Abstract

We have theoretically investigated the general properties of photonic crystals without time-reversal and space-inversion symmetries by examining the case of one-dimensional periodic, lossless dielectric helical media (HM) with magneto-optic (MO) activity. We show that photonic bandgap formation in the absence of these two symmetry elements leads to a remarkable set of properties: indirect photonic bandgaps (edges not aligned in k space), backward wave propagating eigenmodes (which allow for negative refraction), unusual nonpropagating modes in the gap (their complex-valued wave vectors have frequency-dependent, nonzero real parts, which do not change sign for opposite decay directions), anomalous propagation, and group-velocity-based unidirectional superprism effects. Particular properties of MO HM are discussed in detail.

© 2005 Optical Society of America

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  2. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
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  4. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).
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  7. A. Lakhtakia, "Sculptured thin films: accomplishments and emerging uses," Mater. Sci. Eng. C 19, 427-434 (2002).
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  8. A. Lakhtakia and W. S. Weiglhofer, "On light propagation in helicoidal bianisotropic mediums," Proc. R. Soc. London Ser. A 448, 419-437 (1995).
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  9. A. K. Zvedin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (Institute of Physics, Philadelphia, Pa., 1997).
  10. I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, "Magnetic photonic crystals," J. Phys. D 36, 277-287 (2003).
    [CrossRef]
  11. C. Koerdt, G. Düchs, and G. L. J. A. Rikken, "Magnetochiral anisotropy in Bragg scattering," Phys. Rev. Lett. 91, 073902 (2003).
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  12. O. S. Eritsyan, "Diffraction reflection of light in a cholesteric liquid crystal in the presence of wave irreversibility and Bragg formula for media with nonidentical forward and return wavelengths," J. Exp. Theor. Phys. 90, 102-108 (2000).
    [CrossRef]
  13. A. H. Gevorgyan, "Magneto-optics of a thin film layer with helical structure and enormous anisotropy," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 382, 1-19 (2002).
    [CrossRef]
  14. A. H. Gevorgyan, "Optical diode based on a highly anisotropic layer of a helical periodic medium subjected to a magnetic field," Tech. Phys. 47, 1008-1013 (2002).
    [CrossRef]
  15. A. Lakhtakia, "Anomalous axial propagation in a gyrotropic, locally uniaxial, dielectric helicoidally nonhomogeneous medium," Int. J. Electron Commun. 53, 45-48 (1999).
  16. M. D. Pickett and A. Lakhtakia, "On gyrotropic chiral sculptured thin films for magneto-optics," Optik 113, 367-371 (2002).
    [CrossRef]
  17. R. E. Collin, Foundations for Microwave Engineering (McGraw-Hill, New York, 1965).
  18. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  19. D. N. Chigrin and C. M. S. Torres, "Periodic thin-film interference filters as one-dimensional photonic crystals," Opt. Spectrosc. 91, 484-489 (2001).
    [CrossRef]
  20. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
    [CrossRef]
  21. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
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  22. A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
    [CrossRef]
  23. H. C. Chen, Theory of Electromagnetic Waves: A Coordinate-Free Approach (McGraw-Hill, New York, 1983).
  24. J. A. Kong, Electromagnetic Wave Theory (EMW, Cambridge, Mass., 2000).
  25. I. Bita and E. L. Thomas are preparing a manuscript that will describe the effects of further reducing the symmetry of the repeat unit, for example by departing from the linear rotation in Eqs. .
  26. G. H. Wagnière, "The magnetochiral effect and related optical phenomena," Chem. Phys. 245, 165-173 (1999).
    [CrossRef]
  27. P. Kleindienst and G. H. Wagnière, "Interferometric detection of magnetochiral birefringence," Chem. Phys. Lett. 288, 89-97 (1998).
    [CrossRef]
  28. M. Vallet, R. Ghosh, A. Le Floch, T. Ruchon, F. Bretenaker, and J.-Y. Thépot, "Observation of magnetochiral birefringence," Phys. Rev. Lett. 87, 183003 (2001).
    [CrossRef]
  29. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Elmsford, N.Y., 1984).
  30. G. Wagnière and 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]
  31. G. Wagnière, "Magnetochiral dichroism in emission. Photoselection and the polarization of transitions," Chem. Phys. Lett. 110, 546-551 (1984).
    [CrossRef]
  32. L. D. Barron and J. Vrbancich, "Magneto-chiral birefringence and dichroism," Mol. Phys. 51, 715-730 (1984).
    [CrossRef]
  33. G. L. J. A. Rikken and E. Raupach, "Pure and cascaded magnetochiral anisotropy in optical absorption," Phys. Rev. E 58, 5081-5084 (1998).
    [CrossRef]
  34. G. L. J. A. Rikken and E. Raupach, "Observation of magneto-chiral dichroism," Nature 390, 493-494 (1997).
    [CrossRef]
  35. F. A. Pinheiro and B. A. van Tiggelen, "Magnetochiral scattering of light: optical manifestation of chirality," Phys. Rev. E 66, 016607 (2002).
    [CrossRef]
  36. N. Engeta, D. L. Jaggard, and M. W. Kowarz, "Electromagnetic waves in Faraday chiral media," IEEE Trans. Antennas Propag. 40, 367-374 (1992).
    [CrossRef]
  37. H. Taouk, "Optical wave propagation in active media: gyrotropic-gyrochiral media," J. Opt. Soc. Am. A 14, 2006-2012 (1997).
    [CrossRef]
  38. W. S. Weiglhofer, A. Lakhtakia, and B. Michel, "On the constitutive parameters of a chiroferrite composite medium," Microwave Opt. Technol. Lett. 18, 342-345 (1998).
    [CrossRef]
  39. H. L. de Vries, "Rotatory power and other optical properties of certain liquid crystals," Acta Crystallogr. 4, 219-226 (1951).
    [CrossRef]
  40. C. W. Oseen, "The theory of liquid crystals," J. Chem. Soc. 29, 883-899 (1933).
  41. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  42. I. Abdulhalim, R. Weil, and L. Benguigui, "Dispersion and attenuation of the eigenwaves for light propagation in helicoidal liquid crystals," Liq. Cryst. 1, 155-167 (1986).
    [CrossRef]
  43. V. C. Venugopal and A. Lakhtakia, "Electromagnetic plane-wave response characteristics of nonaxially excited slabs of dielectric thin-film helicoidal bianisotropic mediums," Proc. R. Soc. London, Ser. A 456, 125-161 (2000).
    [CrossRef]
  44. J. A. Polo, Jr. and A. Lakhtakia, "Comparison of two methods for oblique propagation in helicoidal bianisotropic mediums," Opt. Commun. 230, 369-386 (2004).
    [CrossRef]
  45. V. I. Kopp, Z.-Q. Zhang, and A. Z. Genack, "Lasing in chiral photonic structures," Prog. Quantum Electron. 27, 369-416 (2003).
    [CrossRef]
  46. I. Bita and E. L. Thomas, 'Tunneling time for barriers lacking space-inversion and time-reversal symmetries,' Phys. Rev. Lett., submitted for publication.
  47. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  48. D. R. Smith and N. Kroll, "Negative refraction index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
    [CrossRef] [PubMed]
  49. G. L. J. A. Rikken, A. Sparenberg, and B. A. van Tiggelen, "Photonic magneto-transport," Physica B 246-247, 188-194 (1998).
    [CrossRef]

