Abstract

We investigated the interface modes in a heterostructure consisting of a semi-infinite metallic layer and a semi-infinite Fibonacci quasiperiodic structure. Various properties of the interface modes, such as their spatial localizations, self-similarities, and multifractal properties, are studied. The interface modes decay exponentially in different ways, and the highest localized mode is found to be a mode in the lower stable gap with the largest gap width. A localization index is introduced to understand the localization properties of the interface modes. We found that the localization index of the interface modes in some of the stable gaps will converge to two slightly different constants related to the parity of the Fibonacci generation. In addition, the localization-delocalization transition is also found in the interface modes of the transient gaps.

© 2010 Optical Society of America

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  1. P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438 (1977).
    [CrossRef]
  2. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
  3. P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32, 104–105 (1978).
    [CrossRef]
  4. F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112–15120 (1999).
    [CrossRef]
  5. T. B. Wang, C. P. Yin, W. Y. Liang, J. W. Dong, and H. Z. Wang, “Electromagnetic surface modes in one-dimensional photonic crystals with dispersive metamaterials,” J. Opt. Soc. Am. B 26, 1635–1640 (2009).
    [CrossRef]
  6. M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
    [CrossRef]
  7. M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
    [CrossRef]
  8. S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B 79, 085416 (2009).
    [CrossRef]
  9. A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans. Antennas Propag. 51, 2558–2571 (2003).
    [CrossRef]
  10. J. W. Dong, J. Zeng, Q. F. Dai, and H. Z. Wang, “Universal condition for the existence of interface modes in the whole momentum space with arbitrary materials,” arXiv:0801.4117.
  11. X. B. Kang, W. Tan, Z. G. Wang, and H. Chen, “Optic Tamm states: The Bloch-wave-expansion method,” Phys. Rev. A 79, 043832 (2009).
    [CrossRef]
  12. G. Guan, H. Jiang, H. Li, Y. Zhang, H. Chen, and S. Zhu, “Tunneling modes of photonic heterostructures consisting of single-negative materials,” Appl. Phys. Lett. 88, 211112 (2006).
    [CrossRef]
  13. A. V. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
    [CrossRef]
  14. L. L. Lin and Z. Y. Li, “Interface states in photonic crystal heterostructures,” Phys. Rev. B 63, 033310 (2001).
    [CrossRef]
  15. Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006).
    [CrossRef]
  16. A. G. Barriuso, J. J. Monzón, L. L. Sánchez-Soto, and A. Felipe, “Comparing omnidirectional reflection from periodic and quasiperiodic one-dimensional photonic crystals,” Opt. Express 13, 3913–3920 (2005).
    [CrossRef] [PubMed]
  17. R. Merlin, K. Bajema, R. Clarke, F.-Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
    [CrossRef] [PubMed]
  18. L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
    [CrossRef] [PubMed]
  19. G. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. 60, 1081–1084 (1988).
    [CrossRef] [PubMed]
  20. F. Nori and J. P. Rodriguez, “Acoustic and electronic properties of one-dimensional quasicrystals,” Phys. Rev. B 34, 2207–2211 (1986).
    [CrossRef]
  21. R. B. Capaz, B. Koiller, and S. L. A. de Queiroz, “Gap states and localization properties of one-dimensional Fibonacci quasicrystals,” Phys. Rev. B 42, 6402–6407 (1990).
    [CrossRef]
  22. C. M. Soukoulis and E. N. Economou, “Localization in one-dimensional lattices in the presence of incommensurate potentials,” Phys. Rev. Lett. 48, 1043–1046 (1982).
    [CrossRef]
  23. M. Kohmoto, B. Sutherland, and C. Tang, “Critical wave functions and a Cantor-set spectrum of a one-dimensional quasicrystal model,” Phys. Rev. B 35, 1020–1033 (1987).
    [CrossRef]
  24. G. J. Jin, S. S. Kang, Z. D. Wang, A. Hu, and S. S. Jiang, “Coupled optical interface modes in a Fibonacci dielectric superlattice,” Phys. Rev. B 54, 11883–11886 (1996).
    [CrossRef]
  25. E. S. Zijlstra, A. Fasolino, and T. Janssen, “Existence and localization of surface states on Fibonacci quasicrystals: A tight-binding study,” Phys. Rev. B 59, 302–307 (1999).
    [CrossRef]
  26. Y. El Hassouani, H. Aynaou, E. H. El Boudouti, B. Djafari-Rouhani, A. Akjouj, and V. R. Velasco, “Surface electromagnetic waves in Fibonacci superlattices: Theoretical and experimental results,” Phys. Rev. B 74, 035314 (2006).
    [CrossRef]
  27. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization in optics: Quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
    [CrossRef] [PubMed]
  28. N. H. Liu, “Propagation of light waves in Thue–Morse dielectric multilayers,” Phys. Rev. B 55, 3543–3547 (1997).
    [CrossRef]
  29. T. Fujiwara, M. Kohmoto, and T. Tokihiro, “Multifractal wave functions on a Fibonacci lattice,” Phys. Rev. B 40, 7413–7416 (1989).
    [CrossRef]

