Abstract

The linear birefringences, optic axes, and linear eigenpolarizations that are familiar features of light propagation in transparent optically inactive anisotropic crystals are fully explained by Fresnel’s ellipsoid model or the related indicatrix ellipsoid. However, these models cannot account for circular birefringence and the linear birefringences of Lorentz and Jones. All birefringences can, nevertheless, be explained by an appropriate multipole eigenvalue theory, of which the electric-dipole description presented in this paper is the formal basis of the ellipsoid models. This description is analytic in form, as opposed to the mainly geometric treatment of the ellipsoid schemes, and sets the latter in the context of a systematic multipole approach for describing other birefringences. Furthermore, it offers certain new insights and results.

© 1998 Optical Society of America

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References

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  1. E. B. Graham, R. E. Raab, “On the Jones birefringence,” Proc. R. Soc. London, Ser. A 390, 73–90 (1983).
    [CrossRef]
  2. E. B. Graham, R. E. Raab, “Light propagation in cubic and other anisotropic crystals,” Proc. R. Soc. London Ser. A 430, 593–614 (1990).
    [CrossRef]
  3. P. N. Argyres, “Theory of the Faraday and Kerr effects in ferromagnetics,” Phys. Rev. 97, 334–345 (1955).
    [CrossRef]
  4. C. Graham, R. E. Raab, “Eigenvector approach to the evaluation of the Jones N matrices of nonabsorbing crystalline media,” J. Opt. Soc. Am. A 11, 2137–2144 (1994).
    [CrossRef]
  5. E. B. Graham, R. E. Raab, “Electric dipole effects in magnetic crystals,” J. Appl. Phys. 69, 2549–2551 (1991).
    [CrossRef]
  6. E. B. Graham, R. E. Raab, “A theory in the electric quadrupole-magnetic dipole approximation of birefringences in antiferromagnetic crystals,” Ferroelectrics 162, 161–171 (1994).
    [CrossRef]
  7. H. A. Lorentz, “Concerning the relation between the velocity of propagation of light and the density and composition of media,” Verh. K. Akad. Wet. 18, 1 (1878);also in H. A. Lorentz, Collected Papers, P. Zeeman, A. D. Fokker, eds. (Nijhoff, The Hague, 1936), Vol. 2, pp. 1–119.
  8. H. A. Lorentz, “Double refraction by regular crystals,” Proc. K. Ned. Acad. Wet. 24, 333–339 (1922);also in H. A. Lorentz, Collected Papers, P. Zeeman, A. D. Fokker, eds. (Nijhoff, The Hague, 1936), Vol. 3, pp. 314–320.
    [CrossRef]
  9. J. Pastrnak, L. E. Cross, “The optical anisotropy of cubic nickel-iodine boracite due to quadrupole transitions,” Phys. Status Solidi B 44, 313–325 (1971).
    [CrossRef]
  10. J. Pastrnak, K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
    [CrossRef]
  11. F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976), pp. 552, 583, 589.
  12. E. U. Condon, F. Seitz, “Lorentz double refraction in the regular system,” J. Opt. Soc. Am. 22, 393–401 (1932).
    [CrossRef]
  13. R. Clark Jones, “A new calculus for the treatment of optical systems. VII. Properties of the N-matrices,” J. Opt. Soc. Am. 38, 671–685 (1948).
    [CrossRef]
