Abstract

The concept of a conducting surface is applied to the description of dielectric multilayers with very thin absorbing films at layer boundaries. Recursive formulas are derived for calculation of multilayer parameters on the basis of the admittance method with arbitrary incidence angles. An expression is found for the characteristic matrix of a conducting surface. Quarter-wavelength dielectric mirrors with boundary losses are investigated, and some simple analytical expressions are found. The possibility of use of the proposed method in the case of boundaries that scatter the light is discussed. Surface radiation conductance is introduced as a characteristic of integral light scattering at a boundary.

© 1998 Optical Society of America

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References

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  1. P. A. Temple, “Measurement of thin-film optical absorption at air–film interface, within the film and at the film-substrate interface,” Appl. Phys. Lett. 34, 677–679 (1979).
    [CrossRef]
  2. F. Coriand, H.-G. Walther, E. Welsch, D. Schafer, and R. Wolf, “Measurement of the thickness dependence of absorption in HfO2 and ZnS single-layer films,” Thin Solid Films 130, 29–35 (1985).
    [CrossRef]
  3. T. Yamaguchi, H. Tamura, S. Taga, and S. Tsuchiya, “Interfacial optical absorption in TiO2-SiO2 multilayer coatings prepared by RF magnetron sputtering,” Appl. Opt. 25, 2703–2706 (1986).
    [CrossRef]
  4. E. N. Kotlikov, “Investigation of absorption in mirrors and films,” Opt. Spektrosk. 70, 838–841 (1991).
  5. K. H. Guenther, “Recent progress in optical coating technology: low voltage ion plating deposition,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. SPIE 1270, 211–221 (1990).
    [CrossRef]
  6. K. H. Guenther, H. L. Gruber, and H. K. Pulker, “Morphology and light scattering of dielectric multilayer systems,” Thin Solid Films 34, 363–367 (1967).
    [CrossRef]
  7. O. Arnon, “Loss mechanisms in dielectric optical interference devices,” Appl. Opt. 16, 2147–2151 (1977).
    [CrossRef] [PubMed]
  8. J. W. Griffin, K. A. Stahl, B. S. Matson, and W. T. Pawlewicz, “Relative importance of surface and volume scattering in all-dielectric mirrors,” Appl. Opt. 25, 1532–1533 (1986).
    [CrossRef] [PubMed]
  9. M. Sparks, “A simple method for calculating the optical properties of multilayer-dielectric reflectors,” J. Opt. Soc. Am. 67, 1590–1594 (1977).
    [CrossRef]
  10. H. G. Walther, E. Welsch, and J. Opfermann, “Calculation and measurement of the absorption in multilayer films by means of photoacoustics,” Thin Solid Films 142, 27–35 (1986).
    [CrossRef]
  11. G. V. Rosenberg, Optics of Thin Film Coatings (Fizmatgiz, Moscow, 1958, in Russian).
  12. H. Wolter, “Optik dünner Schichten,” in Handbuch der Physik (Springer-Verlag, Berlin, 1956), Vol. 24, pp. 461–473.
  13. F. Abelès, “Optical properties of very thin films,” Thin Solid Films 34, 291–302 (1976).
    [CrossRef]
  14. P. W. Smith, M. V. Schneider, and H. G. Danielmeier, “High-power single-frequency lasers using thin-film mode-selection filters,” Bell Syst. Tech. J. 48, 1405–1420 (1969).
    [CrossRef]
  15. W. R. Leeb, “Tunable thin film filters,” Appl. Opt. 15, 681–689 (1976).
  16. Y. V. Troitski, “Conducting surface model for the investigation of the properties of thin metal films,” Avtometriya No. 6, 91–95 (1972). [English transl.: Automatic Monitoring and Measuring No. 6 (1972)].
  17. Y. V. Troitski, Multilayer Coatings with Absorption Localized at Interlayer Boundaries, Preprint No. 471 (Institute of Automation and Electrometry, U.S.S.R. Academy of Sciences, Novosibirsk, U.S.S.R., 1991, in Russian).