2009 (3)

S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B 79, 085416 (2009).
[CrossRef]

X. B. Kang, W. Tan, Z. G. Wang, and H. Chen, “Optic Tamm states: The Bloch-wave-expansion method,” Phys. Rev. A 79, 043832 (2009).
[CrossRef]

T. B. Wang, C. P. Yin, W. Y. Liang, J. W. Dong, and H. Z. Wang, “Electromagnetic surface modes in one-dimensional photonic crystals with dispersive metamaterials,” J. Opt. Soc. Am. B 26, 1635–1640 (2009).
[CrossRef]

2008 (1)

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

2007 (1)

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

2006 (3)

G. Guan, H. Jiang, H. Li, Y. Zhang, H. Chen, and S. Zhu, “Tunneling modes of photonic heterostructures consisting of single-negative materials,” Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006).
[CrossRef]

Y. El Hassouani, H. Aynaou, E. H. El Boudouti, B. Djafari-Rouhani, A. Akjouj, and V. R. Velasco, “Surface electromagnetic waves in Fibonacci superlattices: Theoretical and experimental results,” Phys. Rev. B 74, 035314 (2006).
[CrossRef]

2005 (2)

A. G. Barriuso, J. J. Monzón, L. L. Sánchez-Soto, and A. Felipe, “Comparing omnidirectional reflection from periodic and quasiperiodic one-dimensional photonic crystals,” Opt. Express 13, 3913–3920 (2005).
[CrossRef] [PubMed]

A. V. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

2003 (2)

A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans. Antennas Propag. 51, 2558–2571 (2003).
[CrossRef]

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

2001 (1)

L. L. Lin and Z. Y. Li, “Interface states in photonic crystal heterostructures,” Phys. Rev. B 63, 033310 (2001).
[CrossRef]

1999 (2)

E. S. Zijlstra, A. Fasolino, and T. Janssen, “Existence and localization of surface states on Fibonacci quasicrystals: A tight-binding study,” Phys. Rev. B 59, 302–307 (1999).
[CrossRef]

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112–15120 (1999).
[CrossRef]

1997 (1)

N. H. Liu, “Propagation of light waves in Thue–Morse dielectric multilayers,” Phys. Rev. B 55, 3543–3547 (1997).
[CrossRef]

1996 (1)

G. J. Jin, S. S. Kang, Z. D. Wang, A. Hu, and S. S. Jiang, “Coupled optical interface modes in a Fibonacci dielectric superlattice,” Phys. Rev. B 54, 11883–11886 (1996).
[CrossRef]

1990 (1)

R. B. Capaz, B. Koiller, and S. L. A. de Queiroz, “Gap states and localization properties of one-dimensional Fibonacci quasicrystals,” Phys. Rev. B 42, 6402–6407 (1990).
[CrossRef]

1989 (1)

T. Fujiwara, M. Kohmoto, and T. Tokihiro, “Multifractal wave functions on a Fibonacci lattice,” Phys. Rev. B 40, 7413–7416 (1989).
[CrossRef]

1988 (1)

G. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. 60, 1081–1084 (1988).
[CrossRef] [PubMed]

1987 (2)

M. Kohmoto, B. Sutherland, and C. Tang, “Critical wave functions and a Cantor-set spectrum of a one-dimensional quasicrystal model,” Phys. Rev. B 35, 1020–1033 (1987).
[CrossRef]

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

1986 (1)

F. Nori and J. P. Rodriguez, “Acoustic and electronic properties of one-dimensional quasicrystals,” Phys. Rev. B 34, 2207–2211 (1986).
[CrossRef]

1985 (1)

R. Merlin, K. Bajema, R. Clarke, F.-Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[CrossRef] [PubMed]

1982 (1)

C. M. Soukoulis and E. N. Economou, “Localization in one-dimensional lattices in the presence of incommensurate potentials,” Phys. Rev. Lett. 48, 1043–1046 (1982).
[CrossRef]

1978 (1)

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32, 104–105 (1978).
[CrossRef]

1977 (1)

Abram, R. A.

S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B 79, 085416 (2009).
[CrossRef]

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Akjouj, A.

Y. El Hassouani, H. Aynaou, E. H. El Boudouti, B. Djafari-Rouhani, A. Akjouj, and V. R. Velasco, “Surface electromagnetic waves in Fibonacci superlattices: Theoretical and experimental results,” Phys. Rev. B 74, 035314 (2006).
[CrossRef]

Ali, M. K.

G. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. 60, 1081–1084 (1988).
[CrossRef] [PubMed]

Alù, A.

A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans. Antennas Propag. 51, 2558–2571 (2003).
[CrossRef]

Aynaou, H.

Y. El Hassouani, H. Aynaou, E. H. El Boudouti, B. Djafari-Rouhani, A. Akjouj, and V. R. Velasco, “Surface electromagnetic waves in Fibonacci superlattices: Theoretical and experimental results,” Phys. Rev. B 74, 035314 (2006).
[CrossRef]

Bajema, K.

R. Merlin, K. Bajema, R. Clarke, F.-Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[CrossRef] [PubMed]

Barriuso, A. G.

Bhattacharya, P. K.

R. Merlin, K. Bajema, R. Clarke, F.-Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[CrossRef] [PubMed]

Brand, S.

S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B 79, 085416 (2009).
[CrossRef]

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Capaz, R. B.

R. B. Capaz, B. Koiller, and S. L. A. de Queiroz, “Gap states and localization properties of one-dimensional Fibonacci quasicrystals,” Phys. Rev. B 42, 6402–6407 (1990).
[CrossRef]

Chamberlain, J. M.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Chan, C. H.

Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006).
[CrossRef]

Chen, H.

X. B. Kang, W. Tan, Z. G. Wang, and H. Chen, “Optic Tamm states: The Bloch-wave-expansion method,” Phys. Rev. A 79, 043832 (2009).
[CrossRef]

G. Guan, H. Jiang, H. Li, Y. Zhang, H. Chen, and S. Zhu, “Tunneling modes of photonic heterostructures consisting of single-negative materials,” Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

Cho, A. Y.

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32, 104–105 (1978).
[CrossRef]

Clarke, R.

R. Merlin, K. Bajema, R. Clarke, F.-Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[CrossRef] [PubMed]

Colocci, M.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Dai, Q. F.

J. W. Dong, J. Zeng, Q. F. Dai, and H. Z. Wang, “Universal condition for the existence of interface modes in the whole momentum space with arbitrary materials,” arXiv:0801.4117.

Dal Negro, L.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

de Queiroz, S. L. A.

R. B. Capaz, B. Koiller, and S. L. A. de Queiroz, “Gap states and localization properties of one-dimensional Fibonacci quasicrystals,” Phys. Rev. B 42, 6402–6407 (1990).
[CrossRef]

Djafari-Rouhani, B.

Y. El Hassouani, H. Aynaou, E. H. El Boudouti, B. Djafari-Rouhani, A. Akjouj, and V. R. Velasco, “Surface electromagnetic waves in Fibonacci superlattices: Theoretical and experimental results,” Phys. Rev. B 74, 035314 (2006).
[CrossRef]

Dong, J. W.

