Existence and Stability of Dissipative Solitons in a Dual-Waveguide Lattice with Linear Gain and Nonlinear Losses

TL;DR

This paper explores the existence and stability of dissipative solitons in a dual-waveguide lattice with gain and nonlinear losses, revealing how different nonlinearities affect their stability and properties through numerical analysis.

Contribution

It provides a comprehensive numerical analysis of dissipative solitons in a dual-waveguide lattice, highlighting stability conditions under various nonlinearities and gain/loss parameters, which was previously unexplored.

Findings

In-phase solitons are stable across their entire existence region with defocusing nonlinearity.

Out-of-phase solitons have larger stable regions under focusing nonlinearity.

Stability regions increase with higher nonlinear losses coefficient.

Abstract

In this study, we investigate the existence and stability of in-phase and out-of-phase dissipative solitons in a dual-waveguide lattice with linear localized gain and nonlinear losses under both focusing and defocusing nonlinearities. Numerical results reveal that both types of dissipative solitons bifurcate from the linear amplified modes, and their nonlinear propagation constant changes to a real value when nonlinearity, linear localized gain, and nonlinear losses coexist. We find that increasing the linear gain coefficient leads to an increase in the power and propagation constant of both types of dissipative solitons. For defocusing nonlinearity, in-phase solitons are stable across their entire existence region, while focusing nonlinearity confines them to a small stable region near the lower cutoff value in the propagation constant. In contrast, out-of-phase solitons have a significantly larger stable region under focusing nonlinearity compared to defocusing nonlinearity. The stability regions of both types of dissipative solitons increase with increasing nonlinear losses coefficient. Additionally, we validate the results of linear stability analysis for dissipative solitons using propagation simulations, showing perfect agreement between the two methods.