  18. Y. V. Troitski, “Optical losses in dielectric multilayer coatings and their inlfuence on characteristics of laser resonators,” in Thin Films for Optical Systems, K. H. Guenther, ed., Proc. SPIE 1782, 85–92 (1993).
    [CrossRef]
  19. Y. V. Troitski, Single Frequency Gas Lasers (Nauka, Novosibirsk, U.S.S.R., 1975, in Russian).
  20. Y. V. Troitski, Multiple Beam Interferometers for Reflected Light (Nauka, Novosibirsk, U.S.S.R., 1985, in Russian).
  21. L. N. Hadley and D. M. Dennison, “Reflection and transmission interference filters. 1. Theory,” J. Opt. Soc. Am. 37, 451–465 (1947).
    [CrossRef]
  22. S. Yamaguchi, “Theory of the optical properties of very thin inhomogeneous films,” J. Phys. Soc. Jpn. 17, 184–193 (1962).
    [CrossRef]
  23. Y. V. Troitski, “Absorption and scattering of light obliquely incident on a multilayer structure with absorptive layer boundaries,” Sov. J. Commun. Technol. Electron. 37(5), 23–29 (1992).
  24. P. H. Berning, “Theory and calculations of optical thin films,” in Physics of Thin Films, G. Hass, ed. (Academic, New York, 1963), Vol. 1.
  25. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1968).
  26. A. B. Latyshev, “Metal film as means for matching transparent media in millimeter–submillimeter range,” Radiotekh. Elektron. 34, 1376–1380 (1989).
  27. Y. V. Troitski, “Conducting surface as a model for describing the losses at the layer boundaries in a dielectric multilayered structure,” Opt. Spectrosc. 64, 83–86 (1988).
  28. P. Giacomo, “Les couches réfléchissantes multidieléctriques appliquées à l’interferomètre de Fabry–Perot. Etude théorique et expérimentale des couches réeles,” Rev. d’Opt. 35, 6–354 (1956).
  29. G. Koppelmann, “Zur Theorie der Wechselschichten aus schwachabsorbierenden Substanzen und ihre Verwendung als Interferometerspiegel,” Ann. Physik (Leipzig) 5, 388–396 (1960).
    [CrossRef]
  30. Y. V. Troitski, “Reflecting interferometer based on matched metallic film,” JETP Lett. 11, 183–185 (1970).
  31. Y. V. Troitski, “Present state and future prospects for reflection multiple-beam interferometry,” Optoelectron. Instrum. Data Process. No. 1, 87–105 (1985).
  32. Y. V. Troitski, “Progress in multiple-beam reflection interferometry,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee and J.-F. Houee, eds., Proc. SPIE 2775, 216–225 (1996).
    [CrossRef]
  33. Y. V. Troitski, “Optical resonator with thin absorbing film as a mode selector,” Opt. Spectrosc. 25, 309–313 (1969).
  34. L. N. Hadley and D. M. Dennison, “Reflection and transmission interference filters. 2. Experimental, comparison with theory, results,” J. Opt. Soc. Am. 38, 483–496 (1948).
    [CrossRef] [PubMed]
  35. N. D. Goldina and Y. V. Troitski, “Narrow band filters in reflected light,” Opt. Spectrosc. 40, 532–534 (1976).
  36. N. N. Kamenev and Y. V. Troitski, “Metal-dielectric mirrors with single-sided light reflection,” Opt. Spectrosc. 54, 428–430 (1983).
  37. V. N. Bel’tyugov and Y. V. Troitski, “Polarizing laser mirrors,” Sov. J. Quantum Electron. 18, 627–629 (1988).
    [CrossRef]
  38. D. A. B. Miller, “Laser tuners and wavelength-selective detectors based on absorbers in standing waves,” IEEE J. Quantum Electron. 30, 732–749 (1994).
    [CrossRef]
  39. M. I. Zakharov and Y. V. Troitski, “About the calculation of an optical resonator with absorbing film,” Radiotekh. Elektron. 15, 2644–2645 (1970). English translation in Radio Eng. Electron. Phys. (1970).
  40. H. K. Pulker, “Optical losses in dielectric films,” Thin Solid Films 34, 343–347 (1976).
    [CrossRef]
  41. C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–115 (1979).
    [CrossRef]

1996 (1)

Y. V. Troitski, “Progress in multiple-beam reflection interferometry,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee and J.-F. Houee, eds., Proc. SPIE 2775, 216–225 (1996).
[CrossRef]

