Abstract

We investigate the angular dependence of the reflectance from an isotropic medium consisting of optically large and anisotropic, randomly oriented domains, assuming a highly refractive, isotropic, and homogeneous incidence medium, which is presumed to have a higher refractive index than any of the domains’ principal indices of refraction. By employing average reflectance and transmittance theory, we are able to show that the onset of total reflection is considerably shifted to higher angles of incidence compared with an isotropic medium with domains that are small compared with the wavelength. The onset of total reflection for a random medium with large domains is found to be dependent only on the largest principal index of refraction of the domains, assuming that all domains have the same optical properties. Therefore the shift of the onset depends on the magnitude of the optical anisotropy of the domains. Even in the case of a small optical anisotropy, large cross-polarization terms are predicted in the vicinity of the onset of total reflection. These terms show a pronounced maximum near that onset and extend beyond it.

© 2005 Optical Society of America

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References

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  1. T. G. Mayerhöfer, J. Musfeldt, “Angular dependence of the reflectance from an isotropic medium: surprising results regarding Brewster’s angle,” J. Opt. Soc. Am. A 22, 185–189 (2005).
    [CrossRef]
  2. T. G. Mayerhöfer, “Modelling IR spectra of single-phase polycrystalline materials with random orientation in the large crystallites limit—extension to arbitrary crystal symmetry,” J. Opt. A Pure Appl. Opt. 4, 540–548 (2002).
    [CrossRef]
  3. T. G. Mayerhöfer, Z. Shen, R. Keding, T. Höche, “Modelling IR-spectra of single-phase polycrystalline materials with random orientation—supplementations and refinements for optically uniaxial crystallites,” Optik 114, 351–359 (2003).
    [CrossRef]
  4. T. G. Mayerhöfer, “Modelling IR-spectra of single-phase polycrystalline materials with random orientation—a unified approach,” Vib. Spectrosc. 35, 67–76 (2004).
    [CrossRef]
  5. We assumed optically uniaxial ordered domains in this study.
  6. N. Nagai, Y. Izumi, H. Ishida, Y. Suzuki, A. Hatta, in Proceedings of 11th International Conference of Fourier Transform Spectroscopy, J. A. de Haseth, ed. (American Institute of Physics, Woodbury, N.Y., 1998), pp. 581–585.
  7. N. Nagai, H. Hashimoto, “FT-IR-ATR study of depth profile of SiO2 ultra-thin films,” Appl. Surf. Sci. 172, 307–311 (2001).
    [CrossRef]
  8. A. B. Remizov, “The influence of LO-TO splitting on νSO2 exciton bands in IR and ATR spectra of crystalline dimethyl sulphone,” J. Mol. Struct. 408, 451–453 (1997).
    [CrossRef]
  9. J. P. Devlin, G. Pollard, R. Frech, “ATR infrared spectra of uniaxial nitrate crystals,” J. Chem. Phys. 53, 4147–4151 (1970).
    [CrossRef]
  10. The refractive index of the incidence medium is assumed to be clearly higher than each of the principal refractive indices of one single domain of the polydomain medium.
  11. G. L. Doll, J. Steinbeck, G. Dresselhaus, M. S. Dresselhaus, A. J. Strauss, H. J. Zeiger, “Infrared anisotropy of La1.85Sr0.15CuO4-y,” Phys. Rev. B 36, 8884–8887 (1987).
    [CrossRef]
  12. R. Frech, “Infrared reflectivity of uniaxial microcrystalline powders,” Phys. Rev. B 13, 2342–2348 (1976).
    [CrossRef]
  13. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  14. T. G. Mayerhöfer, “New method of modeling infrared spectra of non-cubic single-phase polycrystalline materials with random orientation,” Appl. Spectrosc. 56, 1194–1205 (2002).
    [CrossRef]
  15. This can be easily verified by a calculation of the reflectance from a medium with cubic crystal symmetry by use of n=nord,2,n=nextraord,2,and ninc=3.
  16. We suggest naming the corresponding effect suppressed total reflection.

