Resolution-Aware Small-Data Inverse Design of Nonlinear Plasmonic Metasurfaces Using Surface-SHG Proxy Targets

Abstract

Machine-learning inverse design of nonlinear plasmonic metasurfaces is limited by the cost of full-wave simulation and by the scarcity of labeled nonlinear optical data. We demonstrate a personal-computer-scale workflow for periodic Au nanorod metasurfaces in which normalized linear finite-difference time-domain (FDTD) fields are extracted on near-surface shell planes and converted into relative second-harmonic-generation (SHG) proxy targets. A 35-sample Latin-hypercube dataset over nanorod length, width, height, lattice period, and pump polarization was generated using MEEP and used to train a radial-basis-function kernel-ridge-regression surrogate. Five-fold cross-validation gives a KRR mean absolute error of 0.493<inline-formula><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula>0.123 log<inline-formula><tex-math notation="LaTeX">$_{10}$</tex-math></inline-formula> units across three SHG-proxy targets, compared with 0.557<inline-formula><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula>0.150 log<inline-formula><tex-math notation="LaTeX">$_{10}$</tex-math></inline-formula> units for degree-1 ridge regression. Direct surrogate maximization overpredicted sparse regions, motivating local active refinement, an offline Bayesian-optimization baseline, and explicit convergence testing. The original sharp-block surface proxy did not pass mesh convergence. A smooth ellipsoid, mesh-locked convergence branch reduced the successive-resolution change from 0.305 log<inline-formula><tex-math notation="LaTeX">$_{10}$</tex-math></inline-formula> at 80–100 px/<inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>m to 0.072 log<inline-formula><tex-math notation="LaTeX">$_{10}$</tex-math></inline-formula> at 120–140 px/<inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>m, with the center-wavelength target reaching the 0.05 log<inline-formula><tex-math notation="LaTeX">$_{10}$</tex-math></inline-formula> criterion but the full three-frequency target still failing. The robust conclusion is therefore a convergence-limited, resolution-aware workflow rather than a mesh-converged optimized-device claim. <bold>Impact Statement</bold>: The primary contribution of this work is a validation protocol and methodological caution for machine-learning inverse design of nonlinear plasmonic metasurfaces, not a mesh-converged device record. Standard practice reports single-resolution surrogate optima as design records without mesh-convergence gating; we show this is unsafe by demonstrating that a coarse-grid 2.51× SHG-proxy gain collapses to 1.05× under finer-grid validation. Our reproducible personal-computer-scale workflow promotes a design only after passing multi-resolution FDTD and energy-sanity gates, distinguishing genuine high-response basins from voxelization artifacts and enabling small laboratories to screen nonlinear plasmonic concepts without producing unconverged claims.