1994 (1)

D. A. B. Miller, “Laser tuners and wavelength-selective detectors based on absorbers in standing waves,” IEEE J. Quantum Electron. 30, 732–749 (1994).
[CrossRef]

1993 (1)

Y. V. Troitski, “Optical losses in dielectric multilayer coatings and their inlfuence on characteristics of laser resonators,” in Thin Films for Optical Systems, K. H. Guenther, ed., Proc. SPIE 1782, 85–92 (1993).
[CrossRef]

1992 (1)

Y. V. Troitski, “Absorption and scattering of light obliquely incident on a multilayer structure with absorptive layer boundaries,” Sov. J. Commun. Technol. Electron. 37(5), 23–29 (1992).

1991 (1)

E. N. Kotlikov, “Investigation of absorption in mirrors and films,” Opt. Spektrosk. 70, 838–841 (1991).

1990 (1)

K. H. Guenther, “Recent progress in optical coating technology: low voltage ion plating deposition,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. SPIE 1270, 211–221 (1990).
[CrossRef]

1989 (1)

A. B. Latyshev, “Metal film as means for matching transparent media in millimeter–submillimeter range,” Radiotekh. Elektron. 34, 1376–1380 (1989).

1988 (2)

Y. V. Troitski, “Conducting surface as a model for describing the losses at the layer boundaries in a dielectric multilayered structure,” Opt. Spectrosc. 64, 83–86 (1988).

V. N. Bel’tyugov and Y. V. Troitski, “Polarizing laser mirrors,” Sov. J. Quantum Electron. 18, 627–629 (1988).
[CrossRef]

1986 (3)

1985 (1)

F. Coriand, H.-G. Walther, E. Welsch, D. Schafer, and R. Wolf, “Measurement of the thickness dependence of absorption in HfO2 and ZnS single-layer films,” Thin Solid Films 130, 29–35 (1985).
[CrossRef]

1983 (1)

N. N. Kamenev and Y. V. Troitski, “Metal-dielectric mirrors with single-sided light reflection,” Opt. Spectrosc. 54, 428–430 (1983).

1979 (2)

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–115 (1979).
[CrossRef]

P. A. Temple, “Measurement of thin-film optical absorption at air–film interface, within the film and at the film-substrate interface,” Appl. Phys. Lett. 34, 677–679 (1979).
[CrossRef]

1977 (2)

1976 (4)

W. R. Leeb, “Tunable thin film filters,” Appl. Opt. 15, 681–689 (1976).

H. K. Pulker, “Optical losses in dielectric films,” Thin Solid Films 34, 343–347 (1976).
[CrossRef]

N. D. Goldina and Y. V. Troitski, “Narrow band filters in reflected light,” Opt. Spectrosc. 40, 532–534 (1976).

F. Abelès, “Optical properties of very thin films,” Thin Solid Films 34, 291–302 (1976).
[CrossRef]

1970 (1)

Y. V. Troitski, “Reflecting interferometer based on matched metallic film,” JETP Lett. 11, 183–185 (1970).

1969 (2)

Y. V. Troitski, “Optical resonator with thin absorbing film as a mode selector,” Opt. Spectrosc. 25, 309–313 (1969).

P. W. Smith, M. V. Schneider, and H. G. Danielmeier, “High-power single-frequency lasers using thin-film mode-selection filters,” Bell Syst. Tech. J. 48, 1405–1420 (1969).
[CrossRef]

1967 (1)

K. H. Guenther, H. L. Gruber, and H. K. Pulker, “Morphology and light scattering of dielectric multilayer systems,” Thin Solid Films 34, 363–367 (1967).
[CrossRef]

1962 (1)

S. Yamaguchi, “Theory of the optical properties of very thin inhomogeneous films,” J. Phys. Soc. Jpn. 17, 184–193 (1962).
[CrossRef]

1960 (1)

G. Koppelmann, “Zur Theorie der Wechselschichten aus schwachabsorbierenden Substanzen und ihre Verwendung als Interferometerspiegel,” Ann. Physik (Leipzig) 5, 388–396 (1960).
[CrossRef]

1948 (1)

1947 (1)

Abelès, F.

