Two-dimensional optical lattices in a ${\mathrm{CO}}_2$ laser

Using a cavity with a large Fresnel number, a nontrivial large-scale order resulting from global multimode-interaction dynamics is found in the transverse structure of a ${\mathrm{CO}}_2$ laser beam. Two-dimensional optical lattices displaying several hundred phase singularities each have been observed. The symmetry properties of these far-field patterns and their associate temporal spectra are studied as a function of two control parameters: the Fresnel number and the transverse intermode spacing.