Acoustical helicoidal waves and Laguerre–Gaussian beams: Applications to scattering and to angular momentum transport

Abstract

Traveling waves having helicoidal wavefronts are cylindrically symmetric except for an azimuthal angular dependence of exp(imφ−iωt), where m is an integer. The amplitude vanishes at the screw-phase dislocation [J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165–190 (1974)] on the z propagation axis. Examples of paraxial helicoidal waves are the Laguerre–Gaussian beam solutions of the parabolic wave equation. Some potentially useful properties of acoustical helicoidal waves are analyzed. Just as for linearly polarized optical Laguerre–Gaussian beams [L. Allen et al., Phys. Rev. A 45, 8185–8189 (1992)], the ratio of the axial angular momentum flux to the acoustical beam power is found to be m/ω so that axial radiation torques are generated when the acoustical energy is absorbed. Helicoidal waves are predicted to backscatter in a way which reveals the axisymmetry of the scatterer when combined with a helicoidal mode-selective detector. Some strategies for acoustical helicoidal wave generation and detection will also be described. [Work supported by the Office of Naval Research.]