Abstract

The reflection from and transmission through a semi-infinite chiral medium are analyzed by obtaining the Fresnel equations in terms of parallel- and perpendicular-polarized modes, and a comparison is made with results reported previously. The chiral medium is described electromagnetically by the constitutive relations D = E + iγB and H = iγE + (1/μ)B. The constants , μ, and γ are real and have values that are fixed by the size, the shape, and the spatial distribution of the elements that collectively compose the medium. The conditions are obtained for the total internal reflection of the incident wave from the interface and for the existence of the Brewster angle. The effects of the chirality on the polarization and the intensity of the reflected wave from the chiral half-space are discussed and illustrated by using the Stokes parameters. The propagation of electromagnetic waves through an infinite slab of chiral medium is formulated for oblique incidence and solved analytically for the case of normal incidence.

© 1988 Optical Society of America

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References

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  1. D. F. Arago, “Sur une modification remarquable qu’ éprouvent les rayons lumineux dans leur passage à travers certains corps diaphanes, et sur quelques autres nouveaux phénomènes d’optique,” Mem. Inst. 1, 93–134 (1811).
  2. J. B. Biot, “Mémoire sur un nouveau genre d’oscillations que les molécules de la lumière éprouvent, en traversant certains cristaux,” Mem. Inst. 1, 1–372 (1812).
  3. J. B. Biot, “Sur les rotations que certaines substances impriment aux axes de polarisation des rayons lumineux,” Mem. Acad. Sci. 2, 41–136 (1817).
  4. J. B. Biot, “Mémoire sur la polarisation circulaire et sur ses applications à la chimie organique,” Mem. Acad. Sci. 13, 39–175 (1835).
  5. J. B. Biot, “Phénomènes de polarisation successive, observés dans des fluides homogènes,” Bull. Soc. Philomath.190–192 (1815).
  6. A. Fresnel, “Mémoire sur la double réfraction que les rayons lumineux éprouvent en traversant les aiguilles de cristal de roche suivant des directions parallèles à l’axe,” Oeuvres 1, 731–751 (1822).
  7. L. Pasteur, “Sur les relations qui peuvent exister entre la forme cristalline, la composition chimique et le sens de la polarisation rotatoire,” Ann. Chim. Phys. 24, 442–459 (1848).
  8. K. F. Lindman, “Über eine durch ein isotropes System von Spiralförmigen Resonatoren erzeugte Rotationspolarisation der elektromagnetischen Wellen,” Ann. Phys. 63, 621–644 (1920).
    [CrossRef]
  9. K. F. Lindman, “Über die durch ein aktives Raumgitter erzeugte Rotationspolarisation der elektromagnetischen Wellen,” Ann. Phys. 69, 270–284 (1922).
    [CrossRef]
  10. W. H. Pickering, California Institute of Technology, Pasadena, California 91125 (personal communication, 1945).
  11. T. M. Lowry, Optical Rotatory Power (Dover, New York, 1964).
  12. M. Born, “Über die natürliche optische Aktivität von Flüssigkeiten und Gasen,” Phys. Z. 16, 251–258 (1915).
  13. C. W. Oseen, “Über die Wechsëlwirkung zwischen zwei elektrischen Dipolen und über in Kristallen und Flüssigkeiten,” Ann. Phys. 48, 1–56 (1915).
    [CrossRef]
  14. F. Gray, The optical activity of liquids and gases,” Phys. Rev. 7, 472–488 (1916).
    [CrossRef]
  15. W. Kuhn, “Quantitative Verhältnisse und Beziehungen bei der natürlichen optischen Aktivität,” Z. Phys. Chem. B 4, 14–36 (1929).
  16. E. U. Condon, W. Altar, H. Eyring, “One-electron rotatory power,” J. Chem. Phys. 5, 753–775 (1937).
    [CrossRef]
  17. E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
    [CrossRef]
  18. C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
    [CrossRef]
  19. C. F. Bohren, “Scattering of electromagnetic waves by an optically active cylinder,” J. Colloid Interface Sci. 66, 105–109 (1975).
    [CrossRef]
  20. B. V. Bokut, F. I. Federov, “Reflection and refraction of light in optically isotropic active media,” Opt. Spektrosk. 9, 334–336 (1960).
  21. J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975).
  22. D. L. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1979).
    [CrossRef]
  23. N. Engheta, A. R. Mickelson, “Transition radiation caused by a chiral plate,” IEEE Trans. Antennas Propag. AP-30, 1213–1216 (1982).
    [CrossRef]
  24. 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]
  25. M. P. Silverman, “Specular light scattering from a chiral medium: unambiguous test of gyrotropic constitutive relations,” Lett. Nuovo Cimento 43, 378–382 (1985).
    [CrossRef]
  26. 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. EM-28, 90–95 (1986).
    [CrossRef]
  27. 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]
  28. M. P. Silverman, R. B. Sohn, “Effects of circular birefringence on light propagation and reflection,” Am. J. Phys. 54, 69–76 (1986).
    [CrossRef]
  29. S. Bassiri, N. Engheta, C. H. Papas, “Dyadic Green’s function and dipole radiation in chiral media,” Alta Freq. 2, 83–88 (1986).
  30. S. Bassiri, “Electromagnetic wave propagation and radiation in chiral media,” doctoral dissertation (Division of Engineering and Applied Science, California Instititute of Technology, Pasadena, Calif., 1987).
  31. A. Sommerfeld, Optics (Academic, New York, 1954).
  32. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).
  33. C. H. Papas, Theory of Electromagnetic Wave Propagation (McGraw-Hill, New York, 1965).
  34. H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, New York, 1983).
  35. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

