Light propagation in anisotropic media

  • Giovanni GiusfrediEmail author
Part of the UNITEXT for Physics book series (UNITEXTPH)


So far, the interaction between light and matter has been treated very succinctly, approximating the polarization P and the magnetization M with linear functions of the fields E and B. In this chapter, we will stick with this assumption, however, we will devote more attention to optical materials and, in particular, to the study of their anisotropic properties. The field of this study is nevertheless very vast and of great applicative importance, for the numerous effects that are encountered there.


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Bibliographical references

  1. Applequist J., Optical activity: Biot’s bequest, American Scientist 75, 59-67 (1987). Reprinted in Lakhtakia (1990).Google Scholar
  2. Azzam R.M.A., Ellipsometry, in Handbook of Optics, Bass M. et al ed., Mc Graw-Hill, New York (1995).Google Scholar
  3. Babinet J., Sur le sens des vibrations dans les rayons polarisés, Comptes Rendus Acad. Sci. Paris 29, 514-515 (1849).Google Scholar
  4. Bass M. et al ed., Handbook of Optics, McGraw-Hill, Inc., New York (1995).Google Scholar
  5. Bekers J.M., Achromatic linear retarders, Appl. Opt. 10, 973-975 (1971).ADSCrossRefGoogle Scholar
  6. Bennett J.M., Polarizer, in Handbook of Optics, Bass M. et al ed., Mc Graw-Hill, New York (1995).Google Scholar
  7. Berry M.V., Jeffrey M.R., and Lunney J.G., Conical diffraction: observations and theory, Proc. R. Soc. A 462, 1629-1642 (2006).ADSMathSciNetCrossRefGoogle Scholar
  8. Bhagavantam S., Crystal Symmetry and Physical Properties, Academic Press, New York (1966).Google Scholar
  9. Bloom A.L., Modes of a laser resonator containing tilted birefringent plates, J. Opt. Soc. Am. 64, 447-452 (1974).ADSCrossRefGoogle Scholar
  10. Bokut B.V. and Fedorov F.I., On the theory of Optical activity in crystals. III. General equation of normal, Opt. and Spectr. 6, 342-344 (1959).Google Scholar
  11. Born M., Über die natürliche optische aktivität von flüssigkeiten und gasen, Zeitschrift für Physik 16, 251-258 (1915). On the theory of optical activity, Proc. Royal Soc. A 150, 84-105 (1935). Reprinted in Lakhtakia (1990).Google Scholar
  12. Born M. and Wolf E., Principles of Optics, Pergamon Press, Paris (1980).Google Scholar
  13. Bragg W.L. and Pippard A.B., The Form Birefringence of Macromolecules, Acta Cryst. 6, 865-867 (1953).CrossRefGoogle Scholar
  14. Brand D.J., Molecular structure and chirality, J. Chemical Education 64, 1035-1038 (1987). Reprinted in Lakhtakia (1990).ADSCrossRefGoogle Scholar
  15. Burns G., Glazer A.M., Space Groups for Solid State Scientists, Academic Press, New York, (1978).Google Scholar
  16. Caldwell D.J. and Eyring H., The theory of optical activity, John Wiley & Sons, Inc., New York (1971).Google Scholar
  17. Chandrasekharan V., Damany H., Birefringence of Sapphire, Magnesium Fluoride, and Quartz in the Vacuum Ultraviolet, and Retardation Plates, Appl. Opt. 7, 939-941 (1968).ADSCrossRefGoogle Scholar
  18. Cheng D.K. and Kong J.A., Time harmonic fields in source free bianisotropic media, J. Appl. Phys. 39, 5792-5796 (1968).ADSCrossRefGoogle Scholar
  19. Chipman R.A., Polarimetry, in Handbook of Optics, Bass M. et al ed., Mc Graw-Hill, New York (1995).Google Scholar
  20. Condon E.U., Theories of Optical Rotatory Power, Rev. Mod. Phys. 9, 432-457 (1937). Reprinted in Lakhtakia (1990).ADSCrossRefGoogle Scholar
