Parity-Time Symmetry in Optics and Photonics

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (31 December 2016) | Viewed by 24933

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Special Issue Information

Dear Colleagues,

Optical systems with balanced linear gain and loss have proved a fertile ground to realize PT-symmetric models. Collections of thin films, engineered volumetric optical potentials, scattering centers in waveguides, discrete systems involving effective coupled modes, in general, any optical systems that obeys a Schrödinger-like equation, where an idea of spacetime reflection is created via linear loss and gain, can be used to realize optical analogs of quantum systems described by non-Hermitian PT-symmetric Hamiltonians.

In this Special Issue of Symmetry, we are interested in such systems, and ask for your help to explore their spectral singularities, underlying symmetries, propagation dynamics, and applications in all fields of optics.

Prof. Dr. Blas Manuel Rodríguez-Lara
Guest Editor

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Keywords

Optical systems with balanced linear gain and loss have proved a fertile ground to realize PT-symmetric models. Collections of thin films, engineered volumetric optical potentials, scattering centers in waveguides, discrete systems involving effective coupled modes, in general, any optical systems that obeys a Schrödinger-like equation, where an idea of spacetime reflection is created via linear loss and gain, can be used to realize optical analogs of quantum systems described by non-Hermitian PT-symmetric Hamiltonians[...]

Published Papers (5 papers)

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Research

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488 KiB  
Article
Small-Amplitude Nonlinear Modes under the Combined Effect of the Parabolic Potential, Nonlocality and PT Symmetry
by Dmitry A. Zezyulin and Vladimir V. Konotop
Symmetry 2016, 8(8), 72; https://doi.org/10.3390/sym8080072 - 28 Jul 2016
Cited by 5 | Viewed by 3877
Abstract
We consider nonlinear modes of the nonlinear Schrödinger equation with nonlocal nonlinearities and and PT -symmetric parabolic potential. We show that there exists a set of continuous families of nonlinear modes and study their linear stability in the limit of small nonlinearity. It [...] Read more.
We consider nonlinear modes of the nonlinear Schrödinger equation with nonlocal nonlinearities and and PT -symmetric parabolic potential. We show that there exists a set of continuous families of nonlinear modes and study their linear stability in the limit of small nonlinearity. It is demonstrated that either PT symmetry or the nonlocality can be used to manage the stability of the small-amplitude nonlinear modes. The stability properties are also found to depend on the particular shape of the nonlocal kernel. Numerical simulations show that the stability results remain valid not only for the infinitesimally small nonlinear modes, but also for the modes of finite amplitude. Full article
(This article belongs to the Special Issue Parity-Time Symmetry in Optics and Photonics)
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640 KiB  
Article
Breathers in Hamiltonian PT -Symmetric Chains of Coupled Pendula under a Resonant Periodic Force
by Alexander Chernyavsky and Dmitry E. Pelinovsky
Symmetry 2016, 8(7), 59; https://doi.org/10.3390/sym8070059 - 8 Jul 2016
Cited by 13 | Viewed by 4358
Abstract
We derive a Hamiltonian version of the PT -symmetric discrete nonlinear Schrödinger equation that describes synchronized dynamics of coupled pendula driven by a periodic movement of their common strings. In the limit of weak coupling between the pendula, we classify the existence and [...] Read more.
We derive a Hamiltonian version of the PT -symmetric discrete nonlinear Schrödinger equation that describes synchronized dynamics of coupled pendula driven by a periodic movement of their common strings. In the limit of weak coupling between the pendula, we classify the existence and spectral stability of breathers (time-periodic solutions localized in the lattice) supported near one pair of coupled pendula. Orbital stability or instability of breathers is proved in a subset of the existence region. Full article
(This article belongs to the Special Issue Parity-Time Symmetry in Optics and Photonics)
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281 KiB  
Article
Parity-Time Symmetry and the Toy Models of Gain-Loss Dynamics near the Real Kato’s Exceptional Points
by Miloslav Znojil
Symmetry 2016, 8(6), 52; https://doi.org/10.3390/sym8060052 - 20 Jun 2016
Cited by 12 | Viewed by 4758
Abstract
For a given operator D ( t ) of an observable in theoretical parity-time symmetric quantum physics (or for its evolution-generator analogues in the experimental gain-loss classical optics, etc.) the instant t c r i t i c a l of a [...] Read more.
For a given operator D ( t ) of an observable in theoretical parity-time symmetric quantum physics (or for its evolution-generator analogues in the experimental gain-loss classical optics, etc.) the instant t c r i t i c a l of a spontaneous breakdown of the parity-time alias gain-loss symmetry should be given, in the rigorous language of mathematics, the Kato’s name of an “exceptional point”, t c r i t i c a l = t ( E P ) . In the majority of conventional applications the exceptional point (EP) values are not real. In our paper, we pay attention to several exactly tractable toy-model evolutions for which at least some of the values of t ( E P ) become real. These values are interpreted as “instants of a catastrophe”, be it classical or quantum. In the classical optical setting the discrete nature of our toy models might make them amenable to simulations. In the latter context the instant of Big Bang is mentioned as an illustrative sample of possible physical meaning of such an EP catastrophe in quantum cosmology. Full article
(This article belongs to the Special Issue Parity-Time Symmetry in Optics and Photonics)
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1101 KiB  
Article
A PT -Symmetric Dual-Core System with the Sine-Gordon Nonlinearity and Derivative Coupling
by Jesús Cuevas-Maraver, Boris A. Malomed and Panayotis G. Kevrekidis
Symmetry 2016, 8(6), 39; https://doi.org/10.3390/sym8060039 - 26 May 2016
Cited by 7 | Viewed by 4522
Abstract
As an extension of the class of nonlinear PT -symmetric models, we propose a system of sine-Gordon equations, with the PT symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling [...] Read more.
As an extension of the class of nonlinear PT -symmetric models, we propose a system of sine-Gordon equations, with the PT symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from local interaction between adjacent particles in coupled Frenkel–Kontorova (FK) chains, while the cross-derivative coupling, which was not considered before, is induced by three-particle interactions, provided that the particles in the parallel FK chains move in different directions. Nonlinear modes are then studied in this system. In particular, kink-kink (KK) and kink-anti-kink (KA) complexes are explored by means of analytical and numerical methods. It is predicted analytically and confirmed numerically that the complexes are unstable for one sign of the sinusoidal coupling and stable for another. Stability regions are delineated in the underlying parameter space. Unstable complexes split into free kinks and anti-kinks that may propagate or become quiescent, depending on whether they are subject to gain or loss, respectively. Full article
(This article belongs to the Special Issue Parity-Time Symmetry in Optics and Photonics)
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Review

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4319 KiB  
Review
Revisiting the Optical PT-Symmetric Dimer
by José Delfino Huerta Morales, Julio Guerrero, Servando López-Aguayo and Blas Manuel Rodríguez-Lara
Symmetry 2016, 8(9), 83; https://doi.org/10.3390/sym8090083 - 24 Aug 2016
Cited by 25 | Viewed by 6318
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Parity-Time Symmetry in Optics and Photonics)
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