Formation of optical vortex lattices in solid-state microchip lasers: Spontaneous transverse mode locking

We experimentally investigate pattern formation in a solid-state microchip laser with a large Fresnel number. Controlling the reflectivity of the output coupler can generate the stable square pattern of optical vortex lattices. The formation of square vortex lattices is found to be a spontaneous process of transverse mode locking within almost-degenerated mode families. The frequency of self-induced oscillation in square vortex lattices agrees well with the numerical calculation. The chaotic relaxation oscillation is found in square vortex lattices due to the multi-longitudinal-mode operation.