Scattering of a Bessel beam by a sphere: Geometric interpretation and resonance excitation

Abstract

The exact solution for the scattering of sound by an isotropic sphere centered on a Bessel beam in an inviscid fluid was recently given [P. L. Marston, J. Acoust. Soc. Am. 121, 753–758 (2007)]. The solution gives insight into the scattering by a broader class of beams and provides a benchmark for the testing of finite-element based scattering algorithms. An important parameter in the Bessel beam solution is the cone angle of the Bessel beam which is related to the ratio of the beam size to the sphere radius and to the wave-number-radius product. For an impenetrable sphere there is a simple geometric interpretation of the scattering pattern verified by quantitative ray theory. The modification of the partial wave series due to Bessel beam illumination may be interpreted using the Van de Hulst localization principle. In the scattering by elastic spheres, specific partial-waves may be suppressed by appropriate selection of the cone angle of the beam. Compared with the plane-wave case, this suppression of partial waves may increase or decrease the backscattering, depending on the situation. [Work supported by the Office of Naval Research.]