Research Database (Denmark)
Færch, Kjartan Ullitz
2003-01-01
The research presented in this phd thesis is concerned about fabrication of waveguide structures in photosensitized germanosilica thin films by exposure to Ultra-violet (UV) radiation. Using a high pressure loading system and a waveguide fabrication setup, planar waveguiding structures with an UV...... induced refractive index change of more than 10-2 have been obtained. New insight, with respect to understanding the UV induced index change obtained by direct UV writing, has been provided, through experiments conducted with such high-pressure loaded germanosilica samples. This include measurements...
Waveguide device and method for making same
Forman, Michael A.
2007-08-14
A monolithic micromachined waveguide device or devices with low-loss, high-power handling, and near-optical frequency ranges is set forth. The waveguide and integrated devices are capable of transmitting near-optical frequencies due to optical-quality sidewall roughness. The device or devices are fabricated in parallel, may be mass produced using a LIGA manufacturing process, and may include a passive component such as a diplexer and/or an active capping layer capable of particularized signal processing of the waveforms propagated by the waveguide.
Waveguide-based optical chemical sensor
Grace, Karen M.; Swanson, Basil I.; Honkanen, Seppo
2007-03-13
The invention provides an apparatus and method for highly selective and sensitive chemical sensing. Two modes of laser light are transmitted through a waveguide, refracted by a thin film host reagent coating on the waveguide, and analyzed in a phase sensitive detector for changes in effective refractive index. Sensor specificity is based on the particular species selective thin films of host reagents which are attached to the surface of the planar optical waveguide. The thin film of host reagents refracts laser light at different refractive indices according to what species are forming inclusion complexes with the host reagents.
Nanofocusing in a tapered graphene plasmonic waveguide
DEFF Research Database (Denmark)
Dai, Yunyun; Zhu, Xiaolong; Mortensen, N. Asger
2015-01-01
Gated or doped graphene can support plasmons making it a promising plasmonic material in the terahertz regime. Here, we show numerically that in a tapered graphene plasmonic waveguide mid- and far-infrared light can be focused in nanometer scales, far beyond the diffraction limit. The underlying...... physics lies in that when propagating along the direction towards the tip both the group and phase velocities of the plasmons supported by the tapered graphene waveguide are reduced accordingly, eventually leading to nanofocusing at the tip with a huge enhancement of optical fields. The nanofocusing...... of optical fields in tapered graphene plasmonic waveguides could be potentially exploited in the enhancement of light–matter interactions....
Spatial Mode Selective Waveguide with Hyperbolic Cladding
Tang, Y; Xu, M; Bäumer, S; Adam, A J L; Urbach, H P
2016-01-01
Hyperbolic Meta-Materials~(HMMs) are anisotropic materials with permittivity tensor that has both positive and negative eigenvalues. Here we report that by using a type II HMM as cladding material, a waveguide which only supports higher order modes can be achieved, while the lower order modes become leaky and are absorbed in the HMM cladding. This counter intuitive property can lead to novel application in optical communication and photonic integrated circuit. The loss in our HMM-Insulator-HMM~(HIH) waveguide is smaller than that of similar guided mode in a Metal-Insulator-Metal~(MIM) waveguide.
Piezoelectric Film Waveguides for Surface Acoustic Waves
Directory of Open Access Journals (Sweden)
M.F. Zhovnir
2016-11-01
Full Text Available The paper presents results of mathematical modeling of piezoelectric film waveguide structures for surface acoustic waves (SAW. Piezoelectric ZnO film is supposed to be placed on a fused quartz substrate. The analytical ratios and numerical results allow to determine the design parameters of the waveguide structures to provide a single-mode SAW propagation mode. The results of amplitude and phase experimental studies of the SAW in the waveguide structures that were carried out on the laser optical sensing set up confirm the theoretical calculations.
Large-bandwidth planar photonic crystal waveguides
DEFF Research Database (Denmark)
Søndergaard, Thomas; Lavrinenko, Andrei
2002-01-01
A general design principle is presented for making finite-height photonic crystal waveguides that support leakage-free guidance of light over large frequency intervals. The large bandwidth waveguides are designed by introducing line defects in photonic crystal slabs, where the material in the line...... defect has appropriate dispersion properties relative to the photonic crystal slab material surrounding the line defect. A three-dimensional theoretical analysis is given for large-bandwidth waveguide designs based on a silicon-air photonic crystal slab suspended in air. In one example, the leakage...