Abstract

The reflection and transmission coefficients of the perpendicular and parallel polarization plane electromagnetic waves of a finite quasi-periodic Fibonacci sequence of chiral and convenient isotropic magnetodielectric layers are obtained using the 2×2-block-representation transfer-matrix formulation. A correlation has been established between geometrical and spectral properties of the structure under consideration. Numerical simulations are carried out for different structures to reveal the dependence of the reflection and transmission coefficients on the frequency, chirality parameter, and the angle of wave incidence.

© 2009 Optical Society of America

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  1. E. Jablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10, 283-295 (1993).
    [CrossRef]
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, 1995).
  3. K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001).
  4. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization in optics: quasiperiodic media,” Phys. Rev. Lett. 58, 2436-2438 (1987).
    [CrossRef] [PubMed]
  5. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci multilayers,” Phys. Rev. Lett. 72, 633-636 (1994).
    [CrossRef] [PubMed]
  6. E. Macia, “Optical engineering with Fibonacci dielectric multilayers,” Appl. Phys. Lett. 73, 3330-3332 (1998).
    [CrossRef]
  7. X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: extensions and applications,” Phys. Rev. B 62, 14020 (2000).
    [CrossRef]
  8. M. Aissaoui, J. Zaghdoudi, M. Kanzari, and B. Rezig, “Optical properties of the quasi-periodic one-dimensional generalized multilayer Fibonacci structures,” Prog. Electromagn. Res. PIER 59, 69-83 (2006).
    [CrossRef]
  9. M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
    [CrossRef]
  10. L. Moretti, I. Rea, L. Rotiroti, I. Rendina, G. Abbate, A. Marino, and L. Du Stefano, “Photonic band gaps analysis of Thue-Morse multilayers made of porous silicon,” Opt. Express 14, 6264-6272 (2006).
    [CrossRef] [PubMed]
  11. H. T. Hattori, V. M. Schneider, and O. Lisboa, “Cantor set Bragg grating,” J. Opt. Soc. Am. A 17, 1583-1589 (2000).
    [CrossRef]
  12. A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
    [CrossRef]
  13. T. Okamoto and A. Fukuyama, “Light amplification from Cantor and asymmetric multilayer resonators,” Opt. Express 13, 8122-8127 (2005).
    [CrossRef] [PubMed]
  14. L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill, 1961).
  15. A. Ishimaru, Wave Propagation and Scattering in Random Media, IEEE/OUP Series on Electromagnetic Wave Theory (IEEE Press, 1997).
  16. A. Lakhtakia, V. K. Varadan, and V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media, Lecture Notes in Physics (Springer-Verlag, 1989).
  17. 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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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  22. D. W. Berreman, “Optics in stratified and anisotropic media: 4×4-matrix formulation,” J. Opt. Soc. Am. A 62, 502-510 (1972).
    [CrossRef]
  23. M. Born and E. Wolf, Principles of Optics (Pergamon, 1968).
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    [CrossRef]
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    [CrossRef]

2008 (1)

2007 (1)

2006 (2)

L. Moretti, I. Rea, L. Rotiroti, I. Rendina, G. Abbate, A. Marino, and L. Du Stefano, “Photonic band gaps analysis of Thue-Morse multilayers made of porous silicon,” Opt. Express 14, 6264-6272 (2006).
[CrossRef] [PubMed]

M. Aissaoui, J. Zaghdoudi, M. Kanzari, and B. Rezig, “Optical properties of the quasi-periodic one-dimensional generalized multilayer Fibonacci structures,” Prog. Electromagn. Res. PIER 59, 69-83 (2006).
[CrossRef]

2005 (2)

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

T. Okamoto and A. Fukuyama, “Light amplification from Cantor and asymmetric multilayer resonators,” Opt. Express 13, 8122-8127 (2005).
[CrossRef] [PubMed]

2002 (1)

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[CrossRef]

2001 (1)

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001).

