Abstract

We present a microscopic approach to study electromagnetic wave propagation in media with broken mirror symmetry. We introduce and calculate the transport mean free path C* associated with the residual polarization of diffuse light in chiral systems. In chiral media subject to an external magnetic field B, all symmetry requirements exist to create a macroscopic “super” light current in the direction of B that persists even in the absence of a spatial photon density gradient. However, we show that such a current is identically zero in our model. We finally show the existence of a linear magnetotransmission in magnetochiral media.

© 2003 Optical Society of America

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  1. B. A. van Tiggelen, “Transverse diffusion of light in Faraday-active media,” Phys. Rev. Lett. 75, 422–424 (1995).
    [CrossRef] [PubMed]
  2. G. L. J. A. Rikken, B. A. van Tiggelen, “Observation of magnetically induced transverse diffusion of light,” Nature (London) 381, 54–55 (1996).
    [CrossRef]
  3. M. P. Silverman, W. Strange, J. Badoz, I. A. Vitkin, “Enhanced optical rotation and diminished depolarization in diffusive scattering from a chiral liquid,” Opt. Commun. 132, 410–416 (1996).
    [CrossRef]
  4. B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
    [CrossRef]
  5. M. P. Groenewege, “A theory of magneto-optical rotation in diamagnetic molecules of low symmetry,” Mol. Phys. 5, 541–563 (1962).
    [CrossRef]
  6. D. L. Portigal, E. Burstein, “Magneto-spatial dispersion effects on propagation of electromagnetic radiation in crystals,” J. Phys. Chem. Solids 32, 603 (1971).
    [CrossRef]
  7. N. B. Baranova, Yu. V. Bogdanov, B. Ya. Zeldovich, “Electrical analog of the Faraday effect and other new optical effects in liquids,” Opt. Commun. 22, 243 (1977).
    [CrossRef]
  8. N. B. Baranova, B. Ya. Zeldovich, “Theory of a new linear magnetorefractive effect in liquids,” Mol. Phys. 38, 1085–1098 (1979).
    [CrossRef]
  9. G. Wagnière, A. Meier, “The influence of a static magnetic field on the absorption coefficient of a chiral molecule,” Chem. Phys. Lett. 93, 78–81 (1982).
    [CrossRef]
  10. G. Wagnière, “Magnetochiral dichroism in emission. Photoselection and the polarization of transition,” Chem. Phys. Lett. 110, 546–551 (1984).
    [CrossRef]
  11. L. D. Barron, J. Vrbancich, “Magneto-chiral birefringence and dichroism,” Mol. Phys. 51, 715–730 (1984).
    [CrossRef]
  12. G. L. J. A. Rikken, E. Raupach, “Observation of magneto-chiral dichroism,” Nature (London) 390, 493–494 (1997).
    [CrossRef]
  13. P. Kleindienst, G. H. Wagnière, “Interferometric detection of magnetochiral birefringence,” Chem. Phys. Lett. 288, 89–97 (1998).
    [CrossRef]
  14. M. Vallet, R. Ghosh, A. Le Floch, T. Ruchon, F. Bretenaker, J.-Y. Thépot, “Observation of magnetochiral birefringence,” Phys. Rev. Lett. 87, 183003 (2001).
    [CrossRef]
  15. F. A. Pinheiro, B. A. van Tiggelen, “Magnetochiral scattering of light: optical manifestation of chirality,” Phys. Rev. E 66, 016607 (2002).
    [CrossRef]
  16. POAN (Propagation des Ondes en Milieux Aleatóires et/ou Non-Linéaires) Research Group, ed., New Aspects of Electromagnetic and Acoustic Wave Diffusion (Springer-Verlag, Heidelberg, 1998).
  17. Yu. N. Barabanenkov, V. D. Ozrin, “Asymptotic solution of the Bethe–Salpeter equation and the Green–Kubo formula for the diffusion constant for wave propagation in random media,” Phys. Lett. A 154, 38–42 (1991).
    [CrossRef]
  18. Yu. N. Barabanenkov, V. D. Ozrin, “Diffusion asymptotics of the Bethe–Salpeter equation for electromagnetic waves in discrete random media,” Phys. Lett. A 206, 116–122 (1995).
    [CrossRef]
  19. F. C. MacKintosh, S. John, “Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media,” Phys. Rev. B 37, 1884–1897 (1988).
    [CrossRef]
  20. B. A. van Tiggelen, R. Maynard, Th. M. Nieuwenhuizen, “Theory for multiple light scattering from Rayleigh scatterers in magnetic fields,” Phys. Rev. E 53, 2881–2908 (1996).
    [CrossRef]
  21. H. Stark, T. C. Lubensky, “Multiple light scattering in nematic liquid crystals,” Phys. Rev. Lett. 77, 2229–2232 (1996).
    [CrossRef] [PubMed]
  22. A. B. Harris, R. D. Kamien, T. C. Lubensky, “Microscopic origin of cholesteric pitch,” Phys. Rev. Lett. 78, 1476–1479 (1997).
    [CrossRef]
  23. A. B. Harris, R. D. Kamien, T. C. Lubensky, “Molecular chirality and chiral parameters,” Rev. Mod. Phys. 71, 1745–1757 (1999).
    [CrossRef]
  24. M. S. Spector, S. K. Prasad, B. T. Weslowski, R. D. Kamien, J. V. Selinger, B. R. Ratna, R. Shashidhar, “Chiral twisting of a smectic-A liquid crystal,” Phys. Rev. E 61, 3977–3983 (2000).
    [CrossRef]
  25. P. Sheng, Wave Scattering, Localization and Mesoscopic Phenomena (Academic, San Diego, Calif., 1995).
  26. G. D. Mahan, Many-Particle Physics (Plenum, New York, 1981).
  27. D. Lacoste, B. A. van Tiggelen, G. L. J. A. Rikken, A. Sparenberg, “Optics of a Faraday-active Mie sphere,” J. Opt. Soc. Am. A 15, 1636–1642 (1998).
    [CrossRef]
  28. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, San Diego, Calif., 1978), Vol. 1.
  29. A. Lagendijk, B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
    [CrossRef]
  30. L. D. Landau, E. M. Lifshitz, L. P. Pitaevski, Electro-dynamics of Continuous Media (Pergamon, Oxford, UK, 1984), Sect. 103, Eq. 103.15.
  31. M. Rusek, A. Orlowski, J. Mostowski, “Localization of light in three-dimensional random dielectric media,” Phys. Rev. E 53, 4122–4130 (1996).
    [CrossRef]
  32. For “point” scatterers with Verdet constant V and line width Γ, μ=12Vc0/Γ. For two-level atoms with Zeeman splitting ℏZB in a magnetic field B, μ=Z/Γ. See, for instance, G. Labeyrie, C. Miniatura, R. Kaiser, “Large Faraday rotation of resonant light in a cold atomic cloud,” Phys. Rev. A 64, 033402 (2001).
    [CrossRef]
  33. A. Sparenberg, G. L. J. A. Rikken, B. A. van Tiggelen, “Observation of photonic magnetoresistance,” Phys. Rev. Lett. 79, 757–759 (1997).
    [CrossRef]
  34. D. Lacoste, B. A. van Tiggelen, “Transport mean free path for magneto-transverse light diffusion,” Europhys. Lett. 45, 721–725 (1999).
    [CrossRef]

