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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 28, Iss. 12 — Dec. 1, 2011
  • pp: 2428–2435

Dispersion analysis of perpendicular modes in anisotropic crystals and layers

Thomas G. Mayerhöfer, Sonja Weber, and Jürgen Popp  »View Author Affiliations

JOSA A, Vol. 28, Issue 12, pp. 2428-2435 (2011)

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Until today dispersion analysis could not be successfully applied to evaluate oscillator parameters of modes that have their transition moments perpendicular to the surface of an anisotropic crystal or a layered medium. The main reason for this failure is that while such modes generate maxima in the external reflection spectra, which are obtained with polarized light parallel to the plane of incidence under nonzero angles of incidence, the positions of these maxima do not allow us to unambiguously trace back the oscillator positions. In contrast, total internal reflection of parallel polarized light generates minima at spectral positions close to the oscillator frequency. Starting from this observation, we found that a combined evaluation of external and total internal reflection spectra by dispersion analysis allows us to gain the oscillator parameters of perpendicular modes unambiguously.

© 2011 Optical Society of America

OCIS Codes
(260.1180) Physical optics : Crystal optics
(260.1440) Physical optics : Birefringence
(260.6970) Physical optics : Total internal reflection
(310.3840) Thin films : Materials and process characterization

ToC Category:
Physical Optics

Original Manuscript: June 13, 2011
Revised Manuscript: September 29, 2011
Manuscript Accepted: September 30, 2011
Published: November 4, 2011

Thomas G. Mayerhöfer, Sonja Weber, and Jürgen Popp, "Dispersion analysis of perpendicular modes in anisotropic crystals and layers," J. Opt. Soc. Am. A 28, 2428-2435 (2011)

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  25. The formulas presented in this paper allow for anisotropic substrate materials down to monoclinic symmetry, where the monoclinic b-axis is oriented perpendicular to the substrate surface, which covers to our best knowledge all common substrate materials. Generally valid formulas can be found in .
  26. The X- and Y-components of the wave vector k, kX and kY, are the same as for the incidence medium and are given by kX=0 and kY=nisin⁡α, wherein α is the angle of incidence and n the index of refraction of the isotropic incidence medium provided that the plane of incidence is the Y–Z plane (cf. Figure ). All components are dimensionless quantities.
  27. For absorbing media, a positive imaginary part of γi determines a forward travelling wave, whereas the same wave in a nonabsorbing medium is characterized by a positive real part of γi.
  28. For a semi-infinte medium the Ψ2,l and the Ψ4,l are zero .
  29. For the wavenumber, traditionally the symbol ν˜ is also in use, especially in the context of spectroscopy [see, e.g., Eq. ].
  30. If for both the sample medium and the substrate the dynamical matrix can be calculated according to Eq. , then the waves are uncoupled and rij=tij=0 holds.
  31. Equation  does not directly transform under the condition of Eq. .
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