Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Reflection spectroscopy for anisotropic materials: Direct determination of phase differences; validity of Fresnel formulas

Ralph H. Young and E. Irene P. Walker

  • Research Laboratories, Eastman Kodak Company, Rochester, New York 14650

Phys. Rev. B 15, 631 – Published 15 January, 1977

DOI: https://doi.org/10.1103/PhysRevB.15.631

Abstract

The reflectance of an anisotropic crystal is generally a tensor quantity even at normal incidence. Phase differences among the tensor components can be obtained from polarized reflectance measurements. A simple method for doing so is described and tested here. Possible applications of phase-difference information range from checking Kramers-Kronig evaluations of absolute phases to substituting for the Kramers-Kronig procedure. In addition, the following is proved, subject to some simple assumptions: If reflection extinction directions exist, the standard Fresnel equations may be used to derive optical constants (n's and k's), regardless of the anisotropy of the crystal. Moreover, extinction directions come in perpendicular pairs.

References (38)

  1. F. Stern, Solid State Phys. 15, 299 (1963)
  2. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), Chap. 7
  3. N. Barakat and N. El-Kadry, J. Opt. Soc. Am. 60, 570 (1970) J. Vincent-Geisse, Nguyen T. T., and J. P. Pinan-Lucarré, J. Phys. (Paris) 28, 26 (1967) J. P. Pinan-Lucarré and Nguyen T. T., Bull. Soc. Fr. Minéral. Cristallogr. 95, 15 (1972)
  4. G. N. Ramachandran and S. Ramasehan, in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1961), Vol. 25/1, Sec. 19-24
  5. , Sec. 14.4
  6. R. H. Muller, Surf. Sci. 56, 19 (1976)
  7. M. Bettini, Solid State Commun. 13, 599 (1973)
  8. C. Jacobsen, T. Skettrup, and I. Filinski, Surf. Sci. 37, 568 (1973)
  9. N. Yamamoto and T. Miyauchi, Jpn. J. Appl. Phys. 13, 1919 (1974)
  10. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. (Cambridge U.P., New York, 1963), p. 75
  11. I. Filinski and T. Skettrup, Solid State Commun. 11, 1651 (1972)
  12. D. C. Hinson and J. R. Stevenson, Phys. Rev. 159, 711 (1967)
  13. L. B. Clark and M. R. Philpott, J. Chem. Phys. 53, 3790 (1970)
  14. J. Bernasconi, P. Brüesch, D. Kuse, and H. R. Zeller, J. Phys. Chem. Solids 35, 145 (1974)
  15. E. I. P. Walker, A. P. Marchetti, and C. D. Salzberg, in Thirtieth Symposium on Molecular Structure and Spectroscopy, Columbus, Ohio, 1975 (unpublished) A. P. Marchetti, C. D. Salzberg, and E. I. P. Walker, J. Chem. Phys. 64, 4693 (1976) Photogr. Sci. Eng. 20, 107 (1976)
  16. A. Bree and L. E. Lyons, J. Chem. Soc. 2662 (1956) B. G. Anex and A. V. Fratini, J. Mol. Spectrosc. 14, 1 (1964) S. V. Marisova, Opt. Spektrosk. 22, 566 (1967) [Opt. Spectrosc. 22, 310 (1967)] M. S. Brodin, S. V. Marisova, and S. A. Shturkhetskaya, Ukr. Fiz. Zh. 13, 353 (1968) [Ukr. Phys. J. 13, 249 (1968).]
