Abstract

The reflectance of an absorbing medium Rθ(ϕ) for incident light of an arbitrary state of polarization is considered as a function of the compex dielectic constant ɛ; ϕ is the angle incidence and θ is an incident polarization parameter, for which cos2θ and sin2θ give the power fractions of incident radiation that are p- and s-polarized, respectively. Our objective is to explore the complex ɛ-plane and define the domains for which the different types of Rθ(ϕ) vs ϕ curves (monotonic, single minimum, and secondary maximum and minimum) occur. An ethanolic solution of Rhodamine B, an organic laser dye luminofor with a well-defined resonance absorption spectrum, was chosen as the absorbing medium. We were able to define the criteria for three distinctly different types of behavior of Rθ(ϕ).

© 1990 Optical Society of America

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References

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  1. R. M. A. Azzam, A. M. El-Saba, “Reflectance of an Absorbing Substrate for Incident Light of Arbitrary Polarization Appearance of a Secondary Maximum at Oblique Incidence,” Appl. Opt. 27, 4034–4037 (1988).
    [CrossRef] [PubMed]
  2. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  3. W. R. Hunter, “Errors in Using Reflectance vs Angle of Incidence Method for Measuring Optical Constants,” J. Opt. Soc. Am. 55, 1197–1204 (1965).
    [CrossRef]
  4. H. B. Holl, “Specular Reflection and Characteristics of Reflected Light,” J. Opt. Soc. Am. 57, 683–690 (1967).
    [CrossRef]
  5. J. M. Bennett, H. E. Bennett, “Polarization,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978).
  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, 985–1008 (1983).
    [CrossRef]
  7. R. M. A. Azzam, “Stationary Property of Normal-Incidence Reflection from Isotropic Surfaces,” J. Opt. Soc. Am. 72, 1187–1189 (1982).
    [CrossRef]
  8. A. Yariv, Quantum Electronics (Wiley, New York, 1975).

1988 (1)

1983 (1)

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, 985–1008 (1983).
[CrossRef]

1982 (1)

1967 (1)

1965 (1)

Aspnes, D. E.

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, 985–1008 (1983).
[CrossRef]

Azzam, R. M. A.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Bennett, H. E.

J. M. Bennett, H. E. Bennett, “Polarization,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978).

Bennett, J. M.

J. M. Bennett, H. E. Bennett, “Polarization,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978).

El-Saba, A. M.

Holl, H. B.

Hunter, W. R.

Studna, A. A.

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, 985–1008 (1983).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

Phys. Rev. B (1)

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, 985–1008 (1983).
[CrossRef]

Other (3)

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

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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Figures (7)

Fig. 1
Fig. 1

Plot of refractive indices (n) and extinction coefficients (k) vs wavelength for 0.4 mole/liter Rhodamine B in ethanol: (—) n (Kramers-Kronig); (- - -) k (experimental).

Fig. 2
Fig. 2

Plot of reflectance Rθ vs angle of incidence ϕ for RhB solution at λ = 552 nm (N 1.356 + j0.22) and for θ = 46, 48, and 50, and 60°; cos2θ and sin2θ give the proportions of incident light that are p- and s-polarized, respectively. All curves in this range of θ indicate a monotonic rise of Rθ with ϕ: (- · -) 46°; (○ ○ ○) 48°;(—) 50°; (- - -) 60°.

Fig. 3
Fig. 3

Same as Fig. 2 except that now N = 1.285 + j2.2, and θ = 46, 47, 48, and 50°. A secondaqry maximum and a minimum appear in this range of θ: (—) 46°; (- · -) 47°; (- - -) 48°; (○ ○ ○) 50°.

Fig. 4
Fig. 4

Same as Fig. 3 except that θ = 52, 53, 54, and 55°: (○ ○ ○) 52°; (- · -) 53°; (—) 54°; (- - -) 55°.

Fig. 5
Fig. 5

Same as Fig. 2 except that N = 1.285 + j2.2, and θ = 55.5, and 70°. The curve at θ = 55.5° represents a limiting case that separates the oscillatory (Figs. 3 and 4) and monotonic (Fig. 2) regimes of the Rθ vs ϕ curve: (—) 55.5°; (- - -) 70°.

Fig. 6
Fig. 6

Same as Fig. 3 except that λ = 535 nm (N = 0.232 + j1.2), and θ = 45.1, 45.5., 46, 47°:(—) 45.1°; (-· -) 45.5°;(○ ○ ○) 46°; (- - -) 47°.

Fig. 7
Fig. 7

Same as Fig. 3 except that λ = 570 nm (N = 2.405 + j1.289), and θ = 45.1, 45.5°: (—) 45.1°; (- - -) 45.5°.

Tables (1)

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Table I Extrema of the Rθ vs ϕ curves (Figs. 3, 4)

Equations (8)

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r p = ɛ cos ϕ - ( ɛ - sin 2 ϕ ) 1 / 2 ɛ cos ϕ + ( ɛ - sin 2 ϕ ) 1 / 2 , r s = cos ϕ - ( ɛ - sin 2 ϕ ) 1 / 2 cos ϕ + ( ɛ - sin 2 ϕ ) 1 / 2 ,
R p = r p r p * ,             R s = r s r s *
R q = q R p + ( 1 - q ) R s .
R θ = ( cos 2 θ ) R p + ( sin 2 θ ) R s .
R θ / ϕ = 0.
Re [ ( cos 2 θ ) r p r p * + ( sin 2 θ ) r s r s * ] = 0 ,
ɛ = ɛ + j ɛ = N 2 = ( n 2 - k 2 ) + j 2 n k ,
n ( ω ) = n 1 + 1 π P . V . - k ( ω ) ( ω - ω ) d ω ,

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