Physics-Informed Fourier Neural Operator for Nanophotonic Scattering in Nonlinear Media

The Fourier Neural Operator (FNO) has shown remarkable success in approximating solutions to partial differential equations in fluid dynamics, yet its potential for nanophotonic systems remains largely unexplored.  We present a physics-informed FNO architecture for solving Maxwell's equations for scattering problems containing nonlinear materials. Trained on finite-difference time-domain (FDTD) simulations, we develop a model that learns the family of solutions mapping electromagnetic field configurations forward in time. Additionally, we construct a model that can predict the optical spectra given initial conditions. We benchmark both approaches against conventional FDTD and experimental data to assess computational efficiency and accuracy. Critically, we explore how well the trained models generalize beyond their training domains, predicting fields and spectra for untested resolutions, geometric configurations, and source parameters. These results suggest FNOs could dramatically accelerate the inverse design and optimization workflows for nonlinear photonic metasurfaces, where conventional solvers remain prohibitively expensive for exploring large parameter spaces.