2005 (1)

2004 (1)

T. G. Mayerhöfer, “Modelling IR-spectra of single-phase polycrystalline materials with random orientation—a unified approach,” Vib. Spectrosc. 35, 67–76 (2004).
[CrossRef]

2003 (1)

T. G. Mayerhöfer, Z. Shen, R. Keding, T. Höche, “Modelling IR-spectra of single-phase polycrystalline materials with random orientation—supplementations and refinements for optically uniaxial crystallites,” Optik 114, 351–359 (2003).
[CrossRef]

2002 (2)

T. G. Mayerhöfer, “New method of modeling infrared spectra of non-cubic single-phase polycrystalline materials with random orientation,” Appl. Spectrosc. 56, 1194–1205 (2002).
[CrossRef]

T. G. Mayerhöfer, “Modelling IR spectra of single-phase polycrystalline materials with random orientation in the large crystallites limit—extension to arbitrary crystal symmetry,” J. Opt. A Pure Appl. Opt. 4, 540–548 (2002).
[CrossRef]

2001 (1)

N. Nagai, H. Hashimoto, “FT-IR-ATR study of depth profile of SiO2 ultra-thin films,” Appl. Surf. Sci. 172, 307–311 (2001).
[CrossRef]

1997 (1)

A. B. Remizov, “The influence of LO-TO splitting on νSO2 exciton bands in IR and ATR spectra of crystalline dimethyl sulphone,” J. Mol. Struct. 408, 451–453 (1997).
[CrossRef]

1987 (1)

G. L. Doll, J. Steinbeck, G. Dresselhaus, M. S. Dresselhaus, A. J. Strauss, H. J. Zeiger, “Infrared anisotropy of La1.85Sr0.15CuO4-y,” Phys. Rev. B 36, 8884–8887 (1987).
[CrossRef]

1976 (1)

R. Frech, “Infrared reflectivity of uniaxial microcrystalline powders,” Phys. Rev. B 13, 2342–2348 (1976).
[CrossRef]

1970 (1)

J. P. Devlin, G. Pollard, R. Frech, “ATR infrared spectra of uniaxial nitrate crystals,” J. Chem. Phys. 53, 4147–4151 (1970).
[CrossRef]

Devlin, J. P.

J. P. Devlin, G. Pollard, R. Frech, “ATR infrared spectra of uniaxial nitrate crystals,” J. Chem. Phys. 53, 4147–4151 (1970).
[CrossRef]

Doll, G. L.

G. L. Doll, J. Steinbeck, G. Dresselhaus, M. S. Dresselhaus, A. J. Strauss, H. J. Zeiger, “Infrared anisotropy of La1.85Sr0.15CuO4-y,” Phys. Rev. B 36, 8884–8887 (1987).
[CrossRef]

Dresselhaus, G.

G. L. Doll, J. Steinbeck, G. Dresselhaus, M. S. Dresselhaus, A. J. Strauss, H. J. Zeiger, “Infrared anisotropy of La1.85Sr0.15CuO4-y,” Phys. Rev. B 36, 8884–8887 (1987).
[CrossRef]

Dresselhaus, M. S.

G. L. Doll, J. Steinbeck, G. Dresselhaus, M. S. Dresselhaus, A. J. Strauss, H. J. Zeiger, “Infrared anisotropy of La1.85Sr0.15CuO4-y,” Phys. Rev. B 36, 8884–8887 (1987).
[CrossRef]

Frech, R.

R. Frech, “Infrared reflectivity of uniaxial microcrystalline powders,” Phys. Rev. B 13, 2342–2348 (1976).
[CrossRef]

J. P. Devlin, G. Pollard, R. Frech, “ATR infrared spectra of uniaxial nitrate crystals,” J. Chem. Phys. 53, 4147–4151 (1970).
[CrossRef]

Hashimoto, H.

