The complex reflection coefficients Rv(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 Rp and Rs are all presented in the complex plane. Furthermore, the amplitude-reflectance and phase-shift functions, |Rv|(ø,ζ) and argRv(ø,ζ) are plotted vs ζ with ø constant and vs ø with ζ constant. It is shown that Rp or Rs 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
R. M. A. Azzam and M. Emdadur Rahman Khan, "Complex reflection coefficients for the parallel and perpendicular polarizations of a film-substrate system," Appl. Opt. 22, 253-264 (1983)