Abstract

Refraction, reflection, and amplitude relations are derived that apply to polarization ray tracing in anisotropic, optically active media such as quartz. The constitutive relations for quartz are discussed. The refractive indices and polarization states associated with the two modes of propagation are derived as a function of wave direction. A procedure for refracting at any uniaxial or optically active interface is derived that computes both the ray direction and the wave direction. A method for computing the optical path length is given, and Fresnel transmission and reflection equations are derived from boundary conditions on the electromagnetic fields. These ray-tracing formulas apply to uniaxial, optically active media and therefore encompass uniaxial, non-optically active materials and isotropic, optically active materials.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. O. N. Stravroudis, “Ray-tracing formulas for uniaxial crystals,”J. Opt. Soc. Am. 52, 187–191 (1962).
    [Crossref]
  2. W. Swindell, “Extraordinary-ray and -wave tracing in uniaxial crystals,” Appl. Opt. 14, 2298–2301 (1975).
    [Crossref] [PubMed]
  3. M. Simon, “Ray tracing formulas for monoaxial optical components,” Appl. Opt. 22, 354–360 (1983).
    [Crossref] [PubMed]
  4. J. D. Trolinger, R. A. Chipman, D. K. Wilson, “Polarization ray tracing in birefringent media,” Opt. Eng. 30, 461–466 (1991).
    [Crossref]
  5. Q.-T. Liang, “Simple ray tracing formulas for uniaxial optical crystals,” Appl. Opt. 29, 1008–1010 (1990).
    [Crossref] [PubMed]
  6. A. Lakhtakia, ed., Selected Papers on Natural Optical Activity, Vol. MS15 of SPIE Milestone Series, B. J. Thompson, ed. (SPIE Optical Engineering Press, Bellingham, Wash., 1990). This volume contains reprints of Refs. 7–9 and 14 (below).
  7. E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
    [Crossref]
  8. F. I. Fedorov, “On the theory of optical activity in crystals,” Opt. Spektrosk. 6, 49–53 (1959).
  9. E. J. Post, Formal Structure of Electromagnetics (North-Holland, Amsterdam, 1962).
  10. A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer-Verlag, Berlin, 1989), pp. 13–18.
  11. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 69–102.
  12. D. Eimerl, “Quantum electrodynamics of optical activity in birefringent crystals,” J. Opt. Soc. Am. B 5, 1453–1461 (1988).
    [Crossref]
  13. M. P. Silverman, R. B. Sohn, “Effects of circular birefringence on light propagation and reflection,” Am. J. Phys. 54, 69–76 (1986).
    [Crossref]
  14. M. P. Silverman, “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); erratum, 4, 1145 (1987).
    [Crossref]
  15. G. N. Ramachandran, S. Ramaseshan, “Crystal optics,” in Encyclopedia of Physics, S. Fluegge, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV/1, pp. 76–85.
  16. S. C. McClain, L. W. Hillman, R. A. Chipman, “Polarization ray tracing in anisotropic optically active media. I. Algorithms,” J. Opt. Soc. Am. A 10, 2371–2382 (1993).
    [Crossref]
  17. E. Waluschka, “Polarization ray trace,” Opt. Eng. 28, 86–89 (1989).
    [Crossref]
  18. R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).
  19. R. A. Chipman, “Polarization ray tracing,” in Recent Trends in Optical Systems Design and Computer Lens Design Workshop, R. E. Fischer, C. Londono, eds., Proc. Soc. Photo-Opt. Instrum. Eng.766, 61–68 (1987).
    [Crossref]
  20. T. J. Bruegge, “Analysis of polarization in optical systems,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 165–176 (1989).
    [Crossref]
  21. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
  22. E. E. Wahlstrom, Optical Crystallography, 3rd ed. (Wiley, New York, 1960), pp. 155–156.
  23. A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Low-frequency scattering by an imperfectly conducting sphere immersed in a dc magnetic field,” Int. J. Infrared Millimeter Waves 12, 1253–1264 (1991).
