Constant Angle of Incidence Contours for an Air-SiO2-Si System

The ellipsometric function for an ambient-film-substrate system is defined as the ratio of complex-amplitude reflection coefficients for the and polarization:
where are functions of Fresnel interface reflection coefficients , r12p, r01s, and r12s. The pairs and signify the ambient-film and film-substrate interfaces. Here is an exponential function of metric film thickness and is the thickness period. If the ambient and film media are transparent, the point representing moves uniformly in a clockwise direction around the unit circle in the complex plane as increases from 0 to . Because ρr is related to by an analytic rational function, the point representing must trace a closed contour in the complex plane as traces the unit circle in the complex plane.
The figure shows such a family of non-intersecting, constant angle of incidence contours (CAIC) for (normal incidence) to (grazing incidence) for the system at .


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R. M. A. Azzam and N. M. Bashara, "Reflection and Transmission of Polarized Light by Stratified Planar Structures," Ellipsometry and Polarized Light, Amsterdam: North Holland, 2003 pp. 292.
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