Fig. 2: Processes of image encoding and decoding in our proposed OAM- and frequency-dependent acoustic hologram mechanism.

a Pre-processing of spatial sampling on the target images. b The schematic diagram of the derivation of phase and amplitude profiles of the metasurface for realizing the OAM- and frequency-multiplexed acoustic hologram. The formula \({{\bf{x}}}={G}^{-1}{{\bf{y}}}\) indicates matrix inversion to obtain the amplitude-phase profile of the metasurface, where x and y are the complex amplitude profiles of the metasurface’s acoustic response and target image, and G is Green’s function. c Target images (upper) and numerically calculated OAM- and frequency-dependent holographic images (lower) for four cases of different beam incidence with topological orders l = ±1 and frequencies f1 = 13720 Hz and f2 = 17150 Hz.