2004 (1)

J. A. Polo, Jr. and A. Lakhtakia, "Comparison of two methods for oblique propagation in helicoidal bianisotropic mediums," Opt. Commun. 230, 369-386 (2004).
[CrossRef]

2003 (3)

V. I. Kopp, Z.-Q. Zhang, and A. Z. Genack, "Lasing in chiral photonic structures," Prog. Quantum Electron. 27, 369-416 (2003).
[CrossRef]

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, "Magnetic photonic crystals," J. Phys. D 36, 277-287 (2003).
[CrossRef]

C. Koerdt, G. Düchs, and G. L. J. A. Rikken, "Magnetochiral anisotropy in Bragg scattering," Phys. Rev. Lett. 91, 073902 (2003).
[CrossRef] [PubMed]

2002 (5)

A. H. Gevorgyan, "Magneto-optics of a thin film layer with helical structure and enormous anisotropy," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 382, 1-19 (2002).
[CrossRef]

A. H. Gevorgyan, "Optical diode based on a highly anisotropic layer of a helical periodic medium subjected to a magnetic field," Tech. Phys. 47, 1008-1013 (2002).
[CrossRef]

A. Lakhtakia, "Sculptured thin films: accomplishments and emerging uses," Mater. Sci. Eng. C 19, 427-434 (2002).
[CrossRef]

M. D. Pickett and A. Lakhtakia, "On gyrotropic chiral sculptured thin films for magneto-optics," Optik 113, 367-371 (2002).
[CrossRef]

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

2001 (3)

D. N. Chigrin and C. M. S. Torres, "Periodic thin-film interference filters as one-dimensional photonic crystals," Opt. Spectrosc. 91, 484-489 (2001).
[CrossRef]

A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
[CrossRef]

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

2000 (4)

O. S. Eritsyan, "Diffraction reflection of light in a cholesteric liquid crystal in the presence of wave irreversibility and Bragg formula for media with nonidentical forward and return wavelengths," J. Exp. Theor. Phys. 90, 102-108 (2000).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, "Negative refraction index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

V. C. Venugopal and A. Lakhtakia, "Electromagnetic plane-wave response characteristics of nonaxially excited slabs of dielectric thin-film helicoidal bianisotropic mediums," Proc. R. Soc. London, Ser. A 456, 125-161 (2000).
[CrossRef]

1999 (3)

A. Lakhtakia, "Anomalous axial propagation in a gyrotropic, locally uniaxial, dielectric helicoidally nonhomogeneous medium," Int. J. Electron Commun. 53, 45-48 (1999).

