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In this talk, I describe a fast full-wave Maxwell equations solver based on the “augmented partial factorization” (APF) method and our inverse design of nonlocal metasurfaces using APF. 

We derive a fundamental bound on the transmission efficiency of diffraction-limited nonlocal metalenses. We show that high efficiency at large numerical aperture re-quires the entrance aperture to be smaller than the output aperture. 

We realize full-wave single-shot computations of the polarization-resolved scattering matrices of 3D complex media using the “augmented partial factorization” method. Our parallelized solver achieves three orders of magnitude speed-up compared to parallelized iterative FDFD method. 

Abstract Metalenses—flat lenses made with optical metasurfaces—promise to enable thinner, cheaper, and better imaging systems. Achieving a sufficient angular field of view (FOV) is crucial toward that goal and requires a tailored incident-angle-dependent response. Here, we show that there is an intrinsic trade-off between achieving a desired broad-angle response and reducing the thickness of the device. Like the memory effect in disordered media, this thickness bound originates from the Fourier transform duality between space and angle. One can write down the transmission matrix describing the desired angle-dependent response, convert it to the spatial basis where its degree of nonlocality can be quantified through a lateral spreading, and determine the minimal device thickness based on such a required lateral spreading. This approach is general. When applied to wide-FOV lenses, it predicts the minimal thickness as a function of the FOV, lens diameter, and numerical aperture. The bound is tight, as some inverse-designed multi-layer metasurfaces can approach the minimal thickness we found. This work offers guidance for the design of nonlocal metasurfaces, proposes a new framework for establishing bounds, and reveals the relation between angular diversity and spatial footprint in multi-channel systems. 

Topology optimization of nonlocal metasurfaces requires the objective-function gradient considering all angles of interest. We generalize the recent “augmented partial factorization” method to compute such gradient efficiently and inverse design a broad-angle metasurface beam splitter.