T. B. Wang, C. P. Yin, W. Y. Liang, J. W. Dong, and H. Z. Wang, “Electromagnetic surface modes in one-dimensional photonic crystals with dispersive metamaterials,” J. Opt. Soc. Am. B 26, 1635–1640 (2009).
[CrossRef]

J. W. Dong, J. Zeng, Q. F. Dai, and H. Z. Wang, “Universal condition for the existence of interface modes in the whole momentum space with arbitrary materials,” arXiv:0801.4117.

Economou, E. N.

C. M. Soukoulis and E. N. Economou, “Localization in one-dimensional lattices in the presence of incommensurate potentials,” Phys. Rev. Lett. 48, 1043–1046 (1982).
[CrossRef]

Egorov, A. Yu.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

El Boudouti, E. H.

Y. El Hassouani, H. Aynaou, E. H. El Boudouti, B. Djafari-Rouhani, A. Akjouj, and V. R. Velasco, “Surface electromagnetic waves in Fibonacci superlattices: Theoretical and experimental results,” Phys. Rev. B 74, 035314 (2006).
[CrossRef]

El Hassouani, Y.

Y. El Hassouani, H. Aynaou, E. H. El Boudouti, B. Djafari-Rouhani, A. Akjouj, and V. R. Velasco, “Surface electromagnetic waves in Fibonacci superlattices: Theoretical and experimental results,” Phys. Rev. B 74, 035314 (2006).
[CrossRef]

Engheta, N.

A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans. Antennas Propag. 51, 2558–2571 (2003).
[CrossRef]

Fasolino, A.

E. S. Zijlstra, A. Fasolino, and T. Janssen, “Existence and localization of surface states on Fibonacci quasicrystals: A tight-binding study,” Phys. Rev. B 59, 302–307 (1999).
[CrossRef]

Felipe, A.

Fujiwara, T.

T. Fujiwara, M. Kohmoto, and T. Tokihiro, “Multifractal wave functions on a Fibonacci lattice,” Phys. Rev. B 40, 7413–7416 (1989).
[CrossRef]

Gaburro, Z.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Guan, G.

G. Guan, H. Jiang, H. Li, Y. Zhang, H. Chen, and S. Zhu, “Tunneling modes of photonic heterostructures consisting of single-negative materials,” Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

Gumbs, G.

G. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. 60, 1081–1084 (1988).
[CrossRef] [PubMed]

Halevi, P.

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112–15120 (1999).
[CrossRef]

Hong, C. -S.

Hu, A.

G. J. Jin, S. S. Kang, Z. D. Wang, A. Hu, and S. S. Jiang, “Coupled optical interface modes in a Fibonacci dielectric superlattice,” Phys. Rev. B 54, 11883–11886 (1996).
[CrossRef]

Iguchi, K.

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

Iorsh, I.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Janssen, T.

E. S. Zijlstra, A. Fasolino, and T. Janssen, “Existence and localization of surface states on Fibonacci quasicrystals: A tight-binding study,” Phys. Rev. B 59, 302–307 (1999).
[CrossRef]

Jiang, H.

G. Guan, H. Jiang, H. Li, Y. Zhang, H. Chen, and S. Zhu, “Tunneling modes of photonic heterostructures consisting of single-negative materials,” Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

Jiang, S. S.

G. J. Jin, S. S. Kang, Z. D. Wang, A. Hu, and S. S. Jiang, “Coupled optical interface modes in a Fibonacci dielectric superlattice,” Phys. Rev. B 54, 11883–11886 (1996).
[CrossRef]

Jin, G. J.

G. J. Jin, S. S. Kang, Z. D. Wang, A. Hu, and S. S. Jiang, “Coupled optical interface modes in a Fibonacci dielectric superlattice,” Phys. Rev. B 54, 11883–11886 (1996).
[CrossRef]

Johnson, P.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Juang, F. -Y.

R. Merlin, K. Bajema, R. Clarke, F.-Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[CrossRef] [PubMed]

Kaliteevski, M.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Kaliteevski, M. A.

S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B 79, 085416 (2009).
[CrossRef]

Kalitteevski, M. A.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Kang, S. S.