2002 (1)

F. A. Pinheiro, B. A. van Tiggelen, “Magnetochiral scattering of light: optical manifestation of chirality,” Phys. Rev. E 66, 016607 (2002).
[CrossRef]

2001 (2)

M. Vallet, R. Ghosh, A. Le Floch, T. Ruchon, F. Bretenaker, J.-Y. Thépot, “Observation of magnetochiral birefringence,” Phys. Rev. Lett. 87, 183003 (2001).
[CrossRef]

For “point” scatterers with Verdet constant V and line width Γ, μ=12Vc0/Γ. For two-level atoms with Zeeman splitting ℏZB in a magnetic field B, μ=Z/Γ. See, for instance, G. Labeyrie, C. Miniatura, R. Kaiser, “Large Faraday rotation of resonant light in a cold atomic cloud,” Phys. Rev. A 64, 033402 (2001).
[CrossRef]

2000 (1)

M. S. Spector, S. K. Prasad, B. T. Weslowski, R. D. Kamien, J. V. Selinger, B. R. Ratna, R. Shashidhar, “Chiral twisting of a smectic-A liquid crystal,” Phys. Rev. E 61, 3977–3983 (2000).
[CrossRef]

1999 (3)

A. B. Harris, R. D. Kamien, T. C. Lubensky, “Molecular chirality and chiral parameters,” Rev. Mod. Phys. 71, 1745–1757 (1999).
[CrossRef]

D. Lacoste, B. A. van Tiggelen, “Transport mean free path for magneto-transverse light diffusion,” Europhys. Lett. 45, 721–725 (1999).
[CrossRef]

B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

1998 (2)

P. Kleindienst, G. H. Wagnière, “Interferometric detection of magnetochiral birefringence,” Chem. Phys. Lett. 288, 89–97 (1998).
[CrossRef]

D. Lacoste, B. A. van Tiggelen, G. L. J. A. Rikken, A. Sparenberg, “Optics of a Faraday-active Mie sphere,” J. Opt. Soc. Am. A 15, 1636–1642 (1998).
[CrossRef]

1997 (3)

A. Sparenberg, G. L. J. A. Rikken, B. A. van Tiggelen, “Observation of photonic magnetoresistance,” Phys. Rev. Lett. 79, 757–759 (1997).
[CrossRef]

A. B. Harris, R. D. Kamien, T. C. Lubensky, “Microscopic origin of cholesteric pitch,” Phys. Rev. Lett. 78, 1476–1479 (1997).
[CrossRef]

G. L. J. A. Rikken, E. Raupach, “Observation of magneto-chiral dichroism,” Nature (London) 390, 493–494 (1997).
[CrossRef]

1996 (6)

