Eliminating blowing-ups and evanescent waves when using the finite series technique in evaluating beam shape coefficients for some T-matrix approaches, with the example of Gaussian beams

When evaluating beam shape coefficients which encode the description of laser beams, for use in some T-matrix approaches such as generalized Lorenz-Mie theory or Extended Boundary Condition Method for structured beams, by using finite series, blowing-ups are observed. When numerical inaccuracies are ruled out, it has been firmly demonstrated that such blowing-ups correspond to genuine physical phenomena, namely they describe evanescent waves. We propose a method to eliminate these blowing-ups and the corresponding evanescent waves (at least most of them). • Finite series beam shape coefficients exhibit blowing-ups. • These blowing-ups are associated to evanescent waves. • We propose a procedure to eliminate both the blowing-ups and the evanescent waves.