Making the PT symmetry unbreakable
arXiv:1802.08783
Abstract
It is well known that typical PT-symmetric systems suffer symmetry breaking when the strength of the gain-loss terms exceeds a certain critical value. We present a summary of recently published and newly produced results which demonstrate various possibilities of extending the PT symmetry to arbitrarily large values of the gain-loss coefficient. First, we recapitulate the analysis which demonstrates a possibility of the restoration of the PT symmetry and, moreover, complete avoidance of the breaking in a photonic waveguide of a subwavelength width. The analysis is based on the Maxwell's equations, instead of the usual paraxial approximation. Next, we review a recently proposed possibility to construct stable one-dimensional (1D) PT-symmetric solitons in a paraxial model with arbitrarily large values of the gain-loss coefficient, provided that the self-trapping of the solitons is induced by self-defocusing cubic nonlinearity, whose local strength grows sufficiently fast from the center to periphery. The model admits a particular analytical solution for the fundamental soliton, and provides full stability for families of fundamental and dipole solitons. Finally, we report new results for unbreakable PT-symmetric solitons in 2D extensions of the 1D model: one with a quasi-1D modulation profile of the local gain-loss coefficient, and another with the fully-2D modulation. These settings admit particular analytical solutions for 2D solitons, while generic soliton families are found in a numerical form. The quasi-1D modulation profile gives rise to a stable family of single-peak 2D solitons. The soliton stability in the full 2D model is possible if the local gain-loss term is subject to spatial confinement.
arXiv commentTo be published as a chapter in book "Parity-time Symmetry and Its Applications", edited by D. Christodoulides and J. Yang
References in corpus (32)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
- Complex Extension of Quantum Mechanics
- Nonlinear waves in -symmetric systems
- PT-symmetric laser-absorber
- Visualization of Branch Points in PT-Symmetric Waveguides
- Unidirectional Nonlinear PT-symmetric Optical Structures
- Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
- Physical realization of -symmetric potential scattering in a planar slab waveguide
- Nonlinear switching and solitons in PT-symmetric photonic systems
- Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices
- Stability analysis for solitons in PT-symmetric optical lattices
- Optical solitons in -symmetric nonlinear couplers with gain and loss
- Mechanical PT symmetry in coupled optomechanical systems
- Bright solitons from defocusing nonlinearities
- Bragg solitons in nonlinear PT-symmetric periodic potentials
- Twisted toroidal vortex-solitons in inhomogeneous media with repulsive nonlinearity
- Soliton gyroscopes in media with spatially growing repulsive nonlinearity
- Algebraic bright and vortex solitons in defocusing media
- Stability boundaries and collisions of two-dimensional solitons in PT-symmetric couplers with the cubic-quintic nonlinearity
- PT-symmetric Deformations of the Korteweg-de Vries Equation
- PT-Symmetric Extension of the Korteweg-de Vries Equation
- Unbreakable PT-symmetry of solitons supported by inhomogeneous defocusing nonlinearity
- PT-restoration via increased loss-gain in PT-symmetric Aubry-Andre model
- Hamiltonian formulation of the standard -symmetric nonlinear Schrödinger dimer
- Necessity of PT symmetry for soliton families in one-dimensional complex potentials
- PT-symmetry in optics beyond the paraxial approximation
- Localized dark solitons and vortices in defocusing media with spatially inhomogeneous nonlinearity
- Bright solitons from the nonpolynomial Schrödinger equation with inhomogeneous defocusing nonlinearities
- Vortices in Bose-Einstein condensates with -symmetric gain and loss
- Stationary through-flows in a Bose-Einstein condensate with a PT-symmetric impurity
- Stabilization of the coupled pendula chain under parametric PT-symmetric driving force
Cited by in corpus (3)
- Attraction centers and PT-symmetric delta-functional dipoles in critical and supercritical self-focusing media
- Dynamical control of solitons in a parity-time-symmetric coupler by periodic management
- Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity