Microring Resonator Dispersion Metrology With Neural Networks

Precise knowledge of resonator dispersion, from both geometric and material contributions, is essential for reliable high-performance nonlinear integrated photonics devices, such as optical parametric oscillators, frequency doublers, and integrated optical frequency combs. However, direct measurements at the fabrication level provide limited knowledge, whether through destructive cross-section imaging or nondestructive ellipsometry, whereas complete optical characterization that enables precise dispersion metrology is time-consuming and poorly suited for mass-scale foundry fabrication. In this work, we develop a machine learning framework to solve three complementary problems: (i) predicting resonator geometric dimensions, (ii) identifying the correct material dispersion, and last, but not least, (iii) precisely reconstructing the integrated dispersion spectrum directly from ring dimensions. These three neural networks together enable both inverse and forward characterization of microring resonators. Using numerically generated datasets based on Sellmeier-type material models, we demonstrate $<1$  nm ring dimension prediction accuracy without noise, $<8$  nm prediction accuracy with $\approx 45$ dispersion samples under a realistic frequency measurement noise level ( $\pm 50$  MHz), and $\approx$ 16 nm prediction accuracy at a higher noise level ( $\pm 200$  MHz). The Sellmeier model classification exceeds 99% accuracy in all cases. Importantly, dispersion sampled far from the pump resonances proves most informative, reducing full-spectrum characterization requirements. The forward-prediction network reconstructs dispersion spectra from the ring dimensions with high accuracy, providing a rapid alternative to numerical simulations and enabling quick assessment of the dispersion regime. Additionally, we present two experimental case studies: in the first, we demonstrate that machine learning can infer trapezoidal ring cross-sectional geometry, including sidewall angle, from measured integrated dispersion data; in the second, we validate our approach against a publicly available dataset, where ML-predicted width and height show close agreement with independently measured values despite an unconstrained ring radius. By combining both inverse and forward predictions, our results highlight the potential of machine learning applied to dispersion data as a rapid, nondestructive tool for wafer-scale quality control and process monitoring in photonic foundries.