Flat optics for optical image differentiation

The differentiator consists of carefully designed 2D photonic crystal (PhC) slab that can transform an image into its second-order derivative. Based on interference between the direct transmission and low quality factor quasi-guided modes, the PhC slab exhibits angular-dependent transmission for P polarization but remains reflective for S polarization, which avoids polarization mixing in the transmission matrix. Fourier imaging was carried out showing a quadratic transfer function for an NA up to 0.315, which allows one to resolve features on the scale of 1.94λ. To showcase practical applications, the nanophotonic differentiator was directly integrated into an optical microscope and onto a camera sensor demonstrating the ease at which it can be vertically integrated into existing imaging systems. Furthermore, we demonstrate a compound bilayer flat optical by integrating the differentiator with a metalens for realizing a compact and monolithic image processing system. In all cases, the use of the nanophotonic differentiator allows for a significant reduction in size compared to traditional systems as one does not need to pass through the Fourier plane for performing complex image processing. This freedom should open new doors for optical analog image processing in applications involving machine vision.