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Applied Optics

Applied Optics


  • Vol. 24, Iss. 8 — Apr. 15, 1985
  • pp: 1171–1179

Constraint on the optical constants of a film–substrate system for operation as an external-reflection retarder at a given angle of incidence

R. M. A. Azzam and Bruce E. Perilloux  »View Author Affiliations

Applied Optics, Vol. 24, Issue 8, pp. 1171-1179 (1985)

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Given a transparent film of refractive index n1 on an absorbing substrate of complex refractive index n2-jk2, we examine the constraint on n1, n2, and k2 such that the film–substrate system acts as an external-reflection retarder of specified retardance Δ at a specified angle of incidence ϕ. The constraint, which takes the form f(n1,n2,k2;ϕ,Δ) = 0, is portrayed graphically by equi-n1 contours in the n2,k2 plane at ϕ = 45, 70° and for Δ = ±90 and ±180°, corresponding to quarterwave and halfwave retarders (QWR and HWR), respectively. The required film thickness as a fraction of the film thickness period and the polarization-independent device reflectance ℛ are also studied graphically as functions of the optical constants. It is found that as n2 → 0, ℛ → 1, so that a metal substrate such as Ag is best suited for high-reflectance QWR (ϕ > 45°) and HWR (ϕ ≤ 45°). However, films that achieve QWR at ϕ ≤ 45° are excellent antireflection coatings of the underlying dielectric, semiconductor, or metallic substrate.

© 1985 Optical Society of America

Original Manuscript: October 9, 1984
Published: April 15, 1985

R. M. A. Azzam and Bruce E. Perilloux, "Constraint on the optical constants of a film–substrate system for operation as an external-reflection retarder at a given angle of incidence," Appl. Opt. 24, 1171-1179 (1985)

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  1. R. M. A. Azzam, A.-R. M. Zaghloul, N. M. Bashara, “Ellipsometric Function of a Film–Substrate System: Applications to the Design of Reflection-Type Optical Devices and to Ellipsometry,” J. Opt. Soc. Am. 65, 252 (1975). [CrossRef]
  2. A.-R. M. Zaghloul, R. M. A. Azzam, N. M. Bashara, “Design of Film–Substrate Single-Reflection Retarders,” J. Opt. Soc. Am. 65, 1043 (1975). [CrossRef]
  3. R. M. A. Azzam, M. E. R. Khan, “Single-Reflection Film–Substrate Half-Wave Retarders with Nearly Stationary Reflection Properties over a Wide Range of Incidence Angles,” J. Opt. Soc. Am. 73, 160 (1983). [CrossRef]
  4. See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Sec. 4.3.
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 40.
  6. If the incident light is linearly polarized at 45° azimuth with respect to the plane of incidence, so that the p and s components of the incident electric vector are equal and inphase, the p component of the electric vector of the reflected light will lead the s component by 90°, when ρ = j, hence the identification of the p direction as the fast axis. The exp(jωt) harmonic time dependence is assumed.
  7. E. Ritter, “Dielectric Film Materials for Optical Applications,” Phys. Thin Films 8, 1 (1975).
  8. H. K. Pulker, “Characterization of Optical Thin Films,” Appl. Opt. 18, 1969 (1979). [CrossRef] [PubMed]
  9. G. Hass, in Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic, New York, 1965), Vol. 3, Chap. 8.
  10. J. H. Apfel, “Graphical Method to Design Internal Reflection Phase Retarders,” Appl. Opt. 23, 1178 (1984). [CrossRef] [PubMed]
  11. W. R. Hunter, “Measurement of Optical Properties of Materials in the Vacuum Ultraviolet Spectral Region,” Appl. Opt. 21, 2103 (1982). [CrossRef] [PubMed]
  12. S. Kawabata, M. Suzuki, “MgF2–Ag Tunable Reflection Retarder,” Appl. Opt. 19, 484 (1980). [CrossRef] [PubMed]

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