Abstract

A simple analysis is presented of reflectance from a stratified uniaxial media with the optic axes parallel or perpendicular to the plane of incidence.

© 1991 Optical Society of America

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References

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  1. D. W. Berreman, “Optics in stratified anisotropic media: 4 × 4-matrix formulation,” J Opt. Soc. Am. 62, 502–510 (1972).
    [Crossref]
  2. P. Yeh, “Electromagnetic propagation in birefringent layered media,” J Opt. Soc. Am. 69, 742–756 (1979).
    [Crossref]
  3. D. J. Williams, ed., Nonlinear Optical Properties of Organic and Polymeric Materials, ACS Symp. Ser.233 (1983).
    [Crossref]
  4. D. S. Chemla, J. Zyss, eds., Nonlinear Properties of Organic Molecules and Crystals (Academic, New York, 1987).
  5. P.N. Prasad, D. R. Ulrich, eds., Nonlinear Optical and Electroactive Polymers (Plenum Press, New York, 1988).
    [Crossref]
  6. A. J. Heeger, J. Orenstein, D. R. Ulrich, eds., Nonlinear Optical Properties of Polymers, Mater. Res. Soc. Symp. Proc.109 (1988).
  7. K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, “Electro-optic phase modulation and optical second harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
    [Crossref]
  8. M. A. Mortazavi, A. Knoesen, S. T. Kowel, B. G. Higgins, A. Dienes, “Second-harmonic generation and absorption studies of polymer-dye films oriented by corona-onset poling at elevated temperatures,” J. Opt. Soc. Am. B 6, 733–741 (1989).
    [Crossref]
  9. R. H. Page, M. C. Jurich, B. Reck, A. Sen, R. J. Twieg, J. D. Swalen, G. C. Bjorklund, C. G. Wilson, “Electrochromic and optical waveguide studies of corona-poled electro-optic polymer films,” J Opt. Soc. Am. B 7, 1239–1250 (1990).
    [Crossref]
  10. W. H. G. Horsthuis, G. J. M. Krijnen, “Simple measuring method for electro-optic coefficients in poled polymer waveguides,” Appl. Phys. Lett. 55, 616–618 (1989).
    [Crossref]
  11. J. S. Schildkraut, “Determination of the electrooptic coefficient of a poled polymer,” Appl. Opt. 29, 2839–2841 (1990).
    [Crossref] [PubMed]
  12. L. P. Mosteller, F. Wooten, “Optical properties and reflectance of uniaxial absorbing crystals,” J. Opt. Soc. Am. 58, 511–518 (1968).
    [Crossref]
  13. M. J. Dignam, M. Moskovits, R. W. Stobie, “Specular reflectance and ellipsometric spectroscopy of oriented molecular layers,” Trans. Faraday Soc. 67, 3306–3317 (1971).
    [Crossref]
  14. A. Knoesen, M. G. Moharam, T. K. Gaylord, “Electromagnetic propagation at interfaces and in waveguides in uniaxial crystals,” Appl. Phys. B 38, 171–178 (1985).
    [Crossref]
  15. F. Abèles, “Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieux stratifies: application aux couches minces,” Ann. Phys. Paris 5, 598 (1950).
  16. O. S. Heavens, Optical Properties of Thin Films (Butterworth, London, 1955;Dover, New York, 1965).
  17. R. M. A. Azzam, N. M. Bashra, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

1990 (2)

R. H. Page, M. C. Jurich, B. Reck, A. Sen, R. J. Twieg, J. D. Swalen, G. C. Bjorklund, C. G. Wilson, “Electrochromic and optical waveguide studies of corona-poled electro-optic polymer films,” J Opt. Soc. Am. B 7, 1239–1250 (1990).
[Crossref]

J. S. Schildkraut, “Determination of the electrooptic coefficient of a poled polymer,” Appl. Opt. 29, 2839–2841 (1990).
[Crossref] [PubMed]

1989 (2)

1988 (1)

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, “Electro-optic phase modulation and optical second harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[Crossref]

1985 (1)

A. Knoesen, M. G. Moharam, T. K. Gaylord, “Electromagnetic propagation at interfaces and in waveguides in uniaxial crystals,” Appl. Phys. B 38, 171–178 (1985).
[Crossref]

1979 (1)

P. Yeh, “Electromagnetic propagation in birefringent layered media,” J Opt. Soc. Am. 69, 742–756 (1979).
[Crossref]

1972 (1)

D. W. Berreman, “Optics in stratified anisotropic media: 4 × 4-matrix formulation,” J Opt. Soc. Am. 62, 502–510 (1972).
[Crossref]

1971 (1)

M. J. Dignam, M. Moskovits, R. W. Stobie, “Specular reflectance and ellipsometric spectroscopy of oriented molecular layers,” Trans. Faraday Soc. 67, 3306–3317 (1971).
[Crossref]

1968 (1)

1950 (1)

F. Abèles, “Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieux stratifies: application aux couches minces,” Ann. Phys. Paris 5, 598 (1950).

