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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 22, Iss. 11 — Nov. 1, 2005
  • pp: 2557–2563

Angular dependence of the reflectance from an isotropic polydomain medium: the influence of absorption

Thomas G. Mayerhöfer and Jürgen Popp  »View Author Affiliations

JOSA A, Vol. 22, Issue 11, pp. 2557-2563 (2005)

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The angular dependence of the reflectance from an absorbing randomly oriented polydomain medium consisting of domains either small or large compared with the wavelength is investigated. Besides the two conventional cases, where the refractive index of the incidence medium is either smaller or larger than the averaged index of refraction (small-domain limit) or every principal index of refraction of the domains (large-domain limit), we also discuss a third principal case, which exists only in the large-domain limit. In this third case, only one of the principal indices of refraction is larger than that of the incidence medium, while the averaged index of refraction is smaller. Thus, in contrast to the small-domain limit, total reflection is completely suppressed even in the absence of absorption. A characteristic property of such a polydomain medium is its ability to considerably depolarize linear polarized light in spite of being optically isotropic. Additionally, the parallel polarized reflectance R p can exceed the perpendicular polarized reflectance R s over certain angle of incidence ranges. Absorption decreases these domain-size-dependent properties, even under the assumption of constant anisotropy. Nevertheless, for materials with low absorption indices, these effects can affect the optical properties significantly.

© 2005 Optical Society of America

OCIS Codes
(260.1180) Physical optics : Crystal optics
(260.5430) Physical optics : Polarization
(260.6970) Physical optics : Total internal reflection

ToC Category:
Physical Optics

Original Manuscript: January 7, 2005
Revised Manuscript: April 20, 2005
Manuscript Accepted: April 28, 2005
Published: November 1, 2005

Thomas G. Mayerhöfer and Jürgen Popp, "Angular dependence of the reflectance from an isotropic polydomain medium: the influence of absorption," J. Opt. Soc. Am. A 22, 2557-2563 (2005)

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  1. G. L. Doll, J. Steinbeck, G. Dresselhaus, M. S. Dresselhaus, A. J. Strauss, H. J. Zeiger, “Infrared anisotropy of La1.85Sr0.15CuO4−y,” Phys. Rev. B 36, 8884–8887 (1987). [CrossRef]
  2. P. E. Sulewski, T. W. Noh, J. T. McWhirter, A. J. Sievers, “Far-infrared composite-medium study of sintered La2NiO4 and La1.85Sr0.15CuO4−y,” Phys. Rev. B 36, 5735–5738 (1987). [CrossRef]
  3. Z. Schlesinger, R. T. Collins, M. W. Shaver, E. M. Engler, “Normal-state reflectivity and superconducting energy-gap measurement of La2−xSrxCuO4,” Phys. Rev. B 36, 5275–5278 (1987). [CrossRef]
  4. References [2, 3] do not explicitly state the existence of an optical crystallite size effect. Its existence can be deduced, however, from the need to apply different methods of averaging (effective-medium approximation in Ref. [2] and averaging over the reflectances in Ref. [3]). Doll’s approach has been used earlier [R. Frech, “Infrared reflectivity of uniaxial microcrystalline powders,” Phys. Rev. B 13, 2342–2348 (1976)] but without a statement about the range of applicability with regard to the domain size. [CrossRef]
  5. T. G. Mayerhöfer, “New method of modeling infrared spectra of non-cubic single-phase polycrystalline materials with random orientation,” Appl. Spectrosc. 56, 1194–1205 (2002). [CrossRef]
  6. The critical size of the crystallites may be one tenth of a wavelength. Below this size, it is assumed that light is unable to detect the anisotropic nature of the individual crystallite so that an averaged index of refraction results.[5] In the case of the effective-medium approach, the crystallites must be small compared with wavelength to justify this quasi-static approach. Accordingly, the critical size is usually presumed to be λ∕10.[1] Up to now the exact critical size has not been experimentally determined. On the basis of the experiments carried out so far,[5] the actual critical size lies between about λ∕5 and λ∕20.
  7. As an alternative, average refractive index theory[5] can be used.
  8. P. Yeh, Optical Waves in Layered Media (Wiley, 1988)..
  9. I. Abdulhalim, “Analytic propagation matrix method for linear optics of arbitrary biaxial layered media,” J. Opt. A, Pure Appl. Opt. 1, 646–653 (1999). [CrossRef]
  10. W. Berreman, “Optics in stratified and anisotropic media: 4×4-matrix formulation,” J. Opt. Soc. Am. 62, 502–510 (1972). [CrossRef]
  11. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).
  12. T. G. Mayerhöfer, “Modelling IR spectra of single-phase polycrystalline materials with random orientation in the large crystallites limit—extension to arbitrary crystal symmetry,” J. Opt. A, Pure Appl. Opt. 4, 540–548 (2002). [CrossRef]
  13. T. G. Mayerhöfer, Z. Shen, R. Keding, T. Höche, “Modelling IR-spectra of single-phase polycrystalline materials with random orientation—supplementations and refinements for optically uniaxial crystallites,” Optik (Stuttgart) 114, 351–359 (2003). [CrossRef]
  14. T. G. Mayerhöfer, “Modelling IR-spectra of single-phase polycrystalline materials with random orientation—a unified approach,” Vib. Spectrosc. 35, 67–76 (2004). [CrossRef]
  15. T. G. Mayerhöfer, Z. Shen, R. Keding, J. Musfeldt, “Optical isotropy in polycrystalline Ba2TiSi2O8: testing the limits of a well-established concept,” Phys. Rev. B 71, 184116 (2005). [CrossRef]
  16. T. G. Mayerhöfer, J. Musfeldt, “Angular dependence of the reflectance from an isotropic medium: surprising results regarding Brewster’s angle,” J. Opt. Soc. Am. A 22, 185–189 (2005). [CrossRef]
  17. T. G. Mayerhöfer, J. Popp, “Angular dependence of the reflectance from an isotropic polydomain medium: effect of large domain size on total reflection,” J. Opt. Soc. Am. A 22, 569–573 (2005). [CrossRef]
  18. A comparison of different orientation representations and their usefulness for orientational averaging can be found in T. G. Mayerhöfer, “Symmetric Euler orientation representations for Orientational averaging,” Spectrochim. Acta, Part A 61, 2611–2621 (2005). [CrossRef]
  19. M. Born, E. Wolf, Principles of Optics (Pergamon, 1999). [CrossRef]
  20. The average has to be carried out over the reflection coefficients r(Ω) instead of the reflectances R(Ω) if a coherent light source is used.
  21. M. V. Belousov, V. F. Pavinich, “Infrared reflection spectra of monoclinic crystals,” Opt. Spectrosc. 45, 771–774 (1978).
  22. Francis M. Mirabella, ed., Internal Reflection Spectroscopy (Marcel Dekker, 1993).
  23. P. Parayanthal, F. H. Pollak, “Raman scattering in alloy semiconductors: ‘Spatial correlation’ model,” Phys. Rev. Lett. 52, 1822–1825 (1984). [CrossRef]

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