    [Crossref]
  24. H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, New York, 1983).
  25. S. Visnovsky, “Optics of magnetic multilayers,” Czech. J. Phys. 41, 663–694 (1991).
    [Crossref]
  26. C. M. Krowne, “Spectral-domain determination of the propagation constant in biaxial planar media,” Int. J. Electron. 59, 315–332 (1985).
    [Crossref]
  27. J. J. Kyame, “Wave propagation in piezoelectric crystals,” J. Acoust. Soc. Am. 21, 159–167 (1945).
    [Crossref]
  28. O. Schwelb, “Stratified lossy anisotropic media: general characteristics,” J. Opt. Soc. Am. A 3, 188–193 (1986).
    [Crossref]
  29. H. Unz, “Drifting plasma magneto-ionic theory for oblique incidence,”IEEE Trans. Antennas Propag. AP-13, 595–600 (1965).
    [Crossref]
  30. T. M. Roberts, “Explicit eigenmodes for anisotropic media,”IEEE Trans. Magn. 26, 3064–3071 (1990).
    [Crossref]
  31. L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1987), pp. 54, 331–357.
  32. P. K. L. Drude, The Theory of Optics (Dover, New York, 1959).
  33. E. Charney, The Molecular Basis of Optical Activity (Wiley, 1979), pp. 18–57.
  34. W. Weiglhofer, “Scalarization of Maxwell’s equations in general inhomogeneous bianisotropic media,” Proc. Inst. Electr. Eng. Ser. H 134, 357–360 (1987).
  35. A. Lakhtakia, “Polarizability dyadics of small bianisotropic spheres,”J. Phys. (Paris) 51, 2235–2242 (1990).
    [Crossref]
  36. M. Born, Optik (Springer-Verlag, Berlin, 1965), pp. 403–420.
  37. A. Sommerfeld, Optics, Vol. IV of Lectures in Theoretical Physics (Academic, New York, 1949), pp. 154–160.
  38. R. M. Peterson, “Comparison of two theories of optical activity,” Am. J. Phys. 43, 969–972 (1975).
    [Crossref]
  39. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 17–19.
  40. F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976), p. 589.
  41. G. Szivessy, C. Muenster, “Ueber die Prufung der Gitteroptik bei Aktiven Kristallen,” Ann. Phys. (Leipzig) 20, 703–736 (1934).
  42. D. E. Gray, ed., American Institute of Physics Handbook, 3rd ed. (McGraw-Hill, New York, 1972), pp. 6–248.
  43. W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1986), p. 12.
  44. S. Bassiri, C. H. Papas, N. Engheta, “Electromagnetic wave propagation through a dielectric–chiral interface and through a chiral slab,” J. Opt. Soc. Am. A 5, 1450–1459 (1988); erratum, 7, 2154 (1990).
    [Crossref]
  45. A. Lakhtakia, J. R. Diamond, “Reciprocity and the concept of the Brewster wavenumber,” Int. J. Infrared Millimeter Waves 12, 1167–1174 (1991).
    [Crossref]
  46. A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Reflection and transmission of plane waves at the planar interface of a general uniaxial medium and free space,” J. Mod. Opt. 38, 649–657 (1991).
    [Crossref]
  47. A. Lakhtakia, “On extending the Brewster law at planar interfaces,” Optik 84, 160–162 (1990).
  48. O. Schwelb, “Fresnel coefficients for anisotropic media with gain or loss,” J. Mod. Opt. 34, 443–453 (1987).
    [Crossref]
  49. Y. A. Tsvirko, M. A. Tolmazina, “On the boundary conditions for electromagnetic waves at the surface of an optically active crystal,” Soy. Phys. Solid State 3, 1011–1015.
  50. B. R. Chawla, H. Unz, “Reflection and transmission of electromagnetic waves normally incident on a plasma slab moving uniformly along a magnetostatic field,”IEEE Trans. Antennas Propag. AP-17, 771–777 (1969).
    [Crossref]
  51. J. E. Greivenkamp, “Color dependent optical prefilter for suppression of aliasing artifacts,” Appl. Opt. 29, 676–684 (1990).
    [Crossref] [PubMed]
  52. S. C. McClain, R. A. Chipman, L. W. Hillman, “Aberrations of a horizontal-vertical depolarizer,” Appl. Opt. 31, 2326–2331 (1992).
    [Crossref] [PubMed]

