Preprint Article Version 1 This version is not peer-reviewed

On a Laser (3+1)-Dimensional Vectorial Cubic-Quintic Complex Ginzburg-Landau Equation and Modulational Instability

Version 1 : Received: 14 October 2019 / Approved: 16 October 2019 / Online: 16 October 2019 (04:09:00 CEST)

How to cite: Djazet, A.; Fewo, S.I.; Tabi, C.B.; Kofané, T.C. On a Laser (3+1)-Dimensional Vectorial Cubic-Quintic Complex Ginzburg-Landau Equation and Modulational Instability. Preprints 2019, 2019100171 (doi: 10.20944/preprints201910.0171.v1). Djazet, A.; Fewo, S.I.; Tabi, C.B.; Kofané, T.C. On a Laser (3+1)-Dimensional Vectorial Cubic-Quintic Complex Ginzburg-Landau Equation and Modulational Instability. Preprints 2019, 2019100171 (doi: 10.20944/preprints201910.0171.v1).

Abstract

Interaction of an electromagnetic field with matter in a laser cavity without the assumption of a fixed direction of the transverse electric field, described by the two-level Maxwell-Bloch equations, is studied. By using a perturbative nonlinear analysis, performed near the laser threshold, we report on the derivation of the laser (3+1)D vectorial complex cubic-quintic complex Ginzburg-Landau equation. Furthermore, we study the modulational instability of the plane waves both theoretically using the linear stability analysis, and numerically, using direct simulations via the split-step Fourier method. The linear theory predicts instability for any amplitude of the primary waves. Our numerical simulations confirm the theoretical predictions of the linear theory as well as the threshold of the amplitude of perturbations. The system understudy shows a deep dependence on the laser cavity parameters, for which there appear wave patterns in accordance with the predictions from the gain spectrum.

Subject Areas

laser cavity; two-level Maxwell-Bloch equations; complex Ginzburg-Landau equation; modulational instability; pattern formation

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