The complex reflection coefficients R_v(ø,ζ) of a film-substrate system for the parallel (v = p) and perpendicular (v = s) polarizations are examined in detail as functions of the angle of incidence ø(0 ≤ ø ≤ 90°) and the reduced normalized film thickness ζ(0 ≤ ζ < 1). For definiteness, the reflection of light of wavelength λ = 0.6328 µm by the air–SiO₂–Si system is assumed. Families of circles that represent the constant-angle-of-incidence contours, their envelopes, and the associated constant-thickness contours of R_p and R_s are all presented in the complex plane. Furthermore, the amplitude-reflectance and phase-shift functions, |R_v|(ø,ζ) and argR_v(ø,ζ) are plotted vs ζ with ø constant and vs ø with ζ constant. It is shown that R_p or R_s can assume the same complex value at two different angles of incidence (i.e., the film-substrate system can have identical reflection characteristics for a given polarization at two angles) for certain ranges of film thickness. The distinct case of internal reflection is represented by a separate example.

© 1983 Optical Society of America

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