Scattering of focused beams by spheres: Understanding the high-frequency angular structure

Previous work on scattering of Bessel beams by spheres [P. L. Marston, J. Acoust. Soc. Am. 122, 247–252 (2007)] and recent work expanding linear focused beams in terms of a Bessel beam superposition [T. D. Daniel et al., J. Acoust. Soc. Am. 144, 3076–3083 (2018)] provide a framework for exploring the scattering of focused beams by spheres. In analogy with the work done on the scattering of Gaussian beams by spheres [P. L. Marston, J. Acoust. Soc. Am. 129, 1773–1782 (2011)], the angular scattering pattern of a sphere in a focused beam is calculated from a partial wave series with appropriate weighting factors (also known as beam shape coefficients). The high-frequency pattern for rigid spheres is found to have distinctive shadow boundaries in both the forward and backward scattering hemispheres. The sphere is centered on the beam axis. A physical optics model of the scattering reproduces the location and general shape of the shadow boundaries in both scattering hemispheres, confirming the calculated beam shape coefficients for a spherical cap focused source. [Work supported by ONR.]