1993 (1)

1992 (1)

1991 (5)

A. Lakhtakia, J. R. Diamond, “Reciprocity and the concept of the Brewster wavenumber,” Int. J. Infrared Millimeter Waves 12, 1167–1174 (1991).
[Crossref]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Reflection and transmission of plane waves at the planar interface of a general uniaxial medium and free space,” J. Mod. Opt. 38, 649–657 (1991).
[Crossref]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Low-frequency scattering by an imperfectly conducting sphere immersed in a dc magnetic field,” Int. J. Infrared Millimeter Waves 12, 1253–1264 (1991).
[Crossref]

S. Visnovsky, “Optics of magnetic multilayers,” Czech. J. Phys. 41, 663–694 (1991).
[Crossref]

J. D. Trolinger, R. A. Chipman, D. K. Wilson, “Polarization ray tracing in birefringent media,” Opt. Eng. 30, 461–466 (1991).
[Crossref]

1990 (5)

Q.-T. Liang, “Simple ray tracing formulas for uniaxial optical crystals,” Appl. Opt. 29, 1008–1010 (1990).
[Crossref] [PubMed]

A. Lakhtakia, “On extending the Brewster law at planar interfaces,” Optik 84, 160–162 (1990).

T. M. Roberts, “Explicit eigenmodes for anisotropic media,”IEEE Trans. Magn. 26, 3064–3071 (1990).
[Crossref]

A. Lakhtakia, “Polarizability dyadics of small bianisotropic spheres,”J. Phys. (Paris) 51, 2235–2242 (1990).
[Crossref]

J. E. Greivenkamp, “Color dependent optical prefilter for suppression of aliasing artifacts,” Appl. Opt. 29, 676–684 (1990).
[Crossref] [PubMed]

1989 (2)

E. Waluschka, “Polarization ray trace,” Opt. Eng. 28, 86–89 (1989).
[Crossref]

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

1988 (2)

1987 (2)

W. Weiglhofer, “Scalarization of Maxwell’s equations in general inhomogeneous bianisotropic media,” Proc. Inst. Electr. Eng. Ser. H 134, 357–360 (1987).

O. Schwelb, “Fresnel coefficients for anisotropic media with gain or loss,” J. Mod. Opt. 34, 443–453 (1987).
[Crossref]

1986 (3)

1985 (1)

C. M. Krowne, “Spectral-domain determination of the propagation constant in biaxial planar media,” Int. J. Electron. 59, 315–332 (1985).
[Crossref]

1983 (1)

1975 (2)

W. Swindell, “Extraordinary-ray and -wave tracing in uniaxial crystals,” Appl. Opt. 14, 2298–2301 (1975).
[Crossref] [PubMed]

R. M. Peterson, “Comparison of two theories of optical activity,” Am. J. Phys. 43, 969–972 (1975).
[Crossref]

1969 (1)

B. R. Chawla, H. Unz, “Reflection and transmission of electromagnetic waves normally incident on a plasma slab moving uniformly along a magnetostatic field,”IEEE Trans. Antennas Propag. AP-17, 771–777 (1969).
[Crossref]

1965 (1)

H. Unz, “Drifting plasma magneto-ionic theory for oblique incidence,”IEEE Trans. Antennas Propag. AP-13, 595–600 (1965).
[Crossref]

1962 (1)

1959 (1)

F. I. Fedorov, “On the theory of optical activity in crystals,” Opt. Spektrosk. 6, 49–53 (1959).

1945 (1)

J. J. Kyame, “Wave propagation in piezoelectric crystals,” J. Acoust. Soc. Am. 21, 159–167 (1945).
[Crossref]

1937 (1)

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
[Crossref]

1934 (1)

G. Szivessy, C. Muenster, “Ueber die Prufung der Gitteroptik bei Aktiven Kristallen,” Ann. Phys. (Leipzig) 20, 703–736 (1934).

Bassiri, S.

Born, M.

M. Born, Optik (Springer-Verlag, Berlin, 1965), pp. 403–420.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Bruegge, T. J.

T. J. Bruegge, “Analysis of polarization in optical systems,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 165–176 (1989).
[Crossref]

Charney, E.

E. Charney, The Molecular Basis of Optical Activity (Wiley, 1979), pp. 18–57.

Chawla, B. R.

B. R. Chawla, H. Unz, “Reflection and transmission of electromagnetic waves normally incident on a plasma slab moving uniformly along a magnetostatic field,”IEEE Trans. Antennas Propag. AP-17, 771–777 (1969).
[Crossref]

Chen, H. C.

H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, New York, 1983).

Chipman, R. A.

