Cylindrical wave spectrum decomposition method for evaluating the expansion coefficients of the shaped beams in spherical coordinates

Abstract

In the analysis of light scattering by spherical particles, the incident beam is expanded into an infinite series of spherical wave functions weighted by the beam shape coefficients (BSCs). Different techniques have been developed for evaluating the BSCs in the context of generalized Lorenz-Mie theory (GLMT). In this work, the spectrum decomposition method which we call cylindrical wave spectrum decomposition (CWSD) is recast and is extended to beams having simple dependence on the azimuth angle. The method first expands the beam field in the cylindrical coordinate system and then expands the cylindrical waves into the spherical waves based on the relations between the cylindrical and spherical waves. The CWSD method offers a deep insight into the effects of the beam distribution and the beam's location to the BSCs. Numerical calculations are performed to verify the method. The CWSD method may serve as a powerful tool for studying the light scattering, in the similar way to the angular spectrum decomposition (ASD) method.