G. J. Jin, S. S. Kang, Z. D. Wang, A. Hu, and S. S. Jiang, “Coupled optical interface modes in a Fibonacci dielectric superlattice,” Phys. Rev. B 54, 11883–11886 (1996).
[CrossRef]

Kang, X. B.

X. B. Kang, W. Tan, Z. G. Wang, and H. Chen, “Optic Tamm states: The Bloch-wave-expansion method,” Phys. Rev. A 79, 043832 (2009).
[CrossRef]

Kavokin, A. V.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

A. V. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

Kohmoto, M.

T. Fujiwara, M. Kohmoto, and T. Tokihiro, “Multifractal wave functions on a Fibonacci lattice,” Phys. Rev. B 40, 7413–7416 (1989).
[CrossRef]

M. Kohmoto, B. Sutherland, and C. Tang, “Critical wave functions and a Cantor-set spectrum of a one-dimensional quasicrystal model,” Phys. Rev. B 35, 1020–1033 (1987).
[CrossRef]

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

Koiller, B.

R. B. Capaz, B. Koiller, and S. L. A. de Queiroz, “Gap states and localization properties of one-dimensional Fibonacci quasicrystals,” Phys. Rev. B 42, 6402–6407 (1990).
[CrossRef]

Lagendijk, A.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Lai, Y.

Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006).
[CrossRef]

Li, H.

G. Guan, H. Jiang, H. Li, Y. Zhang, H. Chen, and S. Zhu, “Tunneling modes of photonic heterostructures consisting of single-negative materials,” Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

Li, Z. Y.

L. L. Lin and Z. Y. Li, “Interface states in photonic crystal heterostructures,” Phys. Rev. B 63, 033310 (2001).
[CrossRef]

Liang, W. Y.

Lin, L. L.

L. L. Lin and Z. Y. Li, “Interface states in photonic crystal heterostructures,” Phys. Rev. B 63, 033310 (2001).
[CrossRef]

Liu, N. H.

N. H. Liu, “Propagation of light waves in Thue–Morse dielectric multilayers,” Phys. Rev. B 55, 3543–3547 (1997).
[CrossRef]

Malpuech, G.

A. V. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

Merlin, R.

R. Merlin, K. Bajema, R. Clarke, F.-Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[CrossRef] [PubMed]

Mikhrin, V. S.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Monzón, J. J.

Nori, F.

F. Nori and J. P. Rodriguez, “Acoustic and electronic properties of one-dimensional quasicrystals,” Phys. Rev. B 34, 2207–2211 (1986).
[CrossRef]

Oton, C. J.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Pavesi, L.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Ramos-Mendieta, F.

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112–15120 (1999).
[CrossRef]

Righini, R.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Rodriguez, J. P.

F. Nori and J. P. Rodriguez, “Acoustic and electronic properties of one-dimensional quasicrystals,” Phys. Rev. B 34, 2207–2211 (1986).
[CrossRef]

Sánchez-Soto, L. L.

Sasin, M. E.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Seisyan, R. P.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Shelykh, I. A.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

A. V. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis and E. N. Economou, “Localization in one-dimensional lattices in the presence of incommensurate potentials,” Phys. Rev. Lett. 48, 1043–1046 (1982).
[CrossRef]

Sutherland, B.

M. Kohmoto, B. Sutherland, and C. Tang, “Critical wave functions and a Cantor-set spectrum of a one-dimensional quasicrystal model,” Phys. Rev. B 35, 1020–1033 (1987).
[CrossRef]

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

Tan, W.

X. B. Kang, W. Tan, Z. G. Wang, and H. Chen, “Optic Tamm states: The Bloch-wave-expansion method,” Phys. Rev. A 79, 043832 (2009).
[CrossRef]

Tang, C.

M. Kohmoto, B. Sutherland, and C. Tang, “Critical wave functions and a Cantor-set spectrum of a one-dimensional quasicrystal model,” Phys. Rev. B 35, 1020–1033 (1987).
[CrossRef]

Tokihiro, T.

T. Fujiwara, M. Kohmoto, and T. Tokihiro, “Multifractal wave functions on a Fibonacci lattice,” Phys. Rev. B 40, 7413–7416 (1989).
[CrossRef]

Tsang, L.

Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006).
[CrossRef]

Vasil’ev, A. P.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Velasco, V. R.

