Rigorous justification of a localized approximation to encode on-axis Gaussian acoustical waves

Abstract

Generalized Lorenz–Mie theory (GLMT) describes the interaction between electromagnetic waves (more specifically, laser beams) and homogeneous spherical particles. An acoustical GLMT-like framework can be used to deal with acoustical wave scattering. The incident acoustical wave may then be encoded in a set of beam shape coefficients (BSCs) similar to the ones used in electromagnetic scattering. One method to evaluate the acoustical BSCs is the localized approximation which takes the form of a variant of a localized approximation used to evaluate the electromagnetic BSCs. These acoustical BSCs are discussed and rigorously justified in the case of on-axis Gaussian beams. Examples of field reconstruction and remodeling using the localized approximation are presented which reinforce the robustness of such a method for very small confinement parameters. We expect that the results presented here will encourage a wider use of localized approximation schemes in acoustic scattering problems.