  14. J. W. Gibbs, “Notes on the electromagnetic theory of light. No. II—on refraction in perfectly transparent media which exhibit the phenomena of circular birefringence,” Am. J. Sci. 23, 460–476 (1882).
    [CrossRef]
  15. H. Nakano, H. Kimura, “Quantum statistical-mechanical theory of optical activity,” J. Phys. Soc. Jpn. 27, 519–535 (1969).
    [CrossRef]
  16. A. D. Buckingham, M. B. Dunn, “Optical activity of oriented molecules,” J. Chem. Soc. A1988–1991 (1971).
    [CrossRef]
  17. L. D. Barron, A. D. Buckingham, “Rayleigh and Raman scattering from optically active molecules,” Molec. Phys. 20, 1111–1119 (1971).
    [CrossRef]
  18. R. E. Raab, J. H. Cloete, “An eigenvalue theory of circular birefringence and dichroism in a non-magnetic chiral medium,” J. Electromagn. Waves Appl. 8, 1073–1089 (1994).
    [CrossRef]
  19. E. B. Graham, R. E. Raab, “Non-reciprocal optical rotation in cubic antiferromagnetics,” Philos. Mag. B 64, 267–274 (1991).
    [CrossRef]
  20. T. A. Maldonado, T. K. Gaylord, “Accurate method to determine the eigenstates of polarization in gyrotropic media,” Appl. Opt. 28, 2075–2086 (1989).
    [CrossRef] [PubMed]
  21. E. B. Graham, J. Pierrus, R. E. Raab, “Multipole moments and Maxwell’s equations,” J. Phys. B 25, 4673–4684 (1992).
    [CrossRef]
  22. L. Rosenfeld, Theory of Electrons (North-Holland, Amsterdam, 1951), Chap. 2.
  23. F. N. H. Robinson, Macroscopic Electromagnetism (Pergamon, Oxford, UK, 1973), pp. 56–62.
  24. A. D. Buckingham, “Permanent and induced molecular moments and long-range intermolecular forces,” in Intermolecular Forces, J. O. Hirschfelder, ed., Adv. Chem. Phys.12, 107–142 (1967).
  25. L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, Cambridge, UK, 1982), p. 76.
  26. I. M. B. de Figueiredo, R. E. Raab, “A molecular theory of new differential light scattering effects in a fluid,” Proc. R. Soc. London Ser. A 375, 425–441 (1981).
    [CrossRef]
  27. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 142.
  28. R. R. Birss, Symmetry and Magnetism, 2nd ed. (North-Holland, Amsterdam, 1966).
  29. S. I. Pekar, Crystal Optics and Additional Light Waves (Benjamin/Cummings, Menlo Park, Calif., 1983), p. XV.
  30. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 73, 75, 79.
  31. E. B. Graham, R. E. Raab, “Magnetic effects in antiferromagnetic crystals in the electric quadrupole-magnetic dipole approximation,” Philos. Mag. B 66, 269–284 (1992).
    [CrossRef]
  32. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 14.
  33. J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, UK, 1985), Appendix H, p. 271.
  34. T. A. Maldonado, T. K. Gaylord, “Electrooptic effect calculations: simplified procedure for arbitrary cases,” Appl. Opt. 27, 5051–5066 (1988).
    [CrossRef] [PubMed]
  35. G. N. Ramachandran, S. Ramaseshan, “Crystal optics,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV/1, p. 63.
  36. V. M. Agranovich, V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, 2nd ed. (Springer-Verlag, Berlin, 1984), pp. 167–173.
  37. D. E. Gray, American Institute of Physics Handbook, 3rd ed. (McGraw-Hill, New York, 1972), pp. 6–115.

