Metasurface enabled high-order differentiator

Metasurface-enabled optical analog differentiation has garnered significant attention due to its inherent capacity of parallel operation, compactness, and low power consumption. Most previous works focused on the first- and second-order operations, while several significant works have also achieved higher-order differentiation in both real space and k-space. However, how to construct the desired optical transfer function in a practical system to realize scalable and multi-order-parallel high-order differentiation of images in real space, and particularly how to leverage it to tackle practical problems, have not been fully explored. Here, drawing on the basic mathematical feature of the Fourier transform, we theoretically propose universal phase-gradient functions of the Pancharatnam-Berry-phase-based meta-device for performing arbitrary order differentiation. The fifth-order optical differentiations for both intensity and phase images are realized in the experiment. More importantly, by exploring this elaborately designed spatial differentiator, we construct another scheme for optical super-resolution and achieve the estimation of the distance between two incoherent point sources within 0.015 of the Rayleigh distance, which thereby provides a potential toolkit for optical alignment in high-precision semiconductor nano-fabrication. Our findings hold promise for image processing, microscopy imaging, and optical super-resolution imaging.