## Abstract

The pseudo-Brewster angle of minimum reflectance for the *p* polarization, the corresponding angle for the *s* polarization, and the second-Brewster angle of minimum ratio of the *p* and *s* reflectances are all determined as functions of the thickness of a transparent film coating an absorbing substrate by numerical solution of the exact equations that govern such angles of the form Re(*Z′/Z*) = 0, where *Z* = *R _{p}, R_{s}*, or

*ρ*represent the complex amplitude-reflection coefficients for the

*p*and

*s*polarizations and their ratio (

*ρ*=

*R*), respectively, and

_{p}/R_{s}*Z′*is the angle-of-incidence derivative of

*Z*. Results that show these angles and their associated reflectance and reflectance-ratio minima are presented for the SiO

_{2}–Si film–substrate system at wavelength λ = 0.6328

*μ*m and film thickness of up to four periods (≃1.2

*μ*m). Applications of these results are proposed in film-thickness measurement and control.

© 1983 Optical Society of America

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