Two-dimensional dissipative gap solitons

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.

8 pages, 6 figures

References in corpus (2)

• Spontaneous soliton symmetry breaking in two-dimensional coupled Bose-Einstein condensates supported by optical lattices
• Symbiotic gap and semi-gap solitons in Bose-Einstein condensates

Cited by in corpus (7)

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• Nonlinear patterns in Bose-Einstein condensates in dissipative optical lattices
• Replication of dissipative vortices modeled by the complex Ginzburg-Landau equation
• Two-dimensional intra-band solitons in lattice potentials with local defects and self-focusing nonlinearity
• Induced Waveform Transitions of Dissipative Solitons
• Global well-posedness for cubic NLS with nonlinear damping