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Two-dimensional dissipative gap solitons

Hidetsugu Sakaguchi1 and Boris A. Malomed2

  • 1Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
  • 2Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel

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Phys. Rev. E 80, 026606 – Published 26 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.026606

Abstract

We introduce a model which integrates the complex Ginzburg-Landau equation in two dimensions (2Ds) with the linear-cubic-quintic combination of loss and gain terms, self-defocusing nonlinearity, and a periodic potential. In this system, stable 2D dissipative gap solitons (DGSs) are constructed, both fundamental and vortical ones. The soliton families belong to the first finite band gap 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.

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Phys. Rev. E 80, 026606– Published 26 August, 2009
  • Received 20 May 2009

© 2009 American Physical Society

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