Dynamic power balance for nonlinear waves in unbalanced gain and loss landscapes

TL;DR

This paper establishes conditions for stable wave trapping in nonlinear photonic structures with unbalanced gain and loss, based on a dynamic power balance mechanism that ensures stable propagation across various initial conditions.

Contribution

It introduces generic sufficient conditions linking gain-loss and refractive index profiles to achieve stable wave propagation in nonlinear unbalanced landscapes.

Findings

Derived conditions for stable wave trapping

Identified a conserved quantity related to power balance

Demonstrated stability across diverse initial conditions

Abstract

The presence of losses in nonlinear photonic structures is a crucial issue for modern applications. Active parts are introduced for wave power compensation resulting in unbalanced gain and loss landscapes where localized beam propagation is, in general, dynamically unstable. Here we provide generic sufficient conditions for the relation between the gain-loss and the refractive index profiles in order to ensure efficient wave trapping and stable propagation for a wide range of beam launching conditions such as initial power, angle of incidence and position. The stability is a consequence of an underlying dynamic power balance mechanism related to a conserved quantity of wave dynamics.