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 ϕ≥ 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: −tanh2x=tanδptanδs , in whichx=2πn1(d/λ)(N2sin2ϕ−1)1/2 , N=n0/n1 , and δp , δs are 01 interface Fresnel reflection phase shifts for the pand 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=−sin2δs/sin2δp and tan2ψt=−tanδp/tanδs , respectively. At a unique principal angle ϕegiven by sin2ϕe=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 byτp=tanδp/tan(δp−δs) and τs=−tanδs/tan(δp−δs) , respectively. The efficiency of linear-to-circular polarization conversion in optical tunneling is maximum at ϕe .
Journal of the Optical Society of America A
R. M. A. Azzam and F. F. Sudradjat, "Principal angles and principal azimuths of frustrated total internal reflection and optical tunneling by an embedded low-index thin film," J. Opt. Soc. Am. A 28, 1256-1261 (2011