Hermite–Gaussian beams in the generalized Lorenz–Mie theory through finite–series Laguerre–Gaussian beam shape coefficients

Abstract

Scalar Hermite–Gaussian beams (HGBs) are natural higher-order solutions to the paraxial wave equation in Cartesian coordinates. Their particular shapes make them a valuable tool in the domain of light–matter interaction. Describing these beams in the generalized Lorenz–Mie theory (GLMT) requires a set of beam shape coefficients (BSCs), which may be quite challenging to evaluate. Since their exact analytic form expressions are unlikely to be found in the foreseeable future, we resort to a particular set of strategies. The main idea is to write HGBs as combinations of Laguerre–Gaussian beams (LGBs), which have already been studied in the GLMT framework by using a finite-series algorithm. This paper describes how to deduce the HGB BSCs directly from LGB BSCs, analyzes their behavior, and compares the resulting GLMT-remodeled solutions with their ideal paraxial counterparts.