Pattern formation by kicked solitons in the two-dimensionnal Ginzburg-Landau medium with a transverse grating

TL;DR

This paper investigates how two-dimensional dissipative solitons in a Ginzburg-Landau medium with a transverse grating can be mobilized by kicks, leading to pattern formation, with potential applications in laser cavity control.

Contribution

It provides a systematic analysis of the depinning threshold and pattern formation mechanisms for 2D solitons in a complex Ginzburg-Landau model with a periodic potential, including analytical and simulation results.

Findings

Depinning threshold depends on kick orientation.

Pattern formation occurs as solitons hop between potential cells.

Elastic and inelastic collisions between solitons and patterns are characterized.

Abstract

We consider the kick-induced mobility of two-dimensional (2D) fundamental dissipative solitons in models of lasing media based on the 2D complex Ginzburg-Landau (CGL) equation including a spatially periodic potential (transverse grating). The depinning threshold is identified by means of systematic simulations, and described by means of an analytical approximation, depending on the orientation of the kick. Various pattern-formation scenarios are found above the threshold. Most typically, the soliton, hopping between potential cells, leaves arrayed patterns of different sizes in its wake. In the laser cavity, this effect may be used as a mechanism for selective pattern formation controlled by the tilt of the seed beam. Freely moving solitons feature two distinct values of the established velocity. Elastic and inelastic collisions between free solitons and pinned arrayed patterns are studied too.