Polarization-Conditioned Fourier-enhanced DeepONet for Electric Field Reconstruction from EFISH Measurements

Abstract

Electric-field-induced second-harmonic generation (EFISH) is an established laser diagnostic for quantifying electric fields in plasmas, yet ensuring field accuracy remains challenging given the coherent, path-integrated nature of the signal. We address this via machine learning, developing a Polarization-Conditioned Fourier-enhanced Deep Operator Network (PC-FDON) -- a unified operator-learning model that reconstructs field profiles from EFISH measurements across both polarizations and various optical parameters. Its architecture incorporates three advances: (i) a Fourier-enhanced branch providing inductive bias for the Gouy phase shift and wave-vector mismatch; (ii) a polarization-conditioning branch encoding signal polarization via Feature-wise Linear Modulation (FiLM) and gated units, enabling one model to handle both polarizations; and (iii) a physics-informed loss enforcing self-consistency with the governing EFISH equation. Trained on data spanning multiple function families, polarization states, and phase-mismatch values, PC-FDON achieves promising reconstruction under noise-free, incomplete, and noisy inputs, with generalizability comparable to our previous polarization-specific model. Pointwise epistemic uncertainty estimates via Monte Carlo dropout reflect model confidence and enable out-of-distribution (OOD) detection through a location-dependent exceedance fraction metric. Validation is performed on realistic electrode configurations under both polarizations and varying Rayleigh ranges, including a simulated surface dielectric barrier discharge where the framework correctly flags OOD inputs, and experimental data showing good agreement with simulations. The architecture -- spectral inductive bias, conditional modulation, and dataset-specific uncertainty -- shows strong potential for broader application beyond plasma diagnostics.