Abstract

The polarization properties of perfectly periodical and defective one-dimensional photonic bandgap structures with nonreciprocal chiral (bi-isotropic) layers are studied. The method of solution is based on the 2×2 block-representation transfer-matrix formulation. Numerical simulations are carried out for different types of structures (symmetrical or asymmetrical) in order to reveal the dependence of the reflection and transmission coefficients on frequency, chirality, nonreciprocity parameters, and angle of wave incidence.

© 2009 Optical Society of America

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  21. L. Poladian, “Resonance mode expansions and exact solutions for nonuniform gratings,” Phys. Rev. E 54, 2963-2975 (1996).
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  22. A. H. Gevorgyan, “Nonreciprocal waves in absorbing multilayer systems,” Tech. Phys. Lett. 29, 819-823 (2003).
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  23. D. N. Astrov, “Magnetoelectric effect in chromium oxide,” Sov. Phys. JETP 13, 729-733 (1961).
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    [CrossRef]
  25. J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573-1575 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  28. J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Mater. 4, 383-387 (2005).
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    [CrossRef]
  31. L. J. Dickey, “High powers of matrices,” ACM SIGAPL APL Quote Quad. 18, 96-99 (1987).
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    [CrossRef]

2009 (3)

2008 (4)

A. H. Gevorgyan, “Optical diodes and omnidirectional reflectors based on one-dimensional quasiperiodic photonic crystals,” Tech. Phys. Lett. 34, 22-25 (2008).
[CrossRef]

V. R. Tuz, “Three-dimensional Gaussian beam scattering from a periodic sequence of bi-isotropic and material layers,” Prog. Electromagn. Res. 7, 53-73 (2008).
[CrossRef]

V. R. Tuz and V. B. Kazanskiy, “Depolarization properties of a periodic sequence of chiral and material layers,” J. Opt. Soc. Am. A 25, 2704-2709 (2008).
[CrossRef]

C.-W. Qiu, N. Burokur, S. Zouhd, and L.-W. Li, “Chiral nihility effects on energy flow in chiral materials,” J. Opt. Soc. Am. A 25, 55-63 (2008).
[CrossRef]

2007 (2)

2006 (2)

J. Li, L. Jin, L. Li and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photonics Technol. Lett. 18, 1261-1263 (2006).
[CrossRef]

J.-Y. Chen and L.-W. Chen, “Color separating with integrated photonic bandgap optical diodes: a numerical study,” Opt. Express 14, 10733-10739 (2006).
[CrossRef] [PubMed]

2005 (3)

2004 (1)

A. Grande, I. Barba, A. C. L. Cabeceira, J. Represa, P. P. M. So, and W. J. R. Hoefer, “FDTD modeling of transient microwave signals in dispersive and lossy bi-isotropic media,” IEEE Trans. Microwave Theory Tech. 52, 773-783 (2004).
[CrossRef]

2003 (1)

A. H. Gevorgyan, “Nonreciprocal waves in absorbing multilayer systems,” Tech. Phys. Lett. 29, 819-823 (2003).
[CrossRef]

2000 (1)

A. Lakhtakia and W. S. Weiglhofer, “A comparative study of planewave propagation in helicoidal bianisotropic mediums and isotropic chiral mediums,” J. Opt. A 2, 107-111 (2000).
[CrossRef]

1998 (1)

1997 (1)

W. S. Weiglhofer and A. Lakhtakia, “On the nonexistence of linear nonreciprocal bi-isotropic (NRBI) media,” J. Phys. A 30, 2597-2600 (1997).
[CrossRef]

1996 (1)

L. Poladian, “Resonance mode expansions and exact solutions for nonuniform gratings,” Phys. Rev. E 54, 2963-2975 (1996).
[CrossRef]

1994 (4)

A. Lakhtakia and W. S. Weiglhofer, “Are linear, nonreciprocal, biisotropic media forbidden?” IEEE Trans. Microwave Theory Tech. 42, 1715-1716 (1994).
[CrossRef]

K. M. Flood and D. L. Jaggard, “Distributed feedback lasers in chiral media,” IEEE J. Quantum Electron. 30, 339-345 (1994).
[CrossRef]