S. C. McClain, L. W. Hillman, R. A. Chipman, “Polarization ray tracing in anisotropic optically active media. I. Algorithms,” J. Opt. Soc. Am. A 10, 2371–2382 (1993).
[Crossref]

S. C. McClain, R. A. Chipman, L. W. Hillman, “Aberrations of a horizontal-vertical depolarizer,” Appl. Opt. 31, 2326–2331 (1992).
[Crossref] [PubMed]

J. D. Trolinger, R. A. Chipman, D. K. Wilson, “Polarization ray tracing in birefringent media,” Opt. Eng. 30, 461–466 (1991).
[Crossref]

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

R. A. Chipman, “Polarization ray tracing,” in Recent Trends in Optical Systems Design and Computer Lens Design Workshop, R. E. Fischer, C. Londono, eds., Proc. Soc. Photo-Opt. Instrum. Eng.766, 61–68 (1987).
[Crossref]

Condon, E. U.

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
[Crossref]

Diamond, J. R.

A. Lakhtakia, J. R. Diamond, “Reciprocity and the concept of the Brewster wavenumber,” Int. J. Infrared Millimeter Waves 12, 1167–1174 (1991).
[Crossref]

Drude, P. K. L.

P. K. L. Drude, The Theory of Optics (Dover, New York, 1959).

Eimerl, D.

Engheta, N.

Fedorov, F. I.

F. I. Fedorov, “On the theory of optical activity in crystals,” Opt. Spektrosk. 6, 49–53 (1959).

Greivenkamp, J. E.

Hillman, L. W.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 17–19.

Jenkins, F. A.

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

Krowne, C. M.

C. M. Krowne, “Spectral-domain determination of the propagation constant in biaxial planar media,” Int. J. Electron. 59, 315–332 (1985).
[Crossref]

Kyame, J. J.

J. J. Kyame, “Wave propagation in piezoelectric crystals,” J. Acoust. Soc. Am. 21, 159–167 (1945).
[Crossref]

Lakhtakia, A.

A. Lakhtakia, J. R. Diamond, “Reciprocity and the concept of the Brewster wavenumber,” Int. J. Infrared Millimeter Waves 12, 1167–1174 (1991).
[Crossref]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Reflection and transmission of plane waves at the planar interface of a general uniaxial medium and free space,” J. Mod. Opt. 38, 649–657 (1991).
[Crossref]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Low-frequency scattering by an imperfectly conducting sphere immersed in a dc magnetic field,” Int. J. Infrared Millimeter Waves 12, 1253–1264 (1991).
[Crossref]

A. Lakhtakia, “On extending the Brewster law at planar interfaces,” Optik 84, 160–162 (1990).

A. Lakhtakia, “Polarizability dyadics of small bianisotropic spheres,”J. Phys. (Paris) 51, 2235–2242 (1990).
[Crossref]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer-Verlag, Berlin, 1989), pp. 13–18.

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1987), pp. 54, 331–357.

Liang, Q.-T.

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1987), pp. 54, 331–357.

McClain, S. C.

Muenster, C.

G. Szivessy, C. Muenster, “Ueber die Prufung der Gitteroptik bei Aktiven Kristallen,” Ann. Phys. (Leipzig) 20, 703–736 (1934).

Papas, C. H.

Peterson, R. M.

R. M. Peterson, “Comparison of two theories of optical activity,” Am. J. Phys. 43, 969–972 (1975).
[Crossref]

Post, E. J.

E. J. Post, Formal Structure of Electromagnetics (North-Holland, Amsterdam, 1962).

Ramachandran, G. N.

G. N. Ramachandran, S. Ramaseshan, “Crystal optics,” in Encyclopedia of Physics, S. Fluegge, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV/1, pp. 76–85.

Ramaseshan, S.

G. N. Ramachandran, S. Ramaseshan, “Crystal optics,” in Encyclopedia of Physics, S. Fluegge, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV/1, pp. 76–85.

Roberts, T. M.

T. M. Roberts, “Explicit eigenmodes for anisotropic media,”IEEE Trans. Magn. 26, 3064–3071 (1990).
[Crossref]

Schwelb, O.

O. Schwelb, “Fresnel coefficients for anisotropic media with gain or loss,” J. Mod. Opt. 34, 443–453 (1987).
[Crossref]

O. Schwelb, “Stratified lossy anisotropic media: general characteristics,” J. Opt. Soc. Am. A 3, 188–193 (1986).
[Crossref]

Silverman, M. P.

