Two-dimensional dissipative gap solitons

TL;DR

This paper introduces a 2D dissipative gap soliton model combining the complex Ginzburg-Landau equation with a periodic potential, demonstrating stable solitons through numerical and analytical methods, with potential optical applications.

Contribution

The study presents the first construction of stable 2D dissipative gap solitons in a complex Ginzburg-Landau model with a periodic potential, using both numerical and analytical approaches.

Findings

Stable fundamental and vortical DGSs are found within the first finite bandgap.

Analytical approximations agree well with numerical results.

Potential implementation in laser media with transverse 2D gratings.

Abstract

We introduce a model which integrates the complex Ginzburg-Landau (CGL) equation in two dimensions (2D) with the linear-cubic-quintic combination of loss and gain terms, self-defocusing nonlinearity, and a periodic potential. In this system, stable 2D \textit{dissipative gap solitons} (DGSs) are constructed, both fundamental and vortical ones. The soliton families belong to the first finite bandgap of the system's linear spectrum. The solutions are obtained in a numerical form and also by means of an analytical approximation, which combines the variational description of the shape of the fundamental and vortical solitons and the balance equation for their total power. The analytical results agree with numerical findings. The model may be implemented as a laser medium in a bulk self-defocusing optical waveguide equipped with a transverse 2D grating, the predicted DGSs representing spatial solitons in this setting.