  Optical metasurfaces are planar arrangements of subwavelength meta-atoms that
implement a wide range of transformations on incident light. The design of
efficient metasurfaces requires that the responses of and interactions among
meta-atoms are accurately modeled. Conventionally, each meta-atom's response is
approximated by that of a meta-atom located in a periodic array. Although this
approximation is accurate for metastructures with slowly varying meta-atoms, it
does not accurately model the complex interactions among meta-atoms in more
rapidly varying metasurfaces. Optimization-based design techniques that rely on
full-wave simulations mitigate this problem but thus far have been mostly
applied to topology optimization of small metasurfaces. Here, we describe an
adjoint-optimization-based design technique that uses parameterized meta-atoms.
Our technique has a lower computational cost than topology optimization
approaches, enabling the design of large-scale metasurfaces that can be readily
fabricated. As proof of concept, we present the design and experimental
demonstration of high numerical aperture metalenses with significantly higher
efficiencies than their conventionally-designed counterparts.
