Arbitrary acoustic scattering of a high‐order Bessel vortex beam by a sphere.

Abstract

The arbitrary acoustic scattering of a high‐order Bessel vortex beam by a sphere is investigated. It is shown here that shifting the sphere off of the axis of wave propagation induces a dependence of the scattering on the azimuthal angle. Theoretical expressions for the incident and scattered fields from a rigid immovable sphere are derived. The near‐ and far‐field acoustic scattering fields are expressed using partial wave series involving the mth‐order spherical harmonics, the scattering coefficients of the sphere, the half‐conical angle of the wave number components of the beam, its order, and the beam‐shape coefficients. The scattering coefficients of the sphere and the three‐dimensional (3‐D) scattering directivity plots in the near‐ and far‐field regions are evaluated using a numerical integration procedure. The calculations indicate that the scattering directivity patterns near the sphere and in the far‐field are strongly dependent on the position of the sphere facing the incident high‐order Bessel vortex beam. In addition to providing physical insight into the off‐axial scattering of acoustic Bessel vortex beams, this investigation would potentially assist in the development of the transverse acoustic radiation force and could provide a useful test of finite element codes for the evaluation of the scattering.