1986 (4)

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. EM-28, 90–95 (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]

S. Bassiri, N. Engheta, C. H. Papas, “Dyadic Green’s function and dipole radiation in chiral media,” Alta Freq. 2, 83–88 (1986).

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]

1985 (2)

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]

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

1982 (1)

N. Engheta, A. R. Mickelson, “Transition radiation caused by a chiral plate,” IEEE Trans. Antennas Propag. AP-30, 1213–1216 (1982).
[CrossRef]

1979 (1)

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

1975 (1)

C. F. Bohren, “Scattering of electromagnetic waves by an optically active cylinder,” J. Colloid Interface Sci. 66, 105–109 (1975).
[CrossRef]

1974 (1)

C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
[CrossRef]

1960 (1)

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

1937 (2)

E. U. Condon, W. Altar, H. Eyring, “One-electron rotatory power,” J. Chem. Phys. 5, 753–775 (1937).
[CrossRef]

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

1929 (1)

W. Kuhn, “Quantitative Verhältnisse und Beziehungen bei der natürlichen optischen Aktivität,” Z. Phys. Chem. B 4, 14–36 (1929).

1922 (1)

K. F. Lindman, “Über die durch ein aktives Raumgitter erzeugte Rotationspolarisation der elektromagnetischen Wellen,” Ann. Phys. 69, 270–284 (1922).
[CrossRef]

1920 (1)

K. F. Lindman, “Über eine durch ein isotropes System von Spiralförmigen Resonatoren erzeugte Rotationspolarisation der elektromagnetischen Wellen,” Ann. Phys. 63, 621–644 (1920).
[CrossRef]

1916 (1)

F. Gray, The optical activity of liquids and gases,” Phys. Rev. 7, 472–488 (1916).
[CrossRef]

1915 (2)

M. Born, “Über die natürliche optische Aktivität von Flüssigkeiten und Gasen,” Phys. Z. 16, 251–258 (1915).

C. W. Oseen, “Über die Wechsëlwirkung zwischen zwei elektrischen Dipolen und über in Kristallen und Flüssigkeiten,” Ann. Phys. 48, 1–56 (1915).
[CrossRef]

1848 (1)

L. Pasteur, “Sur les relations qui peuvent exister entre la forme cristalline, la composition chimique et le sens de la polarisation rotatoire,” Ann. Chim. Phys. 24, 442–459 (1848).

