Neural Adjoint Inverse Design of Three‐Dimensional Nanophotonic Devices

ABSTRACT 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 . These results establish a pathway toward fast large‐scale volumetric meta‐optical design enabled by neural‐operator surrogates.