Discrete vortex solitons and PT symmetry

Abstract

We study the effect of lifting the degeneracy of vortex modes with a PT symmetric defect, using discrete vortices in a circular array of nonlinear waveguides as an example. When the defect is introduced, the degenerate linear vortex modes spontaneously break PT symmetry and acquire complex eigenvalues, but nonlinear propagating modes with real propagation constants can still exist. The stability of nonlinear modes depends on both the magnitude and the sign of the vortex charge, thus PT symmetric systems offer new mechanisms to control discrete vortices.

3 figures, to appear in Optics Letters

References in corpus (4)

• Nonlinear modes in finite-dimensional PT-symmetric systems
• Asymmetric vortex solitons in nonlinear periodic lattices
• Perturbation theory of PT-symmetric Hamiltonians
• PT-symmetry breaking and universal chirality in a PT-symmetric ring

Cited by in corpus (26)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Stability boundaries and collisions of two-dimensional solitons in PT-symmetric couplers with the cubic-quintic nonlinearity
• Instabilities, solitons, and rogue waves in PT-coupled nonlinear waveguides
• Discrete solitons and vortices on two-dimensional lattices of $\mathcal{P}\mathcal{T}$-symmetric couplers
• A solvable model for solitons pinned to a PT-symmetric dipole
• Vortex solitons in twisted circular waveguide arrays
• Revisiting the PT-symmetric Trimer: Bifurcations, Ghost States and Associated Dynamics
• Nonlinear modes in a generalized $\mathcal{P}\mathcal{T}$-symmetric discrete nonlinear Schrödinger equation
• Vortices in Bose-Einstein condensates with $\mathcal{P}\mathcal{T}$-symmetric gain and loss
• Stationary modes and integrals of motion in nonlinear lattices with PT-symmetric linear part
• Pseudo-Hermiticity protects the energy-difference conservation in the scattering
• $\mathcal{P}\mathcal{T}$-symmetric coupler with ${\chi }^{(2)}$ nonlinearity
• CP symmetry in optical systems
• Staggered $\mathcal{P}\mathcal{T}$-symmetric ladders with cubic nonlinearity
• Multisoliton Newton's cradles and supersolitons in regular and PT-symmetric nonlinear couplers
• PT-symmetry Management in Oligomer Systems
• Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity
• Quasi-energies, parametric resonances, and stability limits in ac-driven $\mathcal{P}\mathcal{T}$-symmetric systems
• Generalized Dimers and their Stokes-variable Dynamics
• Gyrating solitons in a necklace of optical waveguides
• Nonlinear Parity-Time (PT) symmetric closed-form optical quadrimer waveguides: Attractor perspective
• Tunable Aharonov-Bohm cages through anti-$\mathcal{P}\mathcal{T}$-symmetric imaginary couplings
• Stable high-charge vortex dissipative solitons in azimuthally modulated waveguide arrays with localized gain
• Existence and stability of PT-symmetric vortices in nonlinear two-dimensional square lattices
• Vortex solitons in star networks