G. L. J. A. Rikken, B. A. van Tiggelen, “Observation of magnetically induced transverse diffusion of light,” Nature (London) 381, 54–55 (1996).
[CrossRef]

M. P. Silverman, W. Strange, J. Badoz, I. A. Vitkin, “Enhanced optical rotation and diminished depolarization in diffusive scattering from a chiral liquid,” Opt. Commun. 132, 410–416 (1996).
[CrossRef]

A. Lagendijk, B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[CrossRef]

M. Rusek, A. Orlowski, J. Mostowski, “Localization of light in three-dimensional random dielectric media,” Phys. Rev. E 53, 4122–4130 (1996).
[CrossRef]

B. A. van Tiggelen, R. Maynard, Th. M. Nieuwenhuizen, “Theory for multiple light scattering from Rayleigh scatterers in magnetic fields,” Phys. Rev. E 53, 2881–2908 (1996).
[CrossRef]

H. Stark, T. C. Lubensky, “Multiple light scattering in nematic liquid crystals,” Phys. Rev. Lett. 77, 2229–2232 (1996).
[CrossRef] [PubMed]

1995 (2)

Yu. N. Barabanenkov, V. D. Ozrin, “Diffusion asymptotics of the Bethe–Salpeter equation for electromagnetic waves in discrete random media,” Phys. Lett. A 206, 116–122 (1995).
[CrossRef]

B. A. van Tiggelen, “Transverse diffusion of light in Faraday-active media,” Phys. Rev. Lett. 75, 422–424 (1995).
[CrossRef] [PubMed]

1991 (1)

Yu. N. Barabanenkov, V. D. Ozrin, “Asymptotic solution of the Bethe–Salpeter equation and the Green–Kubo formula for the diffusion constant for wave propagation in random media,” Phys. Lett. A 154, 38–42 (1991).
[CrossRef]

1988 (1)

F. C. MacKintosh, S. John, “Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media,” Phys. Rev. B 37, 1884–1897 (1988).
[CrossRef]

1984 (2)

G. Wagnière, “Magnetochiral dichroism in emission. Photoselection and the polarization of transition,” Chem. Phys. Lett. 110, 546–551 (1984).
[CrossRef]

L. D. Barron, J. Vrbancich, “Magneto-chiral birefringence and dichroism,” Mol. Phys. 51, 715–730 (1984).
[CrossRef]

1982 (1)

G. Wagnière, A. Meier, “The influence of a static magnetic field on the absorption coefficient of a chiral molecule,” Chem. Phys. Lett. 93, 78–81 (1982).
[CrossRef]

1979 (1)

N. B. Baranova, B. Ya. Zeldovich, “Theory of a new linear magnetorefractive effect in liquids,” Mol. Phys. 38, 1085–1098 (1979).
[CrossRef]

1977 (1)

N. B. Baranova, Yu. V. Bogdanov, B. Ya. Zeldovich, “Electrical analog of the Faraday effect and other new optical effects in liquids,” Opt. Commun. 22, 243 (1977).
[CrossRef]

1971 (1)

D. L. Portigal, E. Burstein, “Magneto-spatial dispersion effects on propagation of electromagnetic radiation in crystals,” J. Phys. Chem. Solids 32, 603 (1971).
[CrossRef]

1962 (1)

M. P. Groenewege, “A theory of magneto-optical rotation in diamagnetic molecules of low symmetry,” Mol. Phys. 5, 541–563 (1962).
[CrossRef]

Ablitt, B. P.

B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

Badoz, J.

M. P. Silverman, W. Strange, J. Badoz, I. A. Vitkin, “Enhanced optical rotation and diminished depolarization in diffusive scattering from a chiral liquid,” Opt. Commun. 132, 410–416 (1996).
[CrossRef]

Barabanenkov, Yu. N.

Yu. N. Barabanenkov, V. D. Ozrin, “Diffusion asymptotics of the Bethe–Salpeter equation for electromagnetic waves in discrete random media,” Phys. Lett. A 206, 116–122 (1995).
[CrossRef]

Yu. N. Barabanenkov, V. D. Ozrin, “Asymptotic solution of the Bethe–Salpeter equation and the Green–Kubo formula for the diffusion constant for wave propagation in random media,” Phys. Lett. A 154, 38–42 (1991).
[CrossRef]

Baranova, N. B.

N. B. Baranova, B. Ya. Zeldovich, “Theory of a new linear magnetorefractive effect in liquids,” Mol. Phys. 38, 1085–1098 (1979).
[CrossRef]

N. B. Baranova, Yu. V. Bogdanov, B. Ya. Zeldovich, “Electrical analog of the Faraday effect and other new optical effects in liquids,” Opt. Commun. 22, 243 (1977).
[CrossRef]

Barron, L. D.

L. D. Barron, J. Vrbancich, “Magneto-chiral birefringence and dichroism,” Mol. Phys. 51, 715–730 (1984).
[CrossRef]

Bogdanov, Yu. V.

N. B. Baranova, Yu. V. Bogdanov, B. Ya. Zeldovich, “Electrical analog of the Faraday effect and other new optical effects in liquids,” Opt. Commun. 22, 243 (1977).
[CrossRef]

Bretenaker, F.

