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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 22, Iss. 2 — Jan. 15, 1983
  • pp: 253–264

Complex reflection coefficients for the parallel and perpendicular polarizations of a film–substrate system

R. M. A. Azzam and M. Emdadur Rahman Khan  »View Author Affiliations


Applied Optics, Vol. 22, Issue 2, pp. 253-264 (1983)
http://dx.doi.org/10.1364/AO.22.000253


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Abstract

The complex reflection coefficients Rν(ϕ,ζ) of a film–substrate system for the parallel (ν = p) and perpendicular (ν = s) polarizations are examined in detail as functions of the angle of incidence ϕ(0 ≤ ϕ ≤ 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, |Rν|(ϕ,ζ) and argRν(ϕ,ζ), are plotted vs ζ with ϕ constant and vs ϕ 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

History
Original Manuscript: August 27, 1982
Published: January 15, 1983

Citation
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)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-22-2-253

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