A. H. Sihvola, “Electromagnetic modeling of bi-isotropic media,” Prog. Electromagn. Res. 9, 45-86 (1994).

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023-2029 (1994).
[CrossRef]

1993 (1)

1987 (2)

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization in optics: quasiperiodic media,” Phys. Rev. Lett. 58, 2436-2438 (1987).
[CrossRef] [PubMed]

L. J. Dickey, “High powers of matrices,” ACM SIGAPL APL Quote Quad. 18, 96-99 (1987).
[CrossRef]

1963 (1)

S. Shtrikman and D. Treves, “Observation of the magnetoelectric effect in Cr2O3 powders,” Phys. Rev. 130, 986-988 (1963).
[CrossRef]

1961 (1)

D. N. Astrov, “Magnetoelectric effect in chromium oxide,” Sov. Phys. JETP 13, 729-733 (1961).

Astrov, D. N.

D. N. Astrov, “Magnetoelectric effect in chromium oxide,” Sov. Phys. JETP 13, 729-733 (1961).

Autschbach, J.

Baev, A.

Barba, I.

A. Grande, I. Barba, A. C. L. Cabeceira, J. Represa, P. P. M. So, and W. J. R. Hoefer, “FDTD modeling of transient microwave signals in dispersive and lossy bi-isotropic media,” IEEE Trans. Microwave Theory Tech. 52, 773-783 (2004).
[CrossRef]

Bloemer, M. J.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023-2029 (1994).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1968).

Bowden, C. M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023-2029 (1994).
[CrossRef]

Burokur, N.

Cabeceira, A. C. L.

A. Grande, I. Barba, A. C. L. Cabeceira, J. Represa, P. P. M. So, and W. J. R. Hoefer, “FDTD modeling of transient microwave signals in dispersive and lossy bi-isotropic media,” IEEE Trans. Microwave Theory Tech. 52, 773-783 (2004).
[CrossRef]

Chan, C. T.

Chen, J.-Y.

Chen, L.-W.

Dickey, L. J.

L. J. Dickey, “High powers of matrices,” ACM SIGAPL APL Quote Quad. 18, 96-99 (1987).
[CrossRef]

Dowling, J. P.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023-2029 (1994).
[CrossRef]

Fan, S.

Fink, Y.

Flood, K. M.

K. M. Flood and D. L. Jaggard, “Distributed feedback lasers in chiral media,” IEEE J. Quantum Electron. 30, 339-345 (1994).
[CrossRef]

Fukuyama, A.

Gevorgyan, A. H.

A. H. Gevorgyan, “Optical diodes and omnidirectional reflectors based on one-dimensional quasiperiodic photonic crystals,” Tech. Phys. Lett. 34, 22-25 (2008).
[CrossRef]

A. H. Gevorgyan, “Nonreciprocal waves in absorbing multilayer systems,” Tech. Phys. Lett. 29, 819-823 (2003).
[CrossRef]

Grande, A.

A. Grande, I. Barba, A. C. L. Cabeceira, J. Represa, P. P. M. So, and W. J. R. Hoefer, “FDTD modeling of transient microwave signals in dispersive and lossy bi-isotropic media,” IEEE Trans. Microwave Theory Tech. 52, 773-783 (2004).
[CrossRef]

Hoefer, W. J. R.

A. Grande, I. Barba, A. C. L. Cabeceira, J. Represa, P. P. M. So, and W. J. R. Hoefer, “FDTD modeling of transient microwave signals in dispersive and lossy bi-isotropic media,” IEEE Trans. Microwave Theory Tech. 52, 773-783 (2004).
[CrossRef]

Hwang, J.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Mater. 4, 383-387 (2005).
[CrossRef]

Iguchi, K.

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization in optics: quasiperiodic media,” Phys. Rev. Lett. 58, 2436-2438 (1987).
[CrossRef] [PubMed]

Ishikawa, K.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Mater. 4, 383-387 (2005).
[CrossRef]

Jablonovitch, E.

Jaggard, D. L.

K. M. Flood and D. L. Jaggard, “Distributed feedback lasers in chiral media,” IEEE J. Quantum Electron. 30, 339-345 (1994).
[CrossRef]

Jin, L.

J. Li, L. Jin, L. Li and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photonics Technol. Lett. 18, 1261-1263 (2006).
[CrossRef]

Joannopoulos, J. D.

