We report the optimal focusing of acoustic vortex beams by using flat lenses based on a Fresnel-spiral diffraction grating. The flat lenses are designed by spiral-shaped Fresnel zone plates composed of one or several arms. The constructive and destructive interferences of the diffracted waves by the spiral grating result in sharp acoustic vortex beams, following the focal laws obtained in analogy with the Fresnel zone plate lenses. In addition, we show that the number of arms determines the topological charge of the vortex, allowing the precise manipulation of the acoustic wave field by flat lenses. The experimental results in the ultrasonic regime show excellent agreement with the theory and full-wave numerical simulations. A comparison with beam focusing by Archimedean spirals also showing vortex focusing is given. The results of this work may have potential applications for particle trapping, ultrasound therapy, imaging, or underwater acoustic transmitters.

Acoustic vortex beams have great potential for contactless particle manipulation and torque-based biomedical applications. However, focusing acoustic waves through highly aberrating layers such as the human skull at ultrasonic frequencies results in strong phase aberrations, which prevent the generation of sharp acoustic images. In the case of a wavefront containing phase dislocations, skull aberrations can inhibit the focusing of acoustic vortex beams inside the cranial cavity. In this paper, we demonstrate that phase-conjugated acoustic holograms can encode time-reversed fields, allowing compensation of the aberrations of the skull and, simultaneously, the generation of a focused vortex inside an ex vivo human skull. The method is applied to single-element geometrically focused sources and results in a very simple and compact ultrasonic system. This work will pave the way to designing low-cost particle-trapping systems, clot manipulation, and the exertion of acoustic-radiation forces and torques in the brain for biomedical applications.