Exact partial wave expansion of optical beams with respect to an arbitrary origin
Antonio Alvaro Ranha Neves, Adriana Fontes, Lazaro Aurelio Padilha, Eugenio Rodriguez, Carlos Henrique de Brito Cruz, Luiz Carlos Barbosa, Carlos Lenz Cesar
Using an analytical expression for an integral involving Bessel and Legendre functions, we succeed in obtaining the partial wave decomposition of a general optical beam at an arbitrary location relative to the origin. We also showed that solid angle integration will eliminate the radial dependence of the expansion coefficients. The beam shape coefficients obtained are given by an exact expression in terms of single or double integrals. These integrals can be evaluated numerically on a short time scale. We present the results for the case of a linear-polarized Gaussian beam. (c) 2006 Optical Society of America.