Correlation‐Aware Uncertainty Quantification and Robustness Assessment of Dual One‐Dimensional Photonic‐Crystal Refractive‐Index Sensors: A Numerical Study

This purely numerical study develops a correlation‐aware framework for quantifying fabrication‐induced uncertainty in a dual one‐dimensional photonic‐crystal refractive‐index sensor; no device was fabricated, and no spectrum was measured. The geometry‐error model is prescribed rather than measured: Layer‐specific thickness errors have a relative standard deviation of 0.5%, a global thickness‐scale error of 0.3% is shared exactly by both channels, and matched layer‐specific errors have a cross‐channel correlation of 0.90. A verified transfer‐matrix model is combined with finite‐difference Jacobians, covariance propagation, bounded candidate screening, and paired full‐spectrum Monte Carlo simulation. The original 300‐design pool was frozen, and nested stratified/LHS‐style expansions were used to construct 500‐ and 1000‐design pools in three independent expansion replicates. The expanded pools retained the same maximum‐figure‐of‐merit (FOM) endpoint and showed only small changes at the low‐variability endpoint, while denser sampling resolved the intermediate trade‐off and the more restrictive variability‐ratio‐constrained portion of the sampled trade‐off more clearly. Seventeen representatives chosen by prespecified rules were refined with 900 paired Monte Carlo realizations each, and six designs (F0–F5) were then validated with five independent random seeds with 1000 paired realizations per seed, giving 5000 paired realizations per design. Among the six validated designs, F1 had the smallest differential wavelength standard deviation, with a baseline‐normalized ratio of 0.9500 (95% bootstrap confidence interval: 0.9256–0.9743). Among the six validated designs, F3 combined a nominal FOM of 1152.25 RIU ⁻¹ with a wavelength‐variability ratio of 0.9728 (0.9489–0.9979), while among the six validated designs, F5 reached the largest nominal FOM, 1303.55 RIU ⁻¹ , and the smallest sensitivity‐normalized equivalent refractive‐index uncertainty ratio, 0.8849 (0.8626–0.9077). The correlation threshold of about 0.5 for layer errors follows algebraically from the near symmetry of the two channels and is not a design constant; the design information lies in the Jacobians, the covariance structure, and the resulting absolute uncertainty. All quantitative conclusions are therefore conditional on the prescribed optical and fabrication models.