Abstract

Fresnel reflection amplitude coefficients (fractional amplitudes) at the surface of an isotropic, intrinsically nonmagnetic chiral medium are derived on the basis of the Drude–Condon model of optical activity. The eigenvalue–eigenvector solution is obtained with use of Berreman’s 4 × 4 matrix method. Self-consistent results are obtained when the calculations are based on a new 4 × 4 matrix for reflection from an isotropic chiral medium.

© 1995 Optical Society of America

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  1. V. A. Kizel, V. I. Burkov, Gyrotropy of Crystals (Nauka, Moscow, 1980).
  2. L. D. Baron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, New York, 1982).
  3. L. Velluz, M. Legrand, M. Grosjean, Optical Circular Dichroism (Academic, London, 1965).
  4. R. W. Ditchburn, Light (Blackie, London, 1963), p. 637.
  5. I. S. Zheludev, “Axial tensors of third rank and the physical phenomena they describe,” Sov. Phys. Crystallogr. 9, 501–505 (1964).
  6. K. Aizu, “Ferroelectric transformation of tensorial properties in regular ferroelectrics,” Phys. Rev. A 133, 1350–1359 (1964).
  7. S. Balakrishna, M. Krishnamurthi, B. Rao, Physics of the Solid State (Academic, London, 1969), p. 447.
  8. D. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in a chiral medium,” Appl. Phys. 18, 211–216 (1979).
    [Crossref]
  9. T. Takizawa, “Effects of optical activity on the reflectance of paratelurite TeO2,” J. Phys. Soc. Jpn. 50, 3054–3062 (1981).
    [Crossref]
  10. M. P. Silverman, “Specular light scattering from a chiral medium: unambiguous test of gyrotropic constitutive relations,” Lett. Nuovo Cimento Soc. Ital. Fis. 43, 378–382 (1985).
    [Crossref]
  11. M. P. Silverman, “Test of gyrotropic constitutive relations by specular light reflection,” J. Opt. Soc. Am. A 2, (13), p. 99 (1985).
  12. 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).
    [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. I. J. Lalov, “Effects of vibrational optical activity in the reflection spectra of crystals for the frequency regions of nondegenerate vibrations,” Phys. Rev. B 32, 6884–6891 (1985).
    [Crossref]
  15. I. J. Lalov, A. I. Miteva, “Reflection optical activity of uniaxial media,” J. Chem. Phys. 85, 5505–5511 (1986).
    [Crossref]
  16. A. Lakhtakia, V. V. Varadan, V. K. Varadan, “What happens to plane waves at the planar interfaces of mirror-conjugate chiral media,” J. Opt. Soc. Am. 6, 23–26 (1989).
    [Crossref]
  17. S. Bassiri, C. H. Papas, N. Engeta, “Electromagnetic wave propagation through a dielectric chiral interface and through a chiral slab,” J. Opt. Soc. Am. A 5, 1450–1459 (1988).
    [Crossref]
  18. B. V. Bokut, F. I. Fedorov, “Reflection and refraction of light in optically isotropic active media,” Opt. Spectrosk. 9, 334–336 (1960).
  19. B. V. Bokut, B. A. Sotski, “The passage of light through an optically active absorbing plate,” Opt. Spektrosk. 14, 117–120 (1963).
  20. F. I. Fedorov, B. V. Bokut, A. F. Konstantinova, “Optical activity of the planar classes of the middle groups,” Sov. Phys. Crystallogr. 7, 738–744 (1963).
  21. A. Lakhtakia, V. V. Varadan, V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral–chiral interface,” IEEE Trans. Electromagn. Compat. 28, 90–95 (1986).
    [Crossref]
  22. A. Lakhtakia, V. V. Varadan, V. K. Varadan, “The extended boundary condition method for scattering by a chiral scatterer in a chiral medium: formulation and analysis,” Optik 86, 155–161 (1991).
  23. A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Scattering by periodic achiral–chiral interfaces,” J. Opt. Soc. Am. A 6, 1675–1681 (1989); errata: 7, 951 (1990).
    [Crossref]
  24. A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Eigen-modes of a chiral sphere with a perfectly conducting coating,” J. Phys. D Appl. Phys. 22, 825–829 (1989).
    [Crossref]
  25. A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Reflection of plane waves at planar achiral–chiral interfaces: independence of the reflected polarization state from the incident polarization state,” J. Opt. Soc. Am. A 7, 1654–1660 (1990).
    [Crossref]
  26. A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Scattering and absorption characteristics of lossy dielectric chiral, nonspherical objects,” Appl. Opt. 24, 4146–4154 (1985).
    [Crossref] [PubMed]
  27. A. I. Miteva, I. J. Lalov, “Reflection of electromagnetic waves from isotropic optically active media,” J. Condens. Matter 2, 529–538 (1991).
    [Crossref]
  28. I. J. Lalov, A. I. Miteva, “Optically active Fabry–Perot étalon,” J. Mod. Opt. 38, 395–411 (1991).
    [Crossref]
  29. H. Cory, I. Rosenhonse, “Electromagnetic wave reflection and transmission at a chiral–dielectric interface,” J. Mod. Opt. 38, 1229–1241 (1991).
    [Crossref]
  30. M. P. Silverman, N. Ritchie, G. M. Cushman, B. Fisher, “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).
    [Crossref]
  31. E. M. Georgieva, “Jones and Mueller matrices for specular reflection from a chiral medium: determination of the basic chiral parameters using the elements of the Mueller matrix and experimental configurations to measure the basic chiral parameters,” Appl. Opt. 30, 5081–5085 (1991).
    [Crossref] [PubMed]
  32. D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire scatterers in chiral media,” Opt. Lett. 16, 781–783 (1991).
    [Crossref] [PubMed]
  33. D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire antennas in chiral media,” Electron. Lett. 27, 243–244 (1991).
    [Crossref]
  34. D. L. Jaggard, N. Engeta, “‘Chirosorb’ as an invisible medium,” Electron. Lett. 25, 173–174 (1989).
    [Crossref]
  35. D. L. Jaggard, J. C. Liu, X. Sun, “Spherical chiroshield,” Electron. Lett. 27, 77–79 (1991).
    [Crossref]
  36. J. C. Liu, D. L. Jaggard, “Chiral layers on planar surfaces,” J. Electromagn. Waves Applic. 6, 705–721 (1992).
  37. D. L. Jaggard, X. Sun, “Theory of chiral multilayers,” J. Opt. Soc. Am. A 9, 804–813 (1992).
    [Crossref]
  38. E. U. Condon, “Theory of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
    [Crossref]
  39. P. Drude, The Theory of Optics (Longmans, Green, New York, 1992), Chap. 6, Eqs. (7) and (8).
  40. W. Kauzmann, Quantum Chemistry (Academic, New York, 1957), p. 703.
  41. V. M. Agranovich, V. Ginsburg, Crystal Optics with Spatial Dispersion and Exitons (Springer-Verlag, Berlin, 1984), Chap. 4.
  42. S. Teitler, B. W. Henvis, “Reflection in stratified anisotropic media,” J. Opt. Soc. Am. 60, 830–834 (1970).
    [Crossref]
  43. P. Allia, C. Oldano, L. Trossi, “Light propagation in anisotropic stratified media in the quasi adiabatic limit,” Mol. Cryst. Liq. Cryst. 143, 17–20 (1987).
    [Crossref]
  44. K. Eidner, G. Mayer, M. Schmidt, H. Schmidel, “Optics in stratified media—the use of optical eigenmodes of uniaxial crystals in the 4 × 4 matrix formalism,” Mol. Cryst. Liq. Cryst. 172, 191–200 (1989).
  45. D. W. Berreman, T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid-crystal films,” Phys. Rev. Lett. 25, 577–581 (1970).
    [Crossref]
  46. D. W. Berreman, “Optics in stratified and anisotropic media: 4 × 4 matrix formulation,” J. Opt. Soc. Am. 62, 502–510 (1972).
    [Crossref]
  47. D. W. Berreman, “Optics in smoothly varying anisotropic planar structures: application to liquid-crystal twist cells,” J. Opt. Soc. Am. 63, 1374–1380 (1973).
    [Crossref]
  48. Lin-Ching, S. Teitler, “4 × 4 matrix formalism for optics in stratified anisotropic media,” J. Opt. Soc. Am. A 1, 703–705 (1984).
    [Crossref]
  49. R. M. Azzam, N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, Amsterdam, 1977) (Russian translation, 1981), p. 394.
  50. A. Gerrard, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975).
  51. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap. 7.