1994 (3)

E. B. Graham, R. E. Raab, “A theory in the electric quadrupole-magnetic dipole approximation of birefringences in antiferromagnetic crystals,” Ferroelectrics 162, 161–171 (1994).
[CrossRef]

R. E. Raab, J. H. Cloete, “An eigenvalue theory of circular birefringence and dichroism in a non-magnetic chiral medium,” J. Electromagn. Waves Appl. 8, 1073–1089 (1994).
[CrossRef]

C. Graham, R. E. Raab, “Eigenvector approach to the evaluation of the Jones N matrices of nonabsorbing crystalline media,” J. Opt. Soc. Am. A 11, 2137–2144 (1994).
[CrossRef]

1992 (2)

E. B. Graham, R. E. Raab, “Magnetic effects in antiferromagnetic crystals in the electric quadrupole-magnetic dipole approximation,” Philos. Mag. B 66, 269–284 (1992).
[CrossRef]

E. B. Graham, J. Pierrus, R. E. Raab, “Multipole moments and Maxwell’s equations,” J. Phys. B 25, 4673–4684 (1992).
[CrossRef]

1991 (2)

E. B. Graham, R. E. Raab, “Non-reciprocal optical rotation in cubic antiferromagnetics,” Philos. Mag. B 64, 267–274 (1991).
[CrossRef]

E. B. Graham, R. E. Raab, “Electric dipole effects in magnetic crystals,” J. Appl. Phys. 69, 2549–2551 (1991).
[CrossRef]

1990 (1)

E. B. Graham, R. E. Raab, “Light propagation in cubic and other anisotropic crystals,” Proc. R. Soc. London Ser. A 430, 593–614 (1990).
[CrossRef]

1989 (1)

1988 (1)

1983 (1)

E. B. Graham, R. E. Raab, “On the Jones birefringence,” Proc. R. Soc. London, Ser. A 390, 73–90 (1983).
[CrossRef]

1981 (1)

I. M. B. de Figueiredo, R. E. Raab, “A molecular theory of new differential light scattering effects in a fluid,” Proc. R. Soc. London Ser. A 375, 425–441 (1981).
[CrossRef]

1971 (4)

A. D. Buckingham, M. B. Dunn, “Optical activity of oriented molecules,” J. Chem. Soc. A1988–1991 (1971).
[CrossRef]

L. D. Barron, A. D. Buckingham, “Rayleigh and Raman scattering from optically active molecules,” Molec. Phys. 20, 1111–1119 (1971).
[CrossRef]

J. Pastrnak, L. E. Cross, “The optical anisotropy of cubic nickel-iodine boracite due to quadrupole transitions,” Phys. Status Solidi B 44, 313–325 (1971).
[CrossRef]

J. Pastrnak, K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
[CrossRef]

1969 (1)

H. Nakano, H. Kimura, “Quantum statistical-mechanical theory of optical activity,” J. Phys. Soc. Jpn. 27, 519–535 (1969).
[CrossRef]

1955 (1)

P. N. Argyres, “Theory of the Faraday and Kerr effects in ferromagnetics,” Phys. Rev. 97, 334–345 (1955).
[CrossRef]

1948 (1)

1932 (1)

1922 (1)

H. A. Lorentz, “Double refraction by regular crystals,” Proc. K. Ned. Acad. Wet. 24, 333–339 (1922);also in H. A. Lorentz, Collected Papers, P. Zeeman, A. D. Fokker, eds. (Nijhoff, The Hague, 1936), Vol. 3, pp. 314–320.
[CrossRef]

1882 (1)

J. W. Gibbs, “Notes on the electromagnetic theory of light. No. II—on refraction in perfectly transparent media which exhibit the phenomena of circular birefringence,” Am. J. Sci. 23, 460–476 (1882).
[CrossRef]

1878 (1)

H. A. Lorentz, “Concerning the relation between the velocity of propagation of light and the density and composition of media,” Verh. K. Akad. Wet. 18, 1 (1878);also in H. A. Lorentz, Collected Papers, P. Zeeman, A. D. Fokker, eds. (Nijhoff, The Hague, 1936), Vol. 2, pp. 1–119.

Agranovich, V. M.

V. M. Agranovich, V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, 2nd ed. (Springer-Verlag, Berlin, 1984), pp. 167–173.

Argyres, P. N.

P. N. Argyres, “Theory of the Faraday and Kerr effects in ferromagnetics,” Phys. Rev. 97, 334–345 (1955).
[CrossRef]

Barron, L. D.

L. D. Barron, A. D. Buckingham, “Rayleigh and Raman scattering from optically active molecules,” Molec. Phys. 20, 1111–1119 (1971).
[CrossRef]

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, Cambridge, UK, 1982), p. 76.

Birss, R. R.

R. R. Birss, Symmetry and Magnetism, 2nd ed. (North-Holland, Amsterdam, 1966).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 14.

Buckingham, A. D.