2000 (2)

X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: extensions and applications,” Phys. Rev. B 62, 14020 (2000).
[CrossRef]

H. T. Hattori, V. M. Schneider, and O. Lisboa, “Cantor set Bragg grating,” J. Opt. Soc. Am. A 17, 1583-1589 (2000).
[CrossRef]

1998 (1)

E. Macia, “Optical engineering with Fibonacci dielectric multilayers,” Appl. Phys. Lett. 73, 3330-3332 (1998).
[CrossRef]

1997 (2)

V. B. Kazanskiy and V. V. Podlozny, “Quasiperiodic layered structure with resistive films,” Electromagnetics 17, 131-146 (1997).
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media, IEEE/OUP Series on Electromagnetic Wave Theory (IEEE Press, 1997).

1995 (2)

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

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

1994 (3)

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci multilayers,” Phys. Rev. Lett. 72, 633-636 (1994).
[CrossRef] [PubMed]

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

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

1993 (1)

1989 (1)

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

1987 (1)

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

1977 (1)

1972 (1)

D. W. Berreman, “Optics in stratified and anisotropic media: 4×4-matrix formulation,” J. Opt. Soc. Am. A 62, 502-510 (1972).
[CrossRef]

1968 (1)

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

1961 (1)

L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill, 1961).

Abbate, G.

Aissaoui, M.

M. Aissaoui, J. Zaghdoudi, M. Kanzari, and B. Rezig, “Optical properties of the quasi-periodic one-dimensional generalized multilayer Fibonacci structures,” Prog. Electromagn. Res. PIER 59, 69-83 (2006).
[CrossRef]

Berreman, D. W.

D. W. Berreman, “Optics in stratified and anisotropic media: 4×4-matrix formulation,” J. Opt. Soc. Am. A 62, 502-510 (1972).
[CrossRef]

Born, M.

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

Chernov, L. A.

L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill, 1961).

Colocci, M.

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

Dal Negro, L.

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

Du Stefano, L.

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.

Gaponenko, S. V.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Gellermann, W.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci multilayers,” Phys. Rev. Lett. 72, 633-636 (1994).
[CrossRef] [PubMed]

Ghulinyan, M.

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

Grimm, U.

X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: extensions and applications,” Phys. Rev. B 62, 14020 (2000).
[CrossRef]

Ha, N. Y.

Hattori, H. T.

He, S.

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

Hong, C.-S.

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.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media, IEEE/OUP Series on Electromagnetic Wave Theory (IEEE Press, 1997).

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]

Joannopoulos, J. D.

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

Kanzari, M.

M. Aissaoui, J. Zaghdoudi, M. Kanzari, and B. Rezig, “Optical properties of the quasi-periodic one-dimensional generalized multilayer Fibonacci structures,” Prog. Electromagn. Res. PIER 59, 69-83 (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. B. Kazanskiy and V. V. Podlozny, “Quasiperiodic layered structure with resistive films,” Electromagnetics 17, 131-146 (1997).
[CrossRef]

Kohmoto, M.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci multilayers,” Phys. Rev. Lett. 72, 633-636 (1994).
[CrossRef] [PubMed]

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

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).

Lavrinenko, A. V.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[CrossRef]

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).

Lisboa, O.

Macia, E.

E. Macia, “Optical engineering with Fibonacci dielectric multilayers,” Appl. Phys. Lett. 73, 3330-3332 (1998).
[CrossRef]

Marino, A.

Meade, R. D.

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

Moretti, L.

Norgen, M.

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

Okamoto, T.

Oton, C. J.

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

Pavesi, L.

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

Podlozny, V. V.

V. B. Kazanskiy and V. V. Podlozny, “Quasiperiodic layered structure with resistive films,” Electromagnetics 17, 131-146 (1997).
[CrossRef]

Rea, I.

Rendina, I.

Rezig, B.