1992 (2)

J. C. Liu, D. L. Jaggard, “Chiral layers on planar surfaces,” J. Electromagn. Waves Applic. 6, 705–721 (1992).

D. L. Jaggard, X. Sun, “Theory of chiral multilayers,” J. Opt. Soc. Am. A 9, 804–813 (1992).
[Crossref]

1991 (8)

D. L. Jaggard, J. C. Liu, X. Sun, “Spherical chiroshield,” Electron. Lett. 27, 77–79 (1991).
[Crossref]

A. I. Miteva, I. J. Lalov, “Reflection of electromagnetic waves from isotropic optically active media,” J. Condens. Matter 2, 529–538 (1991).
[Crossref]

I. J. Lalov, A. I. Miteva, “Optically active Fabry–Perot étalon,” J. Mod. Opt. 38, 395–411 (1991).
[Crossref]

H. Cory, I. Rosenhonse, “Electromagnetic wave reflection and transmission at a chiral–dielectric interface,” J. Mod. Opt. 38, 1229–1241 (1991).
[Crossref]

E. M. Georgieva, “Jones and Mueller matrices for specular reflection from a chiral medium: determination of the basic chiral parameters using the elements of the Mueller matrix and experimental configurations to measure the basic chiral parameters,” Appl. Opt. 30, 5081–5085 (1991).
[Crossref] [PubMed]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire scatterers in chiral media,” Opt. Lett. 16, 781–783 (1991).
[Crossref] [PubMed]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire antennas in chiral media,” Electron. Lett. 27, 243–244 (1991).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “The extended boundary condition method for scattering by a chiral scatterer in a chiral medium: formulation and analysis,” Optik 86, 155–161 (1991).

1990 (1)

1989 (5)

K. Eidner, G. Mayer, M. Schmidt, H. Schmidel, “Optics in stratified media—the use of optical eigenmodes of uniaxial crystals in the 4 × 4 matrix formalism,” Mol. Cryst. Liq. Cryst. 172, 191–200 (1989).

D. L. Jaggard, N. Engeta, “‘Chirosorb’ as an invisible medium,” Electron. Lett. 25, 173–174 (1989).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Scattering by periodic achiral–chiral interfaces,” J. Opt. Soc. Am. A 6, 1675–1681 (1989); errata: 7, 951 (1990).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Eigen-modes of a chiral sphere with a perfectly conducting coating,” J. Phys. D Appl. Phys. 22, 825–829 (1989).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “What happens to plane waves at the planar interfaces of mirror-conjugate chiral media,” J. Opt. Soc. Am. 6, 23–26 (1989).
[Crossref]

1988 (2)

1987 (1)

P. Allia, C. Oldano, L. Trossi, “Light propagation in anisotropic stratified media in the quasi adiabatic limit,” Mol. Cryst. Liq. Cryst. 143, 17–20 (1987).
[Crossref]

1986 (4)

I. J. Lalov, A. I. Miteva, “Reflection optical activity of uniaxial media,” J. Chem. Phys. 85, 5505–5511 (1986).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral–chiral interface,” IEEE Trans. Electromagn. Compat. 28, 90–95 (1986).
[Crossref]

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).
[Crossref]

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

1985 (4)

I. J. Lalov, “Effects of vibrational optical activity in the reflection spectra of crystals for the frequency regions of nondegenerate vibrations,” Phys. Rev. B 32, 6884–6891 (1985).
[Crossref]

M. P. Silverman, “Specular light scattering from a chiral medium: unambiguous test of gyrotropic constitutive relations,” Lett. Nuovo Cimento Soc. Ital. Fis. 43, 378–382 (1985).
[Crossref]

M. P. Silverman, “Test of gyrotropic constitutive relations by specular light reflection,” J. Opt. Soc. Am. A 2, (13), p. 99 (1985).