  21. Condon E.U., Altar W., and Eyring H., One-Electron Rotatory Power, J. Chem. Phys. 5, 753-775 (1937).ADSCrossRefGoogle Scholar
  22. Dodge M.J., Refractive properties of magnesium fluoride, Appl. Opt. 23, 1980-1985 (1984).ADSCrossRefGoogle Scholar
  23. Evans J.W., The birefringent filter, J. Opt. Soc. Am. 39, 229-242 (1949).ADSCrossRefGoogle Scholar
  24. Fedorov F.I., On the theory of Optical activity in crystals. I. The law of conservation of energy and the Optical activity tensor, Optics and Spectroscopy 6, 49-53 (1959a), Reprinted in Lakhtakia (1990). On the theory of Optical activity in crystals. II. Crystal of cubic symmetry and planar classes of central symmetry, Opt. and Spectr. 6, 237-240 (1959b).Google Scholar
  25. Feynman R.P., Leighton R.B., Sands M., The Feynman Lectures on Physics, Vol II, Addison-Wesley publishing company, Reading MA (1969).Google Scholar
  26. Fowles G.R., Introduction to Modern Optics, Holt, Rinehart, and Winston, New York (1968).Google Scholar
  27. Guenther R., Modern Optics, John Wiley & Sons, New York (1990).Google Scholar
  28. Hamilton W.R., On some results of the view of a characteristic function in optics, British Association Report, Cambridge 360-370 (1833). Third supplement to an essay on the theory of systems of rays, Trans. Roy. Irish Acad. 17, 1-144 (1837).Google Scholar
  29. Hammond C., Introduction to crystallography, Oxford University Press, Royal Microscopical Society (1992).Google Scholar
  30. Hermann C.H. and Mauguin C., International Tables for X-ray Crystallography, Vol I, edited by K. Lonsdale. Birmingham: Kynoch Press (1952). See also the last edition at International Tables for Crystallography, Vol. A: Space-group symmetry, edited by Th. Hahn, International Union of Crystallography (2006).Google Scholar
  31. Hobden M.V., Optical activity in a non-enantiomorphous crystal: AgGaS2, Acta Cryst. A 24, 676-680 (1968).CrossRefGoogle Scholar
  32. Hodgkinson I.J. and Wu Q.H., Birefringent thin films and polarizing elements, World Scientific Publ. Co. Pte. Ltd., Singapore (1997).Google Scholar
  33. Hopf F.A. and Stegeman G.I., Applied Classical Electrodynamics, Vol. I: Linear Optics, John Wiley & Sons, New York (1985).Google Scholar
  34. Huard S., Polarization of Light, John Wiley & Sons, New York, Masson, Paris (1997).Google Scholar
  35. Jackson J.D., Classical Electrodynamics, John Wiley & Sons, New York (1974).Google Scholar
  36. Jenkins F.A. and White H.E., Fundamental of Optics, McGraw-Hill (1957).Google Scholar
  37. Jerphagnon J. and Chemla D.S., Optical activity of crystals, J. Chem. Phys. 65, 1522-1529 (1976).ADSCrossRefGoogle Scholar
  38. Jones R.C., A new calculus for the treatment of optical system, Part I, J. Opt. Soc. Am. 31, 488-493 (1941a); … Part II, J. Opt. Soc. Am. 31, 500-503 (1941b); … Part III, J. Opt. Soc. Am. 32, 486-493 (1942).Google Scholar
  39. Kaminow I.P., An introduction to electrooptic devices, Academic Press (1974).Google Scholar
  40. Kong J.A., Theorems of bianisotropic media, Proc. IEEE 60, 1036-1046 (1972). Reprinted in Lakhtakia (1990).MathSciNetCrossRefGoogle Scholar
  41. Lakhtakia A., ed., Selected Papers on Natural Optical Activity, SPIE Milestone Series 15, B.J. Thompson gen. ed., SPIE, Bellingham (1990). On the genesis of Post constraint in modern electromagnetism, Optik, Intern. J. for Light and Electron Optics 115, 151-158 (2004).Google Scholar