L. D. Barron, A. D. Buckingham, “Rayleigh and Raman scattering from optically active molecules,” Molec. Phys. 20, 1111–1119 (1971).
[CrossRef]

A. D. Buckingham, M. B. Dunn, “Optical activity of oriented molecules,” J. Chem. Soc. A1988–1991 (1971).
[CrossRef]

A. D. Buckingham, “Permanent and induced molecular moments and long-range intermolecular forces,” in Intermolecular Forces, J. O. Hirschfelder, ed., Adv. Chem. Phys.12, 107–142 (1967).

Clark Jones, R.

Cloete, J. H.

R. E. Raab, J. H. Cloete, “An eigenvalue theory of circular birefringence and dichroism in a non-magnetic chiral medium,” J. Electromagn. Waves Appl. 8, 1073–1089 (1994).
[CrossRef]

Condon, E. U.

Cross, L. E.

J. Pastrnak, L. E. Cross, “The optical anisotropy of cubic nickel-iodine boracite due to quadrupole transitions,” Phys. Status Solidi B 44, 313–325 (1971).
[CrossRef]

de Figueiredo, I. M. B.

I. M. B. de Figueiredo, R. E. Raab, “A molecular theory of new differential light scattering effects in a fluid,” Proc. R. Soc. London Ser. A 375, 425–441 (1981).
[CrossRef]

Dunn, M. B.

A. D. Buckingham, M. B. Dunn, “Optical activity of oriented molecules,” J. Chem. Soc. A1988–1991 (1971).
[CrossRef]

Gaylord, T. K.

Gibbs, J. W.

J. W. Gibbs, “Notes on the electromagnetic theory of light. No. II—on refraction in perfectly transparent media which exhibit the phenomena of circular birefringence,” Am. J. Sci. 23, 460–476 (1882).
[CrossRef]

Ginzburg, V. L.

V. M. Agranovich, V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, 2nd ed. (Springer-Verlag, Berlin, 1984), pp. 167–173.

Graham, C.

Graham, E. B.

E. B. Graham, R. E. Raab, “A theory in the electric quadrupole-magnetic dipole approximation of birefringences in antiferromagnetic crystals,” Ferroelectrics 162, 161–171 (1994).
[CrossRef]

E. B. Graham, J. Pierrus, R. E. Raab, “Multipole moments and Maxwell’s equations,” J. Phys. B 25, 4673–4684 (1992).
[CrossRef]

E. B. Graham, R. E. Raab, “Magnetic effects in antiferromagnetic crystals in the electric quadrupole-magnetic dipole approximation,” Philos. Mag. B 66, 269–284 (1992).
[CrossRef]

E. B. Graham, R. E. Raab, “Electric dipole effects in magnetic crystals,” J. Appl. Phys. 69, 2549–2551 (1991).
[CrossRef]

E. B. Graham, R. E. Raab, “Non-reciprocal optical rotation in cubic antiferromagnetics,” Philos. Mag. B 64, 267–274 (1991).
[CrossRef]

E. B. Graham, R. E. Raab, “Light propagation in cubic and other anisotropic crystals,” Proc. R. Soc. London Ser. A 430, 593–614 (1990).
[CrossRef]

E. B. Graham, R. E. Raab, “On the Jones birefringence,” Proc. R. Soc. London, Ser. A 390, 73–90 (1983).
[CrossRef]

Gray, D. E.

D. E. Gray, American Institute of Physics Handbook, 3rd ed. (McGraw-Hill, New York, 1972), pp. 6–115.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 142.

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976), pp. 552, 583, 589.

Kimura, H.

H. Nakano, H. Kimura, “Quantum statistical-mechanical theory of optical activity,” J. Phys. Soc. Jpn. 27, 519–535 (1969).
[CrossRef]

Lorentz, H. A.