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Scattering and absorption characteristics of lossy dielectric chiral, nonspherical objects,” Appl. Opt. 24, 4146–4154 (1985).
[Crossref] [PubMed]

1984 (1)

1981 (1)

T. Takizawa, “Effects of optical activity on the reflectance of paratelurite TeO2,” J. Phys. Soc. Jpn. 50, 3054–3062 (1981).
[Crossref]

1979 (1)

D. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in a chiral medium,” Appl. Phys. 18, 211–216 (1979).
[Crossref]

1973 (1)

1972 (1)

1970 (2)

D. W. Berreman, T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid-crystal films,” Phys. Rev. Lett. 25, 577–581 (1970).
[Crossref]

S. Teitler, B. W. Henvis, “Reflection in stratified anisotropic media,” J. Opt. Soc. Am. 60, 830–834 (1970).
[Crossref]

1964 (2)

I. S. Zheludev, “Axial tensors of third rank and the physical phenomena they describe,” Sov. Phys. Crystallogr. 9, 501–505 (1964).

K. Aizu, “Ferroelectric transformation of tensorial properties in regular ferroelectrics,” Phys. Rev. A 133, 1350–1359 (1964).

1963 (2)

B. V. Bokut, B. A. Sotski, “The passage of light through an optically active absorbing plate,” Opt. Spektrosk. 14, 117–120 (1963).

F. I. Fedorov, B. V. Bokut, A. F. Konstantinova, “Optical activity of the planar classes of the middle groups,” Sov. Phys. Crystallogr. 7, 738–744 (1963).

1960 (1)

B. V. Bokut, F. I. Fedorov, “Reflection and refraction of light in optically isotropic active media,” Opt. Spectrosk. 9, 334–336 (1960).

1937 (1)

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

Agranovich, V. M.

V. M. Agranovich, V. Ginsburg, Crystal Optics with Spatial Dispersion and Exitons (Springer-Verlag, Berlin, 1984), Chap. 4.

Aizu, K.

K. Aizu, “Ferroelectric transformation of tensorial properties in regular ferroelectrics,” Phys. Rev. A 133, 1350–1359 (1964).

Allia, P.

P. Allia, C. Oldano, L. Trossi, “Light propagation in anisotropic stratified media in the quasi adiabatic limit,” Mol. Cryst. Liq. Cryst. 143, 17–20 (1987).
[Crossref]

Azzam, R. M.

R. M. Azzam, N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, Amsterdam, 1977) (Russian translation, 1981), p. 394.

Balakrishna, S.

S. Balakrishna, M. Krishnamurthi, B. Rao, Physics of the Solid State (Academic, London, 1969), p. 447.

Baron, L. D.

L. D. Baron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, New York, 1982).

Bashara, N. M.

R. M. Azzam, N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, Amsterdam, 1977) (Russian translation, 1981), p. 394.

Bassiri, S.

Berreman, D. W.

Bokut, B. V.

B. V. Bokut, B. A. Sotski, “The passage of light through an optically active absorbing plate,” Opt. Spektrosk. 14, 117–120 (1963).

F. I. Fedorov, B. V. Bokut, A. F. Konstantinova, “Optical activity of the planar classes of the middle groups,” Sov. Phys. Crystallogr. 7, 738–744 (1963).

B. V. Bokut, F. I. Fedorov, “Reflection and refraction of light in optically isotropic active media,” Opt. Spectrosk. 9, 334–336 (1960).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap. 7.

Burch, J. M.

A. Gerrard, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975).

Burkov, V. I.

V. A. Kizel, V. I. Burkov, Gyrotropy of Crystals (Nauka, Moscow, 1980).

Condon, E. U.

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

Cory, H.

H. Cory, I. Rosenhonse, “Electromagnetic wave reflection and transmission at a chiral–dielectric interface,” J. Mod. Opt. 38, 1229–1241 (1991).
[Crossref]

Cushman, G. M.

Ditchburn, R. W.

R. W. Ditchburn, Light (Blackie, London, 1963), p. 637.

Drude, P.

P. Drude, The Theory of Optics (Longmans, Green, New York, 1992), Chap. 6, Eqs. (7) and (8).

Eidner, K.

K. Eidner, G. Mayer, M. Schmidt, H. Schmidel, “Optics in stratified media—the use of optical eigenmodes of uniaxial crystals in the 4 × 4 matrix formalism,” Mol. Cryst. Liq. Cryst. 172, 191–200 (1989).

Engeta, N.

Fedorov, F. I.

F. I. Fedorov, B. V. Bokut, A. F. Konstantinova, “Optical activity of the planar classes of the middle groups,” Sov. Phys. Crystallogr. 7, 738–744 (1963).

B. V. Bokut, F. I. Fedorov, “Reflection and refraction of light in optically isotropic active media,” Opt. Spectrosk. 9, 334–336 (1960).

Fisher, B.

Georgieva, E. M.

Gerrard, A.

A. Gerrard, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975).

Ginsburg, V.

V. M. Agranovich, V. Ginsburg, Crystal Optics with Spatial Dispersion and Exitons (Springer-Verlag, Berlin, 1984), Chap. 4.

Grosjean, M.

L. Velluz, M. Legrand, M. Grosjean, Optical Circular Dichroism (Academic, London, 1965).

Grot, A.

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire scatterers in chiral media,” Opt. Lett. 16, 781–783 (1991).
[Crossref] [PubMed]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire antennas in chiral media,” Electron. Lett. 27, 243–244 (1991).
[Crossref]

Henvis, B. W.

Jaggard, D.

D. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in a chiral medium,” Appl. Phys. 18, 211–216 (1979).
[Crossref]

Jaggard, D. L.

J. C. Liu, D. L. Jaggard, “Chiral layers on planar surfaces,” J. Electromagn. Waves Applic. 6, 705–721 (1992).

D. L. Jaggard, X. Sun, “Theory of chiral multilayers,” J. Opt. Soc. Am. A 9, 804–813 (1992).
[Crossref]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire antennas in chiral media,” Electron. Lett. 27, 243–244 (1991).
[Crossref]

D. L. Jaggard, J. C. Liu, X. Sun, “Spherical chiroshield,” Electron. Lett. 27, 77–79 (1991).
[Crossref]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire scatterers in chiral media,” Opt. Lett. 16, 781–783 (1991).
[Crossref] [PubMed]

D. L. Jaggard, N. Engeta, “‘Chirosorb’ as an invisible medium,” Electron. Lett. 25, 173–174 (1989).
[Crossref]

Kauzmann, W.

W. Kauzmann, Quantum Chemistry (Academic, New York, 1957), p. 703.

Kizel, V. A.