M. Vallet, R. Ghosh, A. Le Floch, T. Ruchon, F. Bretenaker, J.-Y. Thépot, “Observation of magnetochiral birefringence,” Phys. Rev. Lett. 87, 183003 (2001).
[CrossRef]

Burstein, E.

D. L. Portigal, E. Burstein, “Magneto-spatial dispersion effects on propagation of electromagnetic radiation in crystals,” J. Phys. Chem. Solids 32, 603 (1971).
[CrossRef]

Chang, P. C. Y.

B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

Ghosh, R.

M. Vallet, R. Ghosh, A. Le Floch, T. Ruchon, F. Bretenaker, J.-Y. Thépot, “Observation of magnetochiral birefringence,” Phys. Rev. Lett. 87, 183003 (2001).
[CrossRef]

Groenewege, M. P.

M. P. Groenewege, “A theory of magneto-optical rotation in diamagnetic molecules of low symmetry,” Mol. Phys. 5, 541–563 (1962).
[CrossRef]

Harris, A. B.

A. B. Harris, R. D. Kamien, T. C. Lubensky, “Molecular chirality and chiral parameters,” Rev. Mod. Phys. 71, 1745–1757 (1999).
[CrossRef]

A. B. Harris, R. D. Kamien, T. C. Lubensky, “Microscopic origin of cholesteric pitch,” Phys. Rev. Lett. 78, 1476–1479 (1997).
[CrossRef]

Hopcraft, K. I.

B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, San Diego, Calif., 1978), Vol. 1.

Jakeman, E.

B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

John, S.

F. C. MacKintosh, S. John, “Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media,” Phys. Rev. B 37, 1884–1897 (1988).
[CrossRef]

Kaiser, R.

For “point” scatterers with Verdet constant V and line width Γ, μ=12Vc0/Γ. For two-level atoms with Zeeman splitting ℏZB in a magnetic field B, μ=Z/Γ. See, for instance, G. Labeyrie, C. Miniatura, R. Kaiser, “Large Faraday rotation of resonant light in a cold atomic cloud,” Phys. Rev. A 64, 033402 (2001).
[CrossRef]

Kamien, R. D.

M. S. Spector, S. K. Prasad, B. T. Weslowski, R. D. Kamien, J. V. Selinger, B. R. Ratna, R. Shashidhar, “Chiral twisting of a smectic-A liquid crystal,” Phys. Rev. E 61, 3977–3983 (2000).
[CrossRef]

A. B. Harris, R. D. Kamien, T. C. Lubensky, “Molecular chirality and chiral parameters,” Rev. Mod. Phys. 71, 1745–1757 (1999).
[CrossRef]

A. B. Harris, R. D. Kamien, T. C. Lubensky, “Microscopic origin of cholesteric pitch,” Phys. Rev. Lett. 78, 1476–1479 (1997).
[CrossRef]

Kleindienst, P.

P. Kleindienst, G. H. Wagnière, “Interferometric detection of magnetochiral birefringence,” Chem. Phys. Lett. 288, 89–97 (1998).
[CrossRef]

Labeyrie, G.

For “point” scatterers with Verdet constant V and line width Γ, μ=12Vc0/Γ. For two-level atoms with Zeeman splitting ℏZB in a magnetic field B, μ=Z/Γ. See, for instance, G. Labeyrie, C. Miniatura, R. Kaiser, “Large Faraday rotation of resonant light in a cold atomic cloud,” Phys. Rev. A 64, 033402 (2001).
[CrossRef]

Lacoste, D.

D. Lacoste, B. A. van Tiggelen, “Transport mean free path for magneto-transverse light diffusion,” Europhys. Lett. 45, 721–725 (1999).
[CrossRef]

D. Lacoste, B. A. van Tiggelen, G. L. J. A. Rikken, A. Sparenberg, “Optics of a Faraday-active Mie sphere,” J. Opt. Soc. Am. A 15, 1636–1642 (1998).
[CrossRef]

Lagendijk, A.

A. Lagendijk, B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, L. P. Pitaevski, Electro-dynamics of Continuous Media (Pergamon, Oxford, UK, 1984), Sect. 103, Eq. 103.15.

Le Floch, A.

M. Vallet, R. Ghosh, A. Le Floch, T. Ruchon, F. Bretenaker, J.-Y. Thépot, “Observation of magnetochiral birefringence,” Phys. Rev. Lett. 87, 183003 (2001).
[CrossRef]

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, L. P. Pitaevski, Electro-dynamics of Continuous Media (Pergamon, Oxford, UK, 1984), Sect. 103, Eq. 103.15.

Lubensky, T. C.

A. B. Harris, R. D. Kamien, T. C. Lubensky, “Molecular chirality and chiral parameters,” Rev. Mod. Phys. 71, 1745–1757 (1999).
[CrossRef]

A. B. Harris, R. D. Kamien, T. C. Lubensky, “Microscopic origin of cholesteric pitch,” Phys. Rev. Lett. 78, 1476–1479 (1997).
[CrossRef]

H. Stark, T. C. Lubensky, “Multiple light scattering in nematic liquid crystals,” Phys. Rev. Lett. 77, 2229–2232 (1996).
[CrossRef] [PubMed]

MacKintosh, F. C.

