Abstract

The Cojocaru generalization of the 2 × 2 extended Jones matrix method, placed in a wider context of previous approaches to anisotropic optical thin films, is analyzed from a complementary perspective. This, contrary to initial belief, allows for a simple proof that one may include multiple reflections by taking into account total fields into the anisotropic film, and this therefore provides support for a more widespread use of the method.

© 1998 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. M. Born, E. Wolf, Principles of Optics, 5th ed. (Oxford, Pergamon Press, 1975).
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  6. I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Measurement of the principal refractive indices of thin films deposited at oblique incidence,” J. Opt. Soc. Am. A 2, 1693–1697 (1985).
    [CrossRef]
  7. M. Sikkens, I. J. Hodgkinson, F. Horowitz, H. A. Macleod, J. J. Wharton, “Computer simulation of thin film growth,” in Advances in Optical Materials, S. Musikant, ed., Proc. SPIE505, 236–243 (1984).
    [CrossRef]
  8. A. J. Dirks, H. J. Leamy, “Columnar microstructure in vapor-deposited thin films,” Thin Solid Films 47, 219–233 (1977).
    [CrossRef]
  9. H. Schopper, “Zur optik düner dopplelbrechender und dichroitischer schichten,” Z. Phys. 132, 146–170 (1952).
    [CrossRef]
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  23. Well known from the G. Stokes’s “Mathematical and physical papers” mentioned, for example, in F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (New York, McGraw-Hill, 1976).

1997 (1)

1996 (1)

1993 (1)

1990 (1)

1985 (1)

1982 (1)

1979 (1)

1977 (1)

A. J. Dirks, H. J. Leamy, “Columnar microstructure in vapor-deposited thin films,” Thin Solid Films 47, 219–233 (1977).
[CrossRef]

1972 (2)

1970 (1)

1966 (1)

1963 (1)

A. M. Goncharenko, F. I. Fedorov, “Optical properties of crystalline plates,” Opt. Spectrosc. 14, 48–50 (1963).

1957 (1)

P. Bousquet, “Étude théoretique des propriétés optiques des couches minces transparentes,” Ann. Phys. (Paris) 13, 5–15 (1957).

1952 (1)

H. Schopper, “Zur optik düner dopplelbrechender und dichroitischer schichten,” Z. Phys. 132, 146–170 (1952).
[CrossRef]

1948 (1)

F. Abelès, “Sur la propagation des ondes electromagnétiques dans les milieux stratifiés,” Ann. Phys. (Paris) 3, 504–520 (1948); Ann. Phys. (Paris), 12th series, 5, 596 (1950).

1886 (1)

A. Kundt, “Ueber dopplelbrechung des lichtes in metall-schichten, welche durch zerstäuben einer kathode hergestellt sind,” Ann. Physik Chem. 27, 59–71 (1886).
[CrossRef]

Abelès, F.

F. Abelès, “Sur la propagation des ondes electromagnétiques dans les milieux stratifiés,” Ann. Phys. (Paris) 3, 504–520 (1948); Ann. Phys. (Paris), 12th series, 5, 596 (1950).

Berreman, D. W.

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Oxford, Pergamon Press, 1975).

Bousquet, P.

P. Bousquet, “Étude théoretique des propriétés optiques des couches minces transparentes,” Ann. Phys. (Paris) 13, 5–15 (1957).

Cojocaru, E.

Dirks, A. J.

A. J. Dirks, H. J. Leamy, “Columnar microstructure in vapor-deposited thin films,” Thin Solid Films 47, 219–233 (1977).
[CrossRef]

Eichmann, G.

Fedorov, F. I.

A. M. Goncharenko, F. I. Fedorov, “Optical properties of crystalline plates,” Opt. Spectrosc. 14, 48–50 (1963).

Feucht, D. L.

Goncharenko, A. M.

A. M. Goncharenko, F. I. Fedorov, “Optical properties of crystalline plates,” Opt. Spectrosc. 14, 48–50 (1963).

Gu, C.

