Optical Solitons in PT-symmetric Potentials with Competing Cubic-Quintic Nonlinearity: Existence, Stability, and Dynamics

TL;DR

This paper investigates the existence, stability, and dynamics of optical solitons in PT-symmetric media with competing cubic-quintic nonlinearity, revealing how eigenvalue spectra merge at specific gain-loss thresholds and analyzing their robustness.

Contribution

It provides a comprehensive analysis of soliton solutions in PT-symmetric systems with cubic-quintic nonlinearity, including stability and spectral properties, which is a novel exploration in this context.

Findings

Eigenvalue spectra for fundamental and dipole solitons merge at Wc1.

Tripole and quadrupole spectra merge at Wc2.

Beyond merging points, eigenvalue spectra cease to exist.

Abstract

We address the properties of optical solitons that form in media with competing cubic-quintic nonlinearity and parity-time(PT)-symmetric complex-valued external potentials. The model describes the propagation of solitons in nonlinear optical waveguides with balanced gain and loss. We study the existence, stability, and robustness of fundamental, dipole, and multipole stationary solutions in this PT-symmetric system. The corresponding eigenvalue spectra diagrams for fundamental, dipole, tripole, and quadrupole solitons are presented. We show that the eigenvalue spectra diagrams for fundamental and dipole solitons merge at a coalescence point Wc1, whereas the corresponding diagrams for tripole and quadrupole solitons merge at a larger coalescence point Wc2. Beyond these two merging points, i.e., when the gain-loss strength parameter W0 exceeds the corresponding coalescence points, the eigenvalue spectra cease to exist. The stability of the stationary solutions is investigated by performing the linear stability analysis and the robustness to propagation of these stationary solutions is checked by using direct numerical simulations.