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Stable vortex solitons in the Ginzburg-Landau model of a two-dimensional lasing medium with a transverse grating

Abstract :

We introduce a two-dimensional model of a laser cavity based on the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity and a lattice potential accounting for the transverse grating. A remarkable fact is that localized vortices, built as sets of four peaks pinned to the periodic potential, may be stable without the unphysical diffusion term, which was necessary for the stabilization in previously studied models. The vortices are chiefly considered in the onsite (rhombic) form, but the stabilization of offsite vortices (square-shaped ones) and quadrupoles is demonstrated too. Stability regions for the rhombic vortices and fundamental solitons are identified in the model’s parameter space, and scenarios of the evolution of unstable vortices are described. An essential result is a minimum strength of the lattice potential which is necessary to stabilize the vortices. The stability border is also identified in the case of the self-focusing quintic term in the underlying model, which suggests a possibility of the supercritical collapse. Beyond this border, the stationary vortex turns into a vortical breather, which is subsequently replaced by a dipolar breather and eventually by a single-peak breather.

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https://hal.univ-angers.fr/hal-03423791
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Soumis le : mercredi 10 novembre 2021 - 11:06:10
Dernière modification le : samedi 18 décembre 2021 - 04:04:08
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Hervé Leblond, Boris Malomed, Dumitru Mihalache. Stable vortex solitons in the Ginzburg-Landau model of a two-dimensional lasing medium with a transverse grating. Physical Review A, American Physical Society, 2009, 80 (3), pp.033835. ⟨10.1103/PhysRevA.80.033835⟩. ⟨hal-03423791⟩

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