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 , r_12p, r_01s, and r_12s. 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 ρ_r 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 .