  42. Lakhtakia A., Varadan V.V., and Varadan V.K., Field equations, Huygens’s principle, integral equations, and theorems for radiation and scattering of electromagnetic waves in isotropic chiral media, J. Opt. Soc. Am. A 5, 175-184 (1988). Reprinted in Lakhtakia (1990).Google Scholar
  43. Landau L. and Lifchitz E., (II), Théorie du Champ, MIR, Mosca (1966a). (III), Physique Statistique, MIR, Mosca (1966b). (VIII), Électrodynamique des Milieux Continus, MIR, Mosca (1966c).Google Scholar
  44. Landsberg G.S., Ottica, MIR, Mosca (1979).Google Scholar
  45. Lang S., Linear Algebra, Springer-Verlag, New York (1987).Google Scholar
  46. H. Lloyd, On the phænomena presented by light in its passage along the axes of biaxal crystals, The London and Edinburgh Philosophical Magazine 2, 112-120 (1833).Google Scholar
  47. Lyot Bernard, Le filtre monochromatique polarizant et ses applications en physique solaire, Annales d’Astrophysique 7, 1-49 (1944).Google Scholar
  48. Maillard J.P., Direct measurement of the birefringence of quartz at 3.39 and 3.50 μ, Opt. Comm. 4, 175-177 (1971).Google Scholar
  49. Mason S.F., Optical activity and molecular dissymmetry, Contemp. Phys. 9, 239 (1968).Google Scholar
  50. Medenbach G. and Shannon R.D., Refractive indices and optical dispersion of 103 synthetic and mineral oxides and silicates measured by a small-prism technique, JOSA B 14, 3299-3318 (1997).Google Scholar
  51. Medhat M. and El-Zaiat S.Y., Interferometric determination of the birefringence dispersion of anisotropic materials, Optics Comm. 141, 145-149 (1997).ADSCrossRefGoogle Scholar
  52. Nakano H. and Kimura H., Quantum statistical-mechanical theory of optical activity, J. Phys. Soc. Japan 27, 519-535 (1969). Reprinted in Lakhtakia (1990).ADSCrossRefGoogle Scholar
  53. Nikogosyan D.N., Properties of Optical and Laser-Related Materials. A Handbook, John Wiley & Sons, New York (1997).Google Scholar
  54. Öhman Y., A New Monochromator, Nature 141, n°3560, 157-158, and n°3563, 291-291 (1938).Google Scholar
  55. Pancharatnam, S., Achromatic combinations of birefringent plates, Proceedings of the Indian Academy of Sciences 41, 130 (1955)CrossRefGoogle Scholar
  56. Peterson R.M., Comparison of two theories of optical activity, Am. J. of Physics 43, 969-972 (1975).ADSCrossRefGoogle Scholar
  57. Poggendorff J.C., Ueber die konische refraction, Ann. der Physik 129, 461-462 (1839).ADSCrossRefGoogle Scholar
  58. Post E.J., Formal structure of electromagnetics, (North-Holland, Amsterdam, 1962). Partially reprinted in Lakhtakia (1990).Google Scholar
  59. Potton R.J., Reciprocity in optics, Reports on Progress in Physics 67, 717-754 (2004).ADSCrossRefGoogle Scholar
  60. Pujol M.C. et al, Growth, optical characterization, and laser operation of a stoichiometric crystal KYb(WO4)2, Phys. Rev. B 65, 165121 (2002).Google Scholar
  61. Roberts N.W., Chiou T.-H., Marshall N.J. and Cronin T.W., A biological quarter-wave retarder with excellent achromaticity in the visible wavelength region, Nature Photonics 3, 641-644 (2009).ADSCrossRefGoogle Scholar
  62. Robinson C.C., The Faraday Rotation of Diamagnetic Glasses from 0.334 μ to 1.9 μ, Appl. Optics 3, 1163-1166 (1964).Google Scholar
  63. Shields J.H. and Ellis J.W., Dispersion of Birefringence of Quartz in the Near Infrared, J. Opt. Soc. Am. 46, 363-365 (1956).ADSCrossRefGoogle Scholar