Simon, M.

Sohn, R. B.

M. P. Silverman, R. B. Sohn, “Effects of circular birefringence on light propagation and reflection,” Am. J. Phys. 54, 69–76 (1986).
[Crossref]

Sommerfeld, A.

A. Sommerfeld, Optics, Vol. IV of Lectures in Theoretical Physics (Academic, New York, 1949), pp. 154–160.

Stravroudis, O. N.

Swindell, W.

Szivessy, G.

G. Szivessy, C. Muenster, “Ueber die Prufung der Gitteroptik bei Aktiven Kristallen,” Ann. Phys. (Leipzig) 20, 703–736 (1934).

Tolmazina, M. A.

Y. A. Tsvirko, M. A. Tolmazina, “On the boundary conditions for electromagnetic waves at the surface of an optically active crystal,” Soy. Phys. Solid State 3, 1011–1015.

Trolinger, J. D.

J. D. Trolinger, R. A. Chipman, D. K. Wilson, “Polarization ray tracing in birefringent media,” Opt. Eng. 30, 461–466 (1991).
[Crossref]

Tsvirko, Y. A.

Y. A. Tsvirko, M. A. Tolmazina, “On the boundary conditions for electromagnetic waves at the surface of an optically active crystal,” Soy. Phys. Solid State 3, 1011–1015.

Unz, H.

B. R. Chawla, H. Unz, “Reflection and transmission of electromagnetic waves normally incident on a plasma slab moving uniformly along a magnetostatic field,”IEEE Trans. Antennas Propag. AP-17, 771–777 (1969).
[Crossref]

H. Unz, “Drifting plasma magneto-ionic theory for oblique incidence,”IEEE Trans. Antennas Propag. AP-13, 595–600 (1965).
[Crossref]

Varadan, V. K.

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Reflection and transmission of plane waves at the planar interface of a general uniaxial medium and free space,” J. Mod. Opt. 38, 649–657 (1991).
[Crossref]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Low-frequency scattering by an imperfectly conducting sphere immersed in a dc magnetic field,” Int. J. Infrared Millimeter Waves 12, 1253–1264 (1991).
[Crossref]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer-Verlag, Berlin, 1989), pp. 13–18.

Varadan, V. V.

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Low-frequency scattering by an imperfectly conducting sphere immersed in a dc magnetic field,” Int. J. Infrared Millimeter Waves 12, 1253–1264 (1991).
[Crossref]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Reflection and transmission of plane waves at the planar interface of a general uniaxial medium and free space,” J. Mod. Opt. 38, 649–657 (1991).
[Crossref]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer-Verlag, Berlin, 1989), pp. 13–18.

Visnovsky, S.

S. Visnovsky, “Optics of magnetic multilayers,” Czech. J. Phys. 41, 663–694 (1991).
[Crossref]

Wahlstrom, E. E.

E. E. Wahlstrom, Optical Crystallography, 3rd ed. (Wiley, New York, 1960), pp. 155–156.

Waluschka, E.

E. Waluschka, “Polarization ray trace,” Opt. Eng. 28, 86–89 (1989).
[Crossref]

Weiglhofer, W.

W. Weiglhofer, “Scalarization of Maxwell’s equations in general inhomogeneous bianisotropic media,” Proc. Inst. Electr. Eng. Ser. H 134, 357–360 (1987).

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1986), p. 12.

White, H. E.

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

Wilson, D. K.

J. D. Trolinger, R. A. Chipman, D. K. Wilson, “Polarization ray tracing in birefringent media,” Opt. Eng. 30, 461–466 (1991).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 69–102.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 69–102.

Am. J. Phys. (2)

M. P. Silverman, R. B. Sohn, “Effects of circular birefringence on light propagation and reflection,” Am. J. Phys. 54, 69–76 (1986).
[Crossref]

R. M. Peterson, “Comparison of two theories of optical activity,” Am. J. Phys. 43, 969–972 (1975).
[Crossref]

Ann. Phys. (Leipzig) (1)

G. Szivessy, C. Muenster, “Ueber die Prufung der Gitteroptik bei Aktiven Kristallen,” Ann. Phys. (Leipzig) 20, 703–736 (1934).

