Elastic computational metasurfaces for subwavelength differentiations

Analog computations enable information processing with negligible energy costs and massively parallel architectures, but currently are limited to process macroscale waveforms with characteristic lengths much larger than the operating wavelength λ0. We explore here, in contrast, the differentiation of subwavelength waveforms by using an elastic computational metasurface. We find that the numerical aperture of metasurface governs the threshold of the characteristic length of waveforms, below which the metasurface outputs an identical differentiated pattern. Remarkably, for a subwavelength waveform below the threshold, the metasurface can locate the source because the differentiated pattern is of cylindrical wavefronts centered at the source, which can be harnessed to detect single or multiple subwavelength-scaled scatterers. The detectability reaches a deep subwavelength of 0.12λ0, and the localization error stays smaller than λ0. Our work elucidates the physical image of subwavelength differentiations, which may promote promising applications in nondestructive testing, signal processing, and computational acoustics.