Spherical harmonics expansion of the evanescent waves in angular spectrum decomposition of shaped beams

Abstract

The angular spectrum decomposition (ASD) is a powerful tool for analyzing the interaction between spherical particles and shaped beams, in which homogeneous plane waves and/or evanescent waves are expanded into series of vector spherical harmonics (VSH). The paper presents a numerical study on the VSH expansion of the evanescent wave and its behavior in the field reconstruction of the shaped beam. It is revealed that the beam shape coefficients (BSCs) of the evanescent waves increase exponentially along the increasing partial wave number, consequently extending the convergence of the series and restricting the field reconstruction into a limited space.