Partially-PT-symmetric optical potentials with all-real spectra and soliton families in multi-dimensions

Abstract

Multi-dimensional complex optical potentials with partial parity-time (PT) symmetry are proposed. The usual PT symmetry requires that the potential is invariant under complex conjugation and simultaneous reflection in all spatial directions. However, we show that if the potential is only partially PT-symmetric, i.e., it is invariant under complex conjugation and reflection in a single spatial direction, then it can also possess all-real spectra and continuous families of solitons. These results are established analytically and corroborated numerically.

4 pages, 3 figures

References in corpus (5)

• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Solitons in PT-symmetric nonlinear lattices
• Breathers in PT-symmetric optical couplers
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a necklace of coupled optical waveguides
• Discrete solitons in PT-symmetric lattices

Cited by in corpus (14)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Symmetry breaking of solitons in two-dimensional complex potentials
• Coupled Oscillator Systems Having Partial PT Symmetry
• New classes of non-parity-time-symmetric optical potentials with all-real spectra and exceptional-point-free phase transition
• Realizing PT-symmetric BEC subsystems in closed hermitian systems
• Continuous families of solitary waves in non-symmetric complex potentials: A Melnikov theory approach
• Experimental Observation of Partial Parity-Time Symmetry and Its Phase Transition with a Laser-Driven Cesium Atomic Gas
• Light propagation in periodically modulated complex waveguides
• PT-symmetric sine-Gordon breathers
• Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations
• Existence and stability of PT-symmetric vortices in nonlinear two-dimensional square lattices
• Construction of non-PT-symmetric complex potentials with all-real spectra
• Eigenvalues bifurcating from the continuum in two-dimensional potentials generating non-Hermitian gauge fields