H. A. Lorentz, “Double refraction by regular crystals,” Proc. K. Ned. Acad. Wet. 24, 333–339 (1922);also in H. A. Lorentz, Collected Papers, P. Zeeman, A. D. Fokker, eds. (Nijhoff, The Hague, 1936), Vol. 3, pp. 314–320.
[CrossRef]

H. A. Lorentz, “Concerning the relation between the velocity of propagation of light and the density and composition of media,” Verh. K. Akad. Wet. 18, 1 (1878);also in H. A. Lorentz, Collected Papers, P. Zeeman, A. D. Fokker, eds. (Nijhoff, The Hague, 1936), Vol. 2, pp. 1–119.

Maldonado, T. A.

Nakano, H.

H. Nakano, H. Kimura, “Quantum statistical-mechanical theory of optical activity,” J. Phys. Soc. Jpn. 27, 519–535 (1969).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, UK, 1985), Appendix H, p. 271.

Pastrnak, J.

J. Pastrnak, L. E. Cross, “The optical anisotropy of cubic nickel-iodine boracite due to quadrupole transitions,” Phys. Status Solidi B 44, 313–325 (1971).
[CrossRef]

J. Pastrnak, K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
[CrossRef]

Pekar, S. I.

S. I. Pekar, Crystal Optics and Additional Light Waves (Benjamin/Cummings, Menlo Park, Calif., 1983), p. XV.

Pierrus, J.

E. B. Graham, J. Pierrus, R. E. Raab, “Multipole moments and Maxwell’s equations,” J. Phys. B 25, 4673–4684 (1992).
[CrossRef]

Raab, R. E.

E. B. Graham, R. E. Raab, “A theory in the electric quadrupole-magnetic dipole approximation of birefringences in antiferromagnetic crystals,” Ferroelectrics 162, 161–171 (1994).
[CrossRef]

C. Graham, R. E. Raab, “Eigenvector approach to the evaluation of the Jones N matrices of nonabsorbing crystalline media,” J. Opt. Soc. Am. A 11, 2137–2144 (1994).
[CrossRef]

R. E. Raab, J. H. Cloete, “An eigenvalue theory of circular birefringence and dichroism in a non-magnetic chiral medium,” J. Electromagn. Waves Appl. 8, 1073–1089 (1994).
[CrossRef]

E. B. Graham, R. E. Raab, “Magnetic effects in antiferromagnetic crystals in the electric quadrupole-magnetic dipole approximation,” Philos. Mag. B 66, 269–284 (1992).
[CrossRef]

E. B. Graham, J. Pierrus, R. E. Raab, “Multipole moments and Maxwell’s equations,” J. Phys. B 25, 4673–4684 (1992).
[CrossRef]

E. B. Graham, R. E. Raab, “Non-reciprocal optical rotation in cubic antiferromagnetics,” Philos. Mag. B 64, 267–274 (1991).
[CrossRef]

E. B. Graham, R. E. Raab, “Electric dipole effects in magnetic crystals,” J. Appl. Phys. 69, 2549–2551 (1991).
[CrossRef]

E. B. Graham, R. E. Raab, “Light propagation in cubic and other anisotropic crystals,” Proc. R. Soc. London Ser. A 430, 593–614 (1990).
[CrossRef]

E. B. Graham, R. E. Raab, “On the Jones birefringence,” Proc. R. Soc. London, Ser. A 390, 73–90 (1983).
[CrossRef]

I. M. B. de Figueiredo, R. E. Raab, “A molecular theory of new differential light scattering effects in a fluid,” Proc. R. Soc. London Ser. A 375, 425–441 (1981).
[CrossRef]

Ramachandran, G. N.

G. N. Ramachandran, S. Ramaseshan, “Crystal optics,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV/1, p. 63.

Ramaseshan, S.

G. N. Ramachandran, S. Ramaseshan, “Crystal optics,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV/1, p. 63.

Robinson, F. N. H.

F. N. H. Robinson, Macroscopic Electromagnetism (Pergamon, Oxford, UK, 1973), pp. 56–62.

Rosenfeld, L.

L. Rosenfeld, Theory of Electrons (North-Holland, Amsterdam, 1951), Chap. 2.

Seitz, F.