Y. El Hassouani, H. Aynaou, E. H. El Boudouti, B. Djafari-Rouhani, A. Akjouj, and V. R. Velasco, “Surface electromagnetic waves in Fibonacci superlattices: Theoretical and experimental results,” Phys. Rev. B 74, 035314 (2006).
[CrossRef]

Wang, H. Z.

T. B. Wang, C. P. Yin, W. Y. Liang, J. W. Dong, and H. Z. Wang, “Electromagnetic surface modes in one-dimensional photonic crystals with dispersive metamaterials,” J. Opt. Soc. Am. B 26, 1635–1640 (2009).
[CrossRef]

J. W. Dong, J. Zeng, Q. F. Dai, and H. Z. Wang, “Universal condition for the existence of interface modes in the whole momentum space with arbitrary materials,” arXiv:0801.4117.

Wang, T. B.

Wang, Z. D.

G. J. Jin, S. S. Kang, Z. D. Wang, A. Hu, and S. S. Jiang, “Coupled optical interface modes in a Fibonacci dielectric superlattice,” Phys. Rev. B 54, 11883–11886 (1996).
[CrossRef]

Wang, Z. G.

X. B. Kang, W. Tan, Z. G. Wang, and H. Chen, “Optic Tamm states: The Bloch-wave-expansion method,” Phys. Rev. A 79, 043832 (2009).
[CrossRef]

Wiersma, D. S.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Yariv, A.

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32, 104–105 (1978).
[CrossRef]

P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438 (1977).
[CrossRef]

Yeh, P.

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32, 104–105 (1978).
[CrossRef]

P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438 (1977).
[CrossRef]

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

Yin, C. P.

Zeng, J.

J. W. Dong, J. Zeng, Q. F. Dai, and H. Z. Wang, “Universal condition for the existence of interface modes in the whole momentum space with arbitrary materials,” arXiv:0801.4117.

Zhang, Y.

G. Guan, H. Jiang, H. Li, Y. Zhang, H. Chen, and S. Zhu, “Tunneling modes of photonic heterostructures consisting of single-negative materials,” Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

Zhang, Z. Q.

Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006).
[CrossRef]

Zhu, S.

G. Guan, H. Jiang, H. Li, Y. Zhang, H. Chen, and S. Zhu, “Tunneling modes of photonic heterostructures consisting of single-negative materials,” Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

Zijlstra, E. S.

E. S. Zijlstra, A. Fasolino, and T. Janssen, “Existence and localization of surface states on Fibonacci quasicrystals: A tight-binding study,” Phys. Rev. B 59, 302–307 (1999).
[CrossRef]

Appl. Phys. Lett. (3)

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

G. Guan, H. Jiang, H. Li, Y. Zhang, H. Chen, and S. Zhu, “Tunneling modes of photonic heterostructures consisting of single-negative materials,” Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32, 104–105 (1978).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans. Antennas Propag. 51, 2558–2571 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Express (1)

Phys. Rev. A (1)

X. B. Kang, W. Tan, Z. G. Wang, and H. Chen, “Optic Tamm states: The Bloch-wave-expansion method,” Phys. Rev. A 79, 043832 (2009).
[CrossRef]

Phys. Rev. B (14)

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112–15120 (1999).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B 79, 085416 (2009).
[CrossRef]

A. V. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

L. L. Lin and Z. Y. Li, “Interface states in photonic crystal heterostructures,” Phys. Rev. B 63, 033310 (2001).
[CrossRef]

Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006).
[CrossRef]

M. Kohmoto, B. Sutherland, and C. Tang, “Critical wave functions and a Cantor-set spectrum of a one-dimensional quasicrystal model,” Phys. Rev. B 35, 1020–1033 (1987).
[CrossRef]

G. J. Jin, S. S. Kang, Z. D. Wang, A. Hu, and S. S. Jiang, “Coupled optical interface modes in a Fibonacci dielectric superlattice,” Phys. Rev. B 54, 11883–11886 (1996).
[CrossRef]

E. S. Zijlstra, A. Fasolino, and T. Janssen, “Existence and localization of surface states on Fibonacci quasicrystals: A tight-binding study,” Phys. Rev. B 59, 302–307 (1999).
[CrossRef]

