<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">CP</mml:mi></mml:math>symmetry in optical systems

Dana, Brenda; Bahabad, Alon; Malomed, Boris A.

doi:10.1103/physreva.91.043808

Cited by 13 publications

(17 citation statements)

References 58 publications

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“…We also emphasize that the C operator used here should not be confused with the C operator introduced by Bender, Brody, and Jones (2002) as an observable representing the signature of the PT -norm which allows the definition of an inner product having positivedefinite signatures. Recently C-operator was discussed also in optical context (Dana, Bahabad, and Malomed, 2015).…”

Section: H Spin-orbit Coupled Bose-einstein Condensatesmentioning

confidence: 99%

Nonlinear waves inPT-symmetric systems

2016

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Recent progress on nonlinear properties of parity-time (PT -) symmetric systems is comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying 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 PT -symmetric system. The natural inclusion of nonlinearity into these 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 PTsymmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear PT -symmetric systems arising from various physical disciplines are presented; nonlinear properties of these systems are thoroughly elucidated; and relevant experimental results are described. In addition, emerging applications of PT symmetry are pointed out.

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Section: H Spin-orbit Coupled Bose-einstein Condensatesmentioning

confidence: 99%

Nonlinear waves inPT-symmetric systems

2016

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“…Another variant of interesting dimers where the coupling between the oscillators provide gain to the system was considered in [68,73,74]. Such a system may model the propagation of electromagnetic waves in coupled waveguides embedded in an active medium.…”

Section: Dimersmentioning

confidence: 99%

Discrete solitons dynamics in $$\mathscr {PT}$$-symmetric oligomers with complex-valued couplings

Kirikchi

Karjanto

2021

Nonlinear Dyn

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We consider an array of double oligomers in an optical waveguide device. A mathematical model for the system is the coupled discrete nonlinear Schrödinger (NLS) equations, where the gain-and-loss parameter contributes to the complex-valued linear coupling. The array caters to an optical simulation of the parity-time (PT )-symmetry property between the coupled arms. The system admits fundamental bright discrete soliton solutions. We investigate their existence and spectral stability using perturbation theory analysis. These analytical findings are verified further numerically using the Newton-Raphson method and a standard eigenvalueproblem solver. Our study focuses on two natural discrete modes of the solitons: single-and double-excited-sites, also known as onsite and intersite modes, respectively. Each of these modes acquires three distinct configurations between the dimer arms, i.e., symmetric, asymmetric, and antisymmetric. Although both intersite and onsite discrete solitons are generally unstable, the latter can be stable, depending on the combined values of the propagation constant, horizontal linear coupling coefficient, and gain-loss parameter.

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“…As concerns the emulation of fundamental properties of quantum systems in terms of classical optics and in semiclassical BEC, (quasi-) CP symmetries may be implemented too, in continuous [37][38][39] and discrete [40] media alike.…”

Section: Introductionmentioning

confidence: 99%

Dynamical control of solitons in a parity-time-symmetric coupler by periodic management

Fan

Malomed

2019

Communications in Nonlinear Science and Numerical Simulation

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We consider a dual-core nonlinear waveguide with the parity-time (PT ) symmetry, realized in the form of equal gain and loss terms carried by the coupled cores. To expand a previously found stability region for solitons in this system, and explore possibilities for the development of dynamical control of the solitons, we introduce "management" in the form of periodic sinusoidal variation of the loss-gain (LG) coefficients, along with synchronous variation of the inter-core coupling (ICC) constant. This system, which can be realized in optics (in the temporal and spatial domains alike), features strong robustness when amplitudes of the variation of the LG and ICC coefficients keep a ratio equal to that of their constant counterparts, allowing one to find exact solutions for PTsymmetric solitons. A stability region for the solitons is identified in terms of the management amplitude and period, as well as the soliton's amplitude. In the long-period regime, the solitons evolve adiabatically, making it possible to predict their stability boundaries in an analytical form. The system keeping the Galilean invariance, collisions between moving solitons are considered too. Slowly moving solitons undergo multiple collisions, but eventually separate.

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CPsymmetry in optical systems

Cited by 13 publications

References 58 publications

Nonlinear waves inPT-symmetric systems

Nonlinear waves inPT-symmetric systems

Discrete solitons dynamics in $$\mathscr {PT}$$-symmetric oligomers with complex-valued couplings

Dynamical control of solitons in a parity-time-symmetric coupler by periodic management

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