Partial wave series expansions in spherical coordinates for the acoustic field of vortex beams generated from a finite circular aperture

摘要

Stemming from the Rayleigh-Sommerfeld surface integral, the addition theoremsfor the spherical wave and Legendre functions, and a weighing functiondescribing the behavior of the radial component of the normal velocity at thesurface of a finite circular radiating source, partial-wave series expansionsare derived for the incident field of acoustic spiraling (vortex) beams in aspherical coordinate system centered on the axis of wave propagation. Examplesfor vortex beams, comprising \rho-vortex, zeroth-order and higher-orderBessel-Gauss and Bessel, truncated Neumann-Gauss and Hankel-Gauss,Laguerre-Gauss, and other Gaussian-type vortex beams are considered. Themathematical expressions are exact solutions of the Helmholtz equation. Theresults presented here are particularly useful to accurately evaluateanalytically and compute numerically the acoustic scattering and othermechanical effects of finite vortex beams, such as the axial and 3D acousticradiation force and torque components on a sphere of any (isotropic,anisotropic etc.) material (fluid, elastic, viscoelastic etc.). Numericalpredictions allow optimal design of parameters in applications including butnot limited to acoustical tweezers, acousto-fluidics, beam-forming design andimaging to name a few.