1835 (1)

J. B. Biot, “Mémoire sur la polarisation circulaire et sur ses applications à la chimie organique,” Mem. Acad. Sci. 13, 39–175 (1835).

1822 (1)

A. Fresnel, “Mémoire sur la double réfraction que les rayons lumineux éprouvent en traversant les aiguilles de cristal de roche suivant des directions parallèles à l’axe,” Oeuvres 1, 731–751 (1822).

1817 (1)

J. B. Biot, “Sur les rotations que certaines substances impriment aux axes de polarisation des rayons lumineux,” Mem. Acad. Sci. 2, 41–136 (1817).

1815 (1)

J. B. Biot, “Phénomènes de polarisation successive, observés dans des fluides homogènes,” Bull. Soc. Philomath.190–192 (1815).

1812 (1)

J. B. Biot, “Mémoire sur un nouveau genre d’oscillations que les molécules de la lumière éprouvent, en traversant certains cristaux,” Mem. Inst. 1, 1–372 (1812).

1811 (1)

D. F. Arago, “Sur une modification remarquable qu’ éprouvent les rayons lumineux dans leur passage à travers certains corps diaphanes, et sur quelques autres nouveaux phénomènes d’optique,” Mem. Inst. 1, 93–134 (1811).

Altar, W.

E. U. Condon, W. Altar, H. Eyring, “One-electron rotatory power,” J. Chem. Phys. 5, 753–775 (1937).
[CrossRef]

Arago, D. F.

D. F. Arago, “Sur une modification remarquable qu’ éprouvent les rayons lumineux dans leur passage à travers certains corps diaphanes, et sur quelques autres nouveaux phénomènes d’optique,” Mem. Inst. 1, 93–134 (1811).

Bassiri, S.

S. Bassiri, N. Engheta, C. H. Papas, “Dyadic Green’s function and dipole radiation in chiral media,” Alta Freq. 2, 83–88 (1986).

S. Bassiri, “Electromagnetic wave propagation and radiation in chiral media,” doctoral dissertation (Division of Engineering and Applied Science, California Instititute of Technology, Pasadena, Calif., 1987).

Biot, J. B.

J. B. Biot, “Mémoire sur la polarisation circulaire et sur ses applications à la chimie organique,” Mem. Acad. Sci. 13, 39–175 (1835).

J. B. Biot, “Sur les rotations que certaines substances impriment aux axes de polarisation des rayons lumineux,” Mem. Acad. Sci. 2, 41–136 (1817).

J. B. Biot, “Phénomènes de polarisation successive, observés dans des fluides homogènes,” Bull. Soc. Philomath.190–192 (1815).

J. B. Biot, “Mémoire sur un nouveau genre d’oscillations que les molécules de la lumière éprouvent, en traversant certains cristaux,” Mem. Inst. 1, 1–372 (1812).

Bohren, C. F.

C. F. Bohren, “Scattering of electromagnetic waves by an optically active cylinder,” J. Colloid Interface Sci. 66, 105–109 (1975).
[CrossRef]

C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
[CrossRef]

Bokut, B. V.

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

Born, M.

M. Born, “Über die natürliche optische Aktivität von Flüssigkeiten und Gasen,” Phys. Z. 16, 251–258 (1915).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Chen, H. C.

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

Condon, E. U.

E. U. Condon, W. Altar, H. Eyring, “One-electron rotatory power,” J. Chem. Phys. 5, 753–775 (1937).
[CrossRef]

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

Engheta, N.

S. Bassiri, N. Engheta, C. H. Papas, “Dyadic Green’s function and dipole radiation in chiral media,” Alta Freq. 2, 83–88 (1986).