F. C. MacKintosh, S. John, “Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media,” Phys. Rev. B 37, 1884–1897 (1988).
[CrossRef]

Mahan, G. D.

G. D. Mahan, Many-Particle Physics (Plenum, New York, 1981).

Maynard, R.

B. A. van Tiggelen, R. Maynard, Th. M. Nieuwenhuizen, “Theory for multiple light scattering from Rayleigh scatterers in magnetic fields,” Phys. Rev. E 53, 2881–2908 (1996).
[CrossRef]

Meier, A.

G. Wagnière, A. Meier, “The influence of a static magnetic field on the absorption coefficient of a chiral molecule,” Chem. Phys. Lett. 93, 78–81 (1982).
[CrossRef]

Miniatura, C.

For “point” scatterers with Verdet constant V and line width Γ, μ=12Vc0/Γ. For two-level atoms with Zeeman splitting ℏZB in a magnetic field B, μ=Z/Γ. See, for instance, G. Labeyrie, C. Miniatura, R. Kaiser, “Large Faraday rotation of resonant light in a cold atomic cloud,” Phys. Rev. A 64, 033402 (2001).
[CrossRef]

Mostowski, J.

M. Rusek, A. Orlowski, J. Mostowski, “Localization of light in three-dimensional random dielectric media,” Phys. Rev. E 53, 4122–4130 (1996).
[CrossRef]

Nieuwenhuizen, Th. M.

B. A. van Tiggelen, R. Maynard, Th. M. Nieuwenhuizen, “Theory for multiple light scattering from Rayleigh scatterers in magnetic fields,” Phys. Rev. E 53, 2881–2908 (1996).
[CrossRef]

Orlowski, A.

M. Rusek, A. Orlowski, J. Mostowski, “Localization of light in three-dimensional random dielectric media,” Phys. Rev. E 53, 4122–4130 (1996).
[CrossRef]

Ozrin, V. D.

Yu. N. Barabanenkov, V. D. Ozrin, “Diffusion asymptotics of the Bethe–Salpeter equation for electromagnetic waves in discrete random media,” Phys. Lett. A 206, 116–122 (1995).
[CrossRef]

Yu. N. Barabanenkov, V. D. Ozrin, “Asymptotic solution of the Bethe–Salpeter equation and the Green–Kubo formula for the diffusion constant for wave propagation in random media,” Phys. Lett. A 154, 38–42 (1991).
[CrossRef]

Pinheiro, F. A.

F. A. Pinheiro, B. A. van Tiggelen, “Magnetochiral scattering of light: optical manifestation of chirality,” Phys. Rev. E 66, 016607 (2002).
[CrossRef]

Pitaevski, L. P.

L. D. Landau, E. M. Lifshitz, L. P. Pitaevski, Electro-dynamics of Continuous Media (Pergamon, Oxford, UK, 1984), Sect. 103, Eq. 103.15.

Portigal, D. L.

D. L. Portigal, E. Burstein, “Magneto-spatial dispersion effects on propagation of electromagnetic radiation in crystals,” J. Phys. Chem. Solids 32, 603 (1971).
[CrossRef]

Prasad, S. K.

M. S. Spector, S. K. Prasad, B. T. Weslowski, R. D. Kamien, J. V. Selinger, B. R. Ratna, R. Shashidhar, “Chiral twisting of a smectic-A liquid crystal,” Phys. Rev. E 61, 3977–3983 (2000).
[CrossRef]

Ratna, B. R.

M. S. Spector, S. K. Prasad, B. T. Weslowski, R. D. Kamien, J. V. Selinger, B. R. Ratna, R. Shashidhar, “Chiral twisting of a smectic-A liquid crystal,” Phys. Rev. E 61, 3977–3983 (2000).
[CrossRef]

Raupach, E.

G. L. J. A. Rikken, E. Raupach, “Observation of magneto-chiral dichroism,” Nature (London) 390, 493–494 (1997).
[CrossRef]

Rikken, G. L. J. A.

D. Lacoste, B. A. van Tiggelen, G. L. J. A. Rikken, A. Sparenberg, “Optics of a Faraday-active Mie sphere,” J. Opt. Soc. Am. A 15, 1636–1642 (1998).
[CrossRef]

G. L. J. A. Rikken, E. Raupach, “Observation of magneto-chiral dichroism,” Nature (London) 390, 493–494 (1997).
[CrossRef]

A. Sparenberg, G. L. J. A. Rikken, B. A. van Tiggelen, “Observation of photonic magnetoresistance,” Phys. Rev. Lett. 79, 757–759 (1997).
[CrossRef]

G. L. J. A. Rikken, B. A. van Tiggelen, “Observation of magnetically induced transverse diffusion of light,” Nature (London) 381, 54–55 (1996).
[CrossRef]

Ruchon, T.

