Reliability of Fisher-information bounds for dielectric metalenses: a site-resolved RCWA audit

Abstract

We assess the reliability of localization precision predicted for a 1716-nanopillar dielectric metalens using a site-resolved complex RCWA library and a vectorial Poisson Fisher model. An independent calculation reproduces the archived local axial Cramer-Rao bound of 20.7738 nm to within 0.0044 nm, yielding 20.7695 nm under the same ideal detector and 3000 detected signal photons. High-order periodic-cell calculations reveal a 0.1335 rad phase difference at a selected diameter; different substrate-index assumptions prevent attributing this difference solely to modal truncation. Replacing the recalculated coefficients at 39 actual sites changes the bound to 20.7522 nm. Restricted phase-mask benchmarks and pixel-integration checks further distinguish a stable statistical prediction from electromagnetic convergence. We provide a reproducible, model-conditional benchmark, not a physical-device performance claim.