N. Engheta, A. R. Mickelson, “Transition radiation caused by a chiral plate,” IEEE Trans. Antennas Propag. AP-30, 1213–1216 (1982).
[CrossRef]

Eyring, H.

E. U. Condon, W. Altar, H. Eyring, “One-electron rotatory power,” J. Chem. Phys. 5, 753–775 (1937).
[CrossRef]

Federov, F. I.

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

Fresnel, A.

A. Fresnel, “Mémoire sur la double réfraction que les rayons lumineux éprouvent en traversant les aiguilles de cristal de roche suivant des directions parallèles à l’axe,” Oeuvres 1, 731–751 (1822).

Gray, F.

F. Gray, The optical activity of liquids and gases,” Phys. Rev. 7, 472–488 (1916).
[CrossRef]

Jaggard, D. L.

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

Kong, J. A.

J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975).

Kuhn, W.

W. Kuhn, “Quantitative Verhältnisse und Beziehungen bei der natürlichen optischen Aktivität,” Z. Phys. Chem. B 4, 14–36 (1929).

Lakhtakia, A.

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. EM-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]

Lindman, K. F.

K. F. Lindman, “Über die durch ein aktives Raumgitter erzeugte Rotationspolarisation der elektromagnetischen Wellen,” Ann. Phys. 69, 270–284 (1922).
[CrossRef]

K. F. Lindman, “Über eine durch ein isotropes System von Spiralförmigen Resonatoren erzeugte Rotationspolarisation der elektromagnetischen Wellen,” Ann. Phys. 63, 621–644 (1920).
[CrossRef]

Lowry, T. M.

T. M. Lowry, Optical Rotatory Power (Dover, New York, 1964).

Mickelson, A. R.

N. Engheta, A. R. Mickelson, “Transition radiation caused by a chiral plate,” IEEE Trans. Antennas Propag. AP-30, 1213–1216 (1982).
[CrossRef]

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

Oseen, C. W.

C. W. Oseen, “Über die Wechsëlwirkung zwischen zwei elektrischen Dipolen und über in Kristallen und Flüssigkeiten,” Ann. Phys. 48, 1–56 (1915).
[CrossRef]

Papas, C. H.

S. Bassiri, N. Engheta, C. H. Papas, “Dyadic Green’s function and dipole radiation in chiral media,” Alta Freq. 2, 83–88 (1986).

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

C. H. Papas, Theory of Electromagnetic Wave Propagation (McGraw-Hill, New York, 1965).

Pasteur, L.

L. Pasteur, “Sur les relations qui peuvent exister entre la forme cristalline, la composition chimique et le sens de la polarisation rotatoire,” Ann. Chim. Phys. 24, 442–459 (1848).

Pickering, W. H.

W. H. Pickering, California Institute of Technology, Pasadena, California 91125 (personal communication, 1945).

Silverman, M. P.

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 43, 378–382 (1985).
[CrossRef]

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 (Academic, New York, 1954).

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Varadan, V. K.

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. EM-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, “A parametric study of microwave reflection characteristics of a planar achiral–chiral interface,” IEEE Trans. Electromagn. Compat. EM-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]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Alta Freq. (1)

S. Bassiri, N. Engheta, C. H. Papas, “Dyadic Green’s function and dipole radiation in chiral media,” Alta Freq. 2, 83–88 (1986).

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]

Ann. Chim. Phys. (1)

L. Pasteur, “Sur les relations qui peuvent exister entre la forme cristalline, la composition chimique et le sens de la polarisation rotatoire,” Ann. Chim. Phys. 24, 442–459 (1848).

