Making sound vortices by metasurfaces

Based on the Huygens-Fresnel principle, a metasurface structure is designed to generate a sound vortex beam in airborne environment. The metasurface is constructed by a thin planar plate perforated with a circular array of deep subwavelength resonators with desired phase and amplitude responses. The metasurface approach in making sound vortices is validated well by full-wave simulations and experimental measurements. Potential applications of such artificial spiral beams can be anticipated, as exemplified experimentally by the torque effect exerting on an absorbing disk.

Acoustic vortex beams, proposed early by Nye and Berry 26 , are attracting extensive interest in recent years. [27][28][29][30][31][32] Such sound beams, featured by a screwing phase dislocation around the propagation axis, have been anticipated with exciting applications such as acoustic alignment, 27 wave computations, 28 and acoustic spanners for noncontact rotational manipulation. 30,31 Traditionally, the spiral-like sound beams are generated by transducer (or loudspeaker) arrays with controllable phases. [27][28][29][30][31][33][34][35][36][37][38][39] Recently, some passive techniques for making sound vortices have also been developed based on the spiral gratings 40,41 and sonic crystals. 42 Here we propose a simple metasurface design, endowed with merits of compact and low cost, to convert a uniform sound beam into the spiral shape wavefront. The metasurface is built by a planar plate decorated with several deep subwavelength resonators engineered with 3 / 12 prescribed amplitude and phase responses. The design route has been well confirmed in both full-wave simulations and experimental measurements. Furthermore, the mechanical torque effect exerting on an absorbing disk has been demonstrated preliminarily for such a spiral beam, as an evidence of transferring orbital angular momenta from sound to matter.
It is straightforward to prove that the radiation field of a ring-like line source with Since the diameter of the exit d is in deep subwavelength, the sound wave emitting from the resonator can be safely regarded as a point-like source. Throughout the paper, all full-wave simulations are performed by the commercial finite-element solver (COMSOL Multiphysics), where the solid (epoxy) is modeled as acoustically rigid considering the great impedance mismatch with respect to air.
To search the resonators with sound responses prescribed as above, a plane wave is normally incident upon the planar plate perforated with a single resonator, in which the rotational symmetry can be applied to reduce the computational time. From the far-field sound response, it is easy to extract the amplitude and phase shift at the exit.
(Note that the zero point of phase is fixed at the entrance of the resonator.) As an example, in the inset of Fig. 2 Fig. 4(a), the sound field scanned above the metasurface displays a well-shaped spiral field at the preset frequency 1.51 kHz, consistent with the numerical prediction in Fig. 2(c) again. A test of the frequency response of the wavefront is necessary for the design route based on subwavelength resonators. In Fig. 4(b) we provide the data for 1.47 kHz. Despite of the field distortion displayed in the instant pressure field, the phase pattern manifests an obvious singularity around the field center, an important feature of the screwing field. This is consistent with the fact that the resonance employed here is not too narrow band [see Fig. 2 It is well-known that an acoustic vortex beam carries orbital angular momentum. 43,44 When interacting with an absorbing object, the spiral field can transfer orbital angular momentum to the object and hence exert a mechanical torque on it, as confirmed by several pioneering experiments. 31,34,43,45 Potential applications have been anticipated for the acoustically-induced torque effect, such as for noncontact rotational manipulations on particles. 30,31 Here we experimentally demonstrate the capability of rotating objects by the sound vortex sent from the metasurface. As shown in Fig. 5(a), an absorbing foam disk (of radius 5.0 cm and thickness 0.8 cm) is hung 1.0 cm above the structured metasurface by a fine thread.
When the sound of 1.51 Hz is launched onto the metasurface, a vortex beam is generated and the foam disk is rotated immediately (see the video in the supplementary material). Finally, the disk is balanced with the torque produced by the twisted thread with more or less rigidity, associated with an angle distinct from the 7 / 12 initial one, as shown in Fig. 5(b).
In summary, a metasurface structure has been designed to generate a first-order sound vortex. Good agreement is demonstrated between the sound profiles obtained from full-wave simulations and experimental measurements. Besides, the capability of rotating an absorbing object has been demonstrated experimentally by the vortex beam generated here. The metasurface approach can be conveniently extended to design a vortex of higher order by using more resonant units. It worth pointing out that, the design route proposed here is much simpler than that used for realizing optical vortices by a metasurface, 21