M. Aissaoui, J. Zaghdoudi, M. Kanzari, and B. Rezig, “Optical properties of the quasi-periodic one-dimensional generalized multilayer Fibonacci structures,” Prog. Electromagn. Res. PIER 59, 69-83 (2006).
[CrossRef]

Rotiroti, L.

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001).

Sandomirski, K. S.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Sapienza, R.

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

Schneider, V. M.

Schreiber, M.

X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: extensions and applications,” Phys. Rev. B 62, 14020 (2000).
[CrossRef]

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).

Sutherland, B.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci multilayers,” Phys. Rev. Lett. 72, 633-636 (1994).
[CrossRef] [PubMed]

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

Takanishi, Y.

Takezoe, H.

Taylor, P. C.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci multilayers,” Phys. Rev. Lett. 72, 633-636 (1994).
[CrossRef] [PubMed]

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.

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

Wang, X.

X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: extensions and applications,” Phys. Rev. B 62, 14020 (2000).
[CrossRef]

Wiersma, D.

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

Winn, J. N.

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).

Yariv, A.

Yeh, P.

Zaghdoudi, J.

M. Aissaoui, J. Zaghdoudi, M. Kanzari, and B. Rezig, “Optical properties of the quasi-periodic one-dimensional generalized multilayer Fibonacci structures,” Prog. Electromagn. Res. PIER 59, 69-83 (2006).
[CrossRef]

Zhukovsky, S. V.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

E. Macia, “Optical engineering with Fibonacci dielectric multilayers,” Appl. Phys. Lett. 73, 3330-3332 (1998).
[CrossRef]

Electromagnetics (1)

V. B. Kazanskiy and V. V. Podlozny, “Quasiperiodic layered structure with resistive films,” Electromagnetics 17, 131-146 (1997).
[CrossRef]

IEE Proc., Part H: Microwaves, Antennas Propag. (1)

M. Norgen and S. He, “General scheme for electromagnetic reflection and transmission for composite structures of complex materials,” IEE Proc., Part H: 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]

J. Opt. Soc. Am. (1)

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

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

Opt. Express (3)

Phys. Rev. B (2)

X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: extensions and applications,” Phys. Rev. B 62, 14020 (2000).
[CrossRef]

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

Phys. Rev. E (1)

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

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

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci multilayers,” Phys. Rev. Lett. 72, 633-636 (1994).
[CrossRef] [PubMed]

Prog. Electromagn. Res. (1)

M. Aissaoui, J. Zaghdoudi, M. Kanzari, and B. Rezig, “Optical properties of the quasi-periodic one-dimensional generalized multilayer Fibonacci structures,” Prog. Electromagn. Res. PIER 59, 69-83 (2006).
[CrossRef]

Other (7)

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

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

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001).

L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill, 1961).

A. Ishimaru, Wave Propagation and Scattering in Random Media, IEEE/OUP Series on Electromagnetic Wave Theory (IEEE Press, 1997).

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 (6)

Fig. 1
Fig. 1

Quasi-periodic generalized Fibonacci structure of chiral layers.

Fig. 2
Fig. 2

Frequency dependences of the reflection and transmission coefficient magnitudes for a generalized Fibonacci sequence of isotropic layers (without chirality): ɛ j = μ j = 1 , j 2 , ɛ 2 = 2 + i ɛ 2 , μ 2 = 1 , ρ = 0 , ϕ 0 = 25 ° .

Fig. 3
Fig. 3

Transmission coefficient magnitude of (a) co-polarized and (b) cross-polarized waves as function of the frequency k 0 D and the chirality parameter ρ for a classical Fibonacci sequence of chiral layers: ɛ j = μ j = 1 , j 2 , ɛ 2 = 2 , μ 2 = 1 .

Fig. 4
Fig. 4

Frequency dependences of the reflection and transmission coefficient magnitudes for a generalized Fibonacci sequence of chiral layers with (a) even and (b) odd values of m: ɛ j = μ j = 1 , j 2 , ɛ 2 = 2 , μ 2 = 1 , ρ = 0.2 , ϕ 0 = 25 ° .