Vedam, K.

J. Pastrnak, K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
[CrossRef]

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976), pp. 552, 583, 589.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 14.

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 73, 75, 79.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 73, 75, 79.

Am. J. Sci. (1)

J. W. Gibbs, “Notes on the electromagnetic theory of light. No. II—on refraction in perfectly transparent media which exhibit the phenomena of circular birefringence,” Am. J. Sci. 23, 460–476 (1882).
[CrossRef]

Appl. Opt. (2)

Ferroelectrics (1)

E. B. Graham, R. E. Raab, “A theory in the electric quadrupole-magnetic dipole approximation of birefringences in antiferromagnetic crystals,” Ferroelectrics 162, 161–171 (1994).
[CrossRef]

J. Appl. Phys. (1)

E. B. Graham, R. E. Raab, “Electric dipole effects in magnetic crystals,” J. Appl. Phys. 69, 2549–2551 (1991).
[CrossRef]

J. Chem. Soc. A (1)

A. D. Buckingham, M. B. Dunn, “Optical activity of oriented molecules,” J. Chem. Soc. A1988–1991 (1971).
[CrossRef]

J. Electromagn. Waves Appl. (1)

R. E. Raab, J. H. Cloete, “An eigenvalue theory of circular birefringence and dichroism in a non-magnetic chiral medium,” J. Electromagn. Waves Appl. 8, 1073–1089 (1994).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Phys. B (1)

E. B. Graham, J. Pierrus, R. E. Raab, “Multipole moments and Maxwell’s equations,” J. Phys. B 25, 4673–4684 (1992).
[CrossRef]

J. Phys. Soc. Jpn. (1)

H. Nakano, H. Kimura, “Quantum statistical-mechanical theory of optical activity,” J. Phys. Soc. Jpn. 27, 519–535 (1969).
[CrossRef]

Molec. Phys. (1)

L. D. Barron, A. D. Buckingham, “Rayleigh and Raman scattering from optically active molecules,” Molec. Phys. 20, 1111–1119 (1971).
[CrossRef]

Philos. Mag. B (2)

E. B. Graham, R. E. Raab, “Non-reciprocal optical rotation in cubic antiferromagnetics,” Philos. Mag. B 64, 267–274 (1991).
[CrossRef]

E. B. Graham, R. E. Raab, “Magnetic effects in antiferromagnetic crystals in the electric quadrupole-magnetic dipole approximation,” Philos. Mag. B 66, 269–284 (1992).
[CrossRef]

Phys. Rev. (1)

P. N. Argyres, “Theory of the Faraday and Kerr effects in ferromagnetics,” Phys. Rev. 97, 334–345 (1955).
[CrossRef]

Phys. Rev. B (1)

J. Pastrnak, K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
[CrossRef]

Phys. Status Solidi B (1)

J. Pastrnak, L. E. Cross, “The optical anisotropy of cubic nickel-iodine boracite due to quadrupole transitions,” Phys. Status Solidi B 44, 313–325 (1971).
[CrossRef]

Proc. K. Ned. Acad. Wet. (1)

H. A. Lorentz, “Double refraction by regular crystals,” Proc. K. Ned. Acad. Wet. 24, 333–339 (1922);also in H. A. Lorentz, Collected Papers, P. Zeeman, A. D. Fokker, eds. (Nijhoff, The Hague, 1936), Vol. 3, pp. 314–320.
[CrossRef]

Proc. R. Soc. London Ser. A (2)

E. B. Graham, R. E. Raab, “Light propagation in cubic and other anisotropic crystals,” Proc. R. Soc. London Ser. A 430, 593–614 (1990).
[CrossRef]

I. M. B. de Figueiredo, R. E. Raab, “A molecular theory of new differential light scattering effects in a fluid,” Proc. R. Soc. London Ser. A 375, 425–441 (1981).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

E. B. Graham, R. E. Raab, “On the Jones birefringence,” Proc. R. Soc. London, Ser. A 390, 73–90 (1983).
[CrossRef]

Verh. K. Akad. Wet. (1)

H. A. Lorentz, “Concerning the relation between the velocity of propagation of light and the density and composition of media,” Verh. K. Akad. Wet. 18, 1 (1878);also in H. A. Lorentz, Collected Papers, P. Zeeman, A. D. Fokker, eds. (Nijhoff, The Hague, 1936), Vol. 2, pp. 1–119.