M. Vallet, R. Ghosh, A. Le Floch, T. Ruchon, F. Bretenaker, J.-Y. Thépot, “Observation of magnetochiral birefringence,” Phys. Rev. Lett. 87, 183003 (2001).
[CrossRef]

Rusek, M.

M. Rusek, A. Orlowski, J. Mostowski, “Localization of light in three-dimensional random dielectric media,” Phys. Rev. E 53, 4122–4130 (1996).
[CrossRef]

Selinger, J. V.

M. S. Spector, S. K. Prasad, B. T. Weslowski, R. D. Kamien, J. V. Selinger, B. R. Ratna, R. Shashidhar, “Chiral twisting of a smectic-A liquid crystal,” Phys. Rev. E 61, 3977–3983 (2000).
[CrossRef]

Shashidhar, R.

M. S. Spector, S. K. Prasad, B. T. Weslowski, R. D. Kamien, J. V. Selinger, B. R. Ratna, R. Shashidhar, “Chiral twisting of a smectic-A liquid crystal,” Phys. Rev. E 61, 3977–3983 (2000).
[CrossRef]

Sheng, P.

P. Sheng, Wave Scattering, Localization and Mesoscopic Phenomena (Academic, San Diego, Calif., 1995).

Silverman, M. P.

M. P. Silverman, W. Strange, J. Badoz, I. A. Vitkin, “Enhanced optical rotation and diminished depolarization in diffusive scattering from a chiral liquid,” Opt. Commun. 132, 410–416 (1996).
[CrossRef]

Sparenberg, A.

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[CrossRef]

A. Sparenberg, G. L. J. A. Rikken, B. A. van Tiggelen, “Observation of photonic magnetoresistance,” Phys. Rev. Lett. 79, 757–759 (1997).
[CrossRef]

Spector, M. S.

M. S. Spector, S. K. Prasad, B. T. Weslowski, R. D. Kamien, J. V. Selinger, B. R. Ratna, R. Shashidhar, “Chiral twisting of a smectic-A liquid crystal,” Phys. Rev. E 61, 3977–3983 (2000).
[CrossRef]

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H. Stark, T. C. Lubensky, “Multiple light scattering in nematic liquid crystals,” Phys. Rev. Lett. 77, 2229–2232 (1996).
[CrossRef] [PubMed]

Strange, W.

M. P. Silverman, W. Strange, J. Badoz, I. A. Vitkin, “Enhanced optical rotation and diminished depolarization in diffusive scattering from a chiral liquid,” Opt. Commun. 132, 410–416 (1996).
[CrossRef]

Thépot, J.-Y.

M. Vallet, R. Ghosh, A. Le Floch, T. Ruchon, F. Bretenaker, J.-Y. Thépot, “Observation of magnetochiral birefringence,” Phys. Rev. Lett. 87, 183003 (2001).
[CrossRef]

Turpin, K. D.

B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

Vallet, M.

M. Vallet, R. Ghosh, A. Le Floch, T. Ruchon, F. Bretenaker, J.-Y. Thépot, “Observation of magnetochiral birefringence,” Phys. Rev. Lett. 87, 183003 (2001).
[CrossRef]

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F. A. Pinheiro, B. A. van Tiggelen, “Magnetochiral scattering of light: optical manifestation of chirality,” Phys. Rev. E 66, 016607 (2002).
[CrossRef]

D. Lacoste, B. A. van Tiggelen, “Transport mean free path for magneto-transverse light diffusion,” Europhys. Lett. 45, 721–725 (1999).
[CrossRef]

D. Lacoste, B. A. van Tiggelen, G. L. J. A. Rikken, A. Sparenberg, “Optics of a Faraday-active Mie sphere,” J. Opt. Soc. Am. A 15, 1636–1642 (1998).
[CrossRef]

A. Sparenberg, G. L. J. A. Rikken, B. A. van Tiggelen, “Observation of photonic magnetoresistance,” Phys. Rev. Lett. 79, 757–759 (1997).
[CrossRef]

G. L. J. A. Rikken, B. A. van Tiggelen, “Observation of magnetically induced transverse diffusion of light,” Nature (London) 381, 54–55 (1996).
[CrossRef]

B. A. van Tiggelen, R. Maynard, Th. M. Nieuwenhuizen, “Theory for multiple light scattering from Rayleigh scatterers in magnetic fields,” Phys. Rev. E 53, 2881–2908 (1996).
[CrossRef]

A. Lagendijk, B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[CrossRef]

B. A. van Tiggelen, “Transverse diffusion of light in Faraday-active media,” Phys. Rev. Lett. 75, 422–424 (1995).
[CrossRef] [PubMed]

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M. P. Silverman, W. Strange, J. Badoz, I. A. Vitkin, “Enhanced optical rotation and diminished depolarization in diffusive scattering from a chiral liquid,” Opt. Commun. 132, 410–416 (1996).
[CrossRef]

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L. D. Barron, J. Vrbancich, “Magneto-chiral birefringence and dichroism,” Mol. Phys. 51, 715–730 (1984).
[CrossRef]

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[CrossRef]

G. Wagnière, A. Meier, “The influence of a static magnetic field on the absorption coefficient of a chiral molecule,” Chem. Phys. Lett. 93, 78–81 (1982).
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B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

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M. S. Spector, S. K. Prasad, B. T. Weslowski, R. D. Kamien, J. V. Selinger, B. R. Ratna, R. Shashidhar, “Chiral twisting of a smectic-A liquid crystal,” Phys. Rev. E 61, 3977–3983 (2000).
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[CrossRef]

Chem. Phys. Lett. (3)

G. Wagnière, A. Meier, “The influence of a static magnetic field on the absorption coefficient of a chiral molecule,” Chem. Phys. Lett. 93, 78–81 (1982).
[CrossRef]

G. Wagnière, “Magnetochiral dichroism in emission. Photoselection and the polarization of transition,” Chem. Phys. Lett. 110, 546–551 (1984).
[CrossRef]

P. Kleindienst, G. H. Wagnière, “Interferometric detection of magnetochiral birefringence,” Chem. Phys. Lett. 288, 89–97 (1998).
[CrossRef]

Europhys. Lett. (1)

D. Lacoste, B. A. van Tiggelen, “Transport mean free path for magneto-transverse light diffusion,” Europhys. Lett. 45, 721–725 (1999).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

N. B. Baranova, B. Ya. Zeldovich, “Theory of a new linear magnetorefractive effect in liquids,” Mol. Phys. 38, 1085–1098 (1979).
[CrossRef]

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G. L. J. A. Rikken, B. A. van Tiggelen, “Observation of magnetically induced transverse diffusion of light,” Nature (London) 381, 54–55 (1996).
[CrossRef]

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[CrossRef]

Opt. Commun. (2)

M. P. Silverman, W. Strange, J. Badoz, I. A. Vitkin, “Enhanced optical rotation and diminished depolarization in diffusive scattering from a chiral liquid,” Opt. Commun. 132, 410–416 (1996).
[CrossRef]

N. B. Baranova, Yu. V. Bogdanov, B. Ya. Zeldovich, “Electrical analog of the Faraday effect and other new optical effects in liquids,” Opt. Commun. 22, 243 (1977).
[CrossRef]

Phys. Lett. A (2)

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[CrossRef]

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[CrossRef]

Phys. Rep. (1)

A. Lagendijk, B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[CrossRef]

Phys. Rev. A (1)

For “point” scatterers with Verdet constant V and line width Γ, μ=12Vc0/Γ. For two-level atoms with Zeeman splitting ℏZB in a magnetic field B, μ=Z/Γ. See, for instance, G. Labeyrie, C. Miniatura, R. Kaiser, “Large Faraday rotation of resonant light in a cold atomic cloud,” Phys. Rev. A 64, 033402 (2001).
[CrossRef]

Phys. Rev. B (1)

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[CrossRef]

Phys. Rev. E (4)

B. A. van Tiggelen, R. Maynard, Th. M. Nieuwenhuizen, “Theory for multiple light scattering from Rayleigh scatterers in magnetic fields,” Phys. Rev. E 53, 2881–2908 (1996).
[CrossRef]

M. Rusek, A. Orlowski, J. Mostowski, “Localization of light in three-dimensional random dielectric media,” Phys. Rev. E 53, 4122–4130 (1996).
[CrossRef]

F. A. Pinheiro, B. A. van Tiggelen, “Magnetochiral scattering of light: optical manifestation of chirality,” Phys. Rev. E 66, 016607 (2002).
[CrossRef]

M. S. Spector, S. K. Prasad, B. T. Weslowski, R. D. Kamien, J. V. Selinger, B. R. Ratna, R. Shashidhar, “Chiral twisting of a smectic-A liquid crystal,” Phys. Rev. E 61, 3977–3983 (2000).
[CrossRef]

Phys. Rev. Lett. (5)

A. Sparenberg, G. L. J. A. Rikken, B. A. van Tiggelen, “Observation of photonic magnetoresistance,” Phys. Rev. Lett. 79, 757–759 (1997).
[CrossRef]

H. Stark, T. C. Lubensky, “Multiple light scattering in nematic liquid crystals,” Phys. Rev. Lett. 77, 2229–2232 (1996).
[CrossRef] [PubMed]

A. B. Harris, R. D. Kamien, T. C. Lubensky, “Microscopic origin of cholesteric pitch,” Phys. Rev. Lett. 78, 1476–1479 (1997).
[CrossRef]

M. Vallet, R. Ghosh, A. Le Floch, T. Ruchon, F. Bretenaker, J.-Y. Thépot, “Observation of magnetochiral birefringence,” Phys. Rev. Lett. 87, 183003 (2001).
[CrossRef]

B. A. van Tiggelen, “Transverse diffusion of light in Faraday-active media,” Phys. Rev. Lett. 75, 422–424 (1995).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

A. B. Harris, R. D. Kamien, T. C. Lubensky, “Molecular chirality and chiral parameters,” Rev. Mod. Phys. 71, 1745–1757 (1999).
[CrossRef]

Waves Random Media (1)

B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

Other (5)

P. Sheng, Wave Scattering, Localization and Mesoscopic Phenomena (Academic, San Diego, Calif., 1995).

G. D. Mahan, Many-Particle Physics (Plenum, New York, 1981).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, San Diego, Calif., 1978), Vol. 1.

POAN (Propagation des Ondes en Milieux Aleatóires et/ou Non-Linéaires) Research Group, ed., New Aspects of Electromagnetic and Acoustic Wave Diffusion (Springer-Verlag, Heidelberg, 1998).

L. D. Landau, E. M. Lifshitz, L. P. Pitaevski, Electro-dynamics of Continuous Media (Pergamon, Oxford, UK, 1984), Sect. 103, Eq. 103.15.

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Figures (2)

Fig. 1
Fig. 1

Ratio between the chiral transport mean free path and the transport mean free path C*/* calculated for light scattered by four resonant pointlike scatterers at the vertices of the so-called twisted H (main axis d and secondary axis r) as a function of the angle between its arms α (marked by squares). The parameters used are kr=3.0 and kd=9.0, with k the light wave number. The solid curve corresponds to the chiral parameter ψsin(2α) introduced in Refs. 22 and 23.

Fig. 2
Fig. 2

Ratio C*/* calculated for light scattered by ten resonant pointlike scatterers distributed in a helicoidal structure (height L and radius r) as a function of the number of turns n (marked by squares). The parameters used are kr=1 and kL=100. The solid curve is only a guide for the eyes.

Equations (32)

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J(r, t)=-D(B)·ρ(r, t),
Tpp(g, B)=T-p-pT(g, -B)=TppT(-g, -B).
Φpp(q, g, B)=GpGp*δpp+GpGp*·pUpp(q, g, B)·Φpp(q, g, B),
Σp(g, B)=nTpp(g, B),
Upp(q, g, B)=nTp+p+(g, B)Tp-p-*(g, B).
[-iLp(q)+ΔΣp(q)]·Φpp(q)=ΔGp(q)δpp+ΔGp(q)·pUpp(q)·Φpp(q).
-iWp(q)ΔΣp(q)-pUpp(q)·ΔGp(q),
-l-iΦpp(q, B, g)-k-j=dilp(q, B, g)djk-p(-q, -B, g)D(q, B, g),
k-i-Φpp(q, g, B)-l-j=l-j-Φpp(q, -g, -B)-k-i,
q·D(B, g)·q=12πN(ω) Tr p[Γp(q, B, g)·Gp·Lp(q)·Gp*-(q·p Re Gp)·Lp(q)],
dp(q, B, g)=i(Gp-Gp*)-iGp·Γp(q, B, g)·Gp*.
Γp(q, B, g)=Lp(q)+pΓp(q, B, g)·GpGp*·Upp.
Γp(q, g)=γ0(p·q)Δp+γC(g)(p·q)Ωpˆ,
Γp(q, g)=-Γ-p(q, -g)=Γ-p(-q, -g).
ΔΣp-(Im ΣpS+Im ΣpA)=-(Im Σp0)(U+ξΩpˆ),
γ0=2+gγ0+ξγC1+ξ2+gCγC-ξγ01+ξ2,
γC=-gCγ0+ξγC1+ξ2-gCCγC-ξγ01+ξ2,
g18πσ0  dpˆ4π  dpˆ4π Tr(Δp·Tpp·Δp·Tpp*)×(pˆ·pˆ),
gC18πσ0  dpˆ4π  dpˆ4π Tr(Ωpˆ·Tpp·Δp·Tpp*)×(pˆ·pˆ),
gCC18πσ0  dpˆ4π  dpˆ4π Tr(Ωpˆ·Tpp·Ωpˆ·Tpp*)×(pˆ·pˆ),
dpΔp+i2 s(pˆ·q)γ0+ξγC1+ξ2Δp+γC-ξγ01+ξ2Ωpˆ,
*s2γ0+ξγC1+ξ2,
C*s2γC-ξγ01+ξ2.
Iσ(θ, L)=43 *L+(4/3)* 1+32 cos θ1+C** σ,
V(θ)I(θ)=(3/2)cos θ1+(3/2)cos θ C**,
-ipΦpp(q, g, B)·[Lp(q)+Wp(q, g, B)]sourcep.
q·JρvE=-1N(ω) Tr p[Lp(q)+Wp(q, g, B)]·ΔGp(0, g, B)+O(q2).
Tpp(B)=NNSNN-μ k4π MSNM·Ω(B)·SMN+O(B2)×exp(-ip·rN+ip·rN),
χNMN Im Tr[SNM·(ϵ·rNN)·SMN·G0(rNN)].
Tr Γp(q, B, g)=γ0(pˆ·q)+γMC1(q·B)+γMC2(pˆ·B)(pˆ·q)+γHq·(p×B)+O(B2),
T(θ, B=zˆ)=43 *L+(4/3)* 1+32 cos θ+34 s* BγMC2cos2 θ-12,
δT(θ, B)T(θ)=34 MC** cos2 θ-(1/2)1+(3/2) cos θ,

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