Abstract

A periodic sequence of pairs of isotropic and chiral layers with a defect in the mth period is investigated. The problem is solved using the 2×2-block-representation transfer-matrix formulation. A method that simultaneously allows taking into account different types of defects in the structure is proposed. Analysis of the dynamics of the electromagnetic properties of the investigated structure is carried out for different types of defects.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  9. N. Engheta, D. L. Jaggard, and M. W. Kowarz, “Electromagnetic waves in Faraday chiral media,” IEEE Trans. Antennas Propag. 40, 367-374 (1992).
    [CrossRef]
  10. I. V. Lindell and A. J. Viitanen, “Plane wave propagation in uniaxial bianisotropic medium,” Electron. Lett. 29, 150-151 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. E. L. Tan and S. Y. Tan, “Cylindrical vector wave function representations of electromagnetic fields in gyrotropic bianisotropic media,” J. Electromagn. Waves Appl. 13, 1461-1476 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2008 (2)

A. H. Gevorgyan, “A device for the light polarization selection,” Tech. Phys. Lett. 34, 262-265 (2008) (English translation).
[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]

2007 (3)

2006 (1)

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

2005 (1)

J.-Y. Chen and L.-W. Chen, “Polarization-dependent filters based on chiral photonic structures with defects,” J. Opt. A, Pure Appl. Opt. 7, 558-566 (2005).
[CrossRef]

2003 (1)

2002 (1)

2000 (1)

K. Iga, “Surface-emitting laser--its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 6, 1201-1215 (2000).
[CrossRef]

1999 (1)

E. L. Tan and S. Y. Tan, “Cylindrical vector wave function representations of electromagnetic fields in gyrotropic bianisotropic media,” J. Electromagn. Waves Appl. 13, 1461-1476 (1999).
[CrossRef]

1998 (1)

W. Y. Yin, G. H. Nan, and I. Wolff, “The combined effects of chiral operation in multilayered bianisotropic substrates,” Prog. Electromagn. Res. 20, 153-178 (1998).
[CrossRef]

1995 (1)

M. Norgen and S. He, “General scheme for electromagnetic reflection and transmission for composite structures of complex materials,” IEE Proc. Microwaves, Antennas Propag. 142, 52-56 (1995).
[CrossRef]

1994 (1)

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

1993 (3)

1992 (1)

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

1987 (1)

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

1977 (1)

1972 (1)

Bass, F. G.

F. G. Bass, A. A. Bulgakov, and A. P. Tetervov, High-Frequency Properties of Semiconductors with Super-Lattice (Nauka, 1989) (in Russian).

Berreman, D. W.

Born, M.

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

Bose, R.

Bulgakov, A. A.

F. G. Bass, A. A. Bulgakov, and A. P. Tetervov, High-Frequency Properties of Semiconductors with Super-Lattice (Nauka, 1989) (in Russian).

Chen, J.-Y.

J.-Y. Chen and L.-W. Chen, “Polarization-dependent filters based on chiral photonic structures with defects,” J. Opt. A, Pure Appl. Opt. 7, 558-566 (2005).
[CrossRef]

Chen, L.-W.

J.-Y. Chen and L.-W. Chen, “Polarization-dependent filters based on chiral photonic structures with defects,” J. Opt. A, Pure Appl. Opt. 7, 558-566 (2005).
[CrossRef]

Dalichaouch, R.

Dickey, L. J.

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

Engheta, N.

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

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]

Fujii, A.

H. Yoshida, C. H. Lee, Y. Miura, A. Fujii, and M. Ozaki, “Optical tuning and switching of photonic defect modes in cholesteric liquid crystals,” Appl. Phys. Lett. 90, 071107 (2007).
[CrossRef]

Genack, A. Z.

Gevorgyan, A. H.

A. H. Gevorgyan, “A device for the light polarization selection,” Tech. Phys. Lett. 34, 262-265 (2008) (English translation).
[CrossRef]

Gilles, L.

Ha, N. Y.

He, S.

M. Norgen and S. He, “General scheme for electromagnetic reflection and transmission for composite structures of complex materials,” IEE Proc. Microwaves, Antennas Propag. 142, 52-56 (1995).
[CrossRef]

Hong, C.-S.