N. Nagai, H. Hashimoto, “FT-IR-ATR study of depth profile of SiO2 ultra-thin films,” Appl. Surf. Sci. 172, 307–311 (2001).
[CrossRef]

Hatta, A.

N. Nagai, Y. Izumi, H. Ishida, Y. Suzuki, A. Hatta, in Proceedings of 11th International Conference of Fourier Transform Spectroscopy, J. A. de Haseth, ed. (American Institute of Physics, Woodbury, N.Y., 1998), pp. 581–585.

Höche, T.

T. G. Mayerhöfer, Z. Shen, R. Keding, T. Höche, “Modelling IR-spectra of single-phase polycrystalline materials with random orientation—supplementations and refinements for optically uniaxial crystallites,” Optik 114, 351–359 (2003).
[CrossRef]

Ishida, H.

N. Nagai, Y. Izumi, H. Ishida, Y. Suzuki, A. Hatta, in Proceedings of 11th International Conference of Fourier Transform Spectroscopy, J. A. de Haseth, ed. (American Institute of Physics, Woodbury, N.Y., 1998), pp. 581–585.

Izumi, Y.

N. Nagai, Y. Izumi, H. Ishida, Y. Suzuki, A. Hatta, in Proceedings of 11th International Conference of Fourier Transform Spectroscopy, J. A. de Haseth, ed. (American Institute of Physics, Woodbury, N.Y., 1998), pp. 581–585.

Keding, R.

T. G. Mayerhöfer, Z. Shen, R. Keding, T. Höche, “Modelling IR-spectra of single-phase polycrystalline materials with random orientation—supplementations and refinements for optically uniaxial crystallites,” Optik 114, 351–359 (2003).
[CrossRef]

Mayerhöfer, T. G.

T. G. Mayerhöfer, J. Musfeldt, “Angular dependence of the reflectance from an isotropic medium: surprising results regarding Brewster’s angle,” J. Opt. Soc. Am. A 22, 185–189 (2005).
[CrossRef]

T. G. Mayerhöfer, “Modelling IR-spectra of single-phase polycrystalline materials with random orientation—a unified approach,” Vib. Spectrosc. 35, 67–76 (2004).
[CrossRef]

T. G. Mayerhöfer, Z. Shen, R. Keding, T. Höche, “Modelling IR-spectra of single-phase polycrystalline materials with random orientation—supplementations and refinements for optically uniaxial crystallites,” Optik 114, 351–359 (2003).
[CrossRef]

T. G. Mayerhöfer, “Modelling IR spectra of single-phase polycrystalline materials with random orientation in the large crystallites limit—extension to arbitrary crystal symmetry,” J. Opt. A Pure Appl. Opt. 4, 540–548 (2002).
[CrossRef]

T. G. Mayerhöfer, “New method of modeling infrared spectra of non-cubic single-phase polycrystalline materials with random orientation,” Appl. Spectrosc. 56, 1194–1205 (2002).
[CrossRef]

Musfeldt, J.

Nagai, N.

N. Nagai, H. Hashimoto, “FT-IR-ATR study of depth profile of SiO2 ultra-thin films,” Appl. Surf. Sci. 172, 307–311 (2001).
[CrossRef]

N. Nagai, Y. Izumi, H. Ishida, Y. Suzuki, A. Hatta, in Proceedings of 11th International Conference of Fourier Transform Spectroscopy, J. A. de Haseth, ed. (American Institute of Physics, Woodbury, N.Y., 1998), pp. 581–585.

Pollard, G.

J. P. Devlin, G. Pollard, R. Frech, “ATR infrared spectra of uniaxial nitrate crystals,” J. Chem. Phys. 53, 4147–4151 (1970).
[CrossRef]

Remizov, A. B.

