Design and Optimization of Achromatic High-NA Metalenses Using Graph-Based Electromagnetic Solver

Metasurfaces represent a transformative platform for realizing compact and multifunctional optical devices, enabling precise control over phase, amplitude, and polarization. Metalenses, in particular, have emerged as promising alternatives to bulky refractive optics, with possible uses in imaging, sensing, and metrology. This thesis examines the fundamental principles that dictate light–matter interaction in metasurfaces and evaluates optimisation methodologies for the creation of broadband, high–numerical aperture (NA) metalenses with enhanced efficiency. Present design methodologies encounter inherent physical constraints, and while inverse-design with neural networks expands the search space, reliance on surrogate models introduces errors that full-wave validation could correct, but is computationally infeasible for large devices like metalenses. To address this gap, this work demonstrates that a 2D Graph-BasedElectromagnetic Solver (GEM) offers a fast and accurate solution for training and validation of neural network models, achieving up to forty-fold speed-ups compared to state-of-the-art FDTD solvers. Furthermore, domain decomposition enables parallelization across multiple GPUs, paving the way for efficient three-dimensional simulations. The integration of neural network based optimiza tion tools with this GEM solver, constrained by modern fabrication limits, establishes a practical framework for the inverse design of high-performance, ready to manufacture metalenses.