V. A. Kizel, V. I. Burkov, Gyrotropy of Crystals (Nauka, Moscow, 1980).

Konstantinova, A. F.

F. I. Fedorov, B. V. Bokut, A. F. Konstantinova, “Optical activity of the planar classes of the middle groups,” Sov. Phys. Crystallogr. 7, 738–744 (1963).

Krishnamurthi, M.

S. Balakrishna, M. Krishnamurthi, B. Rao, Physics of the Solid State (Academic, London, 1969), p. 447.

Lakhtakia, A.

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “The extended boundary condition method for scattering by a chiral scatterer in a chiral medium: formulation and analysis,” Optik 86, 155–161 (1991).

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Reflection of plane waves at planar achiral–chiral interfaces: independence of the reflected polarization state from the incident polarization state,” J. Opt. Soc. Am. A 7, 1654–1660 (1990).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Scattering by periodic achiral–chiral interfaces,” J. Opt. Soc. Am. A 6, 1675–1681 (1989); errata: 7, 951 (1990).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Eigen-modes of a chiral sphere with a perfectly conducting coating,” J. Phys. D Appl. Phys. 22, 825–829 (1989).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “What happens to plane waves at the planar interfaces of mirror-conjugate chiral media,” J. Opt. Soc. Am. 6, 23–26 (1989).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral–chiral interface,” IEEE Trans. Electromagn. Compat. 28, 90–95 (1986).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Scattering and absorption characteristics of lossy dielectric chiral, nonspherical objects,” Appl. Opt. 24, 4146–4154 (1985).
[Crossref] [PubMed]

Lalov, I. J.

A. I. Miteva, I. J. Lalov, “Reflection of electromagnetic waves from isotropic optically active media,” J. Condens. Matter 2, 529–538 (1991).
[Crossref]

I. J. Lalov, A. I. Miteva, “Optically active Fabry–Perot étalon,” J. Mod. Opt. 38, 395–411 (1991).
[Crossref]

I. J. Lalov, A. I. Miteva, “Reflection optical activity of uniaxial media,” J. Chem. Phys. 85, 5505–5511 (1986).
[Crossref]

I. J. Lalov, “Effects of vibrational optical activity in the reflection spectra of crystals for the frequency regions of nondegenerate vibrations,” Phys. Rev. B 32, 6884–6891 (1985).
[Crossref]

Legrand, M.

L. Velluz, M. Legrand, M. Grosjean, Optical Circular Dichroism (Academic, London, 1965).

Lin-Ching,

Liu, J. C.

J. C. Liu, D. L. Jaggard, “Chiral layers on planar surfaces,” J. Electromagn. Waves Applic. 6, 705–721 (1992).

D. L. Jaggard, J. C. Liu, X. Sun, “Spherical chiroshield,” Electron. Lett. 27, 77–79 (1991).
[Crossref]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire antennas in chiral media,” Electron. Lett. 27, 243–244 (1991).
[Crossref]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire scatterers in chiral media,” Opt. Lett. 16, 781–783 (1991).
[Crossref] [PubMed]

Mayer, G.

K. Eidner, G. Mayer, M. Schmidt, H. Schmidel, “Optics in stratified media—the use of optical eigenmodes of uniaxial crystals in the 4 × 4 matrix formalism,” Mol. Cryst. Liq. Cryst. 172, 191–200 (1989).

Mickelson, A. R.

D. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in a chiral medium,” Appl. Phys. 18, 211–216 (1979).
[Crossref]

Miteva, A. I.

A. I. Miteva, I. J. Lalov, “Reflection of electromagnetic waves from isotropic optically active media,” J. Condens. Matter 2, 529–538 (1991).
[Crossref]

I. J. Lalov, A. I. Miteva, “Optically active Fabry–Perot étalon,” J. Mod. Opt. 38, 395–411 (1991).
[Crossref]

I. J. Lalov, A. I. Miteva, “Reflection optical activity of uniaxial media,” J. Chem. Phys. 85, 5505–5511 (1986).
[Crossref]

Oldano, C.

P. Allia, C. Oldano, L. Trossi, “Light propagation in anisotropic stratified media in the quasi adiabatic limit,” Mol. Cryst. Liq. Cryst. 143, 17–20 (1987).
[Crossref]

Papas, C. H.

Pelet, P.

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire scatterers in chiral media,” Opt. Lett. 16, 781–783 (1991).
[Crossref] [PubMed]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire antennas in chiral media,” Electron. Lett. 27, 243–244 (1991).
[Crossref]

Rao, B.

S. Balakrishna, M. Krishnamurthi, B. Rao, Physics of the Solid State (Academic, London, 1969), p. 447.

Ritchie, N.

Rosenhonse, I.

H. Cory, I. Rosenhonse, “Electromagnetic wave reflection and transmission at a chiral–dielectric interface,” J. Mod. Opt. 38, 1229–1241 (1991).
[Crossref]

Scheffer, T. J.

D. W. Berreman, T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid-crystal films,” Phys. Rev. Lett. 25, 577–581 (1970).
[Crossref]

Schmidel, H.

K. Eidner, G. Mayer, M. Schmidt, H. Schmidel, “Optics in stratified media—the use of optical eigenmodes of uniaxial crystals in the 4 × 4 matrix formalism,” Mol. Cryst. Liq. Cryst. 172, 191–200 (1989).

Schmidt, M.

K. Eidner, G. Mayer, M. Schmidt, H. Schmidel, “Optics in stratified media—the use of optical eigenmodes of uniaxial crystals in the 4 × 4 matrix formalism,” Mol. Cryst. Liq. Cryst. 172, 191–200 (1989).

Silverman, M. P.

M. P. Silverman, N. Ritchie, G. M. Cushman, B. Fisher, “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).
[Crossref]

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).
[Crossref]

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

M. P. Silverman, “Specular light scattering from a chiral medium: unambiguous test of gyrotropic constitutive relations,” Lett. Nuovo Cimento Soc. Ital. Fis. 43, 378–382 (1985).
[Crossref]

M. P. Silverman, “Test of gyrotropic constitutive relations by specular light reflection,” J. Opt. Soc. Am. A 2, (13), p. 99 (1985).

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]

Sotski, B. A.

B. V. Bokut, B. A. Sotski, “The passage of light through an optically active absorbing plate,” Opt. Spektrosk. 14, 117–120 (1963).

