  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 and apply a technique for the estimation of the efficiency 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.
