Determination of the refractive index and thickness of a transparent film on a transparent substrate from the angles of incidence of zero reflection-induced ellipticity

Abstract

Linearly polarized light incident on a transparent film coating a transparent substrate remains linearly polarized after reflection only at a set of discrete angles of incidence φ m ( m integer). Measurement of these angles of incidence for zero reflection-induced ellipticity (ZRIE) allows simple, direct and explicit determination of the refractive index and thickness of the film, independent of the substrate refractive index. The latter can be separately and easily determined from the azimuths of the incident and reflected linear vibrations at one of the angles of incidence φ m or, alternatively, from the angle of refraction of light into the substrate using Snell's law. The proposed technique requires that the thickness of the film exceed one-fourth the wavelength of light in the medium of the film, and that it does not fall in a “higher-order” thickness gap when the ratio of the refractive index of the film to that of the ambient is greater than 2 √3 .