Ann. Phys. (3)

K. F. Lindman, “Über eine durch ein isotropes System von Spiralförmigen Resonatoren erzeugte Rotationspolarisation der elektromagnetischen Wellen,” Ann. Phys. 63, 621–644 (1920).
[CrossRef]

K. F. Lindman, “Über die durch ein aktives Raumgitter erzeugte Rotationspolarisation der elektromagnetischen Wellen,” Ann. Phys. 69, 270–284 (1922).
[CrossRef]

C. W. Oseen, “Über die Wechsëlwirkung zwischen zwei elektrischen Dipolen und über in Kristallen und Flüssigkeiten,” Ann. Phys. 48, 1–56 (1915).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. (1)

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

Bull. Soc. Philomath. (1)

J. B. Biot, “Phénomènes de polarisation successive, observés dans des fluides homogènes,” Bull. Soc. Philomath.190–192 (1815).

Chem. Phys. Lett. (1)

C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

N. Engheta, A. R. Mickelson, “Transition radiation caused by a chiral plate,” IEEE Trans. Antennas Propag. AP-30, 1213–1216 (1982).
[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. EM-28, 90–95 (1986).
[CrossRef]

J. Chem. Phys. (1)

E. U. Condon, W. Altar, H. Eyring, “One-electron rotatory power,” J. Chem. Phys. 5, 753–775 (1937).
[CrossRef]

J. Colloid Interface Sci. (1)

C. F. Bohren, “Scattering of electromagnetic waves by an optically active cylinder,” J. Colloid Interface Sci. 66, 105–109 (1975).
[CrossRef]

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

Lett. Nuovo Cimento (1)

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

Mem. Acad. Sci. (2)

J. B. Biot, “Sur les rotations que certaines substances impriment aux axes de polarisation des rayons lumineux,” Mem. Acad. Sci. 2, 41–136 (1817).

J. B. Biot, “Mémoire sur la polarisation circulaire et sur ses applications à la chimie organique,” Mem. Acad. Sci. 13, 39–175 (1835).

Mem. Inst. (2)

D. F. Arago, “Sur une modification remarquable qu’ éprouvent les rayons lumineux dans leur passage à travers certains corps diaphanes, et sur quelques autres nouveaux phénomènes d’optique,” Mem. Inst. 1, 93–134 (1811).

J. B. Biot, “Mémoire sur un nouveau genre d’oscillations que les molécules de la lumière éprouvent, en traversant certains cristaux,” Mem. Inst. 1, 1–372 (1812).

Oeuvres (1)

A. Fresnel, “Mémoire sur la double réfraction que les rayons lumineux éprouvent en traversant les aiguilles de cristal de roche suivant des directions parallèles à l’axe,” Oeuvres 1, 731–751 (1822).

Opt. Spektrosk. (1)

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

Phys. Rev. (1)

F. Gray, The optical activity of liquids and gases,” Phys. Rev. 7, 472–488 (1916).
[CrossRef]

Phys. Z. (1)

M. Born, “Über die natürliche optische Aktivität von Flüssigkeiten und Gasen,” Phys. Z. 16, 251–258 (1915).

Rev. Mod. Phys. (1)

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

Z. Phys. Chem. B (1)

W. Kuhn, “Quantitative Verhältnisse und Beziehungen bei der natürlichen optischen Aktivität,” Z. Phys. Chem. B 4, 14–36 (1929).

Other (9)

J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975).

W. H. Pickering, California Institute of Technology, Pasadena, California 91125 (personal communication, 1945).

T. M. Lowry, Optical Rotatory Power (Dover, New York, 1964).

S. Bassiri, “Electromagnetic wave propagation and radiation in chiral media,” doctoral dissertation (Division of Engineering and Applied Science, California Instititute of Technology, Pasadena, Calif., 1987).

