Abstract

In this paper we study the spectral, localization and dispersion properties of dipolar modes in quasi-periodically modulated nanoparticle chains based on the Fibonacci sequence. By developing a transfer matrix approach for the calculation of resonant frequencies, oscillation eigenvectors and integrated density of states (IDS) of spatially-modulated dipole chains, we demonstrate the presence of large spectral gaps and calculate the pseudo-dispersion diagram of Fibonacci plasmonic chains. The presence of plasmonic band-gaps and localized states in metal nanoparticle chains based on quasi-periodic order can have a large impact in the design and fabrication of novel nanophotonics devices.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. D. Levine and P. J. Steinhardt, “Quasicrystals: definition and structure,” Phys. Rev. B 34, 596–616 (1986).
    [Crossref]
  3. C. Janot, Quasicrystals: A Primer (Oxford University Press, NY, 1997).
  4. T. Fujiwara and T. Ogawa, Quasicrystals (Springer-Verlag, Berlin, 1990).
    [Crossref]
  5. 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, 6402–6406 (1990).
    [Crossref]
  6. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization in Optics: Quasiperiodic media,” Phys. Rev. Lett.,  58, 2436–2438 (1987).
    [Crossref] [PubMed]
  7. C. Benoit, G. Poussigue, and A. Azougarh, “Neutron scattering by phonons in quasi-crystals,” J. Phys.: Condens. Matter 2, 2519–2536 (1990).
    [Crossref]
  8. E. L. Albuquerque and M. G. Cottam, “Theory of elementary excitations in quasiperiodic structures,” Phys. Rep. 376, 225–337 (2003).
    [Crossref]
  9. A. Rudinger and F. Piechon, “On the multifractal spectrum of the Fibonacci chain,” J. Phys. A.: Math. Gen. 31, 155–164 (1998).
    [Crossref]
  10. T. Fujiwara, M. Kohmoto, and T. Tokihiro, “Multifractal wavefunctions on a Fibonacci lattice,” Phys. Rev. B 40, 7413–7416 (1989).
    [Crossref]
  11. F. Igloi, L. Turban, and H. Rieger, “Anomalous diffusion in aperiodic environments,” Phys. Rev. E. 59, 1465–1474 (1999).
    [Crossref]
  12. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
    [Crossref] [PubMed]
  13. T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994).
    [Crossref]
  14. L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, L. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
    [Crossref] [PubMed]
  15. R. Zia, J. A. Schuller, and M. L. Brongersma, “Plasmonics: The Next Chip-Scale Technology,” Materials Today 9, 20–27 (2006).
    [Crossref]
  16. S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics -A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501 (2001).
    [Crossref]
  17. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
    [Crossref] [PubMed]
  18. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer-Verlag, 1995).
  19. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B. 62, 356–359 (2000).
    [Crossref]
  20. S. Y. Park and D. Stroud, “Surface-plasmon relations in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B. 69, 125418 (2004).
    [Crossref]
  21. C. Girard and R. Quidant, “Near-field optical transmittance of metal particle chain waveguides,” Opt. Express,  12, 6141 (2004).
    [Crossref] [PubMed]
  22. F. A. B. F. de Moura, L. P. Viana, and A. C. Frery, “Vibrational modes in aperiodic one-dimensional harmonic chains,” Phys. Rev. B. 73, 212302 (2006).
    [Crossref]
  23. P. K. Datta and K. Kundu, “The absence of localization in one-dimensional disordered harmonic chains,” J. Phys: Condens. Matter 6, 4465–4478 (1994).
    [Crossref]
  24. M. Schroeder, Fractals, Chaos, Power Laws (Freeman, NY, 1991).
  25. R. C. Hilborn, Chaos and Nonlinear Dynamics (Oxford University Press, 2000).
  26. U. Frisch, Turbolence (Cambridge University Press, 2004).

2006 (2)

R. Zia, J. A. Schuller, and M. L. Brongersma, “Plasmonics: The Next Chip-Scale Technology,” Materials Today 9, 20–27 (2006).
[Crossref]

F. A. B. F. de Moura, L. P. Viana, and A. C. Frery, “Vibrational modes in aperiodic one-dimensional harmonic chains,” Phys. Rev. B. 73, 212302 (2006).
[Crossref]

2004 (3)

S. Y. Park and D. Stroud, “Surface-plasmon relations in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B. 69, 125418 (2004).
[Crossref]

U. Frisch, Turbolence (Cambridge University Press, 2004).

C. Girard and R. Quidant, “Near-field optical transmittance of metal particle chain waveguides,” Opt. Express,  12, 6141 (2004).
[Crossref] [PubMed]

2003 (3)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[Crossref] [PubMed]

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

E. L. Albuquerque and M. G. Cottam, “Theory of elementary excitations in quasiperiodic structures,” Phys. Rep. 376, 225–337 (2003).
[Crossref]

2001 (1)

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics -A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501 (2001).
[Crossref]

2000 (2)

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B. 62, 356–359 (2000).
[Crossref]

R. C. Hilborn, Chaos and Nonlinear Dynamics (Oxford University Press, 2000).

1999 (1)

F. Igloi, L. Turban, and H. Rieger, “Anomalous diffusion in aperiodic environments,” Phys. Rev. E. 59, 1465–1474 (1999).
[Crossref]

1998 (1)

A. Rudinger and F. Piechon, “On the multifractal spectrum of the Fibonacci chain,” J. Phys. A.: Math. Gen. 31, 155–164 (1998).
[Crossref]

1994 (3)

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

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

P. K. Datta and K. Kundu, “The absence of localization in one-dimensional disordered harmonic chains,” J. Phys: Condens. Matter 6, 4465–4478 (1994).
[Crossref]

1990 (2)

C. Benoit, G. Poussigue, and A. Azougarh, “Neutron scattering by phonons in quasi-crystals,” J. Phys.: Condens. Matter 2, 2519–2536 (1990).
[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, 6402–6406 (1990).
[Crossref]

1989 (1)

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

1987 (2)

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

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]

1986 (1)

D. Levine and P. J. Steinhardt, “Quasicrystals: definition and structure,” Phys. Rev. B 34, 596–616 (1986).
[Crossref]

Albuquerque, E. L.

E. L. Albuquerque and M. G. Cottam, “Theory of elementary excitations in quasiperiodic structures,” Phys. Rep. 376, 225–337 (2003).
[Crossref]

Atwater, H. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[Crossref] [PubMed]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics -A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501 (2001).
[Crossref]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B. 62, 356–359 (2000).
[Crossref]

Azougarh, A.

C. Benoit, G. Poussigue, and A. Azougarh, “Neutron scattering by phonons in quasi-crystals,” J. Phys.: Condens. Matter 2, 2519–2536 (1990).
[Crossref]

Benoit, C.

C. Benoit, G. Poussigue, and A. Azougarh, “Neutron scattering by phonons in quasi-crystals,” J. Phys.: Condens. Matter 2, 2519–2536 (1990).
[Crossref]

Brongersma, M. L.

R. Zia, J. A. Schuller, and M. L. Brongersma, “Plasmonics: The Next Chip-Scale Technology,” Materials Today 9, 20–27 (2006).
[Crossref]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics -A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501 (2001).
[Crossref]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B. 62, 356–359 (2000).
[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, 6402–6406 (1990).
[Crossref]

Colocci, L.

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

Cottam, M. G.

E. L. Albuquerque and M. G. Cottam, “Theory of elementary excitations in quasiperiodic structures,” Phys. Rep. 376, 225–337 (2003).
[Crossref]

Dal Negro, L.

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

Datta, P. K.

P. K. Datta and K. Kundu, “The absence of localization in one-dimensional disordered harmonic chains,” J. Phys: Condens. Matter 6, 4465–4478 (1994).
[Crossref]

de Moura, F. A. B. F.

F. A. B. F. de Moura, L. P. Viana, and A. C. Frery, “Vibrational modes in aperiodic one-dimensional harmonic chains,” Phys. Rev. B. 73, 212302 (2006).
[Crossref]

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, 6402–6406 (1990).
[Crossref]

Frery, A. C.

