Pattern formation in a laser system: spontaneous and hard excitation phenomena

We present a study on pattern formation in an optically pumped three-level laser system. In a pump parameter region below the pattern-forming bifurcation, the system admits travelling solitary pulse solutions in one-dimensional space and rotating spiral waves in two-dimensional space under hard excitations. The pattern forming process and geometry are analysed and numerically simulated, the two showing a good qualitative agreement. When the control parameters are set beyond the bifurcation point, spontaneous emergence of spatiotemporal patterns is observed from an initially uniform background, evolving to rolls, dislocations and turbulence through a defect-mediated turbulence scenario.