F. Abelès, “Optical properties of very thin films,” Thin Solid Films 34, 291–302 (1976).
[CrossRef]

Arnon, O.

Bel’tyugov, V. N.

V. N. Bel’tyugov and Y. V. Troitski, “Polarizing laser mirrors,” Sov. J. Quantum Electron. 18, 627–629 (1988).
[CrossRef]

Carniglia, C. K.

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–115 (1979).
[CrossRef]

Coriand, F.

F. Coriand, H.-G. Walther, E. Welsch, D. Schafer, and R. Wolf, “Measurement of the thickness dependence of absorption in HfO2 and ZnS single-layer films,” Thin Solid Films 130, 29–35 (1985).
[CrossRef]

Danielmeier, H. G.

P. W. Smith, M. V. Schneider, and H. G. Danielmeier, “High-power single-frequency lasers using thin-film mode-selection filters,” Bell Syst. Tech. J. 48, 1405–1420 (1969).
[CrossRef]

Dennison, D. M.

Goldina, N. D.

N. D. Goldina and Y. V. Troitski, “Narrow band filters in reflected light,” Opt. Spectrosc. 40, 532–534 (1976).

Griffin, J. W.

Gruber, H. L.

K. H. Guenther, H. L. Gruber, and H. K. Pulker, “Morphology and light scattering of dielectric multilayer systems,” Thin Solid Films 34, 363–367 (1967).
[CrossRef]

Guenther, K. H.

K. H. Guenther, “Recent progress in optical coating technology: low voltage ion plating deposition,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. SPIE 1270, 211–221 (1990).
[CrossRef]

K. H. Guenther, H. L. Gruber, and H. K. Pulker, “Morphology and light scattering of dielectric multilayer systems,” Thin Solid Films 34, 363–367 (1967).
[CrossRef]

Hadley, L. N.

Kamenev, N. N.

N. N. Kamenev and Y. V. Troitski, “Metal-dielectric mirrors with single-sided light reflection,” Opt. Spectrosc. 54, 428–430 (1983).

Koppelmann, G.

G. Koppelmann, “Zur Theorie der Wechselschichten aus schwachabsorbierenden Substanzen und ihre Verwendung als Interferometerspiegel,” Ann. Physik (Leipzig) 5, 388–396 (1960).
[CrossRef]

Kotlikov, E. N.

E. N. Kotlikov, “Investigation of absorption in mirrors and films,” Opt. Spektrosk. 70, 838–841 (1991).

Latyshev, A. B.

A. B. Latyshev, “Metal film as means for matching transparent media in millimeter–submillimeter range,” Radiotekh. Elektron. 34, 1376–1380 (1989).

Leeb, W. R.

Matson, B. S.

Miller, D. A. B.

D. A. B. Miller, “Laser tuners and wavelength-selective detectors based on absorbers in standing waves,” IEEE J. Quantum Electron. 30, 732–749 (1994).
[CrossRef]

Opfermann, J.

H. G. Walther, E. Welsch, and J. Opfermann, “Calculation and measurement of the absorption in multilayer films by means of photoacoustics,” Thin Solid Films 142, 27–35 (1986).
[CrossRef]

Pawlewicz, W. T.

Pulker, H. K.

H. K. Pulker, “Optical losses in dielectric films,” Thin Solid Films 34, 343–347 (1976).
[CrossRef]

K. H. Guenther, H. L. Gruber, and H. K. Pulker, “Morphology and light scattering of dielectric multilayer systems,” Thin Solid Films 34, 363–367 (1967).
[CrossRef]

Schafer, D.

F. Coriand, H.-G. Walther, E. Welsch, D. Schafer, and R. Wolf, “Measurement of the thickness dependence of absorption in HfO2 and ZnS single-layer films,” Thin Solid Films 130, 29–35 (1985).
[CrossRef]

Schneider, M. V.

P. W. Smith, M. V. Schneider, and H. G. Danielmeier, “High-power single-frequency lasers using thin-film mode-selection filters,” Bell Syst. Tech. J. 48, 1405–1420 (1969).
[CrossRef]

Smith, P. W.

P. W. Smith, M. V. Schneider, and H. G. Danielmeier, “High-power single-frequency lasers using thin-film mode-selection filters,” Bell Syst. Tech. J. 48, 1405–1420 (1969).
[CrossRef]

Sparks, M.