Fig. 5
Fig. 5

Frequency dependences of the reflection and transmission coefficient magnitudes for a generalized Fibonacci sequence of chiral layers with (a) odd and (b) even values of n: ɛ j = μ j = 1 , j 2 , ɛ 2 = 2 , μ 2 = 1 , ρ = 0.2 , ϕ 0 = 25 ° .

Fig. 6
Fig. 6

Angular dependences of the reflection and transmission coefficient magnitudes for a classical Fibonacci sequence of chiral layers: ɛ j = μ j = 1 , j 2 , ɛ 2 = 2 , μ 2 = 1 , ρ = 0.1 , k 0 D = 6 .

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

F 1 = Λ , F 2 = Ψ ,
F v = F v 1 n F v 2 m , for v 3 ,
{ E x 0 e E y 0 h } = ± { A 0 e Y 0 e i A 0 h Y 0 h } exp [ i ( ω t k y y k z 0 z ) ] ,
{ H y 0 e H x 0 h } = { A 0 e Y 0 e i A 0 h Y 0 h } exp [ i ( ω t k y y k z 0 z ) ] ,
Δ E x + k 0 2 ( n 2 2 + ρ 2 ) E x 2 i k 0 2 ρ μ 2 H x = 0 , Δ H x + k 0 2 ( n 2 2 + ρ 2 ) H x + 2 i k 0 2 ρ ɛ 2 E x = 0 ,
E x e = Q e + + Q e , H x e = i η 2 1 ( Q e + Q e ) ,
E x h = i η 2 ( Q h + Q h ) , H x h = Q h + + Q h ,
Δ Q s + + ( γ + ) 2 Q s + = 0 , Δ Q s + ( γ ) 2 Q s = 0 .
Q e ± = 1 2 Y e ± { A e ± exp [ i ( γ y ± y + γ z ± z ) ] + B e ± exp [ i ( γ y ± y γ z ± z ) ] } ,
Q h ± = Y h ± 2 { A h ± exp [ i ( γ y ± y + γ z ± z ) ] + B h ± exp [ i ( γ y ± y γ z ± z ) ] } ,
( A 0 s B 0 s 0 B 0 s ) = T v ( A L s 0 A L s 0 ) = T v 1 n T v 2 m ( A L s 0 A L s 0 ) , T 1 = T Λ = T 01 P 1 T 10 , T 2 = T Ψ = T 02 P 2 T 20 ,
T p ν = ( ( T p ν s ) 0 0 ( T p ν s ) ) , T 02 = ( ( T 02 + s s ) ( T 02 s s ) ( T 02 + s s ) ( T 02 s s ) ) , T 20 = ( ( T 20 + s s ) ( T 20 + s s ) ( T 20 s s ) ( T 20 s s ) ) ,
P 1 = ( ( E 1 ) 0 0 ( E 1 ) ) , P 2 = ( ( E 2 + ) 0 0 ( E 2 ) ) .
T p ν s = 1 2 Y p s Y ν s ( Y p s + Y ν s ± ( Y p s Y ν s ) ± ( Y p s Y ν s ) Y p s + Y ν s ) ,
T 02 ± e e = 1 4 Y 0 e Y 2 e ± ( Y 0 e + Y 2 e ± Y 0 e Y 2 e ± Y 0 e Y 2 e ± Y 0 e + Y 2 e ± ) , T 02 ± e h = ± 1 4 Y 0 h Y 2 h ± ( Y 2 h ± + Y 0 h Y 2 h ± Y 0 h Y 2 h ± Y 0 h Y 2 h ± + Y 0 h ) ,