  64. Silverman M.P., Reflection and refraction at the surface of a chiral medium: comparison of gyrotropic constitutive relations invariant or noninvariant under a duality transformation, J. Opt. Soc. Am. A 3, 830-837 (1986). Reprinted in Lakhtakia (1990).Google Scholar
  65. Silverman M.P. and Badoz J., Light reflection from a naturally active birefringent medium, J. Opt. Soc. Am. A 7, 1163-1173 (1990).ADSCrossRefGoogle Scholar
  66. Silverman M.P., Ritchie N., Cushman G.M., and Fischer B., Experimental configurations using optical phase modulation to measure chiral asymmetries in light specularly reflected from a naturally gyrotropic medium, J. Opt. Soc. Am. A 5, 1852-1862 (1988).ADSCrossRefGoogle Scholar
  67. Sivoukhine D., Optique, MIR, Mosca (1984).Google Scholar
  68. Smartt R.N. and Steel W.H., Birefringence of Quartz and Calcite, J. Opt. Soc. Am. 49, 710-712 (1959).ADSCrossRefGoogle Scholar
  69. Soleil J.B., Nouvel appareil propre ä la mesure des deviations dans les experiences de polarisation rotatoire, C. R. Acad. Sci. (Paris) 21, 426-430 (1845); Note sur un perfectionnement apporté au pointage du saccharimètre, C. R. Acad. Sci. (Paris) 24, 973-975 (1847).Google Scholar
  70. Sommerfeld A., Optics, Academic Press, New York (1949).Google Scholar
  71. Strumia F., Appunti di conduzione elettrica nei gas, Cap. IV - I filtri. Università degli Studi di Pisa, (a.a. 1973-1974).Google Scholar
  72. Tellegen B.D.H., The gyrator, a new electric network element, Phillips Research Report 3, 81-101 (1948). Reprinted in Lakhtakia (1990).Google Scholar
  73. Tinoco I. and Freeman M., The optical activity of oriented copper helices, I, experimental, J. Physical Chemistry 61, 1196-1200 (1957). Reprinted in Lakhtakia (1990).CrossRefGoogle Scholar
  74. Van Kranendonk J. and Sipe J.E., Foundation of the macroscopic electromagnetic theory of dielectric media, in Progress in Optics XV, 245-356, E. Wolf ed., North-Holland Publishing Company, Amsterdam (1977).Google Scholar
  75. Villaverde A.B. et al, Terbium gallium garnet Verdet constant measurements with pulsed magnetic field, J. Phys. C: Solid State Physics 11, L495-498 (1978).ADSCrossRefGoogle Scholar
  76. Voigt W., Bemerkung zur theorie der konischen refraktion, Phys. Z. 6, 672-673 (1905). Ueber die Wellen flaeche zweiachsiger aktiver kristalle und ueber ihre konische refraktion, Phys. Z. 6, 787-790 (1905).Google Scholar
  77. von Haidinger W., Die konische Refraction am Diopsid, nebst Bemerkungen über einige Erscheinungen der konischen Refraction am Arragonit, Annalen Physik 172, 469-487 (1855).ADSCrossRefGoogle Scholar
  78. Wiener O., Allgemeine Sätze über die Dielektrizitätskonstanten der Mischkörper, Abh. Sächs. Ges. Akad. Wiss., Math. Phys. Kl. 6, 574-584 (1912).Google Scholar
  79. Williams P.A. et al, Temperature dependence of the Verdet constant in several diamagnetic glasses, Appl. Optics 30, 1176-1178 (1991).Google Scholar
  80. Wood E.A., Crystals and Light, Dover Publications, Inc., New York (1977).Google Scholar
  81. Yariv A. and Yeh P., Optical waves in crystals, John Wiley, New Jersey (1984).Google Scholar
  82. Zhong H., Levine Z.H., Allan D.C., Wilkins J.W., Band-theoretic calculations of the optical-activity tenor of α-quartz and trigonal Se, Phys. Rev. B 48, 1384-1402 (1993).ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.European Laboratory for Non-Linear Spectroscopy (LENS)Istituto Nazionale di Ottica—Consiglio Nazionale delle Ricerche (INO-CNR)Sesto FiorentinoItaly

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