Ultra-fast simulation and design of nanophotonic devices

This thesis explores advanced methodologies for the ultra-fast simulation and design of nanophotonic devices, emphasizing the efficiency and accuracy of inverse design processes. The study introduces a multi-scale hierarchical inverse design approach that optimizes the fabrication compatibility and performance of nanophotonic components. A significant contribution is the development of a factorization caching method that dramatically reduces computational overhead in the gradient computation phase of inverse design, thereby accelerating the overall optimization process. This method proves particularly effective for two-dimensional finite-difference frequency-domain (FDFD) simulations, offering substantial time savings without compromising physical accuracy. Furthermore, the integration of deep learning techniques into nanophotonic simulations is examined. A dual-stage model trained with physics-based losses is presented, achieving simulation speeds up to 3408 times faster than traditional three-dimensional finite-difference time-domain (FDTD) methods. This model ensures high fidelity in the simulation results, maintaining robustness across various device geometries and sizes. The advancements detailed in this thesis not only enhance the computational efficiency of photonic device design but also expand the feasible design space, paving the way for the development of innovative and practical nanophotonic devices.