Iga, K.

K. Iga, “Surface-emitting laser--its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 6, 1201-1215 (2000).
[CrossRef]

Ishikawa, K.

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]

N. Engheta, D. L. Jaggard, and M. W. Kowarz, “Electromagnetic waves in Faraday chiral media,” IEEE Trans. Antennas Propag. 40, 367-374 (1992).
[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 Photon. Technol. Lett. 18, 1261-1263 (2006).
[CrossRef]

Kazanskiy, V. B.

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]

V. V. Khardikov, V. R. Tuz, and V. B. Kazanskiy, “Influence of defects on electrodynamic properties of the finite series of identical metal-dielectric resonators,” in Tenth International Conference on Mathematical Methods in Electromegnetic Theory (IEEE, 2004), pp. 130-132.
[CrossRef]

Khardikov, V. V.

V. V. Khardikov, V. R. Tuz, and V. B. Kazanskiy, “Influence of defects on electrodynamic properties of the finite series of identical metal-dielectric resonators,” in Tenth International Conference on Mathematical Methods in Electromegnetic Theory (IEEE, 2004), pp. 130-132.
[CrossRef]

Kopp, V. I.

Kowarz, M. W.

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

Kroll, N.

Lakhtakia, A.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Time-harmonic electromagnetic fields in chiral media,” Lecture Notes in Physics (Springer-Verlag, 1989).

Lee, C. H.

H. Yoshida, C. H. Lee, Y. Miura, A. Fujii, and M. Ozaki, “Optical tuning and switching of photonic defect modes in cholesteric liquid crystals,” Appl. Phys. Lett. 90, 071107 (2007).
[CrossRef]

Leung, K. M.

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 Photon. 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 Photon. 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 Photon. Technol. Lett. 18, 1261-1263 (2006).
[CrossRef]

Lindell, I. V.

I. V. Lindell and A. J. Viitanen, “Plane wave propagation in uniaxial bianisotropic medium,” Electron. Lett. 29, 150-151 (1993).
[CrossRef]

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

McCall, S. L.

Miura, Y.

H. Yoshida, C. H. Lee, Y. Miura, A. Fujii, and M. Ozaki, “Optical tuning and switching of photonic defect modes in cholesteric liquid crystals,” Appl. Phys. Lett. 90, 071107 (2007).
[CrossRef]

Nan, G. H.

W. Y. Yin, G. H. Nan, and I. Wolff, “The combined effects of chiral operation in multilayered bianisotropic substrates,” Prog. Electromagn. Res. 20, 153-178 (1998).
[CrossRef]

Norgen, M.

M. Norgen and S. He, “General scheme for electromagnetic reflection and transmission for composite structures of complex materials,” IEE Proc. Microwaves, Antennas Propag. 142, 52-56 (1995).
[CrossRef]

Ozaki, M.

H. Yoshida, C. H. Lee, Y. Miura, A. Fujii, and M. Ozaki, “Optical tuning and switching of photonic defect modes in cholesteric liquid crystals,” Appl. Phys. Lett. 90, 071107 (2007).
[CrossRef]

Platzman, P. M.

Schultz, S.

Sihvola, A. H.

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

Smith, D. R.

Takanishi, Y.

Takezoe, H.

Tan, E. L.

E. L. Tan and S. Y. Tan, “Cylindrical vector wave function representations of electromagnetic fields in gyrotropic bianisotropic media,” J. Electromagn. Waves Appl. 13, 1461-1476 (1999).
[CrossRef]

Tan, S. Y.

E. L. Tan and S. Y. Tan, “Cylindrical vector wave function representations of electromagnetic fields in gyrotropic bianisotropic media,” J. Electromagn. Waves Appl. 13, 1461-1476 (1999).
[CrossRef]

Tetervov, A. P.

F. G. Bass, A. A. Bulgakov, and A. P. Tetervov, High-Frequency Properties of Semiconductors with Super-Lattice (Nauka, 1989) (in Russian).

Thiel, M.

Tran, P.