G. H. Wagnière, "The magnetochiral effect and related optical phenomena," Chem. Phys. 245, 165-173 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

1998 (5)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

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

W. S. Weiglhofer, A. Lakhtakia, and B. Michel, "On the constitutive parameters of a chiroferrite composite medium," Microwave Opt. Technol. Lett. 18, 342-345 (1998).
[CrossRef]

G. L. J. A. Rikken, A. Sparenberg, and B. A. van Tiggelen, "Photonic magneto-transport," Physica B 246-247, 188-194 (1998).
[CrossRef]

G. L. J. A. Rikken and E. Raupach, "Pure and cascaded magnetochiral anisotropy in optical absorption," Phys. Rev. E 58, 5081-5084 (1998).
[CrossRef]

1997 (2)

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

H. Taouk, "Optical wave propagation in active media: gyrotropic-gyrochiral media," J. Opt. Soc. Am. A 14, 2006-2012 (1997).
[CrossRef]

1996 (1)

K. Robbie, M. J. Brett, and A. Lakhtakia, "Chiral sculptured thin films," Nature 384, 616 (1996).
[CrossRef]

1995 (1)

A. Lakhtakia and W. S. Weiglhofer, "On light propagation in helicoidal bianisotropic mediums," Proc. R. Soc. London Ser. A 448, 419-437 (1995).
[CrossRef]

1992 (1)

N. Engeta, D. L. Jaggard, and M. W. Kowarz, "Electromagnetic waves in Faraday chiral media," IEEE Trans. Antennas Propag. 40, 367-374 (1992).
[CrossRef]

1987 (2)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

1986 (1)

I. Abdulhalim, R. Weil, and L. Benguigui, "Dispersion and attenuation of the eigenwaves for light propagation in helicoidal liquid crystals," Liq. Cryst. 1, 155-167 (1986).
[CrossRef]

1984 (2)

G. Wagnière, "Magnetochiral dichroism in emission. Photoselection and the polarization of transitions," Chem. Phys. Lett. 110, 546-551 (1984).
[CrossRef]

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

1982 (1)

G. Wagnière and 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]

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1951 (1)

H. L. de Vries, "Rotatory power and other optical properties of certain liquid crystals," Acta Crystallogr. 4, 219-226 (1951).
[CrossRef]

1933 (1)

C. W. Oseen, "The theory of liquid crystals," J. Chem. Soc. 29, 883-899 (1933).

Abdulhalim, I.

I. Abdulhalim, R. Weil, and L. Benguigui, "Dispersion and attenuation of the eigenwaves for light propagation in helicoidal liquid crystals," Liq. Cryst. 1, 155-167 (1986).
[CrossRef]

Barron, L. D.

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

Benguigui, L.

I. Abdulhalim, R. Weil, and L. Benguigui, "Dispersion and attenuation of the eigenwaves for light propagation in helicoidal liquid crystals," Liq. Cryst. 1, 155-167 (1986).
[CrossRef]

Bita, I.

I. Bita and E. L. Thomas, 'Tunneling time for barriers lacking space-inversion and time-reversal symmetries,' Phys. Rev. Lett., submitted for publication.

I. Bita and E. L. Thomas are preparing a manuscript that will describe the effects of further reducing the symmetry of the repeat unit, for example by departing from the linear rotation in Eqs. .

Bretenaker, F.

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

Brett, M. J.

K. Robbie, M. J. Brett, and A. Lakhtakia, "Chiral sculptured thin films," Nature 384, 616 (1996).
[CrossRef]

Brillouin, L.

L. Brillouin, Wave Propagation in Periodic Structures (Dover, New York, 1953).

Chen, H. C.

H. C. Chen, Theory of Electromagnetic Waves: A Coordinate-Free Approach (McGraw-Hill, New York, 1983).

Chigrin, D. N.

D. N. Chigrin and C. M. S. Torres, "Periodic thin-film interference filters as one-dimensional photonic crystals," Opt. Spectrosc. 91, 484-489 (2001).
[CrossRef]

Collin, R. E.