T 02 ± h h = 1 4 Y 0 h Y 2 h ± ( Y 2 h ± + Y 0 h Y 2 h ± Y 0 h Y 2 h ± Y 0 h Y 2 h ± + Y 0 h ) , T 02 ± h e = 1 4 Y 0 e Y 2 e ± ( Y 0 e + Y 2 e ± Y 0 e Y 2 e ± Y 0 e Y 2 e ± Y 0 e + Y 2 e ± ) ,
T 20 ± e e = 1 4 Y 2 e Y 0 e Y 2 e ± × ( ( Y 2 e + Y 0 e ) ( Y 2 e + Y 2 e ± ) ( Y 2 e Y 0 e ) ( Y 2 e Y 2 e ± ) ( Y 2 e Y 0 e ) ( Y 2 e + Y 2 e ± ) ( Y 2 e + Y 0 e ) ( Y 2 e Y 2 e ± ) ( Y 2 e Y 0 e ) ( Y 2 e + Y 2 e ± ) ( Y 2 e + Y 0 e ) ( Y 2 e Y 2 e ± ) ( Y 2 e + Y 0 e ) ( Y 2 e + Y 2 e ± ) ( Y 2 e Y 0 e ) ( Y 2 e Y 2 e ± ) ) ,
T 20 ± e h = 1 4 Y 2 h Y 0 h Y 2 h ± × ( ( Y 2 h + Y 0 h ) ( Y 2 h + Y 2 h ± ) ( Y 2 h Y 0 h ) ( Y 2 h Y 2 h ± ) ( Y 2 h + Y 0 h ) ( Y 2 h Y 2 h ± ) ( Y 2 h Y 0 h ) ( Y 2 h + Y 2 h ± ) ( Y 2 h + Y 0 h ) ( Y 2 h Y 2 h ± ) ( Y 2 h Y 0 h ) ( Y 2 h + Y 2 h ± ) ( Y 2 h + Y 0 h ) ( Y 2 h + Y 2 h ± ) ( Y 2 h Y 0 h ) ( Y 2 h Y 2 h ± ) ) ,
T 20 ± h h = 1 4 Y 2 h Y 1 h Y 2 h ± × ( ( Y 2 h + Y 0 h ) ( Y 2 h + Y 2 h ± ) ( Y 2 h Y 0 h ) ( Y 2 h Y 2 h ± ) ( Y 2 h + Y 0 h ) ( Y 2 h Y 2 h ± ) ( Y 2 h Y 0 h ) ( Y 2 h + Y 2 h ± ) ( Y 2 h + Y 0 h ) ( Y 2 h Y 2 h ± ) ( Y 2 h Y 0 h ) ( Y 2 h + Y 2 h ± ) ( Y 2 h + Y 0 h ) ( Y 2 h + Y 2 h ± ) ( Y 2 h Y 0 h ) ( Y 2 h Y 2 h ± ) ) ,
T 20 ± h e = 1 4 Y 2 e Y 0 e Y 2 e ± × ( ( Y 2 e + Y 0 e ) ( Y 2 e + Y 2 e ± ) ( Y 2 e Y 0 e ) ( Y 2 e Y 2 e ± ) ( Y 2 e Y 0 e ) ( Y 2 e + Y 2 e ± ) ( Y 2 e + Y 0 e ) ( Y 2 e Y 2 e ± ) ( Y 2 e Y 0 e ) ( Y 2 e + Y 2 e ± ) ( Y 2 e + Y 0 e ) ( Y 2 e Y 2 e ± ) ( Y 2 e + Y 0 e ) ( Y 2 e + Y 2 e ± ) ( Y 2 e Y 0 e ) ( Y 2 e Y 2 e ± ) ) .
E 1 = Diag [ exp ( i k z 1 D ) exp ( i k z 1 D ) ] , E 2 ± = Diag [ exp ( i γ z ± D ) exp ( i γ z ± D ) ] .
S Λ = m n 2 + 4 m ( n + n 2 + 4 m 2 ) v 2 m n 2 + 4 m ( n n 2 + 4 m 2 ) v 2 ,
S Ψ = 1 n 2 + 4 m ( n + n 2 + 4 m 2 ) v 1 1 n 2 + 4 m ( n n 2 + 4 m 2 ) v 1 .

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