  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.