Other (14)

F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976), pp. 552, 583, 589.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 142.

R. R. Birss, Symmetry and Magnetism, 2nd ed. (North-Holland, Amsterdam, 1966).

S. I. Pekar, Crystal Optics and Additional Light Waves (Benjamin/Cummings, Menlo Park, Calif., 1983), p. XV.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 73, 75, 79.

L. Rosenfeld, Theory of Electrons (North-Holland, Amsterdam, 1951), Chap. 2.

F. N. H. Robinson, Macroscopic Electromagnetism (Pergamon, Oxford, UK, 1973), pp. 56–62.

A. D. Buckingham, “Permanent and induced molecular moments and long-range intermolecular forces,” in Intermolecular Forces, J. O. Hirschfelder, ed., Adv. Chem. Phys.12, 107–142 (1967).

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, Cambridge, UK, 1982), p. 76.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 14.

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, UK, 1985), Appendix H, p. 271.

G. N. Ramachandran, S. Ramaseshan, “Crystal optics,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV/1, p. 63.

V. M. Agranovich, V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, 2nd ed. (Springer-Verlag, Berlin, 1984), pp. 167–173.

D. E. Gray, American Institute of Physics Handbook, 3rd ed. (McGraw-Hill, New York, 1972), pp. 6–115.

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Tables (1)

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Table 1 Multipole Origin and Order of Magnitude of Different Birefringences in Nonmagnetic Crystals

Equations (95)

