Design and Optimization of Metasurfaces for Silicon Photonics: PhD Thesis

Abstract

Metasurfaces, two-dimensional arrangements of subwavelength nanopillars, provide local control over the phase of light, enabling flat optical functions beyond conventional refractive components. Their inverse design, finding the pillar distribution producing a target response, faces two obstacles: the immense dimensionality of the design space and the prohibitive cost of rigorous electromagnetic simulations, precluding exhaustive exploration at device scale. This thesis addresses the challenge in three stages. The first assesses the reliability of rigorous Maxwell solvers: comparing three implementations of Li's factorization rules for RCWA shows that spectral convergence does not guarantee physical fidelity, as these rules implicitly distort the simulated permittivity, most severely in the plasmonic regime. FDTD, immune to such artifacts, is retained as ground truth throughout. The second stage removes the computational bottleneck: a local phase-approximation model, then fully convolutional surrogates trained on FDTD simulations of large pillar metasurfaces, predict the near field almost instantaneously. Exploiting problem symmetries quadruples the training database, and the surrogates generalize to much larger apertures while remaining differentiable. The third stage benchmarks three strategies under a common FDTD protocol ($R^2$ between realized and target far fields): Gerchberg-Saxton retrieval and Local Model ($R^2\approx0.925$), surrogate-based and heuristic-initialized gradient descent ($R^2\approx0.975$), and a generative framework based on diffusion models and Schr\"odinger bridges. Hybrid posterior sampling and amplitude constraints restore scale-invariant fidelity on surfaces over 230 times larger than training, with diverse, fabrication-tolerant designs. Database enhancement lifts every approach to $R^2\approx0.97$.