F. A. B. F. de Moura, L. P. Viana, and A. C. Frery, “Vibrational modes in aperiodic one-dimensional harmonic chains,” Phys. Rev. B. 73, 212302 (2006).
[Crossref]

Frisch, U.

U. Frisch, Turbolence (Cambridge University Press, 2004).

Fujiwara, T.

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

T. Fujiwara and T. Ogawa, Quasicrystals (Springer-Verlag, Berlin, 1990).
[Crossref]

Gaburro, Z.

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

Gellermann, W.

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

Girard, C.

Harel, E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[Crossref] [PubMed]

Hartman, J. W.

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B. 62, 356–359 (2000).
[Crossref]

Hattori, T.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

Hilborn, R. C.

R. C. Hilborn, Chaos and Nonlinear Dynamics (Oxford University Press, 2000).

Igloi, F.

F. Igloi, L. Turban, and H. Rieger, “Anomalous diffusion in aperiodic environments,” Phys. Rev. E. 59, 1465–1474 (1999).
[Crossref]

Iguchi, K.

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

Janot, C.

C. Janot, Quasicrystals: A Primer (Oxford University Press, NY, 1997).

Johnson, P.

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

Kawato, S.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

Kik, P. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[Crossref] [PubMed]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics -A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501 (2001).
[Crossref]

Koel, B. E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[Crossref] [PubMed]

Kohmoto, M.

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

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

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

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]

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, 6402–6406 (1990).
[Crossref]

Kreibig, U.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer-Verlag, 1995).

Kundu, K.

P. K. Datta and K. Kundu, “The absence of localization in one-dimensional disordered harmonic chains,” J. Phys: Condens. Matter 6, 4465–4478 (1994).
[Crossref]

Lagendijk, A.

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

Levine, D.

D. Levine and P. J. Steinhardt, “Quasicrystals: definition and structure,” Phys. Rev. B 34, 596–616 (1986).
[Crossref]

Maier, S. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[Crossref] [PubMed]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics -A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501 (2001).
[Crossref]

Meltzer, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[Crossref] [PubMed]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics -A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501 (2001).
[Crossref]

Nakatsuka, H.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

Ogawa, T.

T. Fujiwara and T. Ogawa, Quasicrystals (Springer-Verlag, Berlin, 1990).
[Crossref]

Oton, C. J.

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

Park, S. Y.

S. Y. Park and D. Stroud, “Surface-plasmon relations in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B. 69, 125418 (2004).
[Crossref]

Pavesi, L.

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

Piechon, F.

A. Rudinger and F. Piechon, “On the multifractal spectrum of the Fibonacci chain,” J. Phys. A.: Math. Gen. 31, 155–164 (1998).
[Crossref]

Poussigue, G.

C. Benoit, G. Poussigue, and A. Azougarh, “Neutron scattering by phonons in quasi-crystals,” J. Phys.: Condens. Matter 2, 2519–2536 (1990).
[Crossref]

Quidant, R.

Requicha, A. A. G.

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics -A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501 (2001).
[Crossref]

Requicha, A. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[Crossref] [PubMed]

Rieger, H.

F. Igloi, L. Turban, and H. Rieger, “Anomalous diffusion in aperiodic environments,” Phys. Rev. E. 59, 1465–1474 (1999).
[Crossref]

Righini, R.

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

Rudinger, A.

A. Rudinger and F. Piechon, “On the multifractal spectrum of the Fibonacci chain,” J. Phys. A.: Math. Gen. 31, 155–164 (1998).
[Crossref]

Schroeder, M.

M. Schroeder, Fractals, Chaos, Power Laws (Freeman, NY, 1991).

Schuller, J. A.

R. Zia, J. A. Schuller, and M. L. Brongersma, “Plasmonics: The Next Chip-Scale Technology,” Materials Today 9, 20–27 (2006).
[Crossref]

Steinhardt, P. J.

D. Levine and P. J. Steinhardt, “Quasicrystals: definition and structure,” Phys. Rev. B 34, 596–616 (1986).
[Crossref]

Stroud, D.

S. Y. Park and D. Stroud, “Surface-plasmon relations in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B. 69, 125418 (2004).
[Crossref]

Sutherland, B.

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

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]

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]

Taylor, P. C.

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

Tokihiro, T.

