General theory on electromagnetic scattering of an off-axis Hermite-Gaussian beam by a rotationally uniaxial anisotropic spheroid

Abstract

This letter presents a field expansion of the solution to three-dimensional electromagnetic scattering problems of a uniaxial anisotropic spheroidal particle illuminated by an off-axis Hermite-Gaussian (HG) beam. Using the complex-source-point method, and the relationship between spherical and spheroidal vector wave functions (VWFs), a method is put forward to expand the incident Hermite-Gaussian beam in terms of the spheroidal VWFs. By utilizing the complete relationship between spherical and spheroidal VWFs, the expansion formats of the EM fields in a uniaxial anisotropic spheroid in terms of the spheroidal vector wave functions are derived. The unknown expansion coefficients of the internal fields and scattered field are determined by applying the boundary conditions of the continuity of the tangential components of the electric and magnetic vectors across the surface of the spheroid. These theory works are hopeful to provide an effective test for further research on the numerical analysis of the interaction between a uniaxial anisotropic spheroid and laser beam.