Henvis, B. W.

Hodgkinson, I. J.

I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Measurement of the principal refractive indices of thin films deposited at oblique incidence,” J. Opt. Soc. Am. A 2, 1693–1697 (1985).
[CrossRef]

M. Sikkens, I. J. Hodgkinson, F. Horowitz, H. A. Macleod, J. J. Wharton, “Computer simulation of thin film growth,” in Advances in Optical Materials, S. Musikant, ed., Proc. SPIE505, 236–243 (1984).
[CrossRef]

Holmes, D. A.

Horowitz, F.

I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Measurement of the principal refractive indices of thin films deposited at oblique incidence,” J. Opt. Soc. Am. A 2, 1693–1697 (1985).
[CrossRef]

M. Sikkens, I. J. Hodgkinson, F. Horowitz, H. A. Macleod, J. J. Wharton, “Computer simulation of thin film growth,” in Advances in Optical Materials, S. Musikant, ed., Proc. SPIE505, 236–243 (1984).
[CrossRef]

F. Horowitz, “Structure-induced optical anisotropy in thin films,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Arizona, 1983).

F. Horowitz, H. A. Macleod, “Form birefringence in thin films,” in Proceedings of the Los Alamos Conference on Optics ’83, R. S. McDowell, S. C. Stotlar, eds., Proc. SPIE380, 83–87 (1983).
[CrossRef]

Jenkins, F. A.

Well known from the G. Stokes’s “Mathematical and physical papers” mentioned, for example, in F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (New York, McGraw-Hill, 1976).

Kundt, A.

A. Kundt, “Ueber dopplelbrechung des lichtes in metall-schichten, welche durch zerstäuben einer kathode hergestellt sind,” Ann. Physik Chem. 27, 59–71 (1886).
[CrossRef]

Laundry, G. D.

Leamy, H. J.

A. J. Dirks, H. J. Leamy, “Columnar microstructure in vapor-deposited thin films,” Thin Solid Films 47, 219–233 (1977).
[CrossRef]

MacGregor, A. R.

Macleod, H. A.

I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Measurement of the principal refractive indices of thin films deposited at oblique incidence,” J. Opt. Soc. Am. A 2, 1693–1697 (1985).
[CrossRef]

M. Sikkens, I. J. Hodgkinson, F. Horowitz, H. A. Macleod, J. J. Wharton, “Computer simulation of thin film growth,” in Advances in Optical Materials, S. Musikant, ed., Proc. SPIE505, 236–243 (1984).
[CrossRef]

F. Horowitz, H. A. Macleod, “Form birefringence in thin films,” in Proceedings of the Los Alamos Conference on Optics ’83, R. S. McDowell, S. C. Stotlar, eds., Proc. SPIE380, 83–87 (1983).
[CrossRef]

Maldonado, T. A.

Schesser, J.

Schopper, H.

H. Schopper, “Zur optik düner dopplelbrechender und dichroitischer schichten,” Z. Phys. 132, 146–170 (1952).
[CrossRef]

Sikkens, M.

I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Measurement of the principal refractive indices of thin films deposited at oblique incidence,” J. Opt. Soc. Am. A 2, 1693–1697 (1985).
[CrossRef]

M. Sikkens, I. J. Hodgkinson, F. Horowitz, H. A. Macleod, J. J. Wharton, “Computer simulation of thin film growth,” in Advances in Optical Materials, S. Musikant, ed., Proc. SPIE505, 236–243 (1984).
[CrossRef]

Slocum, R. E.

R. E. Slocum, “Evaporative thin metal films as polarizers,” in Polarizers and Applications, G. B. Trapani, ed., Proc. SPIE307, 25–30 (1981).
[CrossRef]

Stokes’s, G.

Well known from the G. Stokes’s “Mathematical and physical papers” mentioned, for example, in F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (New York, McGraw-Hill, 1976).

Teitler, S.

Wharton, J. J.

