Abstract
We interpret the intrinsic mechanism of the transition from geometric modes to eigenmodes in the Gaussian wave-packet representation based on numerical simulation. We then construct multiaxial super-geometric modes and polygonal vortex modes based on Gaussian wave packets. We highlight that the superposition of Gaussian wave packets can build the geometric modes described by Hermite polynomials and that the eigenmodes are the result of the interference of Gaussian wave packets. We conclude that Gaussian wave packets might serve as a complete basis for constructing structured light generated in solid-state laser cavities. Our study may provide meaningful insight into Gaussian wave packets for laser transverse modes.
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