Sun, X.

D. L. Jaggard, X. Sun, “Theory of chiral multilayers,” J. Opt. Soc. Am. A 9, 804–813 (1992).
[Crossref]

D. L. Jaggard, J. C. Liu, X. Sun, “Spherical chiroshield,” Electron. Lett. 27, 77–79 (1991).
[Crossref]

Takizawa, T.

T. Takizawa, “Effects of optical activity on the reflectance of paratelurite TeO2,” J. Phys. Soc. Jpn. 50, 3054–3062 (1981).
[Crossref]

Teitler, S.

Trossi, L.

P. Allia, C. Oldano, L. Trossi, “Light propagation in anisotropic stratified media in the quasi adiabatic limit,” Mol. Cryst. Liq. Cryst. 143, 17–20 (1987).
[Crossref]

Varadan, V. K.

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “The extended boundary condition method for scattering by a chiral scatterer in a chiral medium: formulation and analysis,” Optik 86, 155–161 (1991).

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Reflection of plane waves at planar achiral–chiral interfaces: independence of the reflected polarization state from the incident polarization state,” J. Opt. Soc. Am. A 7, 1654–1660 (1990).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Scattering by periodic achiral–chiral interfaces,” J. Opt. Soc. Am. A 6, 1675–1681 (1989); errata: 7, 951 (1990).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Eigen-modes of a chiral sphere with a perfectly conducting coating,” J. Phys. D Appl. Phys. 22, 825–829 (1989).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “What happens to plane waves at the planar interfaces of mirror-conjugate chiral media,” J. Opt. Soc. Am. 6, 23–26 (1989).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral–chiral interface,” IEEE Trans. Electromagn. Compat. 28, 90–95 (1986).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Scattering and absorption characteristics of lossy dielectric chiral, nonspherical objects,” Appl. Opt. 24, 4146–4154 (1985).
[Crossref] [PubMed]

Varadan, V. V.

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “The extended boundary condition method for scattering by a chiral scatterer in a chiral medium: formulation and analysis,” Optik 86, 155–161 (1991).

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Reflection of plane waves at planar achiral–chiral interfaces: independence of the reflected polarization state from the incident polarization state,” J. Opt. Soc. Am. A 7, 1654–1660 (1990).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Scattering by periodic achiral–chiral interfaces,” J. Opt. Soc. Am. A 6, 1675–1681 (1989); errata: 7, 951 (1990).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Eigen-modes of a chiral sphere with a perfectly conducting coating,” J. Phys. D Appl. Phys. 22, 825–829 (1989).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “What happens to plane waves at the planar interfaces of mirror-conjugate chiral media,” J. Opt. Soc. Am. 6, 23–26 (1989).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral–chiral interface,” IEEE Trans. Electromagn. Compat. 28, 90–95 (1986).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Scattering and absorption characteristics of lossy dielectric chiral, nonspherical objects,” Appl. Opt. 24, 4146–4154 (1985).
[Crossref] [PubMed]

Velluz, L.

L. Velluz, M. Legrand, M. Grosjean, Optical Circular Dichroism (Academic, London, 1965).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap. 7.

Zheludev, I. S.

I. S. Zheludev, “Axial tensors of third rank and the physical phenomena they describe,” Sov. Phys. Crystallogr. 9, 501–505 (1964).

Am. J. Phys. (1)

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

Appl. Opt. (2)

Appl. Phys. (1)

D. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in a chiral medium,” Appl. Phys. 18, 211–216 (1979).
[Crossref]

Electron. Lett. (3)

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire antennas in chiral media,” Electron. Lett. 27, 243–244 (1991).
[Crossref]

D. L. Jaggard, N. Engeta, “‘Chirosorb’ as an invisible medium,” Electron. Lett. 25, 173–174 (1989).
[Crossref]

D. L. Jaggard, J. C. Liu, X. Sun, “Spherical chiroshield,” Electron. Lett. 27, 77–79 (1991).
[Crossref]

IEEE Trans. Electromagn. Compat. (1)

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral–chiral interface,” IEEE Trans. Electromagn. Compat. 28, 90–95 (1986).
[Crossref]

J. Chem. Phys. (1)

I. J. Lalov, A. I. Miteva, “Reflection optical activity of uniaxial media,” J. Chem. Phys. 85, 5505–5511 (1986).
[Crossref]

J. Condens. Matter (1)

A. I. Miteva, I. J. Lalov, “Reflection of electromagnetic waves from isotropic optically active media,” J. Condens. Matter 2, 529–538 (1991).
[Crossref]

J. Electromagn. Waves Applic. (1)

J. C. Liu, D. L. Jaggard, “Chiral layers on planar surfaces,” J. Electromagn. Waves Applic. 6, 705–721 (1992).

J. Mod. Opt. (2)

I. J. Lalov, A. I. Miteva, “Optically active Fabry–Perot étalon,” J. Mod. Opt. 38, 395–411 (1991).
[Crossref]

H. Cory, I. Rosenhonse, “Electromagnetic wave reflection and transmission at a chiral–dielectric interface,” J. Mod. Opt. 38, 1229–1241 (1991).
[Crossref]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (8)

Lin-Ching, S. Teitler, “4 × 4 matrix formalism for optics in stratified anisotropic media,” J. Opt. Soc. Am. A 1, 703–705 (1984).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Reflection of plane waves at planar achiral–chiral interfaces: independence of the reflected polarization state from the incident polarization state,” J. Opt. Soc. Am. A 7, 1654–1660 (1990).
[Crossref]

S. Bassiri, C. H. Papas, N. Engeta, “Electromagnetic wave propagation through a dielectric chiral interface and through a chiral slab,” J. Opt. Soc. Am. A 5, 1450–1459 (1988).
[Crossref]

M. P. Silverman, “Test of gyrotropic constitutive relations by specular light reflection,” J. Opt. Soc. Am. A 2, (13), p. 99 (1985).