A. Sommerfeld, Optics (Academic, New York, 1954).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

C. H. Papas, Theory of Electromagnetic Wave Propagation (McGraw-Hill, New York, 1965).

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

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

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Figures (5)

Fig. 1
Fig. 1

Orientation of the wave vectors of the incident wave, the reflected wave, and the transmitted waves at an oblique incidence on a semi-infinite chiral medium. In the chiral medium the h1 and the h2 waves are right-circularly (RC) and left-circularly (LC) polarized waves, respectively. The two angles of refraction are denoted by θ1 and θ2. For γ = 0, these two angle approach θt.

Fig. 2
Fig. 2

Polarization ellipse for right-elliptically polarized wave having an orientation angle ψ and an ellipticity angle χ.

Fig. 3
Fig. 3

Normalized reflected power (vertical axes) as a function of the incident angle θi (horizontal axes). For Case (a), 1 = 90, = 0; for Case (b), 1 = 0, = 90. The values of γ are shown on each plot. For both cases it is assumed that μ1 = μ = μ0.

Fig. 4
Fig. 4

Ellipticity of the polarization ellipse of the reflected wave (vertical axis) as a function of the incident angle θi (horizontal axis). For Case (a), 1 = 90, = 0; for Case (b), 1 = 0, = 90. The values of γ are shown on each plot. For both cases it is assumed that μ1 = μ = μ0.

Fig. 5
Fig. 5

Oblique incidence on an infinite slab of chiral medium. The dielectrics occupying the regions z < 0 and z > d have the same constitutive parameters. In the chiral slab, the h1 and h2 waves are right-circularly and left-circularly polarized waves, respectively.

Equations (73)

