Acoustic vortex beam created with a continuous phase ramp lens and resulting radiation torque response of a sphere

Abstract

An acoustic vortex beam was created in water using a lens with a phase ramp placed in front of a focused transducer. The lens was made from a polystyrene disk and CAD machine milled to have a continuous ramp in height about the center axis, with the ramp step height corresponding to a 2π phase difference between waves propagating in water and polystyrene at 500 kHz. This causes the transmitted beam through the lens to exit as a vortex beam with an angular phase ramp. It has been predicted [L. Zhang and P. L. Marston, J. Acoust. Soc. Am. 136, 2917–2921 (2014)] that the torque exerted by a vortex beam on an impenetrable sphere in a viscous fluid is proportional to the incident intensity due to dissipation of angular momentum in the viscous boundary layer near the sphere. This should result in steady rotation of the sphere with viscous drag proportional to angular velocity. Our upward-directed vortex beam was used to trap and spin a Styrofoam (closed foam) ball floating at the water surface. The spin rate was approximately proportional to the square of the source voltage as expected. [Work supported by ONR.]