A. B. Remizov, “The influence of LO-TO splitting on νSO2 exciton bands in IR and ATR spectra of crystalline dimethyl sulphone,” J. Mol. Struct. 408, 451–453 (1997).
[CrossRef]

Shen, Z.

T. G. Mayerhöfer, Z. Shen, R. Keding, T. Höche, “Modelling IR-spectra of single-phase polycrystalline materials with random orientation—supplementations and refinements for optically uniaxial crystallites,” Optik 114, 351–359 (2003).
[CrossRef]

Steinbeck, J.

G. L. Doll, J. Steinbeck, G. Dresselhaus, M. S. Dresselhaus, A. J. Strauss, H. J. Zeiger, “Infrared anisotropy of La1.85Sr0.15CuO4-y,” Phys. Rev. B 36, 8884–8887 (1987).
[CrossRef]

Strauss, A. J.

G. L. Doll, J. Steinbeck, G. Dresselhaus, M. S. Dresselhaus, A. J. Strauss, H. J. Zeiger, “Infrared anisotropy of La1.85Sr0.15CuO4-y,” Phys. Rev. B 36, 8884–8887 (1987).
[CrossRef]

Suzuki, Y.

N. Nagai, Y. Izumi, H. Ishida, Y. Suzuki, A. Hatta, in Proceedings of 11th International Conference of Fourier Transform Spectroscopy, J. A. de Haseth, ed. (American Institute of Physics, Woodbury, N.Y., 1998), pp. 581–585.

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

Zeiger, H. J.

G. L. Doll, J. Steinbeck, G. Dresselhaus, M. S. Dresselhaus, A. J. Strauss, H. J. Zeiger, “Infrared anisotropy of La1.85Sr0.15CuO4-y,” Phys. Rev. B 36, 8884–8887 (1987).
[CrossRef]

Appl. Spectrosc. (1)

Appl. Surf. Sci. (1)

N. Nagai, H. Hashimoto, “FT-IR-ATR study of depth profile of SiO2 ultra-thin films,” Appl. Surf. Sci. 172, 307–311 (2001).
[CrossRef]

J. Chem. Phys. (1)

J. P. Devlin, G. Pollard, R. Frech, “ATR infrared spectra of uniaxial nitrate crystals,” J. Chem. Phys. 53, 4147–4151 (1970).
[CrossRef]

J. Mol. Struct. (1)

A. B. Remizov, “The influence of LO-TO splitting on νSO2 exciton bands in IR and ATR spectra of crystalline dimethyl sulphone,” J. Mol. Struct. 408, 451–453 (1997).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

T. G. Mayerhöfer, “Modelling IR spectra of single-phase polycrystalline materials with random orientation in the large crystallites limit—extension to arbitrary crystal symmetry,” J. Opt. A Pure Appl. Opt. 4, 540–548 (2002).
[CrossRef]

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

Optik (1)

T. G. Mayerhöfer, Z. Shen, R. Keding, T. Höche, “Modelling IR-spectra of single-phase polycrystalline materials with random orientation—supplementations and refinements for optically uniaxial crystallites,” Optik 114, 351–359 (2003).
[CrossRef]

Phys. Rev. B (2)

G. L. Doll, J. Steinbeck, G. Dresselhaus, M. S. Dresselhaus, A. J. Strauss, H. J. Zeiger, “Infrared anisotropy of La1.85Sr0.15CuO4-y,” Phys. Rev. B 36, 8884–8887 (1987).
[CrossRef]

R. Frech, “Infrared reflectivity of uniaxial microcrystalline powders,” Phys. Rev. B 13, 2342–2348 (1976).
[CrossRef]

Vib. Spectrosc. (1)

T. G. Mayerhöfer, “Modelling IR-spectra of single-phase polycrystalline materials with random orientation—a unified approach,” Vib. Spectrosc. 35, 67–76 (2004).
[CrossRef]

Other (6)

We assumed optically uniaxial ordered domains in this study.

