Comparison of paraxial and nonparaxial spheroidal-Gaussian modes with Hermite-Gaussian and Laguerre-Gaussian

摘要

Abstract: In previous work, a new family of exact, closed-form, analytic solutions to the scalar Helmholtz equation was derived in the oblate-spheroidal coordinate system. The 0,0 order of this family represents a new mathematical model for the fundamental mode of a propagating Gaussian beam which is not limited to the paraxial region, but reduces to the traditional Kogelnik and Li model in the paraxial limit. This present work compares the higher-order terms of the spheroidal-Gaussian modes with both the Hermite-Gaussian and Laguerre-Gaussian modes. Distinction is made between magnitude and phase results for paraxial modes (Hermite, Laguerre, and spheroidal) and nonparaxial ones (spheroidal only). !5