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Photonic inverse design typically seeks designs parameterized by binaryarrays, where the values of each element correspond to the presence or absenceof material at a particular point in space. Gradient-based approaches tophotonic inverse design often include thresholding of non-binary optimizationarrays; when the thresholding is sufficiently sharp, binary designs areobtained. However, difficulty can arise due to vanishing gradients for sharpthresholds, which cause optimization to stall. Here, we present hypersphereoptimization, a new method of carrying out binarized photonic optimization on ahigh dimensional manifold. We numerically show that, on the manifold, upstreamgradients from the objective function can smoothly transition a design from onenearly-binary array to another with minimal pixel flips. Our method is anapproximate gradient-based optimization method for binary arrays that can beapplied to various photonic inverse design problems and beyond.

Hypersphere Optimization: Approximated Gradient-Based Binary Optimization on Smooth Manifold for Photonic Inverse Design