Appl. Opt. (5)

Czech. J. Phys. (1)

S. Visnovsky, “Optics of magnetic multilayers,” Czech. J. Phys. 41, 663–694 (1991).
[Crossref]

IEEE Trans. Antennas Propag. (2)

H. Unz, “Drifting plasma magneto-ionic theory for oblique incidence,”IEEE Trans. Antennas Propag. AP-13, 595–600 (1965).
[Crossref]

B. R. Chawla, H. Unz, “Reflection and transmission of electromagnetic waves normally incident on a plasma slab moving uniformly along a magnetostatic field,”IEEE Trans. Antennas Propag. AP-17, 771–777 (1969).
[Crossref]

IEEE Trans. Magn. (1)

T. M. Roberts, “Explicit eigenmodes for anisotropic media,”IEEE Trans. Magn. 26, 3064–3071 (1990).
[Crossref]

Int. J. Electron. (1)

C. M. Krowne, “Spectral-domain determination of the propagation constant in biaxial planar media,” Int. J. Electron. 59, 315–332 (1985).
[Crossref]

Int. J. Infrared Millimeter Waves (2)

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Low-frequency scattering by an imperfectly conducting sphere immersed in a dc magnetic field,” Int. J. Infrared Millimeter Waves 12, 1253–1264 (1991).
[Crossref]

A. Lakhtakia, J. R. Diamond, “Reciprocity and the concept of the Brewster wavenumber,” Int. J. Infrared Millimeter Waves 12, 1167–1174 (1991).
[Crossref]

J. Acoust. Soc. Am. (1)

J. J. Kyame, “Wave propagation in piezoelectric crystals,” J. Acoust. Soc. Am. 21, 159–167 (1945).
[Crossref]

J. Mod. Opt. (2)

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Reflection and transmission of plane waves at the planar interface of a general uniaxial medium and free space,” J. Mod. Opt. 38, 649–657 (1991).
[Crossref]

O. Schwelb, “Fresnel coefficients for anisotropic media with gain or loss,” J. Mod. Opt. 34, 443–453 (1987).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

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

J. Phys. (Paris) (1)

A. Lakhtakia, “Polarizability dyadics of small bianisotropic spheres,”J. Phys. (Paris) 51, 2235–2242 (1990).
[Crossref]

Opt. Eng. (3)

E. Waluschka, “Polarization ray trace,” Opt. Eng. 28, 86–89 (1989).
[Crossref]

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

J. D. Trolinger, R. A. Chipman, D. K. Wilson, “Polarization ray tracing in birefringent media,” Opt. Eng. 30, 461–466 (1991).
[Crossref]

Opt. Spektrosk. (1)

F. I. Fedorov, “On the theory of optical activity in crystals,” Opt. Spektrosk. 6, 49–53 (1959).

Optik (1)

A. Lakhtakia, “On extending the Brewster law at planar interfaces,” Optik 84, 160–162 (1990).

Proc. Inst. Electr. Eng. Ser. H (1)

W. Weiglhofer, “Scalarization of Maxwell’s equations in general inhomogeneous bianisotropic media,” Proc. Inst. Electr. Eng. Ser. H 134, 357–360 (1987).

Rev. Mod. Phys. (1)

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
[Crossref]

Soy. Phys. Solid State (1)

Y. A. Tsvirko, M. A. Tolmazina, “On the boundary conditions for electromagnetic waves at the surface of an optically active crystal,” Soy. Phys. Solid State 3, 1011–1015.

Other (19)

D. E. Gray, ed., American Institute of Physics Handbook, 3rd ed. (McGraw-Hill, New York, 1972), pp. 6–248.

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1986), p. 12.

G. N. Ramachandran, S. Ramaseshan, “Crystal optics,” in Encyclopedia of Physics, S. Fluegge, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV/1, pp. 76–85.

R. A. Chipman, “Polarization ray tracing,” in Recent Trends in Optical Systems Design and Computer Lens Design Workshop, R. E. Fischer, C. Londono, eds., Proc. Soc. Photo-Opt. Instrum. Eng.766, 61–68 (1987).
[Crossref]

T. J. Bruegge, “Analysis of polarization in optical systems,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 165–176 (1989).
[Crossref]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

E. E. Wahlstrom, Optical Crystallography, 3rd ed. (Wiley, New York, 1960), pp. 155–156.

E. J. Post, Formal Structure of Electromagnetics (North-Holland, Amsterdam, 1962).

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer-Verlag, Berlin, 1989), pp. 13–18.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 69–102.

