Origin of continuous curves and dotted spots in laser transverse modes with geometric structures.

The transverse structures of geometric modes in degenerate laser resonators with large astigmatism are systematically investigated by starting from the Gaussian wave packet formulation with ray-wave connections. The overlapping degree D between Gaussian wave packets is derived as an analytic expression that manifests the critical overlapping with D=1. The transverse patterns are confirmed to display a structure of continuous curves or dotted spots, depending on D>1 or D<1, respectively. A thorough comparison between experimental results and numerical calculations is performed to validate the theoretical analysis.