Stahl, K. A.

Taga, S.

Tamura, H.

Temple, P. A.

P. A. Temple, “Measurement of thin-film optical absorption at air–film interface, within the film and at the film-substrate interface,” Appl. Phys. Lett. 34, 677–679 (1979).
[CrossRef]

Troitski, Y. V.

Y. V. Troitski, “Progress in multiple-beam reflection interferometry,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee and J.-F. Houee, eds., Proc. SPIE 2775, 216–225 (1996).
[CrossRef]

Y. V. Troitski, “Optical losses in dielectric multilayer coatings and their inlfuence on characteristics of laser resonators,” in Thin Films for Optical Systems, K. H. Guenther, ed., Proc. SPIE 1782, 85–92 (1993).
[CrossRef]

Y. V. Troitski, “Absorption and scattering of light obliquely incident on a multilayer structure with absorptive layer boundaries,” Sov. J. Commun. Technol. Electron. 37(5), 23–29 (1992).

Y. V. Troitski, “Conducting surface as a model for describing the losses at the layer boundaries in a dielectric multilayered structure,” Opt. Spectrosc. 64, 83–86 (1988).

V. N. Bel’tyugov and Y. V. Troitski, “Polarizing laser mirrors,” Sov. J. Quantum Electron. 18, 627–629 (1988).
[CrossRef]

N. N. Kamenev and Y. V. Troitski, “Metal-dielectric mirrors with single-sided light reflection,” Opt. Spectrosc. 54, 428–430 (1983).

N. D. Goldina and Y. V. Troitski, “Narrow band filters in reflected light,” Opt. Spectrosc. 40, 532–534 (1976).

Y. V. Troitski, “Reflecting interferometer based on matched metallic film,” JETP Lett. 11, 183–185 (1970).

Y. V. Troitski, “Optical resonator with thin absorbing film as a mode selector,” Opt. Spectrosc. 25, 309–313 (1969).

Tsuchiya, S.

Walther, H. G.

H. G. Walther, E. Welsch, and J. Opfermann, “Calculation and measurement of the absorption in multilayer films by means of photoacoustics,” Thin Solid Films 142, 27–35 (1986).
[CrossRef]

Walther, H.-G.

F. Coriand, H.-G. Walther, E. Welsch, D. Schafer, and R. Wolf, “Measurement of the thickness dependence of absorption in HfO2 and ZnS single-layer films,” Thin Solid Films 130, 29–35 (1985).
[CrossRef]

Welsch, E.

H. G. Walther, E. Welsch, and J. Opfermann, “Calculation and measurement of the absorption in multilayer films by means of photoacoustics,” Thin Solid Films 142, 27–35 (1986).
[CrossRef]

F. Coriand, H.-G. Walther, E. Welsch, D. Schafer, and R. Wolf, “Measurement of the thickness dependence of absorption in HfO2 and ZnS single-layer films,” Thin Solid Films 130, 29–35 (1985).
[CrossRef]

Wolf, R.

F. Coriand, H.-G. Walther, E. Welsch, D. Schafer, and R. Wolf, “Measurement of the thickness dependence of absorption in HfO2 and ZnS single-layer films,” Thin Solid Films 130, 29–35 (1985).
[CrossRef]

Yamaguchi, S.

S. Yamaguchi, “Theory of the optical properties of very thin inhomogeneous films,” J. Phys. Soc. Jpn. 17, 184–193 (1962).
[CrossRef]

Yamaguchi, T.

Ann. Physik (Leipzig) (1)

G. Koppelmann, “Zur Theorie der Wechselschichten aus schwachabsorbierenden Substanzen und ihre Verwendung als Interferometerspiegel,” Ann. Physik (Leipzig) 5, 388–396 (1960).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

P. A. Temple, “Measurement of thin-film optical absorption at air–film interface, within the film and at the film-substrate interface,” Appl. Phys. Lett. 34, 677–679 (1979).
[CrossRef]

Bell Syst. Tech. J. (1)