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573-1575 (1998).
[CrossRef]

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

Kazanskiy, V. B.

Kohmoto, M.

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization in optics: quasiperiodic media,” Phys. Rev. Lett. 58, 2436-2438 (1987).
[CrossRef] [PubMed]

Krykunov, M.

Lakhtakia, A.

A. Lakhtakia and W. S. Weiglhofer, “A comparative study of planewave propagation in helicoidal bianisotropic mediums and isotropic chiral mediums,” J. Opt. A 2, 107-111 (2000).
[CrossRef]

W. S. Weiglhofer and A. Lakhtakia, “On the nonexistence of linear nonreciprocal bi-isotropic (NRBI) media,” J. Phys. A 30, 2597-2600 (1997).
[CrossRef]

A. Lakhtakia and W. S. Weiglhofer, “Are linear, nonreciprocal, biisotropic media forbidden?” IEEE Trans. Microwave Theory Tech. 42, 1715-1716 (1994).
[CrossRef]

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer-Verlag, 1989).

Lee, H. F.

Lee, J. C. W.

Li, C.

J. Li, L. Jin, L. Li and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photonics Technol. Lett. 18, 1261-1263 (2006).
[CrossRef]

Li, J.

J. Li, L. Jin, L. Li and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photonics Technol. Lett. 18, 1261-1263 (2006).
[CrossRef]

Li, L.

J. Li, L. Jin, L. Li and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photonics Technol. Lett. 18, 1261-1263 (2006).
[CrossRef]

Li, L.-W.

Lindell, I. V.

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).

Linden, S.

M. Wegener and S. Linden, “Giving light yet another new twist,” Physics 2, 3 (2009). Available on: http://link.aps.org/doi/10.1103/Physics.2.3
[CrossRef]

Meade, R. D.

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

Nishimura, S.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Mater. 4, 383-387 (2005).
[CrossRef]

Okamoto, T.

Pang, Y. K.

Park, B.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Mater. 4, 383-387 (2005).
[CrossRef]

Poladian, L.

L. Poladian, “Resonance mode expansions and exact solutions for nonuniform gratings,” Phys. Rev. E 54, 2963-2975 (1996).
[CrossRef]

Prasad, P. N.

Qiu, C.-W.

Represa, J.

A. Grande, I. Barba, A. C. L. Cabeceira, J. Represa, P. P. M. So, and W. J. R. Hoefer, “FDTD modeling of transient microwave signals in dispersive and lossy bi-isotropic media,” IEEE Trans. Microwave Theory Tech. 52, 773-783 (2004).
[CrossRef]

Samoc, M.

Scalora, M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023-2029 (1994).
[CrossRef]

Sheng, P.

Shtrikman, S.

S. Shtrikman and D. Treves, “Observation of the magnetoelectric effect in Cr2O3 powders,” Phys. Rev. 130, 986-988 (1963).
[CrossRef]

Sihvola, A. H.

A. H. Sihvola, “Electromagnetic modeling of bi-isotropic media,” Prog. Electromagn. Res. 9, 45-86 (1994).

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).

So, P. P. M.

A. Grande, I. Barba, A. C. L. Cabeceira, J. Represa, P. P. M. So, and W. J. R. Hoefer, “FDTD modeling of transient microwave signals in dispersive and lossy bi-isotropic media,” IEEE Trans. Microwave Theory Tech. 52, 773-783 (2004).
[CrossRef]

Song, M. H.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Mater. 4, 383-387 (2005).
[CrossRef]

Sutherland, B.

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization in optics: quasiperiodic media,” Phys. Rev. Lett. 58, 2436-2438 (1987).
[CrossRef] [PubMed]

Takanishi, Y.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Mater. 4, 383-387 (2005).
[CrossRef]

Takezoe, H.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Mater. 4, 383-387 (2005).
[CrossRef]

Tam, W. Y.

Thiel, M.

Toyooka, T.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Mater. 4, 383-387 (2005).
[CrossRef]

Tretyakov, S. A.

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).

Treves, D.

S. Shtrikman and D. Treves, “Observation of the magnetoelectric effect in Cr2O3 powders,” Phys. Rev. 130, 986-988 (1963).
[CrossRef]

Tuz, V. R.

