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Large-scale metasurfaces promise nanophotonic performance improvements tomacroscopic optics functionality, for applications from imaging to analogcomputing. Yet the size scale mismatch of centimeter-scale chips versusmicron-scale wavelengths prohibits use of conventional full-wave simulationtechniques, and has necessitated dramatic approximations. Here, we show thattailoring "fast direct" integral-equation simulation techniques to the formfactor of metasurfaces offers the possibility for accurate and efficientfull-wave, large-scale metasurface simulations. For cylindrical(two-dimensional) metasurfaces, we demonstrate accurate simulations whosesolution time scales \emph{linearly} with the metasurface diameter. Moreover,the solver stores compressed information about the simulation domain that isreusable over many design iterations. We demonstrate the capabilities of oursolver through two designs: first, a high-efficiency, high-numerical-aperturemetalens that is 20,000 wavelengths in diameter. Second, a high-efficiency,large-beam-width grating coupler. The latter corresponds to millimeter-scalebeam design at standard telecommunications wavelengths, while the former, at avisible wavelength of 500 nm, corresponds to a design diameter of 1 cm, createdthrough full simulations of Maxwell's equations.

Fullwave design of cm-scale cylindrical metasurfaces via fast direct solvers