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From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency-selective feedback

Paulau, P. V. and Gomila, D. and Colet, P. and Malomed, B. A. and Firth, W. J. (2011) From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency-selective feedback. Physical Review E, 84 (3). ISSN 1539-3755

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We use the cubic complex Ginzburg-Landau equation linearly coupled to a dissipative linear equation as a model for lasers with an external frequency-selective feedback. This system may also serve as a general pattern-formation model in media driven by an intrinsic gain and selective feedback. While, strictly speaking, the approximation of the laser nonlinearity by a cubic term is only valid for small field intensities, it qualitatively reproduces results for dissipative solitons obtained in models with a more complex nonlinearity in the whole parameter region where the solitons exist. The analysis is focused on two-dimensional stripe-shaped and vortex solitons. An analytical expression for the stripe solitons is obtained from the known one-dimensional soliton solution, and its relation with vortex solitons is highlighted. The radius of the vortices increases linearly with their topological charge m, therefore the stripe-shaped soliton may be interpreted as the vortex with m = infinity, and, conversely, vortex solitons can be realized as unstable stripes bent into stable rings. The results for the vortices are applicable for a broad class of physical systems.