N. Nagai, Y. Izumi, H. Ishida, Y. Suzuki, A. Hatta, in Proceedings of 11th International Conference of Fourier Transform Spectroscopy, J. A. de Haseth, ed. (American Institute of Physics, Woodbury, N.Y., 1998), pp. 581–585.

The refractive index of the incidence medium is assumed to be clearly higher than each of the principal refractive indices of one single domain of the polydomain medium.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

This can be easily verified by a calculation of the reflectance from a medium with cubic crystal symmetry by use of n=nord,2,n=nextraord,2,and ninc=3.

We suggest naming the corresponding effect suppressed total reflection.

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Figures (4)

Fig. 1
Fig. 1

(a) Calculated angular dependence of the perpendicular and parallel polarized reflectances, R s and R p , from an isotropic semi-infinite medium consisting of either optically small ( d λ / 10 ) or large ( d λ / 10 ) ordered domains into a highly refractive incidence medium ( n inc = 3 , n ord = 2.02 , and n extraord = 1.96 ) . (b) Close-up view of the calculated angular dependence of the parallel polarized reflectance, R p , for an isotropic medium consisting of optically small ( d λ / 10 ) or large ( d λ / 10 ) ordered regions near α Brew and α Min , respectively. For comparison, we also show the cross-polarization reflectance ( R sp = R ps ) . (c) Close-up view of the calculated angular dependence of the reflectance near the onsets of total reflection.

Fig. 2
Fig. 2

(a) Calculated angular dependence of the perpendicular and parallel polarized reflectances, R s and R p , from an isotropic medium consisting of optically small ( d λ / 10 ) or large ( d λ / 10 ) ordered domains into a highly refractive incidence medium ( n inc = 3 , n ord = 2.2 , and n extraord = 1.6 ) . (b) Close-up view of the calculated angular dependence of the parallel polarized reflectance, R p . For comparison, we also show the cross-polarization reflectance ( R sp = R ps ) . (c) Close-up view of the calculated angular dependence of the reflectance (large-domain case) near the onset of total reflection.

Fig. 3
Fig. 3

Angular dependence of the reflectance from a unixial medium for the three principal orientations and the incoherent averages of R s and R p according to Eq. (4). (a) φ = 0 ° , θ = 0 ° (optical axis parallel to the Z axis), (b) φ = 0 ° , θ = 90 ° (optical axis parallel to the Y axis), (c) φ = 90 ° , θ = 90 ° (optical axis parallel to the X axis), (d) incoherent average ( 1 3 R ( a ) , i + 1 3 R ( b ) , i + 1 3 R ( c ) , i ,   i = s , p ) .

Fig. 4
Fig. 4

Angular dependence of the reflectance from an anisotropic medium for two nonprincipal orientations Ω = Ω ( φ ,   θ ) . Also shown is the corresponding incoherent average. (a) φ = 45 ° , θ = 45 ° . (b) φ = 45 ° , θ = - 45 ° . (c) Incoherent average ( 1 2 R ( a ) , i + 1 2 R ( b ) , i ,   i = s ,   p ,   sp ,   ps ) .

Equations (6)

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R = 1 2   R s + 1 2   R p = N ( 3 ) Ω ( 3 ) R s ( Ω ) 2 + R p ( Ω ) 2 d Ω ,
n = N ( 3 ) Ω ( 3 ) n 1 ( Ω ) 2 + n 2 ( Ω ) 2 d Ω ,
n = 1 3 n a + 1 3 n b + 1 3 n c .
R i = 1 3 R i ( φ ,   θ = 0 ° ) + 1 3 R i ( φ = 0 ° ,   θ = 90 ° ) + 1 3 R i ( φ ,   θ = 90 ° ) , i = s ,   p
R i = 1 2   R i φ = π 4 ,   θ = π 4 + 1 2   R i φ = π 4 ,   θ = - π 4 ,
i = s ,   p ,   sp ,   ps .

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