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D = E + i γ B ,
H = i γ E + ( 1 / μ ) B .
h 1 = ω μ γ + ( ω 2 μ 2 γ 2 + k 2 ) 1 / 2 ,
h 2 = ω μ γ + ( ω 2 μ 2 γ 2 + k 2 ) 1 / 2 ,
k i × e ˆ z = k r × e ˆ z = h 1 × e ˆ z = h 2 × e ˆ z ,
k i sin θ i = k r sin θ r = h 1 sin θ 1 = h 2 sin θ 2 ;
θ 1 = arcsin ( k i sin θ i h 1 ) ,
θ 2 = arcsin ( k i sin θ i h 2 ) ,
θ t = arcsin ( k i sin θ i k ) ,
θ c 1 = arcsin [ μ γ + ( μ 2 γ 2 + μ ) 1 / 2 ( μ 1 1 ) 1 / 2 ] ,
θ c 2 = arcsin [ μ γ + ( μ 2 γ 2 + μ ) 1 / 2 ( μ 1 1 ) 1 / 2 ] .
( E 0 i + E 0 r ) × e ˆ z = ( E 01 + E 02 ) × e ˆ z ,
( H 0 i + H 0 r ) × e ˆ z = ( H 01 + H 02 ) × e ˆ z ,
( E r E r ) = [ R 11 R 12 R 21 R 22 ] ( E i E i )
( E 01 E 02 ) = [ T 11 T 12 T 21 T 22 ] ( E i E i ) ,
R 11 = cos θ i ( 1 g 2 ) ( cos θ 1 + cos θ 2 ) + 2 g ( cos 2 θ i cos θ 1 cos θ 2 ) cos θ i ( 1 + g 2 ) ( cos θ 1 + cos θ 2 ) + 2 g ( cos 2 θ i + cos θ 1 cos θ 2 ) ,
R 12 = 2 i g cos θ i ( cos θ 1 cos θ 2 ) cos θ i ( 1 + g 2 ) ( cos θ 1 + cos θ 2 ) + 2 g ( cos 2 θ i + cos θ 1 cos θ 2 ) ,
R 21 = 2 i g cos θ i ( cos θ 1 cos θ 2 ) cos θ i ( 1 + g 2 ) ( cos θ 1 + cos θ 2 ) + 2 g ( cos 2 θ i + cos θ 1 cos θ 2 ) ,
R 22 = cos θ i ( 1 g 2 ) ( cos θ 1 + cos θ 2 ) 2 g ( cos 2 θ i cos θ 1 cos θ 2 ) cos θ i ( 1 + g 2 ) ( cos θ 1 + cos θ 2 ) + 2 g ( cos 2 θ i + cos θ 1 cos θ 2 ) ,
T 11 = 2 i cos θ i ( g cos θ i + cos θ 2 ) cos θ i ( 1 + g 2 ) ( cos θ 1 + cos θ 2 ) + 2 g ( cos 2 θ i + cos θ 1 cos θ 2 ) ,
T 12 = 2 cos θ i ( cos θ i + g cos θ 2 ) cos θ i ( 1 + g 2 ) ( cos θ 1 + cos θ 2 ) + 2 g ( cos 2 θ i + cos θ 1 cos θ 2 ) ,
T 21 = 2 i cos θ i ( g cos θ i + cos θ 1 ) cos θ i ( 1 + g 2 ) ( cos θ 1 + cos θ 2 ) + 2 g ( cos 2 θ i + cos θ 1 cos θ 2 ) ,
T 22 = 2 cos θ i ( cos θ i + g cos θ 1 ) cos θ i ( 1 + g 2 ) ( cos θ 1 + cos θ 2 ) + 2 g ( cos 2 θ i + cos θ 1 cos θ 2 ) .
R 11 = R 22 = 1 g 1 + g ,
R 12 = R 21 = 0 ,
T 11 = i T 22 = i 1 + g ,
T 12 = i T 21 = 1 1 + g .
tan α i = E i E i ,
tan α r = E r E r ,
tan α r = R 12 + R 11 tan α i R 22 + R 21 tan α i .
R 11 R 22 R 12 R 21 = 0.
tan α r = R 12 R 22 = R 11 R 21 .
( 1 g 2 ) 2 cos 2 θ i ( cos θ 1 + cos θ 2 ) 2 4 g 2 ( cos 2 θ i cos 2 θ 1 ) ( cos 2 θ i cos 2 θ 2 ) ,
E = ( E e ˆ + E e ˆ ) exp ( i k · r i ω t )
S 0 = E E * + E E * ,
S 1 = E E * E E * ,
S 2 = 2 Re { E E * } ,
S 3 = 2 Im { E E * } ,
tan 2 ψ = S 2 S 1 ( 0 ψ π ) ,
tan χ = ( S 3 / S 0 ) 1 + [ 1 ( S 3 / S 0 ) 2 ] 1 / 2 ( π / 4 χ π / 4 ) .
ψ = 1 2 arctan ( S 2 S 1 ) = 0 ;
E i = E 0 i exp [ i k i ( z cos θ i x sin θ i ) ] ,
H i = H 0 i exp [ i k i ( z cos θ i x sin θ i ) ] ,
