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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 24, Iss. 12 — Jun. 15, 1985
  • pp: 1788–1798

Determination of the optical constants of a thin film from transmittance measurements of a single film thickness

Kent F. Palmer and Michael Z. Williams  »View Author Affiliations


Applied Optics, Vol. 24, Issue 12, pp. 1788-1798 (1985)
http://dx.doi.org/10.1364/AO.24.001788


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Abstract

A subtractive Kramers-Kronig method is presented for obtaining the optical constants, n and k, of a uniform absorbing film on a substrate using the transmittance spectrum of a single film thickness. We give the results of tests on the reliability of our method, demonstrate the usefulness of the method when only transmittance data are available, and give examples of thin films whose optical constants depend on their thickness.

© 1985 Optical Society of America

History
Original Manuscript: November 2, 9199
Published: June 15, 1985

Citation
Kent F. Palmer and Michael Z. Williams, "Determination of the optical constants of a thin film from transmittance measurements of a single film thickness," Appl. Opt. 24, 1788-1798 (1985)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-24-12-1788


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References

  1. K. F. Palmer, J. A. Roux, B. E. Wood, “The Infrared Optical Properties of Mixtures of Molecular Species at 20 K,” AEDC-TR-80-30 (AD-A094214) (Jan.1981); also AIAA paper 83-1452.
  2. O. S. Heavens, Optical Properties of Thin Films (Dover, New York, 1965).
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  10. D. W. Johnson, “A Fourier Series Method for Numerical Kramers-Kronig Analysis,” J. Phys. A 8, 490 (1975). [CrossRef]
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  12. R. K. Ahrenkiel, “Modified Kramers-Kronig Analysis of Optical Spectra,” J. Opt. Soc. Am. 61, 1651 (1971). [CrossRef]
  13. K. E. Peiponen, “On the Properties of the Complex Refractive Index of Lorentzian Type,” Phys. Scr. 21, 181 (1980). [CrossRef]
  14. R. W. Ditchburn, Light (Academic, New York, 1976), Vols. 1 and 2.
  15. J. A. Roux, B. F. Wood, A. M. Smith, “IR Optical Properties of Thin H2O, NH3, CO2 Cryofilms,” AEDC-TR-79-57 (AD-A074913) (Sept.1979).
  16. K. E. Tempelmeyer, D. W. Mills, “Refractive Index of Carbon Dioxide Cryodeposit,” J. Appl. Phys. 39, 2968 (1968). [CrossRef]
  17. In cases where some observed transmittance values are negative, we can establish a new base line for the transmittance spectrum by adding a very small constant to every original transmittance value so that the new transmittance spectrum will not have any negative (or zero) values. It is not clear, however, what the additive constant should be. The establishment of the criteria for choosing the constant is very important because relatively small adjustments of the additive constant can cause variances in the smallest transmittances of several hundred percent, or more, and can create very noticeable differences in the n spectra computed by skktrans, as we observed in the case of the thicker N2/CO2 films.
  18. B. E. Wood, Arvin/Calspan Field Services, Inc.; private communication.
  19. K. F. Palmer, M. Z. Williams, “Optical Constant Determination of Thin Films Condensed on Transmitting and Reflecting Surfaces,” AEDC-TR-83-64.
  20. E. A. Lupaskho, V. K. Miloslavskii, I. N. Shklyarevskii, “Use of the Kramers-Kronig Dispersion Relations in Determining the Phase Shift Occurring upon Reflection of Light from Thin Dielectric Layers,” Opt. Spektrosk. 24, 257 (1968)[Opt. Spectrosc. 24, 32 (1968)].
  21. E. A. Lupashko, V. K. Miloslavskii, I. N. Shklyarevskii, “Use of the Kramers-Kronig Dispersion Relationships to Calculate the Phase of the Wave Reflected from Thin Dielectric Layers,” Opt. Spektrosk. 29, 789 (1970)[Opt. Spectrosc. 29, 419 (1970)].
  22. F. Wooten, Optical Properties of Solids (Academic, New York, 1972).
  23. L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon,New York, 1960).

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