Theoretical Study and Modeling of a MgF₂/HfO₂ Double-layer Antireflection Coating for the Optical Detection of Nuclear Radiation

Abstract

Efficient photon transmission from scintillators to photodetectors is important for maximising the optical response of nuclear-radiation detection systems. This theoretical study evaluates a double-layer MgF₂/HfO₂ antireflection coating on a fused-silica optical window and compares its performance with a bare air/silica interface and a quarter-wave MgF₂ monolayer. The optical response was modelled using the transfer matrix method for normal and oblique incidence, and the MgF₂ and HfO₂ thicknesses were numerically optimised over the 380–460 nm NaI(Tl) emission band, with 415 nm as the design wavelength. The optimised thicknesses were approximately 56.4 nm for MgF₂ and 89.3 nm for HfO₂. At 415 nm, the calculated reflectance decreased to approximately 0.03%, compared with about 1.75% for the MgF₂ monolayer and 3.50% for the bare interface. The average reflectance over 380–460 nm was approximately 0.27% for the optimised bilayer and 1.76% for the monolayer. The predicted transmission gain reached approximately 3.6% near 420 nm, and the bilayer retained lower reflectance than the monolayer across the analysed incidence-angle range of 0–40°. The results indicate that joint thickness optimisation is necessary because a simple quarter-wave/quarter-wave bilayer does not satisfy the exact cancellation condition for the selected refractive indices. The study provides a quantitative modelling basis for subsequent fabrication and experimental validation of the proposed coating.