Fig. 1.

Acoustic communication using vortex beams with OAM charges −4 to +4. (A) Experimental setup of acoustic communication with vortex beams. A computer-controlled digital-to-analog circuit generates signal to control 4 rings of transducers (with 16 transducers equally spaced on each ring) and emit information encoded into multiplexed acoustic vortex beams into free space at 16 kHz. The radii of these 4 rings are 3, 6, 9, and 12 wavelengths. (B) Measured orthogonality relations between the bases formed by acoustic vortex beams with OAM charges −4 to +4. Each of the bars is calculated by forming the inner products between the measured pressure fields of the two corresponding bases. The norm of each basis is normalized to unity. The cross-talk between the bases is less than −8.54 dB. (C) Measured pressure-field amplitudes and phases of acoustic vortex beam bases with OAM charges −4 to +4 at 100 wavelengths (2.14 m) away from the emitting plane in air. The scanning area covers 22.4 wavelengths by 22.4 wavelengths (48 cm × 48 cm) with 26 by 26 resolutions. Thermal and rainbow-scale color bars are used for the measured amplitude and phase fields, respectively.