Ab-initio design of realistic Fabry–Perot cavities for accurate refractive index determination of liquids and gases

Abstract

Fabry–Perot cavities (FPCs) provide a simple and precise alternative to measure the refractive indices of gases and liquids. The performance of an FPC is very sensitive to the quality of its dielectric multilayer mirrors. In this article, a combined ab-initio and transfer-matrix study is carried out for a realistic Fabry–Perot microcavity made of TiO2/SiO2, including interface atomic diffusions and possible layer thickness variations. The refractive indices obtained from the density functional theory are used as the input of cavity transmittance calculations. The performance of such a Fabry–Perot cavity is monitored by the quality factor, finesse, and full width at half maximum (FWHM) of its main resonant peaks. The results confirm the exponential decrease of FWHM with the number of layers and then an exponential growth of the finesse. An analytical solution for the optical transmittance of few-layer cavities is also presented. Furthermore, the results reveal non-uniform shifts of the resonant peaks, due to the presence of a finite-layer interface width or layer thickness fluctuation. Finally, simulated measurements of the refractive indices of CO2 and ethanol by using this ab-initio designed realistic Fabry–Perot microcavity are analyzed in detail.