E 0 i = E i e ˆ y + E i ( cos θ i e ˆ x + sin θ i e ˆ z ) ,
H 0 i = η 1 1 [ E i e ˆ y E i ( cos θ i e ˆ x + sin θ i e ˆ z ) ] ,
E r = E 0 r exp [ i k i ( z cos θ i + x sin θ i ) ] ,
H r = H 0 r exp [ i k i ( z cos θ i + x sin θ i ) ] ,
E 0 r = E r e ˆ y + E r ( cos θ i e ˆ x sin θ i e ˆ z ) ,
H 0 r = η 1 1 [ E r e ˆ y + E r ( cos θ i e ˆ x sin θ i e ˆ z ) ] .
E c + = E 01 + exp [ i h 1 ( z cos θ 1 x sin θ 1 ) ] + E 02 + exp [ i h 2 ( z cos θ 2 x sin θ 2 ) ] ,
H c + = H 01 + exp [ i h 1 ( z cos θ 1 x sin θ 1 ) ] + H 02 + exp [ i h 2 ( z cos θ 2 x sin θ 2 ) ] ,
E 01 + = E 01 + ( cos θ 1 e ˆ x + sin θ 1 e ˆ z + i e ˆ y )
H 01 + = i Z 1 E 01 + ( cos θ 1 e ˆ x + sin θ 1 e ˆ z + i e ˆ y ) ,
E 02 + = E 02 + ( cos θ 2 e ˆ x + sin θ 2 e ˆ z i e ˆ y ) ,
H 02 + = i Z 1 E 02 + ( cos θ 2 e ˆ x + sin θ 2 e ˆ z i e ˆ y ) .
E c = E 01 exp [ i h 1 ( z cos θ 1 + x sin θ 1 ) ] + E 02 exp [ i h 2 ( z cos θ 2 + x sin θ 2 ) ] ,
H c = H 01 exp [ i h 1 ( z cos θ 1 + x sin θ 1 ) ] + H 02 exp [ i h 2 ( z cos θ 2 + x sin θ 2 ) ] ,
E 01 = E 01 ( sin θ 1 e ˆ z cos θ 1 e ˆ x + i e ˆ y ) ,
H 01 = i Z 1 E 01 ( sin θ 1 e ˆ z cos θ 1 e ˆ x + i e ˆ y ) ,
E 02 = E 02 ( sin θ 2 e ˆ z cos θ 2 e ˆ x i e ˆ y )
H 02 = i Z 1 E 02 ( sin θ 2 e ˆ z cos θ 2 e ˆ x i e ˆ y )
E t = E 0 t exp [ i k t ( z cos θ t x sin θ t ) ] ,
H t = H 0 t exp [ i k t ( z cos θ t x sin θ t ) ] ,
E 0 t = E t e ˆ y + E t ( cos θ t e ˆ x + sin θ t e ˆ z ) ,
H 0 t = η 1 1 [ E t e ˆ y E t ( cos θ t e ˆ x + sin θ t e ˆ z ) ] ,
[ E r E r E 01 + E 02 + E 01 E 02 E t E t ] = Q 1 [ E i E i E i E i 0 0 0 0 ] ,
Q = [ 0 1 R 1 R 2 R 1 R 2 0 0 1 0 i i i i 0 0 1 0 i g R 1 i g R 2 i g R 1 i g R 2 0 0 0 1 g g g g 0 0 0 0 R 1 exp ( i δ 1 ) R 2 exp ( i δ 2 ) R 1 exp ( i δ 1 ) R 2 exp ( i δ 2 ) 0 exp ( i δ i ) 0 0 i exp ( i δ 1 ) i exp ( i δ 2 ) i exp ( i δ 1 ) i exp ( i δ 2 ) exp ( i δ i ) 0 0 0 i g R 1 exp ( i δ 1 ) i g R 2 exp ( i δ 2 ) i g R 1 exp ( i δ 1 ) i g R 2 exp ( i δ 2 ) exp ( i δ i ) 0 0 0 g exp ( i δ 1 ) g exp ( i δ 2 ) g exp ( i δ 1 ) g exp ( i δ 2 ) 0 exp ( i δ i ) ]
E i = E i e ˆ x exp ( i k i z ) .
E r = E r e ˆ x exp ( i k i z ) ,
E r = E i ( 1 + g 1 g ) 1 exp [ i ( δ 1 + δ 2 ) ] [ ( 1 + g ) / ( 1 g ) ] 2 exp [ i ( δ 1 + δ 2 ) ] .
E t = E t [ e ˆ x + tan ( δ 2 δ 1 2 ) e ˆ y ] exp ( i k i z ) ,
E t = E i 2 g ( 1 g ) 2 exp [ i ( δ 1 δ i ) ] + exp [ i ( δ 2 δ i ) ] [ ( 1 + g ) / ( 1 g ) ] 2 exp [ i ( δ 1 + δ 2 ) ] .
E t y E t x = tan ( δ 2 δ 1 2 ) = tan ( ω μ γ d ) ,

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