Stability analysis for solitons in PT-symmetric optical lattices

TL;DR

This paper investigates the stability of solitons in PT-symmetric optical lattices, revealing how gain-loss strength influences stability, phase transitions, and nonlinear evolution of solitons in one- and two-dimensional systems.

Contribution

It provides analytical and numerical insights into the stability thresholds and dynamics of solitons in PT-symmetric lattices, including effects of gain-loss parameters.

Findings

Infinite Bloch bands become complex above a gain-loss threshold.

Increasing gain-loss reduces stable soliton regions.

Unstable solitons can exhibit unbounded energy growth.

Abstract

Stability of solitons in parity-time (PT)-symmetric periodic potentials (optical lattices) is analyzed in both one- and two-dimensional systems. First we show analytically that when the strength of the gain-loss component in the PT lattice rises above a certain threshold (phase-transition point), an infinite number of linear Bloch bands turn complex simultaneously. Second, we show that while stable families of solitons can exist in PT lattices, increasing the gain-loss component has an overall destabilizing effect on soliton propagation. Specifically, when the gain-loss component increases, the parameter range of stable solitons shrinks as new regions of instability appear. Thirdly, we investigate the nonlinear evolution of unstable PT solitons under perturbations, and show that the energy of perturbed solitons can grow unbounded even though the PT lattice is below the phase transition point.