Simple and explicit expressions for the phase shifts that p- and s-polarized light experience in frustrated total internal reflection (FTIR) and optical tunneling by an embedded low-index thin film are obtained. The differential phase shifts in reflection and transmission Δr,Δt are found to be identical, and the associated ellipsometric parameters ψr,ψt are governed by a simple relation, independent of film thickness. When the Fresnel interface reflection phase shifts for the pand s polarizations or their average are quarter-wave, the corresponding overall reflection phase shifts introduced by the embedded layer are also quarter-wave for all values of film thickness. In the limit of zero film thickness (i.e., for an ultrathin embedded layer), the reflection phase shifts are also quarter-wave independent of polarization (p or s) or angle of incidence (except at grazing incidence). Finally, variable-angle FTIR ellipsometry is shown to be a sensitive technique for measuring the thickness of thin uniform air gaps between transparent bulk media.
Journal of the Optical Society of America A
R. M. A. Azzam, "Phase shifts in frustrated total internal reflection and optical tunneling by an embedded low-index thin film," J. Opt. Soc. Am. A 23, 960-965 (2006)