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

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, 661-676 (2013)] for the force and Gong and Baudoin [J. Acoust. Soc. Am. 148, 3131-3140 (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, 3541-3544 (2011)] and Baresch, Thomas, and Marchiano [J. Acoust. Soc. Am. 133, 25-36 (2013)] for the force, and Silva, Lobo, and Mitri [Europhys. Lett. 97, 54003 (2012)] and Gong, Marston, and Li [Phys. Rev. Appl. 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.