Using interference in the frequency domain for precise determination of thickness and refractive indices of normal dispersive materials

TLDR

Introducing a dispersive medium into one arm of a Michelson interferometer alters the spectral interference pattern, producing a zero‑order fringe at the wavelength where the net path difference vanishes. The study demonstrates spectral interference with a broadband white‑light source and theoretically analyzes the interference law for amplitude‑division interferometers, aiming to relate medium thickness to the zero‑order fringe width. Using a Michelson interferometer with a white‑light source, the authors measure spectral interference and apply a theoretical model of amplitude‑division interferometers to extract thickness from the zero‑order fringe. Experimental data across the visible spectrum yielded the refractive index n(λ) and thickness t of the dispersive medium with an accuracy of ~10⁻⁵.

Abstract

We present an experimental demonstration of the spectral interference phenomenon, using a spectrally broad white-light source in a Michelson interferometer configuration. We also present a theoretical analysis of the spectral interference law for the general case of amplitude-division interferometers. When a dispersive medium is introduced into one of the arms of the interferometer, the spectral interference pattern changes drastically, with a change in the frequency modulation corresponding to the dispersive nature of the medium. A zero-order fringe appears at a wavelength where the net path difference between the two arms of the interferometer is zero. We relate the thickness of the dispersive medium to the width of the zero-order fringe. From the experimental data over the entire visible region of the spectrum we obtain the refractive index n(λ) and the thickness t of the dispersive medium, calculated to an accuracy of the order of 10−5.