Nonresonant Metasurface for Fast Decoding in Acoustic Communications

Acoustic communication is crucial in underwater exploration, where sound is the dominant information carrier, with significantly less loss and scattering than that of electromagnetic waves. However, the capacity of acoustic communication channels is limited due to the intrinsically low speed of sound relative to that of electromagnetic waves and because the attenuation of acoustic waves underwater increases with frequency. Recently, orbital angular momentum (OAM) has emerged as an alternative multiplexing degree of freedom to encode data onto vortex beams for increasing the capacity of acoustic communication. For information retrieval from the multiplexed acoustic vortices, an active scanning method and a passive resonant method are explored. Time-consuming scanning and complex postprocessing significantly restrict the data-transmission speed, while the large amount of resonant cascaded devices in the passive technique intrinsically results in a low efficiency and bulky volume of the system. Here, we propose and experimentally demonstrate a passive and nonresonant approach with the ability to separate different OAM states of multiplexed acoustic vortex beams in parallel using a parabolic-phased metasurface. The metasurface converts the spiral-phase patterns of vortex beams carrying various angular momenta into plane waves with different in-plane linear momenta. Our approach is compatible with multiplexing technologies, significantly enhancing the speed in acoustic communication.

Figure 1

Parallel sorting of the multiplexed vortex beams with the nonresonant metasurface. (a) Schematic of the experimental setup. Two-dimensional (2D) waveguide (transparent plastic glass) with the subwavelength metasurface (green) assembled on one end serves as a reading device. The metasurface is designed to mimic the phase gradient of a parabolic reflector. Sorting includes two processes. (1) The multiplexed vortex beams propagating in free space (spirals) are coupled into the 2D waveguide through an aperture on the top wall at the focal point of the parabola. (2) The decoding metasurface converts the vortex modes (red and blue arrows) radiated from the focal point into modes with different in-plane linear momenta, resulting in reflected plane waves propagating in different directions (purple arrows). Based on this scheme, information encoded on the superimposed OAM multiplexed signal can be read out in parallel by detecting the reflected waves at specific spatial angles. (b) Photograph of the 3D-printed decoding metasurface used in experiments. The metasurface is made from acrylonitrile butadiene styrene (ABS) plastic, with a length of 89.6 cm in the y direction and maximum thickness of 2.8 cm in the x direction.

Figure 2

Parallel sorting of acoustic OAM modes. (a) Simulated phase distributions of acoustic vortex beams with various OAM charges, $m=0,\pm 1,\pm 2,\pm 4$. The twist number in the phase pattern indicates the magnitude of m, and the twist direction determines the sign. (b),(c) Reflected pressure fields for acoustic vortex beams carrying different OAM charges in numerical simulations and experimental measurements. The simulations and measurements match each other, both of which show that vortex beams with positive and negative OAM charges are reflected in opposite directions, and the reflection angle increases with the magnitude of m. Spatial separation of different acoustic OAM modes is used for parallel information decoding in acoustic OAM-based multiplexing.

Figure 3

Analysis of reflection in reciprocal space. (a),(b) Simulated and measured distributions of spectra in reciprocal space with various OAM charges, $m=0,\pm 1,\pm 2,\pm 4$. The spectrum of the beam with $m=0$ has only a wavevector component along the propagating direction (x axis), while the nontrivial OAM charge gives rise to the transverse linear momentum, corresponding to the emergence of $k_y$. The dotted (white) lines show the reference positions $k_y=0$ and the dashed (black) lines indicate the positions where $k_x$ reaches its maximum value. (c),(d) Distributions of the amplitude of the spectra along the dashed (black) lines in the reciprocal space as functions of $k_y$ for various OAM charges, as obtained from numerical simulations and experimental measurements. The emergence of transverse linear momentum and shift of the spatial spectra for nontrivial m are clearly demonstrated. The results are normalized with their corresponding maximum values. (e) Relationship between the reflection angle, $\alpha$, and OAM charge, m. The reflection angle results from the transverse linear momentum by $\alpha ={\tan }^{-1}(k_y/k_x)$. A nearly linear relationship between $\alpha$ and m is observed from both numerical simulations and experimental measurements.

Figure 4

Analytical model and controllability of the reflection angle. (a) Schematic plot of the ray trajectory of vortex beams radiated from the focal point $F(p/2,0)$ and reflected by the parabola. The reflection of the vortex beams with nontrivial OAM charge by the parabola is equivalent to a line source with the phase gradient $\phi (y)$ on the directrix, $x=-p/2$, inducing a transverse linear momentum (along the y axis) and angular shift of the reflection. (b) Reflection angle $\alpha$ as a function of OAM charge m, with wavelengths of the vortex beams of $\lambda =1\mathrm{.62},3.25,6\mathrm{.5,}\mathrm{and\; 9}\mathrm{.75cm}$ and the geometric parameter of the parabola $p=0\mathrm{.8m}$, which is obtained from numerical simulations. The reflection angle shows a linear relationship with both m and $\lambda$, i.e., $\alpha \propto m\lambda$, which agrees with the analytical calculation. (c) Relationship between reflection angle $\alpha \mathrm{and}$ parameter p, with OAM charges $m=0,\pm 2,\pm 4,\pm 6$ and a wavelength $\lambda =6\mathrm{.5}\mathrm{cm}$, which shows that the angular shift is inversely proportional to p, i.e., $\alpha \propto p^{-1}$. The red dots in (b),(c) represent the results obtained with the same parameters used in the experiments.