  Optical metasurfaces have been heralded as the platform to integrate multiple
functionalities in a compact form-factor, potentially replacing bulky
components. A central stepping stone towards realizing this promise is the
demonstration of multifunctionality under several constraints (e.g. at multiple
incident wavelengths and/or angles) in a single device -- an achievement being
hampered by design limitations inherent to single-layer planar geometries.
Here, we propose a general framework for the inverse design of volumetric 3D
metaoptics via topology optimization, showing that even few-wavelength thick
devices can achieve high-efficiency multifunctionality. We embody our framework
in multiple closely-spaced patterned layers of a low-index polymer. We
experimentally demonstrate our approach with an inverse-designed 3d-printed
light concentrator working at five different non-paraxial angles of incidence.
Our framework paves the way towards realizing multifunctional ultra-compact 3D
nanophotonic devices.