A. Lakhtakia, ed., Selected Papers on Natural Optical Activity, Vol. MS15 of SPIE Milestone Series, B. J. Thompson, ed. (SPIE Optical Engineering Press, Bellingham, Wash., 1990). This volume contains reprints of Refs. 7–9 and 14 (below).

H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, New York, 1983).

M. Born, Optik (Springer-Verlag, Berlin, 1965), pp. 403–420.

A. Sommerfeld, Optics, Vol. IV of Lectures in Theoretical Physics (Academic, New York, 1949), pp. 154–160.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 17–19.

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

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1987), pp. 54, 331–357.

P. K. L. Drude, The Theory of Optics (Dover, New York, 1959).

E. Charney, The Molecular Basis of Optical Activity (Wiley, 1979), pp. 18–57.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Ordinary and extraordinary refractive indices of right-handed quartz at 762 nm as a function of propagation angle from the crystal axis. Optical activity splits the degeneracy that would otherwise exist at 0°.

Fig. 2
Fig. 2

Difference between the refractive indices of quartz at 762 nm and the refractive indices without optical activity. Lower curve, ordinary index; upper curve, extraordinary index; the deviation is equal and opposite for the two modes.

Fig. 3
Fig. 3

Ellipticity of the modes as a function of propagation angle from the crystal axis. The modes are nearly circular for angles less than 1.5°, nearly linear for angles greater than 10°.

Fig. 4
Fig. 4

Geometry for refraction at birefringent interfaces. A ray with wave vector k ^ i is incident upon a surface with normal η ^. (a) Birefringent to birefringent. Two rays are transmitted, with wave vectors and k ^ to and k ^ te; two rays are reflected, with wave vectors k ^ ro and k ^ re. (b) Nonbirefringent to birefringent. Two rays are transmitted, with wave vectors k ^ to and k ^ te; one ray is reflected, with wave vector k ^ r. (c) Birefringent to nonbirefringent. One ray is transmitted, with wave vector k ^ t; two rays are reflected, with wave vectors k ^ ro and k ^ re. (d) Nonbirefringent to nonbirefringent. One ray is transmitted, with wave vector k ^ t; one ray is reflected, with wave vector k ^ r.

Fig. 5
Fig. 5

Angle of refraction versus angle of incidence for the ordinary transmitted mode of Fig. 4 with the crystal axis parallel to η ^.

Fig. 6
Fig. 6

Difference between the angle of refraction from Fig. 5 and the angle of refraction in the absence of optical activity. Ray paths are affected little by optical activity.

Fig. 7
Fig. 7

A ray propagates a distance l from surface 1 to surface 2. The ray direction ρ ^ is not parallel to k ^. The optical path length is determined by the projection of the ray in the k ^ direction.

Equations (67)

Equations on this page are rendered with MathJax. Learn more.

