Measured scattering of a first-order vortex beam by a sphere: Cross-helicity and helicity-neutral near-forward scattering and helicity modulation

The wavefield of a traveling wave acoustic vortex beam has an axial null and an angular phase ramp. An appropriately phased four-element transducer array can be used to generate a first order vortex beam [Hefner and Marston, J. Acoust. Soc. Am. 106, 3313–3316 (1999)]. The direction of the phase ramp determines the helicity of the beam. Superposition of signals from an appropriately positioned four-element receiver array gives a helicity selective detector and commutation of diagonal source elements can be used to reverse the source helicity [Marston and Marston, J. Acoust. Soc. Am. 127, 1856 (2010)]. These techniques were used to investigate the near forward scattering by a small sphere placed on or near a beam’s axis. The forward scattering vanishes in the on-axis case [Marston, J. Acoust. Soc. Am. 124, 2905–2910 (2008)]. As the sphere is moved off axis the scattering to a helicity neutral receiver is found to increase linearly in the displacement with a first order phase swirl as a function of the sphere coordinates. For cross-helicity detection (detection opposite the beam’s helicity) as required by symmetry, the signal is approximately quadratic in the displacement with a second-order phase swirl. [Work supported by ONR.]