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Reflection spectroscopy for anisotropic materials: Direct determination of phase differences; validity of Fresnel formulas
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 ('s and 's), regardless of the anisotropy of the crystal. Moreover, extinction directions come in perpendicular pairs.
References (38)
- F. Stern, Solid State Phys. 15, 299 (1963)
- M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), Chap. 7
- 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)
- G. N. Ramachandran and S. Ramasehan, in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1961), Vol. 25/1, Sec. 19-24
- , Sec. 14.4
- R. H. Muller, Surf. Sci. 56, 19 (1976)
- M. Bettini, Solid State Commun. 13, 599 (1973)
- C. Jacobsen, T. Skettrup, and I. Filinski, Surf. Sci. 37, 568 (1973)
- N. Yamamoto and T. Miyauchi, Jpn. J. Appl. Phys. 13, 1919 (1974)
- E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. (Cambridge U.P., New York, 1963), p. 75
- I. Filinski and T. Skettrup, Solid State Commun. 11, 1651 (1972)
- D. C. Hinson and J. R. Stevenson, Phys. Rev. 159, 711 (1967)
- L. B. Clark and M. R. Philpott, J. Chem. Phys. 53, 3790 (1970)
- J. Bernasconi, P. Brüesch, D. Kuse, and H. R. Zeller, J. Phys. Chem. Solids 35, 145 (1974)
- 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P. Marchetti, and C. D. Salzberg, in Thirtieth Symposium on Molecular Structure and Spectroscopy, Columbus, Ohio, 1975 (unpublished) A. P. Marchetti, C. D. Salzberg, and E. I. P. Walker, J. Chem.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)
- 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).]
- 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)
- C. J. Eckhardt and R. R. Pennelly, Chem. Phys. Lett. 9, 572 (1971)
- 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)
- 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
- R. H. Young (unpublished)
- C. J. Eckhardt and G. D. Sturgeon, Chem. Phys. Lett. 8, 300 (1971)
- 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)
- 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)
- B. G. Anex and L. J. Parkhurst, J. Am. Chem. Soc. 85, 3301 (1963)
- 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)
- R. K. Ahrenkiel, J. Opt. Soc. Am. 61, 1651 (1971) ibid.62, 1009 (1972)
- 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)
- E. I. P. Walker, A. P. Marchetti, and C. D. Salzberg, J. Chem. Phys. 63, 2090 (1975)
- 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)
- , Sec. 14.6
- , 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)
- 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
- , Introduction and Chap. 1, Sec. 1
- , Sec. 43 L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960), Sec. 76
- , Sec. 44ff
- B. Cervelle, Bull. Soc. Fr. Minéral Cristallogr. 95, 464 (1972)
- R. M. A. Azzam, Opt. Commun. 19, 122 (1976)