D = E ,
B = H .
D = E .
= [ o 0 0 0 o 0 0 0 e ] .
D = E - X H ˙
B = μ H + X E ˙ .
D = E + i G H ,
B = μ H - i G E .
D = E + i GH ,
B = μ H - i GE .
G = [ g o 0 0 0 g o 0 0 0 g e ] .
D = F ( E + β × E )
B = μ F ( H + β × H ) ,
D = p E + i ξ B
B = μ p ( H - i ξ E ) .
D = E ,
B = μ H ,
i k = i k ( 0 ) + i i k l g l
D = ( 0 ) E + i E × g .
g = g k ^ .
[ F 1 F 2 ] = [ cos t sin t - sin t cos t ] [ F 1 F 2 ] ,
E = R e { E o exp [ i ( n ω / c k ^ · r - ω t ) ] } ,
ME = 0 ,
M = + ( n K + i G ) 2 .
K = [ 0 - k z k y k z 0 - k x - k y k x 0 ] .
[ o - g o 2 - n 2 - 2 i n g o cos θ i n ( g o + g e ) sin θ 2 i n g o cos θ o - g o 2 - n 2 cos 2 θ n 2 sin θ cos θ - i n ( g o + g e ) sin θ n 2 sin θ cos θ e - g e 2 - n 2 sin 2 θ ] E = 0.
( n 2 ) 2 ( e + w ) - n 2 [ o ( e + e ) + v ] + o 2 e = 0 ,
o = o - g o 2 ,
e = e - g e 2 ,
e = cos 2 θ e + sin 2 θ o ,
v = 4 e g o 2 cos 2 θ + o ( g o + g e ) 2 sin 2 θ ,
w = ( g o - g e ) 2 sin 2 θ cos 2 θ .
n 2 = o ( e + e ) + v ± [ o 2 ( e + e ) 2 + 2 o v ( e + e ) + v 2 - 4 ( e + w ) o 2 e ] 1 / 2 2 ( e + w ) .
E ^ * · E ^ = 1.
B ^ = n K E ^ ,
H ^ = ( n K + i G ) E ^ ,
D ^ = ( - G 2 + i n GK ) E ^ .
n e = o + g o ,
n o = o - g o ,
E ^ e = 1 2 ( 1 , - i , 0 ) ,
E ^ o = 1 2 ( 1 , i , 0 ) .
o = 1 / 4 ( n r + n l ) 2 = 2.36904
g o = 1 / 2 ( n r - n l ) = 3 × 10 - 5 .
n = 1 2 { o + e - ( g o + g e ) 2 ± [ ( o - e ) 2 - 2 ( g o + g e ) 2 ( e + o ) + ( g o + g e ) 4 ] 1 / 2 } 1 / 2 .
n o = o .
n e = e .
g e = - 1.92 g o .
ρ = π λ ( n r - n l ) = 2 π λ g o
g o = λ ρ 2 π .
η ^ × ( n i k ^ i ) = η ^ × ( n t k ^ t ) ,
n t k ^ t = n i k ^ i + Γ η ^ ,
Γ = - n i k ^ i · η ^ ± [ n i 2 ( k ^ i · η ^ ) 2 + ( n t 2 - n i 2 ) ] 1 / 2 .
cos θ = k ^ t · c ^ .
ρ ^ = R e ( E ^ × H ^ * ) R e ( E ^ × H ^ * ) ,
OPL = n l k ^ · ρ ^ .
E 1 = R e { E i { E ^ i exp [ i ( n i k ^ i · r - ω t ) ] + a ro E ^ ro × exp [ i ( n ro k ^ ro · r - ω t ) ] + a re E ^ re × exp [ i ( n re k ^ re · r - ω t ) ] } } ,
E 2 = R e { E i { a to E ^ to exp [ i ( n to k ^ to · r - ω t ) ] + a te E ^ te × exp [ i ( n te k ^ te · r - ω t ) ] } } ,
H 1 = R e { H i { H ^ i exp [ i ( n t k ^ t · r - ω t ) ] + a ro H ^ ro × exp [ i ( n ro k ^ ro · r - ω t ) ] + a re H ^ re × exp [ i ( n re k ^ re · r - ω t ) ] } } ,
H 2 = R e ( H ^ i { a to H ^ to exp [ i ( n to k ^ to · r - ω t ) ] + a te H ^ te × exp [ i ( n te k ^ te · r - ω t ) ] } ) .
s 1 = k ^ i × η ^ ,
s 2 = η × s 1 ,
s 1 · ( E ^ i + a ro E ^ ro + a re E ^ re ) = s 1 · ( a to E ^ to + a te E ^ te ) ,
s 2 · ( E ^ i + a ro E ^ ro + a re E ^ re ) = s 2 · ( a to E ^ to + a te E ^ te ) ,
s 1 · ( H ^ i + a ro H ^ ro + a re H ^ re ) = s 1 · ( a to H ^ to + a te H ^ te ) ,
s 2 · ( H ^ i + a ro H ^ ro + a re H ^ re ) = s 2 · ( a to H ^ to + a te H ^ te ) ,
[ a to a te a ro a re ] = F - 1 · [ s 1 · E ^ i s 2 · E ^ i s 1 · H ^ i s 2 · H ^ i ] ,
F = [ s 1 · E ^ to s 1 · E ^ te - s 1 · E ^ ro - s 1 · E ^ re s 2 · E ^ to s 2 · E ^ te - s 2 · E ^ ro - s 2 · E ^ re s 1 · H ^ to s 1 · H ^ te - s 1 · H ^ ro - s 1 · H ^ re s 2 · H ^ to s 2 · H ^ te - s 2 · H ^ ro - s 2 · H ^ re ] .

Metrics