Varadan, V. K.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer-Verlag, 1989).

Varadan, V. V.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer-Verlag, 1989).

Viitanen, A. J.

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).

von Freymann, G.

Wegener, M.

M. Wegener and S. Linden, “Giving light yet another new twist,” Physics 2, 3 (2009). Available on: http://link.aps.org/doi/10.1103/Physics.2.3
[CrossRef]

M. Thiel, G. von Freymann, and M. Wegener, “Layer-by-layer three-dimensional chiral photonic crystals,” Opt. Lett. 32, 2547-2549 (2007).
[CrossRef] [PubMed]

Weiglhofer, W. S.

A. Lakhtakia and W. S. Weiglhofer, “A comparative study of planewave propagation in helicoidal bianisotropic mediums and isotropic chiral mediums,” J. Opt. A 2, 107-111 (2000).
[CrossRef]

W. S. Weiglhofer and A. Lakhtakia, “On the nonexistence of linear nonreciprocal bi-isotropic (NRBI) media,” J. Phys. A 30, 2597-2600 (1997).
[CrossRef]

A. Lakhtakia and W. S. Weiglhofer, “Are linear, nonreciprocal, biisotropic media forbidden?” IEEE Trans. Microwave Theory Tech. 42, 1715-1716 (1994).
[CrossRef]

Winn, J. N.

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573-1575 (1998).
[CrossRef]

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

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1968).

Wu, J. W.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Mater. 4, 383-387 (2005).
[CrossRef]

Zouhd, S.

ACM SIGAPL APL Quote Quad. (1)

L. J. Dickey, “High powers of matrices,” ACM SIGAPL APL Quote Quad. 18, 96-99 (1987).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. M. Flood and D. L. Jaggard, “Distributed feedback lasers in chiral media,” IEEE J. Quantum Electron. 30, 339-345 (1994).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

J. Li, L. Jin, L. Li and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photonics Technol. Lett. 18, 1261-1263 (2006).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

A. Lakhtakia and W. S. Weiglhofer, “Are linear, nonreciprocal, biisotropic media forbidden?” IEEE Trans. Microwave Theory Tech. 42, 1715-1716 (1994).
[CrossRef]

A. Grande, I. Barba, A. C. L. Cabeceira, J. Represa, P. P. M. So, and W. J. R. Hoefer, “FDTD modeling of transient microwave signals in dispersive and lossy bi-isotropic media,” IEEE Trans. Microwave Theory Tech. 52, 773-783 (2004).
[CrossRef]

J. Appl. Phys. (1)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023-2029 (1994).
[CrossRef]

J. Opt. A (1)

A. Lakhtakia and W. S. Weiglhofer, “A comparative study of planewave propagation in helicoidal bianisotropic mediums and isotropic chiral mediums,” J. Opt. A 2, 107-111 (2000).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (2)

J. Phys. A (1)

W. S. Weiglhofer and A. Lakhtakia, “On the nonexistence of linear nonreciprocal bi-isotropic (NRBI) media,” J. Phys. A 30, 2597-2600 (1997).
[CrossRef]

Nature Mater. (1)

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Mater. 4, 383-387 (2005).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. (1)

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[CrossRef]

Phys. Rev. E (1)

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[CrossRef]

Phys. Rev. Lett. (1)

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization in optics: quasiperiodic media,” Phys. Rev. Lett. 58, 2436-2438 (1987).
[CrossRef] [PubMed]

Physics (1)

M. Wegener and S. Linden, “Giving light yet another new twist,” Physics 2, 3 (2009). Available on: http://link.aps.org/doi/10.1103/Physics.2.3
[CrossRef]

Prog. Electromagn. Res. (2)

A. H. Sihvola, “Electromagnetic modeling of bi-isotropic media,” Prog. Electromagn. Res. 9, 45-86 (1994).

V. R. Tuz, “Three-dimensional Gaussian beam scattering from a periodic sequence of bi-isotropic and material layers,” Prog. Electromagn. Res. 7, 53-73 (2008).
[CrossRef]

Sov. Phys. JETP (1)

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Tech. Phys. Lett. (2)

A. H. Gevorgyan, “Optical diodes and omnidirectional reflectors based on one-dimensional quasiperiodic photonic crystals,” Tech. Phys. Lett. 34, 22-25 (2008).
[CrossRef]

A. H. Gevorgyan, “Nonreciprocal waves in absorbing multilayer systems,” Tech. Phys. Lett. 29, 819-823 (2003).
[CrossRef]

Other (4)

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer-Verlag, 1989).

