Theoretical Fisher-Information Limits in Resonant Transmission Through a Single Subwavelenth Aperture

We establish the fundamental limits of nanoscale parameter estimation enabled by the resonant transmission of a single subwavelength slit in a metallic film. Using a refined Fabry–Pérot model that incorporates accurate effective-index and interface-phase corrections—validated against full-wave simulations—we derive closed-form expressions for the Fisher information associated with transmission-based spectroscopy. The resulting Cramér–Rao bounds quantify the minimum achievable uncertainty in estimating both geometric variations, such as changes in slit width, and perturbations in the surrounding refractive index. Contrary to the common assumption that the highest quality factor guarantees optimal precision, we show that the ultimate sensitivity arises in regimes of enhanced spectral responsivity. These results uncover a general physical principle governing information flow in resonant subwavelength apertures and provide a compact, computationally efficient framework for evaluating and optimizing the performance of slit-based optical sensors.