Ince–Gaussian beams in the generalized Lorenz–Mie theory through finite series Laguerre–Gaussian beam shape coefficients

Abstract

The Ince–Gaussian beams (IGBs) are brought under the formalism of the generalized Lorenz–Mie theory (GLMT) through their expansions in terms of Laguerre–Gaussian beams (LGBs). The IG beam shape coefficients (BSCs) are here derived based on the expressions of LG BSCs given by the finite series method. We then analyze how such relationships between LG and IG modes are translated to the domain of BSCs. This avoids complications that arise when computing said BSCs through other methods such as quadratures. Further ahead, the IG electric fields are reconstructed through the finite series BSCs and are then compared to their respective paraxial expressions. Through these results, we are able to make an in-depth analysis of the implications of the finite series method when translating more complex paraxial modes into the framework of the GLMT.