Calculation of beam shape coefficients for elliptical Gaussian light using the scalar translational addition theorem

Abstract

A two-step indirect method for calculating the beam shape coefficients (BSCs) of the electromagnetic field of the circular Gaussian beam was recently presented, based on the spherical wave expansion of the scalar potential function and the scalar translational addition theorem (STAT). In this paper, the indirect method is extended to the shaped beam with non-axisymmetric cross-section, more specifically the elliptical Gaussian beam (EGB). Using the angular spectrum decomposition method, the BSCs of the scalar potential function are formulated in the beam coordinate system. Then, based on the STAT, the scalar BSCs in the particle coordinate system are obtained, which can be further transformed to the electromagnetic BSCs of the EGB. Numerical calculations are carried out to verify the accuracy and efficiency of the indirect method.