On an infinite number of quadratures to evaluate beam shape coefficients in generalized Lorenz-Mie theory and the extended boundary condition method for structured EM beams

When dealing with light scattering theories such as the T-matrix methods for structured laser beams, e.g. Generalized Lorenz-Mie Theory (GLMT) or the Extended Boundary Condition Method (EBCM), EM fields are expanded over a set of Vector Spherical Wave Functions (VSWFs) involving spherical Bessel functions, with expansion coefficients expressed in terms of Beam Shape Coefficients (BSCs). Although spherical Bessel functions are orthogonal over the range (-infinity, +infinity), the GLMT may be expressed using a non-orthogonal set of spherical Bessel functions defined over (0, +infinity), allowing one to generate an infinite number of quadratures for evaluating the BSCs. This paper points out the difference between orthogonal and non-orthogonal spherical Bessel functions, establishes the infinite number of quadratures and discusses its properties. (C) 2019 Elsevier Ltd. All rights reserved.