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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 13, Iss. 4 — Apr. 1, 1996
  • pp: 875–883

Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from uniaxial TiO2

Mathias Schubert, Bernd Rheinländer, John A. Woollam, Blaine Johs, and Craig M. Herzinger  »View Author Affiliations


JOSA A, Vol. 13, Issue 4, pp. 875-883 (1996)
http://dx.doi.org/10.1364/JOSAA.13.000875


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Abstract

For what is the first time, to our knowledge, we report on the extension of spectroscopic rotating-analyzer ellipsometry to generalized ellipsometry to define and to determine three essentially normalized elements of the optical Jones matrix J [ AzzamR. M. A. BasharaN. M., J. Opt. Soc. Am. 62, 1521 ( 1972)]. These elements are measured in reflection over the spectral range of 3.5–4.5 eV on different surface orientations of uniaxial TiO2 cut from the same bulk crystal. With a wavelength-by-wavelength regression and a 4 × 4 generalized matrix algebra, both refractive and absorption indices for the ordinary and the extraordinary waves, no, ko, ne, and ke, are determined. The inclinations and the azimuths of the optic axes with respect to the sample normal and plane of incidence were determined as well. The latter are confirmed by x-ray diffraction and polarization microscopy. Hence the spectrally dependent dielectric function tensor in laboratory coordinates is obtained. Very good agreement between measured and calculated data for the normalized Jones elements for the respective sample orientations and positions are presented. This technique may become an important tool for investigating layered systems with nonscalar dielectric susceptibilities.

© 1996 Optical Society of America

History
Original Manuscript: June 29, 1995
Revised Manuscript: October 19, 1995
Manuscript Accepted: October 24, 1995
Published: April 1, 1996

Citation
Mathias Schubert, John A. Woollam, Blaine Johs, Craig M. Herzinger, and Bernd Rheinländer, "Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from uniaxial TiO2," J. Opt. Soc. Am. A 13, 875-883 (1996)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-13-4-875


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References

  1. R. M. A. Azzam, N. M. Bashara, “Generalized ellipsometry for surfaces with directional preference: application to diffraction gratings,” J. Opt. Soc. Am. 62, 1521–1523 (1972). [CrossRef]
  2. See, e.g.: R. M. A. Azzam, N. M. Bashara, “Polarization transfer function of a biaxial system as a bilinear transformation,” J. Opt. Soc. Am. 62, 222–229 (1972). [CrossRef]
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  9. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985), pp. 798–804.
  10. K. Vos, H. J. Krusemayer, “Reflectance and electroreflectance of TiO2single crystals: I. Optical spectra,” Phys. C 10, 3893–3915 (1977). [CrossRef]
  11. M. Cardona, G. Harbeke, “Optical properties and band structure of wurtzite-type crystals and rutile,” Phys. Rev. A 137, 1467–1476 (1965).

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