R. E. Collin, Foundations for Microwave Engineering (McGraw-Hill, New York, 1965).

Dadoenkova, N. N.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, "Magnetic photonic crystals," J. Phys. D 36, 277-287 (2003).
[CrossRef]

de Vries, H. L.

H. L. de Vries, "Rotatory power and other optical properties of certain liquid crystals," Acta Crystallogr. 4, 219-226 (1951).
[CrossRef]

Düchs, G.

C. Koerdt, G. Düchs, and G. L. J. A. Rikken, "Magnetochiral anisotropy in Bragg scattering," Phys. Rev. Lett. 91, 073902 (2003).
[CrossRef] [PubMed]

Engeta, N.

N. Engeta, D. L. Jaggard, and M. W. Kowarz, "Electromagnetic waves in Faraday chiral media," IEEE Trans. Antennas Propag. 40, 367-374 (1992).
[CrossRef]

Eritsyan, O. S.

O. S. Eritsyan, "Diffraction reflection of light in a cholesteric liquid crystal in the presence of wave irreversibility and Bragg formula for media with nonidentical forward and return wavelengths," J. Exp. Theor. Phys. 90, 102-108 (2000).
[CrossRef]

Figotin, A.

A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
[CrossRef]

Floch, A. Le

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

Genack, A. Z.

V. I. Kopp, Z.-Q. Zhang, and A. Z. Genack, "Lasing in chiral photonic structures," Prog. Quantum Electron. 27, 369-416 (2003).
[CrossRef]

Gevorgyan, A. H.

A. H. Gevorgyan, "Magneto-optics of a thin film layer with helical structure and enormous anisotropy," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 382, 1-19 (2002).
[CrossRef]

A. H. Gevorgyan, "Optical diode based on a highly anisotropic layer of a helical periodic medium subjected to a magnetic field," Tech. Phys. 47, 1008-1013 (2002).
[CrossRef]

Ghosh, R.

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

Jaggard, D. L.

N. Engeta, D. L. Jaggard, and M. W. Kowarz, "Electromagnetic waves in Faraday chiral media," IEEE Trans. Antennas Propag. 40, 367-374 (1992).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

John, S.

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kleindienst, P.

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

Koerdt, C.

C. Koerdt, G. Düchs, and G. L. J. A. Rikken, "Magnetochiral anisotropy in Bragg scattering," Phys. Rev. Lett. 91, 073902 (2003).
[CrossRef] [PubMed]

Kong, J. A.

J. A. Kong, Electromagnetic Wave Theory (EMW, Cambridge, Mass., 2000).

Kopp, V. I.

V. I. Kopp, Z.-Q. Zhang, and A. Z. Genack, "Lasing in chiral photonic structures," Prog. Quantum Electron. 27, 369-416 (2003).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kotov, V. A.

A. K. Zvedin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (Institute of Physics, Philadelphia, Pa., 1997).

Kowarz, M. W.

N. Engeta, D. L. Jaggard, and M. W. Kowarz, "Electromagnetic waves in Faraday chiral media," IEEE Trans. Antennas Propag. 40, 367-374 (1992).
[CrossRef]

Kroll, N.

D. R. Smith and N. Kroll, "Negative refraction index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Lakhtakia, A.

J. A. Polo, Jr. and A. Lakhtakia, "Comparison of two methods for oblique propagation in helicoidal bianisotropic mediums," Opt. Commun. 230, 369-386 (2004).
[CrossRef]

A. Lakhtakia, "Sculptured thin films: accomplishments and emerging uses," Mater. Sci. Eng. C 19, 427-434 (2002).
[CrossRef]

M. D. Pickett and A. Lakhtakia, "On gyrotropic chiral sculptured thin films for magneto-optics," Optik 113, 367-371 (2002).
[CrossRef]

V. C. Venugopal and A. Lakhtakia, "Electromagnetic plane-wave response characteristics of nonaxially excited slabs of dielectric thin-film helicoidal bianisotropic mediums," Proc. R. Soc. London, Ser. A 456, 125-161 (2000).
[CrossRef]

A. Lakhtakia, "Anomalous axial propagation in a gyrotropic, locally uniaxial, dielectric helicoidally nonhomogeneous medium," Int. J. Electron Commun. 53, 45-48 (1999).

W. S. Weiglhofer, A. Lakhtakia, and B. Michel, "On the constitutive parameters of a chiroferrite composite medium," Microwave Opt. Technol. Lett. 18, 342-345 (1998).
[CrossRef]

K. Robbie, M. J. Brett, and A. Lakhtakia, "Chiral sculptured thin films," Nature 384, 616 (1996).
[CrossRef]

A. Lakhtakia and W. S. Weiglhofer, "On light propagation in helicoidal bianisotropic mediums," Proc. R. Soc. London Ser. A 448, 419-437 (1995).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Elmsford, N.Y., 1984).

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Elmsford, N.Y., 1984).

Lyubchanskii, I. L.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, "Magnetic photonic crystals," J. Phys. D 36, 277-287 (2003).
[CrossRef]

Lyubchanskii, M. I.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, "Magnetic photonic crystals," J. Phys. D 36, 277-287 (2003).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Meier, A.

G. Wagnière and 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]

Michel, B.

W. S. Weiglhofer, A. Lakhtakia, and B. Michel, "On the constitutive parameters of a chiroferrite composite medium," Microwave Opt. Technol. Lett. 18, 342-345 (1998).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Oseen, C. W.

C. W. Oseen, "The theory of liquid crystals," J. Chem. Soc. 29, 883-899 (1933).

Pendry, J. B.

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Pickett, M. D.

M. D. Pickett and A. Lakhtakia, "On gyrotropic chiral sculptured thin films for magneto-optics," Optik 113, 367-371 (2002).
[CrossRef]

Pinheiro, F. A.

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

Polo, J. A.

J. A. Polo, Jr. and A. Lakhtakia, "Comparison of two methods for oblique propagation in helicoidal bianisotropic mediums," Opt. Commun. 230, 369-386 (2004).
[CrossRef]

Rasing, Th.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, "Magnetic photonic crystals," J. Phys. D 36, 277-287 (2003).
[CrossRef]

Raupach, E.

G. L. J. A. Rikken and E. Raupach, "Pure and cascaded magnetochiral anisotropy in optical absorption," Phys. Rev. E 58, 5081-5084 (1998).
[CrossRef]

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

Rikken, G. L. J. A.

C. Koerdt, G. Düchs, and G. L. J. A. Rikken, "Magnetochiral anisotropy in Bragg scattering," Phys. Rev. Lett. 91, 073902 (2003).
[CrossRef] [PubMed]

G. L. J. A. Rikken, A. Sparenberg, and B. A. van Tiggelen, "Photonic magneto-transport," Physica B 246-247, 188-194 (1998).
[CrossRef]

G. L. J. A. Rikken and E. Raupach, "Pure and cascaded magnetochiral anisotropy in optical absorption," Phys. Rev. E 58, 5081-5084 (1998).
[CrossRef]

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

Robbie, K.

K. Robbie, M. J. Brett, and A. Lakhtakia, "Chiral sculptured thin films," Nature 384, 616 (1996).
[CrossRef]

Ruchon, T.

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

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Shapovalov, E. A.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, "Magnetic photonic crystals," J. Phys. D 36, 277-287 (2003).
[CrossRef]

Smith, D. R.

D. R. Smith and N. Kroll, "Negative refraction index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Sparenberg, A.

G. L. J. A. Rikken, A. Sparenberg, and B. A. van Tiggelen, "Photonic magneto-transport," Physica B 246-247, 188-194 (1998).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Taouk, H.

Terentjev, E. M.

M. Warner and E. M. Terentjev, Liquid Crystal Elastomers (Oxford U. Press, New York, 2003).

Thépot, J.-Y.

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

Thomas, E. L.

I. Bita and E. L. Thomas are preparing a manuscript that will describe the effects of further reducing the symmetry of the repeat unit, for example by departing from the linear rotation in Eqs. .

I. Bita and E. L. Thomas, 'Tunneling time for barriers lacking space-inversion and time-reversal symmetries,' Phys. Rev. Lett., submitted for publication.

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Torres, C. M. S.

D. N. Chigrin and C. M. S. Torres, "Periodic thin-film interference filters as one-dimensional photonic crystals," Opt. Spectrosc. 91, 484-489 (2001).
[CrossRef]

Vallet, M.

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

van Tiggelen, B. A.

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

G. L. J. A. Rikken, A. Sparenberg, and B. A. van Tiggelen, "Photonic magneto-transport," Physica B 246-247, 188-194 (1998).
[CrossRef]

Venugopal, V. C.

V. C. Venugopal and A. Lakhtakia, "Electromagnetic plane-wave response characteristics of nonaxially excited slabs of dielectric thin-film helicoidal bianisotropic mediums," Proc. R. Soc. London, Ser. A 456, 125-161 (2000).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vitebsky, I.

A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
[CrossRef]

Vrbancich, J.

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

Wagnière, G.

G. Wagnière, "Magnetochiral dichroism in emission. Photoselection and the polarization of transitions," Chem. Phys. Lett. 110, 546-551 (1984).
[CrossRef]

G. Wagnière and 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]

Wagnière, G. H.

G. H. Wagnière, "The magnetochiral effect and related optical phenomena," Chem. Phys. 245, 165-173 (1999).
[CrossRef]

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

Warner, M.

M. Warner and E. M. Terentjev, Liquid Crystal Elastomers (Oxford U. Press, New York, 2003).

Weiglhofer, W. S.

W. S. Weiglhofer, A. Lakhtakia, and B. Michel, "On the constitutive parameters of a chiroferrite composite medium," Microwave Opt. Technol. Lett. 18, 342-345 (1998).
[CrossRef]

A. Lakhtakia and W. S. Weiglhofer, "On light propagation in helicoidal bianisotropic mediums," Proc. R. Soc. London Ser. A 448, 419-437 (1995).
[CrossRef]

Weil, R.

I. Abdulhalim, R. Weil, and L. Benguigui, "Dispersion and attenuation of the eigenwaves for light propagation in helicoidal liquid crystals," Liq. Cryst. 1, 155-167 (1986).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Yablonovitch, E.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

Zhang, Z.-Q.

V. I. Kopp, Z.-Q. Zhang, and A. Z. Genack, "Lasing in chiral photonic structures," Prog. Quantum Electron. 27, 369-416 (2003).
[CrossRef]

Zvedin, A. K.

A. K. Zvedin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (Institute of Physics, Philadelphia, Pa., 1997).

Acta Crystallogr. (1)

H. L. de Vries, "Rotatory power and other optical properties of certain liquid crystals," Acta Crystallogr. 4, 219-226 (1951).
[CrossRef]

Appl. Phys. Lett. (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

Chem. Phys. (1)

G. H. Wagnière, "The magnetochiral effect and related optical phenomena," Chem. Phys. 245, 165-173 (1999).
[CrossRef]

Chem. Phys. Lett. (3)

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

G. Wagnière and 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 transitions," Chem. Phys. Lett. 110, 546-551 (1984).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

N. Engeta, D. L. Jaggard, and M. W. Kowarz, "Electromagnetic waves in Faraday chiral media," IEEE Trans. Antennas Propag. 40, 367-374 (1992).
[CrossRef]

Int. J. Electron Commun. (1)

A. Lakhtakia, "Anomalous axial propagation in a gyrotropic, locally uniaxial, dielectric helicoidally nonhomogeneous medium," Int. J. Electron Commun. 53, 45-48 (1999).

J. Chem. Soc. (1)

C. W. Oseen, "The theory of liquid crystals," J. Chem. Soc. 29, 883-899 (1933).

J. Exp. Theor. Phys. (1)

O. S. Eritsyan, "Diffraction reflection of light in a cholesteric liquid crystal in the presence of wave irreversibility and Bragg formula for media with nonidentical forward and return wavelengths," J. Exp. Theor. Phys. 90, 102-108 (2000).
[CrossRef]

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

J. Phys. D (1)

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, "Magnetic photonic crystals," J. Phys. D 36, 277-287 (2003).
[CrossRef]

Liq. Cryst. (1)

I. Abdulhalim, R. Weil, and L. Benguigui, "Dispersion and attenuation of the eigenwaves for light propagation in helicoidal liquid crystals," Liq. Cryst. 1, 155-167 (1986).
[CrossRef]

Mater. Sci. Eng. C (1)

A. Lakhtakia, "Sculptured thin films: accomplishments and emerging uses," Mater. Sci. Eng. C 19, 427-434 (2002).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

W. S. Weiglhofer, A. Lakhtakia, and B. Michel, "On the constitutive parameters of a chiroferrite composite medium," Microwave Opt. Technol. Lett. 18, 342-345 (1998).
[CrossRef]

Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A (1)

A. H. Gevorgyan, "Magneto-optics of a thin film layer with helical structure and enormous anisotropy," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 382, 1-19 (2002).
[CrossRef]

Mol. Phys. (1)

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

Nature (2)

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

K. Robbie, M. J. Brett, and A. Lakhtakia, "Chiral sculptured thin films," Nature 384, 616 (1996).
[CrossRef]

Opt. Commun. (1)

J. A. Polo, Jr. and A. Lakhtakia, "Comparison of two methods for oblique propagation in helicoidal bianisotropic mediums," Opt. Commun. 230, 369-386 (2004).
[CrossRef]

Opt. Spectrosc. (1)

D. N. Chigrin and C. M. S. Torres, "Periodic thin-film interference filters as one-dimensional photonic crystals," Opt. Spectrosc. 91, 484-489 (2001).
[CrossRef]

Optik (1)

M. D. Pickett and A. Lakhtakia, "On gyrotropic chiral sculptured thin films for magneto-optics," Optik 113, 367-371 (2002).
[CrossRef]

Phys. Rev. B (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Phys. Rev. E (3)

A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
[CrossRef]

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

G. L. J. A. Rikken and E. Raupach, "Pure and cascaded magnetochiral anisotropy in optical absorption," Phys. Rev. E 58, 5081-5084 (1998).
[CrossRef]

Phys. Rev. Lett. (6)

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

C. Koerdt, G. Düchs, and G. L. J. A. Rikken, "Magnetochiral anisotropy in Bragg scattering," Phys. Rev. Lett. 91, 073902 (2003).
[CrossRef] [PubMed]

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, "Negative refraction index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Physica B (1)

G. L. J. A. Rikken, A. Sparenberg, and B. A. van Tiggelen, "Photonic magneto-transport," Physica B 246-247, 188-194 (1998).
[CrossRef]

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

A. Lakhtakia and W. S. Weiglhofer, "On light propagation in helicoidal bianisotropic mediums," Proc. R. Soc. London Ser. A 448, 419-437 (1995).
[CrossRef]

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

V. C. Venugopal and A. Lakhtakia, "Electromagnetic plane-wave response characteristics of nonaxially excited slabs of dielectric thin-film helicoidal bianisotropic mediums," Proc. R. Soc. London, Ser. A 456, 125-161 (2000).
[CrossRef]

Prog. Quantum Electron. (1)

V. I. Kopp, Z.-Q. Zhang, and A. Z. Genack, "Lasing in chiral photonic structures," Prog. Quantum Electron. 27, 369-416 (2003).
[CrossRef]

Sov. Phys. Usp. (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Tech. Phys. (1)

A. H. Gevorgyan, "Optical diode based on a highly anisotropic layer of a helical periodic medium subjected to a magnetic field," Tech. Phys. 47, 1008-1013 (2002).
[CrossRef]

Other (11)

R. E. Collin, Foundations for Microwave Engineering (McGraw-Hill, New York, 1965).

A. K. Zvedin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (Institute of Physics, Philadelphia, Pa., 1997).

L. Brillouin, Wave Propagation in Periodic Structures (Dover, New York, 1953).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

M. Warner and E. M. Terentjev, Liquid Crystal Elastomers (Oxford U. Press, New York, 2003).

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Elmsford, N.Y., 1984).

H. C. Chen, Theory of Electromagnetic Waves: A Coordinate-Free Approach (McGraw-Hill, New York, 1983).

J. A. Kong, Electromagnetic Wave Theory (EMW, Cambridge, Mass., 2000).

I. Bita and E. L. Thomas are preparing a manuscript that will describe the effects of further reducing the symmetry of the repeat unit, for example by departing from the linear rotation in Eqs. .

I. Bita and E. L. Thomas, 'Tunneling time for barriers lacking space-inversion and time-reversal symmetries,' Phys. Rev. Lett., submitted for publication.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

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Figures (7)

Fig. 1
Fig. 1

Conceptual representation of the structural rotation throughout the unit cell of a 1D chiral PC showing the periodic, right-handed continuous twist along the z axis of an arbitrary vector with fixed orientation in the local material coordinate system. The spatial period L is defined for a full 2 π rotation ϕ ( z + L ) = ϕ ( z ) + 2 π .

Fig. 2
Fig. 2

Numerically calculated photonic band structure for axial propagation ω ( k z , k x = k y = 0 ) at two orientations of the magnetogyration vector g z (gray curves) and g x (black curves). Inset shows a magnification of the photonic band structure near the bandgap. Note that the g x band structure is also valid for the case when no MO activity is present, thus describing a simple dielectric helical medium.

Fig. 3
Fig. 3

(b) Numerically calculated photonic band structure for axial propagation ω ( k z , k x = k y = 0 ) in the case of g z . The thick curves correspond to propagation eigenmodes. The evanescent modes are shown with thin curves, the dark curve for the real part of the wave vector Re { k z } and the lighter ellipse for the imaginary part Im { k z } . (a) Transmission of plane waves propagation in the + z direction ( γ > 0 ) through a finite piece of the right-hand PC, showing the total transmissivities of LCP waves ( T LL + T LR ) and stop band for RCP waves ( T RR + T RL ) . The polarization conversion contribution ( T LR = T RL ) is scaled by a factor of 200 for visibility on the same plot. (c) Same as (a), but the magnetogyration vector is reversed ( γ < 0 ) , corresponding to an incident wave propagating in the z direction.

Fig. 4
Fig. 4

Isofrequency cuts through numerically calculated dispersion surfaces, ω ( k x , k y = 0 , k z ) . (a) Effect of MO activity ( γ > 0 ) on the isofrequency contours when ω = 0.65 ( 2 π c L ) and the magnetogyration vector is parallel to the helical axis ( g z ) ;(b) is isofrequency cuts at multiple frequencies for constant MO activity ( γ = 0.1 , g z ) .

