Scattering of a Bessel beam by a sphere: II. Helicoidal case and spherical shell example

In prior work [P. L. Marston, "Scattering of a Bessel beam by a sphere," J. Acoust. Soc. Am. 121, 753-758 (2007)] the partial wave series for the scattering by a sphere centered on a zero-order Bessel beam was derived. The present work extends the analysis of the far-field scattering to the case of a Bessel beam having an angular dependence on phase. The beam considered is an example of a helicoidal beam where "helicoidal" refers to a type of beam that possesses an axial null and has an azimuthal phase gradient. This type of beam is sometimes also referred to as an acoustic vortex. The beam considered here has a phase ramp equal to the azimuthal angle. In agreement with symmetry arguments given previously, the backward scattering and forward scattering vanish for all frequencies. Some of the resulting modifications of the scattering are illustrated for a rigid sphere and an evacuated steel shell in water. For some directions and choices for the frequency, the calculated scattering by the shell increases when shifting to a helicoidal beam illumination.