Near real-time full-wave inverse design of electromagnetic devices.

Inverse design enables automating the discovery and optimization of devices achieving performance significantly exceeding that of traditional human-engineered designs. However, existing methodologies to inverse-design electromagnetic devices require computationally expensive and time-consuming full-wave electromagnetic simulation at each iteration or generation of large datasets for training neural-network surrogate models. This work introduces the Precomputed Numerical Green Function method, an approach for ultrafast electromagnetic inverse design. The static components of the design are incorporated into a numerical Green function obtained from a single fully-parallelized precomputation step, reducing the cost of evaluating candidate designs during optimization to only being proportional to the size of the region under modification. A low-rank matrix update technique is introduced that further decreases the cost of the method to milliseconds per iteration without any approximations or compromises in accuracy. This method is shown to have linear time complexity, reducing the total runtime for an inverse design by several orders of magnitude compared to using conventional electromagnetics solvers. The design examples considered demonstrate speedups of up to 16,000x, shortening the design process from multiple days to weeks down to minutes. The approach enables practical and ultrafast design of complex structures that are prohibitively time-consuming for prior inverse design methods.