We experimentally investigate pattern formation in a solid-state microchip
laser with a large Fresnel number. Controlling the reflectivity of the outp
ut coupler can generate the stable square pattern of optical vortex lattice
s. The formation of square vortex lattices is found to be a spontaneous pro
cess of transverse mode locking within almost-degenerated mode families. Th
e frequency of self-induced oscillation in square vortex lattices agrees we
ll with the numerical calculation. The chaotic relaxation oscillation is fo
und in square vortex lattices due to the multi-longitudinal-mode operation.