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Applied Optics

Applied Optics


  • Vol. 28, Iss. 7 — Apr. 1, 1989
  • pp: 1365–1368

Maximum rate of change of the differential reflection phase shift with respect to the angle of incidence for light reflection at the surface of an absorbing medium

R. M. A. Azzam and A. M. El-Saba  »View Author Affiliations

Applied Optics, Vol. 28, Issue 7, pp. 1365-1368 (1989)

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The differential reflection phase shift, Δ = δpδs, associated with the external reflection of monochromatic light at the surface of an absorbing medium is a monotonically decreasing function of the angle of incidence ϕ which is determined by the complex dielectric function . A new special angle of incidence, denoted by ϕΔ′max, is defined at which the slope Δ′ = ∂Δ/∂ϕ of the Δ–ϕ curve is maximum negative, Δ max , and a transcendental equation is derived that determines this angle. ϕΔ′max differs from the principal angle ϕp at which Δ = 90°. As an example, ϕΔ′ max is calculated by numerical iteration for light reflection at the air–Si interface for photon energies from 1.7 to 5.6 eV in steps of 0.1 eV, and is plotted, along with the associated maximum slope Δ max , vs wavelength λ. It is noted that ϕΔ′ max > ϕp at every λ, a result that may hold in general. Also, for 4.5 ≤ ≤ 5.6 eV, ϕΔ′ max = 90°, so that a maximum negative slope occurs at grazing incidence in this spectral range. Another interesting observation is that, when || ≫ 1 (e.g., for metals in the IR), Δ′(90°) is a direct measure of the extinction coefficient k = Im1/2.

© 1989 Optical Society of America

Original Manuscript: June 24, 1988
Published: April 1, 1989

R. M. A. Azzam and A. M. El-Saba, "Maximum rate of change of the differential reflection phase shift with respect to the angle of incidence for light reflection at the surface of an absorbing medium," Appl. Opt. 28, 1365-1368 (1989)

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  1. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  2. R. H. Muller, “Definitions and Conventions in Ellipsometry,” Surf. Sci. 16, 14 (1969). [CrossRef]
  3. R. M. A. Azzam, “AIDER: Angle-of Incidence Derivative Ellipsometry and Reflectometry,” Opt. Commun. 16, 153 (1976). [CrossRef]
  4. V. M. Bermudez, “AIDER (Angle-of Incidence Derivative Ellipsometry and Reflectometry): Implementation and Application,” Surf. Sci. 94, 29 (1980). [CrossRef]
  5. R. M. A. Azzam, “Stationary Property of Normal-Incidence Reflection from Isotropic Surfaces,” J. Opt. Soc. Am. 72, 1187 (1982). [CrossRef]
  6. D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985 (1983). [CrossRef]
  7. See, for example, J. M. Bennett, H. E. Bennett, “Polarization,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978).

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