P. W. Smith, M. V. Schneider, and H. G. Danielmeier, “High-power single-frequency lasers using thin-film mode-selection filters,” Bell Syst. Tech. J. 48, 1405–1420 (1969).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. A. B. Miller, “Laser tuners and wavelength-selective detectors based on absorbers in standing waves,” IEEE J. Quantum Electron. 30, 732–749 (1994).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Phys. Soc. Jpn. (1)

S. Yamaguchi, “Theory of the optical properties of very thin inhomogeneous films,” J. Phys. Soc. Jpn. 17, 184–193 (1962).
[CrossRef]

JETP Lett. (1)

Y. V. Troitski, “Reflecting interferometer based on matched metallic film,” JETP Lett. 11, 183–185 (1970).

Opt. Eng. (1)

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–115 (1979).
[CrossRef]

Opt. Spectrosc. (4)

N. D. Goldina and Y. V. Troitski, “Narrow band filters in reflected light,” Opt. Spectrosc. 40, 532–534 (1976).

N. N. Kamenev and Y. V. Troitski, “Metal-dielectric mirrors with single-sided light reflection,” Opt. Spectrosc. 54, 428–430 (1983).

Y. V. Troitski, “Optical resonator with thin absorbing film as a mode selector,” Opt. Spectrosc. 25, 309–313 (1969).

Y. V. Troitski, “Conducting surface as a model for describing the losses at the layer boundaries in a dielectric multilayered structure,” Opt. Spectrosc. 64, 83–86 (1988).

Opt. Spektrosk. (1)

E. N. Kotlikov, “Investigation of absorption in mirrors and films,” Opt. Spektrosk. 70, 838–841 (1991).

Proc. SPIE (3)

K. H. Guenther, “Recent progress in optical coating technology: low voltage ion plating deposition,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. SPIE 1270, 211–221 (1990).
[CrossRef]

Y. V. Troitski, “Optical losses in dielectric multilayer coatings and their inlfuence on characteristics of laser resonators,” in Thin Films for Optical Systems, K. H. Guenther, ed., Proc. SPIE 1782, 85–92 (1993).
[CrossRef]

Y. V. Troitski, “Progress in multiple-beam reflection interferometry,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee and J.-F. Houee, eds., Proc. SPIE 2775, 216–225 (1996).
[CrossRef]

Radiotekh. Elektron. (1)

A. B. Latyshev, “Metal film as means for matching transparent media in millimeter–submillimeter range,” Radiotekh. Elektron. 34, 1376–1380 (1989).

Sov. J. Commun. Technol. Electron. (1)

Y. V. Troitski, “Absorption and scattering of light obliquely incident on a multilayer structure with absorptive layer boundaries,” Sov. J. Commun. Technol. Electron. 37(5), 23–29 (1992).

Sov. J. Quantum Electron. (1)

V. N. Bel’tyugov and Y. V. Troitski, “Polarizing laser mirrors,” Sov. J. Quantum Electron. 18, 627–629 (1988).
[CrossRef]

Thin Solid Films (5)

H. K. Pulker, “Optical losses in dielectric films,” Thin Solid Films 34, 343–347 (1976).
[CrossRef]

F. Coriand, H.-G. Walther, E. Welsch, D. Schafer, and R. Wolf, “Measurement of the thickness dependence of absorption in HfO2 and ZnS single-layer films,” Thin Solid Films 130, 29–35 (1985).
[CrossRef]

K. H. Guenther, H. L. Gruber, and H. K. Pulker, “Morphology and light scattering of dielectric multilayer systems,” Thin Solid Films 34, 363–367 (1967).
[CrossRef]

H. G. Walther, E. Welsch, and J. Opfermann, “Calculation and measurement of the absorption in multilayer films by means of photoacoustics,” Thin Solid Films 142, 27–35 (1986).
[CrossRef]

F. Abelès, “Optical properties of very thin films,” Thin Solid Films 34, 291–302 (1976).
[CrossRef]

Other (11)

P. Giacomo, “Les couches réfléchissantes multidieléctriques appliquées à l’interferomètre de Fabry–Perot. Etude théorique et expérimentale des couches réeles,” Rev. d’Opt. 35, 6–354 (1956).

Y. V. Troitski, “Conducting surface model for the investigation of the properties of thin metal films,” Avtometriya No. 6, 91–95 (1972). [English transl.: Automatic Monitoring and Measuring No. 6 (1972)].

