Focusing a Two-Dimensional Acoustic Vortex Beyond Diffraction Limit on an Ultrathin Structured Surface

We propose and experimentally demonstrate a mechanism for focusing two-dimensional (2D) vortex for airborne sound beyond diffraction limit on an ultrathin structured surface in free space. A simple design of unit cell is presented as a practical implementation, which is capable of exciting evanescent wave and modulating its propagation phase over full 0-to-2\ensuremath{\pi} range. By analytically deriving the dispersion relationship and desired azimuthal distribution of effective parameters, we elucidate how to guide the propagation of excited evanescent waves in the vicinity of an unbounded surface decorated with designed structures and focus such surface vortex within a target region despite its compactness and nonaxisymmetry. The effectiveness of our mechanism is demonstrated numerically and experimentally via production and confinement of 2D vortex on a square surface at subwavelength spatial resolution. We anticipate our methodology with no need of a 2D system, bulky device size, geometric symmetry, active elements, or complicated phased array to offer new possibilities for the miniaturization and integration of planar vortex devices and may promote their on-chip applications in various fields such as by significantly boosting the information density and manipulation precision.