Modified finite series technique for the evaluation of beam shape coefficients in the T-matrix methods for structured beams with application to Bessel beams

Abstract

The finite series technique is a rigorous mathematical formulation to exactly calculate the beam shape coefficients gn,TMm and gn,TEm which describe an arbitrary structured beam within the framework of the T-matrix methods for structured beams, e.g. generalized Lorenz–Mie theory or Extended Boundary Condition Method. It allows for fast computation without having recourse to time-consuming quadratures with double or triple integrals. Here, a simpler version of the finite series – the Modified Finite Series – is presented in which gn,TMm and gn,TEm are obtained by using an arbitrary choice of the spherical angle θ in the development of the finite series technique. To illustrate it, a linearly polarized vector Bessel beam is described within this new formalism. We expect that the present method will be an important alternative tool in the field of light scattering and light-matter interaction within the optical domain.