Abèles, F.

F. Abèles, “Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieux stratifies: application aux couches minces,” Ann. Phys. Paris 5, 598 (1950).

Azzam, R. M. A.

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

Bashra, N. M.

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

Berreman, D. W.

D. W. Berreman, “Optics in stratified anisotropic media: 4 × 4-matrix formulation,” J Opt. Soc. Am. 62, 502–510 (1972).
[Crossref]

Bjorklund, G. C.

R. H. Page, M. C. Jurich, B. Reck, A. Sen, R. J. Twieg, J. D. Swalen, G. C. Bjorklund, C. G. Wilson, “Electrochromic and optical waveguide studies of corona-poled electro-optic polymer films,” J Opt. Soc. Am. B 7, 1239–1250 (1990).
[Crossref]

Dienes, A.

Dignam, M. J.

M. J. Dignam, M. Moskovits, R. W. Stobie, “Specular reflectance and ellipsometric spectroscopy of oriented molecular layers,” Trans. Faraday Soc. 67, 3306–3317 (1971).
[Crossref]

Gaylord, T. K.

A. Knoesen, M. G. Moharam, T. K. Gaylord, “Electromagnetic propagation at interfaces and in waveguides in uniaxial crystals,” Appl. Phys. B 38, 171–178 (1985).
[Crossref]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Films (Butterworth, London, 1955;Dover, New York, 1965).

Higgins, B. G.

Holland, W. R.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, “Electro-optic phase modulation and optical second harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[Crossref]

Horsthuis, W. H. G.

W. H. G. Horsthuis, G. J. M. Krijnen, “Simple measuring method for electro-optic coefficients in poled polymer waveguides,” Appl. Phys. Lett. 55, 616–618 (1989).
[Crossref]

Jurich, M. C.

R. H. Page, M. C. Jurich, B. Reck, A. Sen, R. J. Twieg, J. D. Swalen, G. C. Bjorklund, C. G. Wilson, “Electrochromic and optical waveguide studies of corona-poled electro-optic polymer films,” J Opt. Soc. Am. B 7, 1239–1250 (1990).
[Crossref]

Knoesen, A.

Kowel, S. T.

Krijnen, G. J. M.

W. H. G. Horsthuis, G. J. M. Krijnen, “Simple measuring method for electro-optic coefficients in poled polymer waveguides,” Appl. Phys. Lett. 55, 616–618 (1989).
[Crossref]

Kuzyk, M. G.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, “Electro-optic phase modulation and optical second harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[Crossref]

Lalama, S. J.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, “Electro-optic phase modulation and optical second harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[Crossref]

Moharam, M. G.

A. Knoesen, M. G. Moharam, T. K. Gaylord, “Electromagnetic propagation at interfaces and in waveguides in uniaxial crystals,” Appl. Phys. B 38, 171–178 (1985).
[Crossref]

Mortazavi, M. A.

Moskovits, M.

M. J. Dignam, M. Moskovits, R. W. Stobie, “Specular reflectance and ellipsometric spectroscopy of oriented molecular layers,” Trans. Faraday Soc. 67, 3306–3317 (1971).
[Crossref]

Mosteller, L. P.

Page, R. H.

R. H. Page, M. C. Jurich, B. Reck, A. Sen, R. J. Twieg, J. D. Swalen, G. C. Bjorklund, C. G. Wilson, “Electrochromic and optical waveguide studies of corona-poled electro-optic polymer films,” J Opt. Soc. Am. B 7, 1239–1250 (1990).
[Crossref]

Reck, B.

R. H. Page, M. C. Jurich, B. Reck, A. Sen, R. J. Twieg, J. D. Swalen, G. C. Bjorklund, C. G. Wilson, “Electrochromic and optical waveguide studies of corona-poled electro-optic polymer films,” J Opt. Soc. Am. B 7, 1239–1250 (1990).
[Crossref]

Schildkraut, J. S.

Sen, A.

R. H. Page, M. C. Jurich, B. Reck, A. Sen, R. J. Twieg, J. D. Swalen, G. C. Bjorklund, C. G. Wilson, “Electrochromic and optical waveguide studies of corona-poled electro-optic polymer films,” J Opt. Soc. Am. B 7, 1239–1250 (1990).
[Crossref]

Singer, K. D.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, “Electro-optic phase modulation and optical second harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[Crossref]

Sohn, J. E.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, “Electro-optic phase modulation and optical second harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[Crossref]

Stobie, R. W.

M. J. Dignam, M. Moskovits, R. W. Stobie, “Specular reflectance and ellipsometric spectroscopy of oriented molecular layers,” Trans. Faraday Soc. 67, 3306–3317 (1971).
[Crossref]

Swalen, J. D.