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).
[Crossref]

M. P. Silverman, N. Ritchie, G. M. Cushman, B. Fisher, “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).
[Crossref]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Scattering by periodic achiral–chiral interfaces,” J. Opt. Soc. Am. A 6, 1675–1681 (1989); errata: 7, 951 (1990).
[Crossref]

D. L. Jaggard, X. Sun, “Theory of chiral multilayers,” J. Opt. Soc. Am. A 9, 804–813 (1992).
[Crossref]

J. Phys. D Appl. Phys. (1)

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Eigen-modes of a chiral sphere with a perfectly conducting coating,” J. Phys. D Appl. Phys. 22, 825–829 (1989).
[Crossref]

J. Phys. Soc. Jpn. (1)

T. Takizawa, “Effects of optical activity on the reflectance of paratelurite TeO2,” J. Phys. Soc. Jpn. 50, 3054–3062 (1981).
[Crossref]

Lett. Nuovo Cimento Soc. Ital. Fis. (1)

M. P. Silverman, “Specular light scattering from a chiral medium: unambiguous test of gyrotropic constitutive relations,” Lett. Nuovo Cimento Soc. Ital. Fis. 43, 378–382 (1985).
[Crossref]

Mol. Cryst. Liq. Cryst. (2)

P. Allia, C. Oldano, L. Trossi, “Light propagation in anisotropic stratified media in the quasi adiabatic limit,” Mol. Cryst. Liq. Cryst. 143, 17–20 (1987).
[Crossref]

K. Eidner, G. Mayer, M. Schmidt, H. Schmidel, “Optics in stratified media—the use of optical eigenmodes of uniaxial crystals in the 4 × 4 matrix formalism,” Mol. Cryst. Liq. Cryst. 172, 191–200 (1989).

Opt. Lett. (1)

Opt. Spectrosk. (1)

B. V. Bokut, F. I. Fedorov, “Reflection and refraction of light in optically isotropic active media,” Opt. Spectrosk. 9, 334–336 (1960).

Opt. Spektrosk. (1)

B. V. Bokut, B. A. Sotski, “The passage of light through an optically active absorbing plate,” Opt. Spektrosk. 14, 117–120 (1963).

Optik (1)

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “The extended boundary condition method for scattering by a chiral scatterer in a chiral medium: formulation and analysis,” Optik 86, 155–161 (1991).

Phys. Rev. A (1)

K. Aizu, “Ferroelectric transformation of tensorial properties in regular ferroelectrics,” Phys. Rev. A 133, 1350–1359 (1964).

Phys. Rev. B (1)

I. J. Lalov, “Effects of vibrational optical activity in the reflection spectra of crystals for the frequency regions of nondegenerate vibrations,” Phys. Rev. B 32, 6884–6891 (1985).
[Crossref]

Phys. Rev. Lett. (1)

D. W. Berreman, T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid-crystal films,” Phys. Rev. Lett. 25, 577–581 (1970).
[Crossref]

Rev. Mod. Phys. (1)

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

Sov. Phys. Crystallogr. (2)

F. I. Fedorov, B. V. Bokut, A. F. Konstantinova, “Optical activity of the planar classes of the middle groups,” Sov. Phys. Crystallogr. 7, 738–744 (1963).

I. S. Zheludev, “Axial tensors of third rank and the physical phenomena they describe,” Sov. Phys. Crystallogr. 9, 501–505 (1964).

Other (11)

R. M. Azzam, N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, Amsterdam, 1977) (Russian translation, 1981), p. 394.

A. Gerrard, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap. 7.

S. Balakrishna, M. Krishnamurthi, B. Rao, Physics of the Solid State (Academic, London, 1969), p. 447.

V. A. Kizel, V. I. Burkov, Gyrotropy of Crystals (Nauka, Moscow, 1980).

L. D. Baron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, New York, 1982).

L. Velluz, M. Legrand, M. Grosjean, Optical Circular Dichroism (Academic, London, 1965).

R. W. Ditchburn, Light (Blackie, London, 1963), p. 637.

P. Drude, The Theory of Optics (Longmans, Green, New York, 1992), Chap. 6, Eqs. (7) and (8).

W. Kauzmann, Quantum Chemistry (Academic, New York, 1957), p. 703.

V. M. Agranovich, V. Ginsburg, Crystal Optics with Spatial Dispersion and Exitons (Springer-Verlag, Berlin, 1984), Chap. 4.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of polarized light reflected from an isotropic, optically active medium, showing the coordinate system for the surface and the directions of the electric fields for incident and reflected light. Generally, two elliptical polarizations are transmitted in an optically active medium with different angles of refraction and wave vectors k+ and k.

Fig. 2
Fig. 2

Coefficient of reflection rpp versus angle of incidence θ1 for Bi12SiO20 (g = 10−5, n = 2.583, λ = 550 nm).

Fig. 3
Fig. 3

Coefficient of reflection (rpp)2 versus angle of incidence θ1 for Bi12SiO20 (g = 10−5, n = 2.583, λ = 550 nm).

Fig. 4
Fig. 4

Coefficient of reflection rss versus angle of incidence θ1 for Bi12SiO20 (g = 10−5, n = 2.583, λ = 550 nm).

Fig. 5
Fig. 5

Coefficient of reflection (rss)2 versus angle of incidence θ1 for Bi12SiO20 (g = 10−5, n = 2.583, λ = 550 nm).

Fig. 6
Fig. 6

Coefficient of reflection (rps)2 = (rsp)2 versus angle of incidence θ1 for Bi12SiO20 (g = 10−5, n = 2.583, λ = 550 nm).

Fig. 7
Fig. 7

Coefficients of reflection rps and rsp = −rps versus angle of incidence θ1 for Bi12SiO20 (g = 10−5, n = 2.583, λ = 550 nm).

Equations (67)

