Broadband Electromagnetic Field Prediction at Unseen Wavelengths via Physics-Guided Neural Operators

Surrogate solvers that deliver full-wave accuracy across broad spectral ranges can unlock the rapid design and analysis of nanophotonic devices. We present a physics-guided neural-operator surrogate solver that predicts electromagnetic field distributions throughout the visible band from a permittivity map and a query wavelength, including wavelengths unseen during training. Our approach is built on two key ideas: (i) spectral consistency, which formalizes the intrinsic relationship between wavelength-dependent field variations and spatial frequency, and (ii) a conditional embedding framework that comprises a refined wave prior. We validate the approach on three representative nanophotonic platforms-a single-layer metasurface (metalenses), a five-layer volumetric metasurface (spectrum-splitters), and a freeform waveguide for photonic integrated circuits-achieving full-wave fidelity while reducing mean field-prediction error relative to prior operator-learning baselines by up to 80.3% (single-layer), 56.8% (multilayer), and 32.3% (waveguide). The solver remains compact (0.43 M parameters; 86.9% fewer than FNO) and accelerates simulation by $\sim 42\times$ compared with a finite-difference frequency-domain solver while yielding robust broadband generalization. By providing continuous-wavelength field predictions with full-wave accuracy, this surrogate solver eliminates a key bottleneck in modeling and inverse design of metalenses, spectrum splitters, and emerging large-area meta-optics, offering a drop-in engine for system-level co-optimization in nanophotonics.