Stability boundary and collisions of two-dimensional solitons inPT-symmetric couplers with the cubic-quintic nonlinearity

Abstract

We introduce one-and two-dimensional (1D and 2D) models of parity-time (PT ) -symmetric couplers with the mutually balanced linear gain and loss applied to the two cores, and cubic-quintic (CQ) nonlinearity acting in each one. The 2D and 1D models may be realized in dual-core optical waveguides, in the spatiotemporal and spatial domains, respectively. Stationary solutions for PTsymmetric solitons in these systems reduce to their counterparts in the usual coupler. The most essential problem is the stability of the solitons, which become unstable against symmetry breaking with the increase of the energy (norm), and retrieve the stability at still larger energies. The boundary value of the intercore-coupling constant, above which the solitons are completely stable, is found by means of an analytical approximation, based on the CW (zero-dimensional) counterpart of the system. The approximation demonstrates good agreement with numerical findings for the 1D and 2D solitons. Numerical results for the stability limits of the 2D solitons are obtained by means of the computation of eigenvalues for small perturbations, and verified in direct simulations.Although large parts of the solitons families are unstable, the instability is quite weak. Collisions between 2D solitons in the PT -symmetric coupler are studied by means of simulations. Outcomes of the collisions are inelastic but not destructive, as they do not break the PT symmetry.

Nonlinear switching and solitons in PT‐symmetric photonic systems

“…In other cases soliton dynamics is investigated in the two-core systems such as an array of coupled PT-symmetric dimers [85,167] and its continuum version in the form of coupled planar waveguides with gain in one of them and balanced loss in another [77,168]. Two-dimensional generalization of such models was studied in [169]. Soliton scattering by PT defects was first investigated in a nonlinear waveguide array [162,163].…”

Dromion structures in the(2+1)-dimensional nonlinear Schrödinger equation with a parity-time-symmetric potential

“…It may be meaningful to research the solutions of (2+1)-dimensional NLS equation with variable diffraction and nonlinearity coefficients in a PT-symmetric potential. The above analysis also play a potential role in future experiments and applications of synthetic PT-symmetric systems [49][50][51][52].…”

Dynamical behaviors of optical solitons in parity–time (PT) symmetric sextic anharmonic double-well potentials

“…For the fixed amplitude of gain-or-loss distribution, we find that the super-Gaussian frequency modulate the stability of solitons such that the solitons are unstable as the frequency decreases since the stronger effect of gain-or-loss distribution is generated. The idea can also be extended to study solitons of the higher-dimensional NLS equation with parity-time symmetric anharmonic double-well potential (see, e.g., [43]), which will be considered in another literature.…”