  17. H. R. Philipp and E. A. Taft, Phys. Rev. 136, A1445 (1964) G. Anderman, A. Caron, and D. A. Dows, J. Opt. Soc. Am. 55, 1210 (1965) P. O. Nilsson and L. Munkby, Phys. Kondens. Materie 10, 290 (1969) R. Y. Koyama, N. V. Smith, and W. E. Spicer, Phys. Rev. B 8, 2426 (1973)
  18. C. J. Eckhardt and R. R. Pennelly, Chem. Phys. Lett. 9, 572 (1971)
  19. R. S. Bauer, W. E. Spicer, and J. J. White, III, J. Opt. Soc. Am. 64, 830 (1974) C.-K. Wu and G. Anderman, 58, 519 (1968)
  20. E. A. Lupashko, V. K. Miloslavskii, and I. N. Shklyarevskii, Opt. Spektrosk. 29, 789 (1970) [Opt. Spectrosc. 29, 419 (1970)] W. G. Chambers, Infrared Phys. 15, 139 (1975) A. A. Clifford, M. I. Duckels, and B. Walker, J. Chem. Soc. Faraday Trans. II 68, 407 (1972) M. Cardona, in Optical Properties of Solids, edited by S. Nudelman and S. S. Mitra (Plenum, New York, 1969), pp. 137-152
  21. R. H. Young (unpublished)
  22. C. J. Eckhardt and G. D. Sturgeon, Chem. Phys. Lett. 8, 300 (1971)
  23. C. J. Eckhardt and R. R. Pennelly, Spectrosc. Lett. 7, 469 (1974) S. Hiroma, H. Kuroda, and H. Akamatu, Bull. Chem. Soc. Jpn. 43, 3626 (1970)
  24. P. M. Grant, R. L. Greene, G. C. Wrighton, and G. Castro, Phys. Rev. Lett. 31, 1311 (1973) A. A. Bright, A. F. Garito, and A. J. Heeger, Phys. Rev. B 10, 1328 (1974)
  25. B. G. Anex and L. J. Parkhurst, J. Am. Chem. Soc. 85, 3301 (1963)
  26. B. Velický, Czech. J. Phys. B 11, 787 (1961) R. A. MacRae, E. T. Arakawa, and M. W. Williams, Phys. Rev. 162, 615 (1967) E. T. Arakawa and M. W. Williams, J. Phys. Chem. Solids 29, 735 (1968) J. D. Hayes, E. T. Arakawa, and M. W. Williams, J. Appl. Phys. 39, 5527 (1968)
  27. R. K. Ahrenkiel, J. Opt. Soc. Am. 61, 1651 (1971) ibid.62, 1009 (1972)
  28. G. K. T. Conn and G. K. Eaton, J. Opt. Soc. Am. 44, 546 (1954) J. R. Beattie, Philos. Mag. 46, 235 (1955) J. N. Hodgson, Proc. Phys. Soc. Lond. B 68, 593 (1955)
  29. E. I. P. Walker, A. P. Marchetti, and C. D. Salzberg, J. Chem. Phys. 63, 2090 (1975)
  30. H. H. Chen and L. B. Clark, J. Chem. Phys. 51, 1862 (1969) P. F. Williams, M. A. Butler, D. L. Rousseau, and A. N. Bloch, Phys. Rev. B 10, 1109 (1974)
  31. , Sec. 14.6
  32. , Sec. 60 P. Drude, Ann. Phys. Chem. 32, 584 (1887) F. Pockels, Lehrbuch der Kristalloptik (Druck and Verlag von B. G. Teubner, Leipzig, 1906), p. 428ff M. Berek, Fortschr. Mineralogie 22, 1 (1937) A. Wünsche, Ann. Phys. (Leipz.) 25, 201 (1970) H. Damany and E. Uzan, Opt. Acta 17, 131 (1970) T. P. Sosnowski, Opt. Commun. 4, 408 (1972) E. E. Koch, A. Otto, and K. L. Kliewer, Chem. Phys. 3, 362 (1974)
  33. V. M. Agranovich and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Interscience, New York, 1966), Chap. 1, Sec. 2
  34. , Introduction and Chap. 1, Sec. 1
  35. , Sec. 43 L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960), Sec. 76
  36. , Sec. 44ff
  37. B. Cervelle, Bull. Soc. Fr. Minéral Cristallogr. 95, 464 (1972)
  38. R. M. A. Azzam, Opt. Commun. 19, 122 (1976)

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation