Abstract
The paper studies the spontaneous formation of nonlinear optical patterns in broad area lasers. Spatiotemporal transverse dynamics of the laser is described by the Maxwell-Bloch equations (MBE). The instability of the steady-state solution leads to pattern formation. Two different types of instabilities were observed analytically (Hopf and wave). 2D numerical simulation of the MBE with the random initial conditions has been performed using a split-step Fourier method and periodic boundary conditions. Hopf instability leads to homogeneous oscillations, spatiotemporal chaos and spiral waves. In the case of wave instability, the direct numerical simulation showed that space–time (periodic, quasi-periodic, or chaotic) modulation of the uniform profile is observed. The characteristic sizes of excited patterns are in good agreement with analytical predictions. The nonlinear interaction of four travelling waves forms a square optical vortex lattice similar to the vortex lattices observed in superconductors and Bose Einstein condensate.
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