Abstract

The angle-of-incidence dependence of the differential reflection phase shift Δ between p and s polarizations is considered a function of the real and imaginary parts of the relative complex dielectric function ε of an interface in the domain of fractional optical constants, i.e., under conditions of internal reflection. The constraint on complex ε such that oscillatory and monotonic angular responses are obtained is determined. A sensitive and stable technique, which is based on attenuated internal reflection ellipsometry between the Brewster angle and the critical angle, is proposed for measuring small induced absorption (εi10-5) in the medium of refraction.

© 1999 Optical Society of America

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References

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  1. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).
  2. R. M. A. Azzam, 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); erratum, Appl. Opt.35, 213 (1996).
    [CrossRef] [PubMed]
  3. R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
    [CrossRef]
  4. R. M. A. Azzam, “Contours of constant principal angle and constant principal azimuth in the complex plane,” J. Opt. Soc. Am. 71, 1523–1528 (1981).
    [CrossRef]
  5. R. M. A. Azzam, “Extrema of the magnitude and the phase of a complex function of a real variable: application to attenuated internal reflection,” J. Opt. Soc. Am. A 5, 1187–1192 (1988).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  9. R. G. Pinnick, S. G. Jennings, D. C. Boice, J. P. Cruncleton, “Attenuated total reflectance measurements of the complex refractive index of kaolinite powder at CO2 laser wavelengths,” Appl. Opt. 24, 3274–3285 (1985).
    [CrossRef]

1997 (1)

1996 (1)

1989 (1)

1988 (1)

1985 (1)

1981 (2)

1969 (1)

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

Azzam, R. M. A.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

Boice, D. C.

Chiu, M.-H.

Cruncleton, J. P.

El-Saba, A. M.

Jennings, S. G.

Lee, J.-Y.

Li, H.

Muller, R. H.

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

Pinnick, R. G.

Su, D.-C.

Xie, S.

Appl. Opt. (4)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Surf. Sci. (1)

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

Other (1)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

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Figures (7)

Fig. 1
Fig. 1

Differential reflection phase shift Δ versus angle of inci dence ϕ for different values of the imaginary part of the relative dielectric constant εi and the constant real part εr=0.6. The curves marked o, a, b, c, d, e, f, g, and h correspond to εi=0, 0.005, 0.015, 0.045, 0.075, 0.1, 0.1366, 0.2, and 2.0, respectively.

Fig. 2
Fig. 2

Differential reflection phase shift Δ as a function of the angle of incidence ϕ and the imaginary part of the relative dielectric constant εi for a given value of the real part εr=0.6.

Fig. 3
Fig. 3

Angles of incidence ϕmin and ϕmax for minimum and maximum differential reflection phase shift Δ as functions of the imaginary part of the relative dielectric constant εi when εr=0.6, corresponding to the data shown in Fig. 1.

Fig. 4
Fig. 4

Minimum and maximum differential reflection phase shift Δmin and Δmax as functions of the imaginary part of the relative dielectric constant εi when εr=0.6, corresponding to the data shown in Fig. 1.

Fig. 5
Fig. 5

Upper bound on the imaginary part of the relative dielectric constant εi for an oscillatory Δ-versus-ϕ response as a function of the real part εr.

Fig. 6
Fig. 6

Ellipsometric sensitivity S, Eq. (5), as a function of the angle of incidence ϕ for attenuated internal reflection between the Brewster angle and the critical angle of a transparent interface with εr=0.6.

Fig. 7
Fig. 7

Same as in Fig. 6, but for a range of ±1° of the incidence angle ϕ around the minimum.

Equations (5)

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ε=ε1/ε0=εr-jεi,
ρ=[sin ϕ tan ϕ-(ε-sin2 ϕ)1/2][sin ϕ tan ϕ+(ε-sin2 ϕ)1/2] ,
Δ=arg(ρ).
S=[Δ/εi]εi=0.
S=(180°/π)sin ϕ tan ϕ/[(εr-sin2 ϕ)1/2×(tan2 ϕ-εr)].

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