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).

Tuz, V. R.

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]

V. V. Khardikov, V. R. Tuz, and V. B. Kazanskiy, “Influence of defects on electrodynamic properties of the finite series of identical metal-dielectric resonators,” in Tenth International Conference on Mathematical Methods in Electromegnetic Theory (IEEE, 2004), pp. 130-132.
[CrossRef]

Ujihara, K.

H. Yokoyama and K. Ujihara, Spontaneous Emission and Laser Oscillation in Microcavities (CRC Press, 1995).

Varadan, V. K.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Time-harmonic electromagnetic fields in chiral media,” Lecture Notes in Physics (Springer-Verlag, 1989).

Varadan, V. V.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Time-harmonic electromagnetic fields in chiral media,” Lecture Notes in Physics (Springer-Verlag, 1989).

Viitanen, A. J.

I. V. Lindell and A. J. Viitanen, “Plane wave propagation in uniaxial bianisotropic medium,” Electron. Lett. 29, 150-151 (1993).
[CrossRef]

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.

Wolf, E.

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

Wolff, I.

W. Y. Yin, G. H. Nan, and I. Wolff, “The combined effects of chiral operation in multilayered bianisotropic substrates,” Prog. Electromagn. Res. 20, 153-178 (1998).
[CrossRef]

Yariv, A.

Yeh, P.

Yin, W. Y.

W. Y. Yin, G. H. Nan, and I. Wolff, “The combined effects of chiral operation in multilayered bianisotropic substrates,” Prog. Electromagn. Res. 20, 153-178 (1998).
[CrossRef]

Yokoyama, H.

H. Yokoyama and K. Ujihara, Spontaneous Emission and Laser Oscillation in Microcavities (CRC Press, 1995).

Yoshida, H.

H. Yoshida, C. H. Lee, Y. Miura, A. Fujii, and M. Ozaki, “Optical tuning and switching of photonic defect modes in cholesteric liquid crystals,” Appl. Phys. Lett. 90, 071107 (2007).
[CrossRef]

ACM SIGAPL APL Quote Quad. (1)

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

Appl. Phys. Lett. (1)

H. Yoshida, C. H. Lee, Y. Miura, A. Fujii, and M. Ozaki, “Optical tuning and switching of photonic defect modes in cholesteric liquid crystals,” Appl. Phys. Lett. 90, 071107 (2007).
[CrossRef]

Electron. Lett. (1)

I. V. Lindell and A. J. Viitanen, “Plane wave propagation in uniaxial bianisotropic medium,” Electron. Lett. 29, 150-151 (1993).
[CrossRef]

IEE Proc. Microwaves, Antennas Propag. (1)

M. Norgen and S. He, “General scheme for electromagnetic reflection and transmission for composite structures of complex materials,” IEE Proc. Microwaves, Antennas Propag. 142, 52-56 (1995).
[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 J. Sel. Top. Quantum Electron. (1)

K. Iga, “Surface-emitting laser--its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 6, 1201-1215 (2000).
[CrossRef]

IEEE Photon. 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 Photon. Technol. Lett. 18, 1261-1263 (2006).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

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

J. Electromagn. Waves Appl. (1)

E. L. Tan and S. Y. Tan, “Cylindrical vector wave function representations of electromagnetic fields in gyrotropic bianisotropic media,” J. Electromagn. Waves Appl. 13, 1461-1476 (1999).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

J.-Y. Chen and L.-W. Chen, “Polarization-dependent filters based on chiral photonic structures with defects,” J. Opt. A, Pure Appl. Opt. 7, 558-566 (2005).
[CrossRef]

J. Opt. Soc. Am. (2)

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

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

Opt. Express (1)

Opt. Lett. (2)

Prog. Electromagn. Res. (1)

W. Y. Yin, G. H. Nan, and I. Wolff, “The combined effects of chiral operation in multilayered bianisotropic substrates,” Prog. Electromagn. Res. 20, 153-178 (1998).
[CrossRef]

Tech. Phys. Lett. (1)

A. H. Gevorgyan, “A device for the light polarization selection,” Tech. Phys. Lett. 34, 262-265 (2008) (English translation).
[CrossRef]

Other (6)

V. V. Khardikov, V. R. Tuz, and V. B. Kazanskiy, “Influence of defects on electrodynamic properties of the finite series of identical metal-dielectric resonators,” in Tenth International Conference on Mathematical Methods in Electromegnetic Theory (IEEE, 2004), pp. 130-132.
[CrossRef]

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

F. G. Bass, A. A. Bulgakov, and A. P. Tetervov, High-Frequency Properties of Semiconductors with Super-Lattice (Nauka, 1989) (in Russian).