Y. V. Troitski, Multilayer Coatings with Absorption Localized at Interlayer Boundaries, Preprint No. 471 (Institute of Automation and Electrometry, U.S.S.R. Academy of Sciences, Novosibirsk, U.S.S.R., 1991, in Russian).

Y. V. Troitski, “Present state and future prospects for reflection multiple-beam interferometry,” Optoelectron. Instrum. Data Process. No. 1, 87–105 (1985).

G. V. Rosenberg, Optics of Thin Film Coatings (Fizmatgiz, Moscow, 1958, in Russian).

H. Wolter, “Optik dünner Schichten,” in Handbuch der Physik (Springer-Verlag, Berlin, 1956), Vol. 24, pp. 461–473.

P. H. Berning, “Theory and calculations of optical thin films,” in Physics of Thin Films, G. Hass, ed. (Academic, New York, 1963), Vol. 1.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1968).

M. I. Zakharov and Y. V. Troitski, “About the calculation of an optical resonator with absorbing film,” Radiotekh. Elektron. 15, 2644–2645 (1970). English translation in Radio Eng. Electron. Phys. (1970).

Y. V. Troitski, Single Frequency Gas Lasers (Nauka, Novosibirsk, U.S.S.R., 1975, in Russian).

Y. V. Troitski, Multiple Beam Interferometers for Reflected Light (Nauka, Novosibirsk, U.S.S.R., 1985, in Russian).

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Figures (1)

Fig. 1
Fig. 1

Multilayer system with conducting surfaces at layer boundaries.

Equations (30)

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

[Ej(zj)]t=[Ej-1(zj)]t,
[Hj(zj)]t-[Hj-1(zj)]t=YSj[Ej(zj)]t,
Yinpj-1[Hj-1(zj+h)]t/[Ej-1(zj+h)]t.
Yinpj=[Hj(zj+1+h)]t/[Ej(zj+1+h)]t.
Ej=Ej+ exp(-ikjz)+Ej- exp(ikjz),
[Hj]t=cos θjYj[Ej+ exp(-ikjz)-Ej- exp(ikjz)].
Yinpj=Yj cos θjYinpj-1+Ysj+iYj cos θj tan φjYj cos θj+i(Yinpj-1+Ysj)tan φj,
yj=ujyj-1+ξj+iuj tan φjuj+i(yj-1+ξj)tan φj.
ρ=EV-(zN+1)]t[EV+(zN+1)]t=uV-ξN+1-yNuV+ξN+1+yN,
EG+EV+=EG+E1+E1+E2+EN-1+EN+EN+EV+,
Ej-1+(zj+h)Ej+(zj+1+h)=ujuj-1(yj-1+uj-1)exp(-iφj)yj-1+ξj+uj.
EN+(zN+h)EV+(zN-h)=uVuNyN+uNyN+ξN+1+uV.
τ=EG+EV+uGuV1/2=uVuG1/2 yN+uNyN+ξN+1+uV×j=1Nyj-1+uj-1yj-1+ξj+ujexp(-iφj).
1-T-R11-T-R2=n1n2,
1-T-R1T=ξn2.
M=MN+1ξ·MND·MNξ·MN-1D··M1D·M1ξ,
Mjξ=10Y0ξj1.
(ω0nLhL/c)cos θL=(ω0nHhH/c)cos θH=π/2,
AQ=4ξuV/(uH2-uL2)
AQ=4ξnV cos θVnH2-nL2;
AQ=4ξnV/cos θVnH4/(nH2-nV2 sin2 θV)-nL4/(nL2-nV2 sin2 θV).
AQ=4ξnVnH2-nL2.
AQ=4ξuH2/[uV(uH2-uL2)],
AQ=4ξnH2nV(nH2-nL2).
R¯1=R0 exp(-16π2n12σ2/λ2),
R¯2=R0 exp(-16π2n22σ2/λ2),
T¯=T0 exp[-4π2(n1-n2)2σ2/λ2],
ξ¯=4π2(n1+n2)(n1-n2)2σ2/λ2.
TIS=A¯=16π2nV(nH-nL)(σ/λ)2.
TIS=A¯=(16π2/nV)[(nV-nL)2(nV+nL)+nL2(nH-nL)](σ/λ)2.

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