R. H. Page, M. C. Jurich, B. Reck, A. Sen, R. J. Twieg, J. D. Swalen, G. C. Bjorklund, C. G. Wilson, “Electrochromic and optical waveguide studies of corona-poled electro-optic polymer films,” J Opt. Soc. Am. B 7, 1239–1250 (1990).
[Crossref]

Twieg, R. J.

R. H. Page, M. C. Jurich, B. Reck, A. Sen, R. J. Twieg, J. D. Swalen, G. C. Bjorklund, C. G. Wilson, “Electrochromic and optical waveguide studies of corona-poled electro-optic polymer films,” J Opt. Soc. Am. B 7, 1239–1250 (1990).
[Crossref]

Wilson, C. G.

R. H. Page, M. C. Jurich, B. Reck, A. Sen, R. J. Twieg, J. D. Swalen, G. C. Bjorklund, C. G. Wilson, “Electrochromic and optical waveguide studies of corona-poled electro-optic polymer films,” J Opt. Soc. Am. B 7, 1239–1250 (1990).
[Crossref]

Wooten, F.

Yeh, P.

P. Yeh, “Electromagnetic propagation in birefringent layered media,” J Opt. Soc. Am. 69, 742–756 (1979).
[Crossref]

Ann. Phys. Paris (1)

F. Abèles, “Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieux stratifies: application aux couches minces,” Ann. Phys. Paris 5, 598 (1950).

Appl. Opt. (1)

Appl. Phys. B (1)

A. Knoesen, M. G. Moharam, T. K. Gaylord, “Electromagnetic propagation at interfaces and in waveguides in uniaxial crystals,” Appl. Phys. B 38, 171–178 (1985).
[Crossref]

Appl. Phys. Lett. (2)

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, “Electro-optic phase modulation and optical second harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[Crossref]

W. H. G. Horsthuis, G. J. M. Krijnen, “Simple measuring method for electro-optic coefficients in poled polymer waveguides,” Appl. Phys. Lett. 55, 616–618 (1989).
[Crossref]

J Opt. Soc. Am. (2)

D. W. Berreman, “Optics in stratified anisotropic media: 4 × 4-matrix formulation,” J Opt. Soc. Am. 62, 502–510 (1972).
[Crossref]

P. Yeh, “Electromagnetic propagation in birefringent layered media,” J Opt. Soc. Am. 69, 742–756 (1979).
[Crossref]

J Opt. Soc. Am. B (1)

R. H. Page, M. C. Jurich, B. Reck, A. Sen, R. J. Twieg, J. D. Swalen, G. C. Bjorklund, C. G. Wilson, “Electrochromic and optical waveguide studies of corona-poled electro-optic polymer films,” J Opt. Soc. Am. B 7, 1239–1250 (1990).
[Crossref]

J. Opt. Soc. Am. (1)

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

Trans. Faraday Soc. (1)

M. J. Dignam, M. Moskovits, R. W. Stobie, “Specular reflectance and ellipsometric spectroscopy of oriented molecular layers,” Trans. Faraday Soc. 67, 3306–3317 (1971).
[Crossref]

Other (6)

O. S. Heavens, Optical Properties of Thin Films (Butterworth, London, 1955;Dover, New York, 1965).

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

D. J. Williams, ed., Nonlinear Optical Properties of Organic and Polymeric Materials, ACS Symp. Ser.233 (1983).
[Crossref]

D. S. Chemla, J. Zyss, eds., Nonlinear Properties of Organic Molecules and Crystals (Academic, New York, 1987).

P.N. Prasad, D. R. Ulrich, eds., Nonlinear Optical and Electroactive Polymers (Plenum Press, New York, 1988).
[Crossref]

A. J. Heeger, J. Orenstein, D. R. Ulrich, eds., Nonlinear Optical Properties of Polymers, Mater. Res. Soc. Symp. Proc.109 (1988).

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Figures (1)

Fig. 1
Fig. 1

Reflection of a plane wave in a semi-infinite isotropic region from a stratified uniaxial structure (films 2,3, …, m). The electric-field orientation of the TE polarization s and TM polarization p is as indicated.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

E y i E y i + = Z TE j Z TE i Z TE j + Z TE i = ( ρ TE ) i j ,
H y i H y i + = Z TM i Z TM j Z TM i + Z TM j = ( ρ TM ) i j ,
ρ = ( ρ 12 + ρ 23 e j 2 β 2 ) + ( ρ 12 ρ 23 + e j 2 β 2 ) ρ 34 e j 2 β 3 ( 1 + ρ 12 ρ 23 e j 2 β 2 ) + ( ρ 23 + ρ 12 e j 2 β 2 ) ρ 34 e j 2 β 3 ,

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