A neural operator-based surrogate solver for free-form electromagnetic inverse design

Tools for solving Maxwell's equations are essential in nanophotonics for modeling light-matter interaction at the wavelength scale and, in extension, for designing new optical devices. Some of the most established methods for this purpose are finite element solvers (FEM) [1, 2] in the frequency domain and finite difference solvers for both frequency (FDFD) [3, 4] and time domain (FDTD) [5-7]. As full-wave Maxwell solvers, these methods represent the most general and accurate class of tools for modeling electromagnetic systems. However, full-wave solutions often involve significant time and computational cost, placing a practical limit on the scale of problems that can be tackled. This is exacerbated in problems such as inverse design [8-12], where typically on the order of hundreds of simulations have to be performed to reach reasonable solutions. While there are ongoing developments in the search for faster full-wave solvers [13, 14], there exist also a variety of semi-analytical methods [15-18] that can potentially offer order-of-magnitude speedups.