Three-dimensional elements, with refractive index distribution structured at sub-wavelength scale, provide an expansive optical design space that can be harnessed for demonstrating multi-functional free-space optical devices. Here we present 3D dielectric elements, designed to be placed on top of the pixels of image sensors, that sort and focus light based on its color and polarization with efficiency significantly surpassing 2D absorptive and diffractive filters. The devices are designed via iterative gradient-based optimization to account for multiple target functions while ensuring compatibility with existing nanofabrication processes, and experimentally validated using a scaled device that operates at microwave frequencies. This approach combines arbitrary functions into a single compact element even where there is no known equivalent in bulk optics, enabling novel integrated photonic applications.
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