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The pseudo-Brewster angle of minimum reflectance for the p polarization, the corresponding angle for thes 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-sibstrate 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.

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Applied Optics


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