Principal angles and principal azimuths of frustrated total internal reflection and optical tunneling by an embedded low-index thin film

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 ? ≥ the critical angle by a transparent thin film (medium 1) of low refractive index n1 and uniform thickness d, which is embedded in a transparent bulk medium 0 of high refractive index n0 takes the simple form: -tanh2 x = tan δp tan δs, in which x = 2πn1(d/λ)(N2sin2? - 1)(1/2), N = n0/n1, and δp, δs 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/λ are obtained explicitly. At a given principal angle, the associated principal azimuths ψr, ψt in reflection and transmission are determined by tan2ψr = -sin 2δs/sin 2δp and tan2ψt = -tan δp/tan δs, respectively. At a unique principal angle ?e given by sin2?e = 2/(N2 + 1), ψr = ψt = 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 τp = tan δp/tan (δp - δs) and τs = -tan δs/tan (δp - δs), respectively. The efficiency of linear-to-circular polarization conversion in optical tunneling is maximum at ?e.