Neural Adjoint Inverse Design of Three-Dimensional Nanophotonic Devices

Volumetric meta-optics have emerged as a compact high-performance platform for advanced imaging, color routing in image sensors, and on-chip wavefront control. Realizing such devices depends on solving a high-dimensional nonconvex inverse-design problem governed by Maxwell's equations. Adjoint optimization is the standard route to gradients, yet broadband three-dimensional (3D) design typically requires thousands of full-wave forward/adjoint simulations, making industrial-scale optimization prohibitively slow. To address this bottleneck, a neural adjoint method is introduced, in which a solver-supervised Fourier neural operator (FNO) directly predicts dense, per-voxel 3D adjoint gradient fields from a voxelized permittivity volume. To preserve the sharp, resonance-driven sensitivity peaks that single-pass operator networks tend to oversmooth, a stage-wise FNO is proposed, in which successive stages refine residual errors with progressively higher-frequency emphasis. A domain-specific dataset is curated from paired forward/adjoint finite-difference time-domain (FDTD) simulations spanning three volumetric tasks: spectral sorting (color routers), achromatic focusing (metalenses), and waveguide mode conversion. Across all benchmarks, the surrogate-driven optimization attains figures of merit within 86%-99% of rigorous FDTD-based adjoint optimization whilst reducing end-to-end design time from hours to seconds, with speedups exceeding $10^4\times$ . These results establish a pathway toward fast large-scale volumetric meta-optical design enabled by neural-operator surrogates.