H. Yokoyama and K. Ujihara, Spontaneous Emission and Laser Oscillation in Microcavities (CRC Press, 1995).

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Time-harmonic electromagnetic fields in chiral media,” Lecture Notes in Physics (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).

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Figures (4)

Fig. 1
Fig. 1

Bounded periodical sequence of isotropic and chiral layers with the defect period.

Fig. 2
Fig. 2

Frequency dependences of the reflection and transmission coefficient magnitudes of the structure of N = 5 periods with perturbations of the (a) layer thicknesses d 2 and (b) chirality parameter ρ in the middle ( m = 3 ) of the structure. ε j = μ j = 1 , j 2 , ε 2 = 2 , μ 2 = 1 , d 1 L = d 2 L = 0.5 , ρ = 0.1 , φ 0 = 25 ° .

Fig. 3
Fig. 3

Defect modes of the reflection and transmission coefficient magnitudes of the structure of N = 19 periods with perturbations of permittivity ε 2 and chirality parameter ρ in the middle ( m = 10 ) of the structure. ε j = μ j = 1 , j 2 , ε 2 = 2 , μ 2 = 1 , ρ = 0.1 , ρ ̃ = 0 , d 1 L = d 2 L = 0.5 , φ 0 = 25 ° . (a), (b) ε ̃ 2 = 1 ; (c), (d) ε ̃ 2 = 4 .

Fig. 4
Fig. 4

Defect modes of the (a) reflection and (b) transmission coefficient magnitudes of the structure of N = 19 periods with perturbations of the permittivity ε 2 and the chirality ρ parameter in the first half ( m = 6 ) of the structure. ε j = μ j = 1 , j 2 , ε 2 = 2 , μ 2 = 1 , ε ̃ 2 = 1 , ρ = 0.1 , ρ ̃ = 0 , d 1 L = d 2 L = 0.5 , φ 0 = 25 ° .

Equations (10)

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D = ε 2 E i ρ H , B = μ 2 H + i ρ E ,
( A 0 s B 0 s 0 B 0 s ) = T ( 0 ) ( A N + 1 s 0 A N + 1 s 0 ) , T ( 0 ) = T 01 T N 1 T = T 01 T N T 13 ,
T p ν = [ ( T p ν s ) 0 0 ( T p ν s ) ] , T 1 = [ ( T 1 + s s ) ( T 1 s s ) ( T 1 + s s ) ( T 1 s s ) ] ,
T 2 = [ ( T 2 + s s ) ( T 2 + s s ) ( T 2 s s ) ( T 2 s s ) ] ,
T N = n = 1 4 λ n N F n , F n = P I n P 1 ,
T ( Δ X s ) = T 01 ( n = 1 4 λ n m 1 F n ) T ̃ ( n = 1 4 λ n N m F n ) T 13 .
T ̃ = T + δ = 1 M ( T X δ ) Δ X δ T + δ = 1 M T ( δ ) Δ X δ ;
t ̃ j k = t j k + δ = 1 M ( t j k X δ ) Δ X δ = t j k + δ = 1 M t j k δ Δ X δ .
T ( Δ X δ ) = T ( 0 ) + T 01 ( n = 1 4 λ n m 1 F n ) ( δ = 1 M T ( δ ) Δ X δ ) ( n = 1 4 λ n N m F n ) T 13 ,
T ( Δ X δ ) = T ( 0 ) + Δ X δ T 01 ( n = 1 4 λ n m 1 F n ) T ( δ ) ( n = 1 4 λ n N m F n ) T 13 .

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