Equivalence between angular spectrum-based and multipole expansion-based formulas of the acoustic radiation force and torque

TL;DR

This paper demonstrates the formal equivalence between two main methods—angular spectrum decomposition and multipole expansion—for calculating acoustic radiation force and torque on particles, unifying their theoretical frameworks.

Contribution

It establishes the formal mathematical equivalence between the angular spectrum-based and multipole expansion-based formulas for acoustic radiation force and torque.

Findings

Proves the equivalence of the two methods mathematically.

Provides a unified framework for calculating acoustic radiation force and torque.

Enhances understanding of the relationship between different theoretical approaches.

Abstract

Two main methods have been proposed to derive the acoustical radiation force and torque applied by an arbitrary acoustic field on a particle: The first one relies on the plane wave angular spectrum decomposition of the incident field (see [Sapozhnikov and Bailey, J. Acoust. Soc. Am. 133, 661 (2013)] for the force and [Gong and Baudoin, J. Acoust. Soc. Am. 148, 3131 (2020)] for the torque), while the second one relies on the decomposition of the incident field into a sum of spherical waves, the so-called multipole expansion (see [Silva, J. Acoust. Soc. Am. 130, 3541 (2011)] and [Baresh et al., J. Acoust. Soc. Am. 133, 25 (2013)] for the force, and [Silva et al., EPL 97, 54003 (2012)] and [Gong et al., Phys. Rev. Applied 11, 064022 (2019)] for the torque). In this paper, we formally establish the equivalence between the expressions obtained with these two methods for both the force and torque.