  Conventional phased-array metasurfaces utilize resonant nanoparticles or
nanowaveguides to specify spatially-dependent amplitude and phase responses to
light. In nearly all these implementations, subwavelength-scale elements are
stitched together while minimizing coupling between adjacent elements. In this
report, we theoretically analyze an alternate method of metasurface design,
utilizing freeform inverse design methods, which support significantly enhanced
efficiencies compared to conventional designs. Our design process optimizes
wavelength-scale elements, which dramatically increases the design space for
optical engineering. An in-depth coupled mode analysis of ultra-wide-angle beam
deflectors and wavelength splitters shows that the extraordinary performance of
our designs originates from the large number of propagating modes supported by
the metagrating, in combination with complex multiple scattering dynamics
exhibited by these modes. We also apply our coupled mode analysis to
conventional nanowaveguide-based metasurfaces to understand and quantify the
factors limiting the efficiencies of these devices. We envision that freeform
metasurface design methods will open new avenues towards truly
high-performance, multi-functional optics by utilizing strongly coupled
nanophotonic modes and elements.