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rot E = - B / t ,
rot H = D / t ,
D = 0 E + P ,             B = μ 0 ( H + M ) ,
D = E - g ¯ H t ,
B = μ H + g ¯ E t ,
rot H = E t + g ¯ μ t rot E = E t + g ¯ μ t ( - B t ) ,
- rot H = - i ω E + ( + i ω g ¯ ) ( i ω H ) .
rot E = - B t + g ¯ t rot H = - μ H t + g ¯ t ( D t ) ,
- rot E = i ω μ H + ( - i ω g ¯ ) ( i ω E ) .
D = ( E + β × E ) ,
B = μ ( H + β × H ) ,
[ 0 0 0 0 - / z / y 0 0 0 / z 0 - / x 0 0 0 - / y / x 0 0 / z - / y 0 0 0 - / z 0 / x 0 0 0 / y - / x 0 0 0 0 ] × [ E x E y E z H x H y H z ] = i ω [ D x D y D z B x B y B z ] ,
R G = i ω C .
R = [ 0 rot - rot 0 ] .
C = M G ,
M = [ ρ ρ μ ] ,
ρ = + i ω g ¯ = + i g ,             ρ = - i ω g ¯ = - i g ,
R G = i ω M G .
R Γ = i ω M Γ ,
/ x = - i ξ ω / c .
[ 0 0 0 0 - / z 0 0 0 0 / z 0 i ω ξ / c 0 0 0 0 - i ω ξ / c 0 0 / z 0 0 0 0 - / z 0 - i ω ξ / c 0 0 0 0 - i ω ξ / c 0 0 0 0 ] × [ Γ 1 Γ 2 Γ 3 Γ 4 Γ 5 Γ 6 ] = i ω [ 0 0 i g 0 0 0 0 0 i g 0 0 0 0 0 i g - i g 0 0 1 0 0 0 - i g 0 0 1 0 0 0 - i g 0 0 1 ] [ Γ 1 Γ 2 Γ 3 Γ 4 Γ 5 Γ 6 ] .
Γ 1 = E x , Γ 2 = E y , Γ 3 = E z , Γ 4 = H x , Γ 5 = H y , Γ 6 = H z .
Δ = [ 0 1 - n 2 2 sin 2 θ 2 n 2 2 - g 2 - i g ( 1 + n 2 2 sin 2 θ 2 n 2 2 - g 2 ) 0 n 2 2 0 0 - i g i g 0 0 1 0 i g ( 1 + n 2 2 sin 2 θ 2 n 2 2 - g 2 ) n 2 2 ( 1 - n 2 2 sin 2 θ 2 n 2 2 - g 2 ) 0 ] .
z [ E x H y E y - H x ] = - i ω Δ [ E x H y E y - H x ] ,
ψ / z = - i ω Δ ψ ,
ψ ( z ) = [ E x H y E y - H x ] .
ζ = ± ( n 2 2 cos 2 θ 2 + g 2 ± 2 g n 2 ) 1 / 2 .
δ = n 2 2 cos 2 θ 2 + g 2 - 2 g n 2 ,
σ = n 2 2 cos 2 θ 2 + g 2 + 2 g n 2 .
ζ δ = δ 1 / 2 ,             ζ σ = σ 1 / 2 .
r 1 = ψ δ 1 = E x = 1 , r 2 = ψ δ 2 = H y = n 2 ( n 2 - g ) / δ , r 3 = ψ δ 3 = E y = - i ( n 2 - g ) / δ , r 4 = ψ δ 4 = - H x = - i n 2 ;
r 1 = ψ σ 1 = E x = 1 , r 2 = ψ σ 2 = H y = n 2 ( n 2 + g ) / σ , r 3 = ψ σ 3 = E y = i ( n 2 + g ) / σ , r 4 = ψ σ 4 = - H x = i n 2 .
ψ t = k 1 ψ δ + k 2 ψ σ ,
ψ i + ψ r = ψ t .
ψ i = E p , i [ cos θ 1 n 1 0 0 ] + E s , i [ 0 0 1 n 1 cos θ 1 ] .
ψ r = E p , r [ - cos θ 1 n 1 0 0 ] + E s , r [ 0 0 1 - n 1 cos θ 1 ] .
[ cos θ 1 0 - cos θ 1 0 ψ δ 1 ψ σ 1 0 1 0 1 ψ δ 3 ψ σ 3 n 1 0 n 1 0 ψ δ 2 ψ σ 2 0 n 1 cos θ 1 0 - n 1 cos θ 1 ψ δ 4 ψ σ 4 ] × [ E p , i E s , i E p , r E s , r - k 1 - k 2 ] = 0.
[ M 1 M 2 M 3 M 4 M 5 M 6 ] [ E i E r k ] = 0 ,
E i = [ E p , i E s , i ] ,             E r = [ E p , r E s , r ] ,             k = [ - k 1 - k 2 ] .
M 1 E i + M 2 E r + M 3 k = 0 , M 4 E i + M 5 E r + M 6 k = 0 ,
[ M 3 M 6 - 1 M 5 - M 2 ] - 1 [ M 1 - M 3 M 6 - 1 M 4 ] E i = E r .
r = [ M 3 M 6 - 1 M 5 - M 2 ] - 1 [ M 1 - M 3 M 6 - 1 M 4 ] .
r p p = 2 δ σ n 1 n 2 + [ ( n 2 δ + n 2 σ + g δ - g σ ) ( n 1 2 - n 2 2 ) - 2 n 1 n 2 cos θ 1 ( n 2 2 - g 2 ) ] cos θ 1 2 δ σ n 1 n 2 + [ ( n 2 δ + n 2 σ + g δ - g σ ) ( n 1 2 + n 2 2 ) + 2 n 1 n 2 cos θ 1 ( n 2 2 - g 2 ) ] cos θ 1 ,
r p s = i 2 n 1 n 2 [ ( δ - σ ) ( n 2 2 + g 2 ) + 2 g n 2 ( δ + σ ) ] cos θ 1 2 δ σ n 1 n 2 + [ ( n 2 δ + n 2 σ + g δ - g σ ) ( n 1 2 + n 2 2 ) + 2 n 1 n 2 cos θ 1 ( n 2 2 - g 2 ) ] cos θ 1 ,
r s p = - i 2 n 1 n 2 [ ( δ - σ ) ( n 2 2 + g 2 ) + 2 g n 2 ( δ + σ ) ] cos θ 1 2 δ σ n 1 n 2 [ ( n 2 δ + n 2 σ + g δ - g σ ) ( n 1 2 + n 2 2 ) + 2 n 1 n 2 cos θ 1 ( n 2 2 - g 2 ) ] cos θ 1 ,