Y. El Hassouani, H. Aynaou, E. H. El Boudouti, B. Djafari-Rouhani, A. Akjouj, and V. R. Velasco, “Surface electromagnetic waves in Fibonacci superlattices: Theoretical and experimental results,” Phys. Rev. B 74, 035314 (2006).
[CrossRef]

F. Nori and J. P. Rodriguez, “Acoustic and electronic properties of one-dimensional quasicrystals,” Phys. Rev. B 34, 2207–2211 (1986).
[CrossRef]

R. B. Capaz, B. Koiller, and S. L. A. de Queiroz, “Gap states and localization properties of one-dimensional Fibonacci quasicrystals,” Phys. Rev. B 42, 6402–6407 (1990).
[CrossRef]

N. H. Liu, “Propagation of light waves in Thue–Morse dielectric multilayers,” Phys. Rev. B 55, 3543–3547 (1997).
[CrossRef]

T. Fujiwara, M. Kohmoto, and T. Tokihiro, “Multifractal wave functions on a Fibonacci lattice,” Phys. Rev. B 40, 7413–7416 (1989).
[CrossRef]

Phys. Rev. Lett. (5)

C. M. Soukoulis and E. N. Economou, “Localization in one-dimensional lattices in the presence of incommensurate potentials,” Phys. Rev. Lett. 48, 1043–1046 (1982).
[CrossRef]

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

R. Merlin, K. Bajema, R. Clarke, F.-Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[CrossRef] [PubMed]

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

G. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. 60, 1081–1084 (1988).
[CrossRef] [PubMed]

Other (2)

J. W. Dong, J. Zeng, Q. F. Dai, and H. Z. Wang, “Universal condition for the existence of interface modes in the whole momentum space with arbitrary materials,” arXiv:0801.4117.

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

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the 1D heterostructure consisting of a semi-infinite Drude-model metal and a semi-infinite structure where each unit cell is composed of the fifth generation Fibonacci generation. Both layers A and B are the quarter-wave plates.

Fig. 2
Fig. 2

(a) Band structures (blue line segments) and the eigen-frequencies (red symbols) with different generation numbers from j = 2 to j = 8 . Full circles represent the modes in the transient gap, while full lower triangles and full upper triangles represent the modes in the stable gaps with the localization index of one and two limits, respectively. Others are marked by open circles. (b)–(d) Same as (a) but for higher generations of frequencies around 1.65, 1.0, and 0.35 eV in order to show the self-similarity.

Fig. 3
Fig. 3

Intensity profiles of (a) the TIM, (b) the SIM-I, and (c) the SIM-II in the heterostructure composed of the eighth generation Fibonacci structure. Their resonant frequencies are 0.9985, 0.8011, and 1.1535 eV, respectively. The solid red lines guide the eyes to indicate the exponential decay. Insets show part of the intensity profiles for clarity.

Fig. 4
Fig. 4

The relationship between the localization index γ and the number of layers F j for (a) the TIM, (b) the SIM-I, and (c) the SIM-II. Their resonant frequencies are at around 1.0, 0.8, and 1.15 eV. The solid curves guide the eyes.

Fig. 5
Fig. 5

Multifractal spectra for (a) the TIM at around 1.65 eV and (b) the SIM-I at around 0.8 eV.

Equations (5)

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

E y ( z ) = { a l e i k l z ( z z l ) + b l e i k l z ( z z l ) z 0 C e α z z < 0 , }
H x ( z ) = 1 i ω μ × { i a l k l z e i k l z ( z z l ) i b l k l z e i k l z ( z z l ) z 0 C α e α z z < 0 , }
( a F j + 1 + a F j + 1 ) = M ( j ) ( a 1 + a 1 ) = ( m 11 ( j ) m 12 ( j ) m 21 ( j ) m 22 ( j ) ) ( a 1 + a 1 ) ,
m 12 ( j ) η metal 2 ( m 11 ( j ) m 22 ( j ) ) η metal m 21 ( j ) = 0 ,
γ = i = 1 F j I i 2 ( i = 1 F j I i ) 2 ,

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