I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Measurement of the principal refractive indices of thin films deposited at oblique incidence,” J. Opt. Soc. Am. A 2, 1693–1697 (1985).
[CrossRef]

M. Sikkens, I. J. Hodgkinson, F. Horowitz, H. A. Macleod, J. J. Wharton, “Computer simulation of thin film growth,” in Advances in Optical Materials, S. Musikant, ed., Proc. SPIE505, 236–243 (1984).
[CrossRef]

White, H. E.

Well known from the G. Stokes’s “Mathematical and physical papers” mentioned, for example, in F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (New York, McGraw-Hill, 1976).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Oxford, Pergamon Press, 1975).

Yeh, P.

Ann. Phys. (Paris) (2)

P. Bousquet, “Étude théoretique des propriétés optiques des couches minces transparentes,” Ann. Phys. (Paris) 13, 5–15 (1957).

F. Abelès, “Sur la propagation des ondes electromagnétiques dans les milieux stratifiés,” Ann. Phys. (Paris) 3, 504–520 (1948); Ann. Phys. (Paris), 12th series, 5, 596 (1950).

Ann. Physik Chem. (1)

A. Kundt, “Ueber dopplelbrechung des lichtes in metall-schichten, welche durch zerstäuben einer kathode hergestellt sind,” Ann. Physik Chem. 27, 59–71 (1886).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (6)

J. Opt. Soc. Am. A (4)

Opt. Spectrosc. (1)

A. M. Goncharenko, F. I. Fedorov, “Optical properties of crystalline plates,” Opt. Spectrosc. 14, 48–50 (1963).

Thin Solid Films (1)

A. J. Dirks, H. J. Leamy, “Columnar microstructure in vapor-deposited thin films,” Thin Solid Films 47, 219–233 (1977).
[CrossRef]

Z. Phys. (1)

H. Schopper, “Zur optik düner dopplelbrechender und dichroitischer schichten,” Z. Phys. 132, 146–170 (1952).
[CrossRef]

Other (6)

R. E. Slocum, “Evaporative thin metal films as polarizers,” in Polarizers and Applications, G. B. Trapani, ed., Proc. SPIE307, 25–30 (1981).
[CrossRef]

F. Horowitz, H. A. Macleod, “Form birefringence in thin films,” in Proceedings of the Los Alamos Conference on Optics ’83, R. S. McDowell, S. C. Stotlar, eds., Proc. SPIE380, 83–87 (1983).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 5th ed. (Oxford, Pergamon Press, 1975).

F. Horowitz, “Structure-induced optical anisotropy in thin films,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Arizona, 1983).

M. Sikkens, I. J. Hodgkinson, F. Horowitz, H. A. Macleod, J. J. Wharton, “Computer simulation of thin film growth,” in Advances in Optical Materials, S. Musikant, ed., Proc. SPIE505, 236–243 (1984).
[CrossRef]

Well known from the G. Stokes’s “Mathematical and physical papers” mentioned, for example, in F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (New York, McGraw-Hill, 1976).

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Figures (1)

Fig. 1
Fig. 1

Multiple reflection and refraction in anisotropic film of thickness d (Region 2), surrounded by isotropic incidence (Region 1) and substrate (Region 3) media. As in Ref. 19, wave vectors k1 + and k1 - correspond to the incident and the reflected waves at interface 1–2; kα + and kβ + correspond to forward-moving α and β waves after double refraction at interface 1–2; kα - and kβ - correspond to backward-moving α and β waves after single reflection at interface 2–3; k3 + corresponds to the transmitted waves after refraction at interface 2–3. In addition, k + and k + correspond to forward-moving α and β waves after second reflection at interface 1–2; k - (not shown) and k - correspond to backward-moving α and β waves after second reflection at interface 2–3 (and so on). Note that all k +, k +, k -, and k -, where n is the number of multiple reflections from the last departed interface, are parallel to kα +, kβ +, kα -, and kβ -.

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