Off-axial acoustic scattering of a high-order Bessel vortex beam by a rigid sphere

Abstract

In this paper, the off-axial acoustic scattering of a high-order Bessel vortex beam by a rigid immovable (fixed) sphere is investigated. It is shown here that shifting the sphere off the axis of wave propagation induces a dependence of the scattering on the azimuthal angle. Theoretical expressions for the incident and scattered field from a rigid immovable sphere are derived. The near-and far-field acoustic scattering fields are expressed using partial wave series involving the 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 3D scattering directivity plots in the near-and farfield 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 upon the position of the sphere facing the incident high-order Bessel vortex beam.

Multipole expansion of acoustical Bessel beams with arbitrary order and location

“…It is noteworthy that the off-axis scattering of Bessel beams from a rigid sphere has been investigated by using numerical quadrature to compute the corresponding beam-shape coefficients. 3,4 In addition, the on-axial 5,6 and off-axial 7 acoustic radiation force properties for spherical shapes in Bessel beams were studied using the partial-wave series expansion method. The geometrical interpretation of negative radiation forces in ideal Bessel beams was also discussed and it was found that negative forces only occur when the scattering into the backward hemisphere is suppressed relative to the scattering into the forward hemisphere.…”

Axial radiation force exerted by general non-diffracting beams

“…One approach would be to use a method based on numerical integration of beam-shape coefficients. 17,18 The results here using momentum conservation, however, are not restricted to spheres and apply to general non-diffracting beams. The asymmetry hcos hi s is relative to the evaluated direction n z with n Á n z ¼ cos h. The oblique angle b only affects as the projection of the extinction into the evaluated direction n z since all of the other parameters (including extinction, absorption, scattering, and asymmetry) are intrinsic properties of the object associated with the incident direction.…”

Radiation force of an arbitrary acoustic beam on an elastic sphere in a fluid

“…There are several alternative descriptions of these waves. For instance, the incident wave can be represented as a series of spherical harmonics; 18,19 the advantage in such an approach is that each spherical harmonic of the incident wave gives rise to the same spherical harmonic of the scattered wave [e.g., compare Eqs. (7) and (11)].…”

“…In particular, analytic methods are especially effective for cases of spherical objects in fluids, for which scattering theory is well-developed. For instance, a multipole expansion can be used to represent the acoustic field, 18,19 which makes it possible to express the radiation force for an arbitrary beam. In Ref.…”