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Dα=0Eα+Pα-12βQαβ+16γβQαβγ-,
Hα=μ0-1Bα - Mα + 12βMαβ-.
E¨α=-ω2Eα,βBα=-ω2βB˙α,etc.,
Pα=ααβEβ+1ωααβE˙β+12aαβγγEβ+12ωaαβγγE˙β+GαβBβ+1ωGαβB˙β+,
Dα=0Eα+Pα,
Hα=μ0-1Bα,
Pα=ααβEβ+(1/ω)ααβE˙β.
P=nqr/ΔV,
E=E(0) exp[-iω(t-nr·σ/c)],
×E=-B˙,
B=nσ×E/c.
×H=D˙,
[n2σασβ-(n2-1)δαβ+χαβ]Eβ(0)=0.
[n2(σx2-1)+1+χxx]Ex(0)+[n2σxσy+χxy]Ey(0)
+[n2σxσz+χxz]Ez(0)=0,
[n2σyσx+χyx]Ex(0)+[n2(σy2-1)+1+χyy]Ey(0)
+[n2σyσz+χyz]Ez(0)=0,
[n2σzσx+χzx]Ex(0)+[n2σzσy+χzy]Ey(0)+[n2(σz2-1)
+1+χzz]Ez(0)=0.
n2(1-σx2)-χxx-n2σxσy-n2σxσz-n2σyσxn2(1-σy2)-χyy-n2σyσz-n2σzσx-n2σzσyn2(1-σz2)-χzzEx(0)Ey(0)Ez(0)=Ex(0)Ey(0)Ez(0).
n2(σx2-1)+1+χxxn2σxσyn2σxσzn2σyσxn2(σy2-1)+1+χyyn2σyσzn2σzσxn2σzσyn2(σz2-1)+1+χzz=0.
n4(xσx2+yσy2+zσz2)-n2[xy(σx2+σy2)+yz(σy2
+σz2)+zx(σz2+σx2)]+xyz=0,
x=1+χxx,y=1+χyy,z=1+χzz.
χxx=χyy=χzz=χ.
n2=1+χ=.
σ·E(0)=0.
χxx=χyyχzz.
n4[x(1-σz2)+zσz2]-n2x[x(1-σz2)+z(1+σz2)]
+x2z=0.
n12=x,
n22=xzx(1-σz2)+zσz2.
σ·E(0)=0,
xσxσzEx(0)+xσyσzEy(0)+[x(σz2-1)+z]Ez(0)=0.
(z-x)Ez(0)=0,
σxEx(0)+σyEy(0)=0.
E(0)=Ex(0)(1,-σx/σy, 0)=Ey(0)(-σy/σx, 1, 0).
x(σxEx(0)+σyEy(0))+zσzEz(0)=0.
xσ·E(0)+(z-x)σzEz(0)=0,
σyEx(0)=σxEy(0).
Ez(0)=-x(σx2+σy2)zσxσzEx(0)=-x(σx2+σy2)zσyσzEy(0).
E=Ex(0)[1, σy/σx,-x(σx2+σy2)/(zσxσz)]=Ey(0)[σx/σy, 1,-x(σx2+σy2)/(zσyσz)].
σ·E(0)=E(0) cos ϕ,
cos ϕ=σz(z-x)1-σz2x2(1-σz2)+z2σz21/2.
χxx>χyy>χzz,
x>y>z.
b2-4ac=0.
b2-4ac0.
σy2+σz2=1.
b2-4ac=[y(x-z)σy2+z(x-y)σz2]2.
σx2+σz2=1.
b2-4ac=[x(y-z)σx2-z(x-y)σz2]2.
σoa=z(x-y)y(x-z)1/2,0,±x(y-z)y(x-z)1/2,
σoa·zˆ=cos θ=±x(y-z)y(x-z)1/2.
n2=(b/2a)=y.
E1(0)=(0, 1, 0),
E2(0)={[z(y-z)]1/2,0,
[x(x-y)1/2]}[z(y-z)+x(x-y)]-1/2.
σ=(σx, σy, 0).
n2(σx2-1)+xn2σxσy0n2σxσyn2(σy2-1)+y000-n2+z=0,
n12=z,withE1(0)=(0, 0, 1).
n22=xyxσx2+yσy2,
withE2(0)=(yσy,-xσx, 0)(x2σx2+y2σy2)-1/2.
Dα=αβEβ,
Hα=μ-1Bα,
μμ0.
Hα=μ0-1Bα,
Dα=αβEβ,
αβ=0δαβ+ααβ+(in/c)σγ[βγδGαδ+12ω(aαβγ-aβαγ)].
an4-bn2+c=0,
a=xσx2+yσy2+zσz2,
b=xy(σx2+σy2)+yz(σy2+σz2)+zx(σz2+σx2),
c=xyz.
b2-4ac0.
b2-4ac=αx2+βx+γ,
α=[y(1-σz2)-z(1-σy2)]2+4yzσy2σz2>0,
β=2yz{(σy2+σz2)[y(1-σz2)+z(1-σy2)]-2(yσy2+zσz2)},
γ=[yz(σy2+σz2)]20.
σ2=σx2+σy2+σz2=1.
x=-β±{β2-4α[γ-(b2-4ac)]}1/22α.
β2-4α[γ-(b2-4ac)]0,
b2-4ac4αγ-β24α.
4αγ-β20.
4αγ-β2=16y2z2(y-z)2σx2σy2σz2.
E(0)=nσxn2-x,nσyn2-y,nσzn2-z.
tan α=|E1(0)×E2(0)|E1(0)·E2(0)
=[(b2-4ac)(x2σx2+y2σy2+z2σz2)]1/2(x-y)(y-z)(z-x)σxσyσz,
x=5.6169,y=6.2500,z=7.0225,37
σx2=3/12,σy2=4/12,σz2=5/12,
α=89.778°.
n1=2.4109083,
E1(0)=(0.87371359;-0.45098329;-0.18231472),
n2=2.5715952,
E2(0)=(0.21871419, 0.69288996;-0.68707175).
ϕ1=86.629°,ϕ2=86.222°.

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