Nonlinear localized modes in PT-symmetric optical media with competing gain and loss

TL;DR

This paper explores the existence, stability, and properties of nonlinear localized modes in PT-symmetric optical media with complex refractive index profiles, providing analytical solutions and stability analysis for various nonlinear regimes.

Contribution

It presents exact analytical expressions for localized modes in PT-symmetric media with competing gain and loss, including stability analysis and extensions to two-dimensional geometries.

Findings

Localized modes exist for all competing parameter values.

Stability depends on the gain/loss profile and nonlinearity type.

Localized modes are characterized by specific power-flow patterns.

Abstract

The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expressions of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effect of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined.