Intrinsic method for the evaluation of beam shape coefficients in spheroidal coordinates for oblique illumination

Abstract

When dealing with T-matrix scattering, e.g. in the framework of Generalized Lorenz-Mie Theory (GLMT) or of Extended Boundary Condition Method (EBCM), the incident electromagnetic fields are expanded over a set of vectorial wave functions, with expansion coefficients expressed in terms of beam shape coefficients (BSCs). In the case of structured beams, the evaluation of these BSCs may constitute a challenging issue, particularly in the case of spheroidal coordinates. BSCs in spheroidal coordinates have been originally evaluated using an extrinsic method, i.e. they have been expressed in terms of more conventional BSCs in spherical coordinates. Later on, it has been possible to provide expressions to evaluate spheroidal BSCs using an intrinsic approach, i.e. by working only inside the spheroidal coordinate system used to deal with the scattering problem. Fairly recently, the intrinsic method for the evaluation of BSCs in spheroidal coordinates for on-axis standard configuration has been released in the archival literature. The present paper extends the intrinsic method to the case of oblique illumination. It also serves as a review devoted to GLMTs in spheroidal coordinates.