r s s = - 2 δ σ n 1 n 2 + [ ( n 2 δ + n 2 σ + g δ - g σ ) ( n 1 2 - n 2 2 ) + 2 n 1 n 2 cos θ 1 ( n 2 2 - g 2 ) ] cos θ 1 2 δ σ n 1 n 2 + [ ( n 2 δ + n 2 σ + g δ - g σ ) ( n 1 2 + n 2 2 ) + 2 n 1 n 2 cos θ 1 ( n 2 2 - g 2 ) ] cos θ 1 .
n ± 2 = ξ 2 + ζ 2 = n 1 2 sin 2 θ 1 + n 2 2 cos 2 θ 2 + g 2 ± 2 g n 2
n ± = ( n 2 2 + g 2 ± 2 g n 2 ) 1 / 2 = ± ( n ± g ) ,
Δ n = n + - n - = 2 g .
E z = - i n 2 g sin θ 2 n 2 2 - g 2 E y - n 2 sin θ 2 n 2 2 - g 2 H y = - n 2 sin θ 2 δ , H z = n 2 3 sin θ 2 n 2 2 - g 2 E y - i g n 2 sin θ 2 n 2 2 - g 2 H y = - i n 2 2 sin θ 2 δ .
E x = 1 , H x = i n 2 , E y = - i n 2 - g δ , H y = n 2 ( n 2 - g ) δ , E z = - n 2 sin θ 2 δ , H z = - i n 2 2 sin θ 2 δ .
E z = - i n 2 g sin θ 2 n 2 2 - g 2 E y - n 2 2 sin θ 2 n 2 2 - g 2 H y = - n 2 sin θ 2 σ , H z = n 2 3 sin θ 2 n 2 2 - g 2 E y - i n 2 g sin θ 2 n 2 2 - g 2 H y = + i n 2 2 sin θ 2 σ .
E x = 1 , H x = - i n 2 , E y = i n 2 + g σ , H y = n 2 ( n 2 + g ) σ , E z = - n 2 sin θ 2 σ , H z = + i n 2 2 sin θ 2 σ .
tan θ ± = ξ ζ = n 2 sin θ 2 ( n 2 2 cos 2 θ 2 + g 2 ± 2 g n 2 ) 1 / 2 = tan θ 2 1 + ( g 2 ± 2 g n 2 ) / ( n 2 2 cos 2 θ 2 ) .
S x ~ n 2 2 ( n 2 - g ) sin θ 2 δ , S y ~ 0 , S z ~ n 2 ( n 2 - g ) δ 1 / 2 ,
S x ~ n 2 2 ( n 2 + g ) sin θ 2 σ , S y ~ 0 , S z ~ n 2 ( n 2 + g ) σ 1 / 2 .
Δ = [ 0 cos 2 θ 2 - i g sin 2 θ 2 0 n 2 2 0 0 - i g 0 0 0 1 0 i g n 2 2 0 ] .
ζ = ± ( 2 n 0 2 cos 2 θ 2 + g 2 ± 4 n 0 2 g 2 + g 4 2 ) 1 / 2 ,
δ = 1 2 ( 2 n 0 2 cos 2 θ 2 + g 2 - 4 g 2 n 0 2 + g 4 ) ,
σ = 1 2 ( 2 n 0 2 cos 2 θ 2 + g 2 + 4 g 2 n 0 2 + g 4 ) ,
ζ δ = δ 1 / 2 ,             ζ σ = σ 1 / 2 ,
r 1 = ψ δ 1 = - δ 1 / 2 ( δ - g 2 - n 0 2 cos 2 θ 2 ) , r 2 = ψ δ 2 = n 0 2 ( δ - n 0 2 cos 2 θ 2 ) , r 3 = ψ δ 3 = - i n 0 2 g , r 4 = ψ δ 4 = - i δ 1 / 2 n 0 2 g , r 1 = ψ σ 1 = E x = - σ 1 / 2 ( σ - g 2 - n 0 2 cos 2 θ 2 ) , r 2 = ψ σ 2 = H y = - n 0 2 ( σ - n 0 2 cos 2 θ 2 ) , r 3 = ψ σ 3 = E y = i n 0 2 g , r 4 = - H x = - i σ 1 / 2 n 0 2 g .
r s s = n 1 a { [ n 2 2 ( cos 2 θ 1 - cos 2 θ 2 ) - a n 1 cos θ 1 - b ] b + n 2 4 cos 2 θ 1 cos 2 θ 2 } + n 2 2 cos θ 1 b c + f - n 1 2 cos θ 1 ( d n 2 2 cos 2 θ 2 - e ) n 1 a { [ n 2 2 ( cos 2 θ 1 + cos 2 θ 2 ) + a n 1 cos θ 1 + b ] b + n 2 4 cos 2 θ 1 cos 2 θ 2 } + n 2 2 cos θ 1 b c + f + n 1 2 cos θ 1 ( d n 2 2 cos 2 θ 2 - e ) ,
r p p = n 1 a { [ n 2 2 ( cos 2 θ 1 - cos 2 θ 2 ) + a n 1 cos θ 1 - b ] b + n 2 4 cos 2 θ 2 } - n 2 2 cos θ 1 b c - f + n 1 2 cos θ 1 ( d n 2 2 cos 2 θ 2 - e ) n 1 a { [ n 2 2 ( cos 2 θ 1 + cos 2 θ 2 ) + a n 1 cos θ 1 + b ] b + n 2 4 cos 2 θ 1 cos 2 θ 2 } + n 2 2 cos θ 1 b c + f + n 1 2 cos θ 1 ( d n 2 2 cos 2 θ 2 - e ) ,
r s p = i 2 g n 1 n 2 2 cos θ 1 ( b + n 2 2 cos 2 θ 2 ) n 1 a { [ n 2 2 ( cos 2 θ 1 + cos 2 θ 2 ) + a n 1 cos θ 1 + b ] b + n 2 4 cos 2 θ 1 cos θ 2 } + n 2 2 cos θ 1 b c + f + n 1 2 cos θ 1 ( d n 2 2 cos 2 θ 2 - e ) ,
r p s = i 2 n 1 cos θ 1 ( b + n 2 2 cos 2 θ 2 ) ( d n 2 2 cos 2 θ 2 - e ) g { [ n 1 a b + n 2 2 cos θ 1 ( b + n 2 2 cos 2 θ 2 ) ] [ n 1 cos θ 1 a + b + n 2 2 cos 2 θ 2 ] + n 1 2 cos θ 1 ( d n 2 2 cos 2 θ 2 - b 2 - b g 2 ) } ,
a = σ 1 / 2 + δ 1 / 2 , b = σ 1 / 2 δ 1 / 2 , c = σ 1 / 2 δ 1 / 2 + 2 n 2 2 cos 2 θ 2 , d = σ + δ - g 2 - n 2 2 cos 2 θ 2 , e = σ δ + g 2 σ 1 / 2 δ 1 / 2 , f = n 2 6 cos θ 1 cos 4 θ 2 .

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