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).

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

M. Born and E. Wolf, Principles of Optics (Pergamon, 1968).

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Figures (7)

Fig. 1
Fig. 1

Finite photonic bandgap structure of isotropic and bi-isotropic layers.

Fig. 2
Fig. 2

(a) Frequency and (b) angular dependences of the reflection and transmission spectra of a finite photonic structure of isotropic and bi-isotropic layers. ε j = μ j = 1 , j 2 , ε 2 = 2 , μ 2 = 1 , ρ = 0.1 , χ = 0.05 , d 1 L = d 2 L = 0.5 , N = 5 . (a) φ 0 = 25 ° . (b) k 0 L = 10 .

Fig. 3
Fig. 3

Transmission coefficient magnitude of (a) copolarized and (b) cross-polarized waves as function of frequency k 0 L and chirality parameter ρ for a finite photonic structure of isotropic and bi-isotropic layers. ε j = μ j = 1 , j 2 , ε 2 = 2 , μ 2 = 1 , χ = 0.05 , d 1 L = d 2 L = 0.5 , N = 5 .

Fig. 4
Fig. 4

Finite photonic bandgap structure of isotropic and bi-isotropic layers with periodicity defect.

Fig. 5
Fig. 5

(a), (c) Reflection and (b), (d) transmission spectra of a finite symmetrical bi-isotropic photonic structure of N = 19 periods with the isotropic defect in the middle ( m = 10 ) of the structure. ε j = μ j = 1 , j 2 , ε 2 = ε 2 = 2 , ε 2 = 1 , μ 2 = μ 2 = μ 2 = 1 , ρ = χ = 0 , φ 0 = 25 ° , d 1 L = d 2 L = 0.5 . (a), (b) Tellegen layers. ρ = ρ = 0 , χ = χ = 0.1 . (c), (d) Pasteur layers. ρ = ρ = 0.1 , χ = χ = 0 .

Fig. 6
Fig. 6

(a), (c) Reflection and (b), (d) transmission spectra of a finite asymmetrical bi-isotropic photonic structure of N = 19 periods with the isotropic defect in the middle ( m = 10 ) of the structure. ε j = μ j = 1 , j 2 , ε 2 = ε 2 = 2 , ε 2 = 1 , μ 2 = μ 2 = μ 2 = 1 , ρ = χ = 0 , φ 0 = 25 ° , d 1 L = d 2 L = 0.5 . (a), (b) Tellegen layers. ρ = ρ = 0 , χ = 0.1 , χ = 0.1 . (c), (d) Pasteur layers. ρ = 0.1 , ρ = 0.1 χ = χ = 0 .

Fig. 7
Fig. 7

(a), (c) Reflection and (b), (d) transmission spectra of a finite isotropic photonic structure of N = 19 periods with the bi-isotropic defect in the middle ( m = 10 ) of the structure. ε j = μ j = 1 , j 2 , ε 2 = ε 2 = 2 , ε 2 = 3 , μ 2 = μ 2 = μ 2 = 1 , ρ = ρ = χ = χ = 0 , φ 0 = 25 ° , d 1 L = d 2 L = 0.5 . (a), (b) Tellegen defective layer. ρ = 0 , χ = 0.1 . (c), (d) Pasteur defective layer. ρ = 0.1 , χ = 0 .

Equations (4)

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D = ϵ E + ξ H , B = μ H + ζ E .
V 0 = T Σ V N + 1 = ( T 01 T N 1 T ̃ ) V N + 1 = ( T 01 T N T 13 ) V N + 1 ,
V 0 = [ T 01 ( n = 1 4 λ n N F n ) T 13 ] V N + 1 .
V 0 = { T 01 ( T ) m 1 T ( T ) N m T 13 } V N + 1 = { T 01 ( n = 1 4 ( λ n ) m 1 F n ) T ( n = 1 4 ( λ n ) N m F n ) T 13 } V N + 1 ,

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