Sensitivity and tolerance analysis of single-layer MgF₂ and SiO₂ anti-reflection coatings

Anti-reflection (AR) coatings are integral to enhancing the performance of optical systems. This paper presents a comprehensive simulation-based sensitivity analysis of single-layer magnesium fluoride ([Formula: see text]) and silicon dioxide ([Formula: see text]) AR coatings on a glass substrate. The investigation focuses on the influence of critical design parameters, namely layer thickness, angle of incidence, and light polarization (s and p), on the spectral reflectance within the visible range. The results demonstrate that the optical performance of these coatings is strongly dependent on the aforementioned parameters. For s-polarized light, reflectance consistently increases with the angle of incidence. In contrast, for p-polarized light, reflectance initially decreases, reaching a minimum near zero at an optimal angle, a phenomenon associated with the Brewster angle. Furthermore, the study reveals that reflectance is highly sensitive to variations in layer thickness, particularly to thickness reduction. Quantitative sensitivity metrics are introduced to evaluate robustness against manufacturing errors. This analysis provides critical insights for the design optimization and the determination of manufacturing tolerances for AR coatings, aimed at maximizing light transmission in practical optical devices.