One of the important advantages of optical metasurfaces over conventional diffractive optical elements is their capability
to efficiently deflect light by large angles. However, metasurfaces are conventionally designed using approaches that are
optimal for small deflection angles and their performance for designing high numerical aperture devices is not well quantified.
Here we introduce a technique for the estimation of the efficiency and the design of high numerical aperture metasurfaces.
The technique is based on a particular coherent averaging of diffraction coefficients of periodic blazed gratings and can be
used to compare the performance of different metasurface designs in implementing high numerical aperture devices. Unlike
optimization-based methods that rely on full-wave simulations and are only practicable in designing small metasurfaces, the
gradient averaging technique allows for the design of arbitrarily large metasurfaces. Using this technique, we identify an
unconventional metasurface design and experimentally demonstrate a metalens with a numerical aperture of 0.78 and a
measured focusing efficiency of 77％. The grating averaging is a versatile technique applicable to many types of gradient
metasurfaces, thus enabling highly efficient metasurface components and systems.