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 = Rp, Rs, or ρ represent the complex amplitude-reflection coefficients for the p and s polarizations and their ratio (ρ = Rp/Rs), respectively, and 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 SiO2–Si film–substrate system at wavelength λ = 0.6328 μm and film thickness of up to four periods (≃1.2 μm). Applications of these results are proposed in film-thickness measurement and control.
© 1983 Optical Society of America
Original Manuscript: August 9, 1983
Published: December 15, 1983
R. M. A. Azzam and T. F. Thonn, "Pseudo-Brewster and second-Brewster angles of an absorbing substrate coated by a transparent thin film," Appl. Opt. 22, 4155-4165 (1983)