Fig. 5
Fig. 5

Isofrequency cut at ω = 0.67 ( 2 π c L ) through numerically calculated dispersion surfaces ω ( k x , k y = 0 , k z ) when g z ( γ = 0.1 ) showing the directions of the Poynting vectors of four eigenmodes phase matched to a particular value of the parallel wave vector.

Fig. 6
Fig. 6

Isofrequency cuts through numerically calculated dispersion surfaces ω ( k x , k y = 0 , k z ) . (a) Effect of MO activity ( γ > 0 ) on the ω = 0.65 ( 2 π c L ) contours, when the magnetogyration vector is perpendicular to the helical axis ( g x ) ; (b) isofrequency cuts at multiple frequencies for constant MO activity ( γ = 0.2 , g x ) .

Fig. 7
Fig. 7

Isofrequency cut at ω = 0.65 ( 2 π c L ) through numerically calculated dispersion surfaces ω ( k x , k y = 0 , k z ) showing three different regimes of transmission when g x ( γ = 0.2 ) ; (i) and (iii) depict normal refraction at the air–PC interface; (ii) shows negative refraction at the air–PC interface

Equations (28)

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D = ϵ 0 ϵ ͇ x y z ( r ) E ,
B = μ 0 H .
ϵ ͇ x y z ( z ) = S ͇ z ( z ) ϵ ͇ ref S ͇ z 1 ( z ) + i γ g × I ͇ ,
ϵ ͇ ref = ϵ 11 x x + ϵ 22 y y + ϵ 33 z z ,
S ͇ z = ( x x + y y ) cos [ ϕ ( z ) ] + ( y x x y ) sin [ ϕ ( z ) ] + z z ,
g = x cos ( θ g ) + z sin ( θ g ) ,
ϕ ( z ) = q z ,
q = q 0 ( 2 π L ) ,
D = ϵ 0 ϵ ͇ E ,
ϵ ͇ ( ω , k , B 0 ) = ϵ ( ω ) I ͇ + i α ( ω ) ( k × I ͇ ) + i β ( ω ) ( B 0 × I ͇ ) + γ ( ω ) ( k B 0 ) ,
D = ϵ 0 ϵ ͇ E + i ϵ 0 μ o ξ c H ,
B = i ϵ 0 μ o ξ c E + μ 0 μ ͇ H ,
ϵ ͇ = ϵ a I ͇ + ϵ b g g + i ϵ g g × I ͇ ,
μ ͇ = μ a I ͇ + μ b g g + i μ g g × I ͇ ,
v p = ω ( k ) k ,
v g = ω ( k ) k .
× × E ( r ) = ω 2 μ 0 D ( r ) .
z z 2 E ( z ) = ( ω c ) 2 ϵ ͇ x y z E ( z ) ,
ϵ ͇ = ϵ ͇ ref + i γ z × I ͇ .
E ( z ) = S ͇ z ( z ) E ( z ) ,
[ z z 2 ( z ϕ ) 2 ( z z 2 ϕ ) 2 ( z ϕ ) ( z z 2 ϕ ) + 2 ( z ϕ ) z z 2 ( z ϕ ) 2 ] [ E 1 E 2 ] = ω 2 c 2 ϵ ͇ [ E 1 E 2 ] ,
[ ω 2 c 2 ϵ 11 k z 2 q 2 ω 2 c 2 ϵ 12 2 i q k z ω 2 c 2 ϵ 21 + 2 i q k z ω 2 c 2 ϵ 22 k z 2 q 2 ] [ E 1 E 2 ] = 0 ,
ω 4 c 4 ( ϵ 11 ϵ 22 γ 2 ) ω 2 c 2 [ ( ϵ 11 + ϵ 22 ) ( k z 2 + q 2 ) 4 γ k z q ] + ( k z 2 q 2 ) 2 = 0 .
Ψ ( z + L ) = P ͇ Ψ ( z ) ,
det [ P ͇ exp ( i k z L ) ] = 0 .
ω ̃ 4 ( ϵ 11 ϵ 22 γ 2 ) ω ̃ 2 [ ( ϵ 11 + ϵ 22 ) ( k ̃ z 2 + 1 ) 4 γ k ̃ z q 0 ] + ( k ̃ z 2 1 ) 2 = 0 ,
ω ̃ i 1 ϵ i i [ 1 + γ 2 2 ϵ i i ( 3 ϵ i i + ϵ j j ) ] ,
k ̃ z , i q 0 γ 3 ϵ i i + ϵ j j ,

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