Abstract

The condition for obtaining a differential (or ellipsometric) quarter-wave retardation when p- and s-polarized light of wavelength λ experience frustrated total internal reflection (FTIR) and optical tunneling at angles of incidence $\varphi \ge$ the critical angle by a transparent thin film (medium 1) of low refractive index $n_1$ and uniform thickness d, which is embedded in a transparent bulk medium 0 of high refractive index $n_0$ takes the simple form: $-{\tanh }^{2}x=\tan {\delta }_p\tan {\delta }_s$, in which $x=2\pi n_1(d/\lambda )(N^2{\sin }^2\varphi -1{)}^{1/2}$, $N=n_0/n_1$, and ${\delta }_p$, ${\delta }_s$ are 01 interface Fresnel reflection phase shifts for the p and s polarizations. From this condition, the ranges of the principal angle and normalized film thickness $d/\lambda$ are obtained explicitly. At a given principal angle, the associated principal azimuths ${\psi }_r$, ${\psi }_t$ in reflection and transmission are determined by ${\tan }^2{\psi }_r=-\sin 2{\delta }_s/\sin 2{\delta }_p$ and ${\tan }^2{\psi }_t=-\tan {\delta }_p/\tan {\delta }_s$, respectively. At a unique principal angle ${\varphi }_e$ given by ${\sin }^2{\varphi }_e=2/(N^2+1)$, ${\psi }_r={\psi }_t=45°$ and linear-to-circular polarization conversion is achieved upon FTIR and optical tunneling simultaneously. The intensity transmittances of p- and s-polarized light at any principal angle are given by ${\tau }_p=\tan {\delta }_p/\tan ({\delta }_p-{\delta }_s)$ and ${\tau }_s=-\tan {\delta }_s/\tan ({\delta }_p-{\delta }_s)$, respectively. The efficiency of linear-to-circular polarization conversion in optical tunneling is maximum at ${\varphi }_e$.

© 2011 Optical Society of America

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