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

Tsurumachi, N.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

Turban, L.

F. Igloi, L. Turban, and H. Rieger, “Anomalous diffusion in aperiodic environments,” Phys. Rev. E. 59, 1465–1474 (1999).
[Crossref]

Viana, L. P.

F. A. B. F. de Moura, L. P. Viana, and A. C. Frery, “Vibrational modes in aperiodic one-dimensional harmonic chains,” Phys. Rev. B. 73, 212302 (2006).
[Crossref]

Vollmer, M.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer-Verlag, 1995).

Wiersma, D. S.

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

Zia, R.

R. Zia, J. A. Schuller, and M. L. Brongersma, “Plasmonics: The Next Chip-Scale Technology,” Materials Today 9, 20–27 (2006).
[Crossref]

Adv. Mater. (1)

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics -A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501 (2001).
[Crossref]

J. Phys. A.: Math. Gen. (1)

A. Rudinger and F. Piechon, “On the multifractal spectrum of the Fibonacci chain,” J. Phys. A.: Math. Gen. 31, 155–164 (1998).
[Crossref]

J. Phys.: Condens. Matter (1)

C. Benoit, G. Poussigue, and A. Azougarh, “Neutron scattering by phonons in quasi-crystals,” J. Phys.: Condens. Matter 2, 2519–2536 (1990).
[Crossref]

J. Phys: Condens. Matter (1)

P. K. Datta and K. Kundu, “The absence of localization in one-dimensional disordered harmonic chains,” J. Phys: Condens. Matter 6, 4465–4478 (1994).
[Crossref]

Materials Today (1)

R. Zia, J. A. Schuller, and M. L. Brongersma, “Plasmonics: The Next Chip-Scale Technology,” Materials Today 9, 20–27 (2006).
[Crossref]

Nat. Mater. (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[Crossref] [PubMed]

Opt. Express (1)

Phys. Rep. (1)

E. L. Albuquerque and M. G. Cottam, “Theory of elementary excitations in quasiperiodic structures,” Phys. Rep. 376, 225–337 (2003).
[Crossref]

Phys. Rev. B (5)

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, 6402–6406 (1990).
[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]

D. Levine and P. J. Steinhardt, “Quasicrystals: definition and structure,” Phys. Rev. B 34, 596–616 (1986).
[Crossref]

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

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

Phys. Rev. B. (3)

F. A. B. F. de Moura, L. P. Viana, and A. C. Frery, “Vibrational modes in aperiodic one-dimensional harmonic chains,” Phys. Rev. B. 73, 212302 (2006).
[Crossref]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B. 62, 356–359 (2000).
[Crossref]

S. Y. Park and D. Stroud, “Surface-plasmon relations in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B. 69, 125418 (2004).
[Crossref]

Phys. Rev. E. (1)

F. Igloi, L. Turban, and H. Rieger, “Anomalous diffusion in aperiodic environments,” Phys. Rev. E. 59, 1465–1474 (1999).
[Crossref]

Phys. Rev. Lett. (3)

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

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

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

Other (6)

C. Janot, Quasicrystals: A Primer (Oxford University Press, NY, 1997).

T. Fujiwara and T. Ogawa, Quasicrystals (Springer-Verlag, Berlin, 1990).
[Crossref]

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer-Verlag, 1995).

M. Schroeder, Fractals, Chaos, Power Laws (Freeman, NY, 1991).

R. C. Hilborn, Chaos and Nonlinear Dynamics (Oxford University Press, 2000).

U. Frisch, Turbolence (Cambridge University Press, 2004).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

(a). Schematics of the aperiodic nanoparticle chain, and real parts of the transfer matrix element Q11 for (b) periodic and (c) aperiodic Fibonacci chains.

Fig. 2.
Fig. 2.

Integrated density of states (IDS) for the (a) periodic and (b) quasi-periodic Fibonacci chains.

Fig. 3.
Fig. 3.

Dipole moments of the (a) extended state of a periodic chain, (b) critical state (ω/ω0 = 0.986) and (c) the most localized states (ω/ω0 = 0.984) of a quasi-periodic Fibonacci chain. The participation ratios for cases (b) and (c) are 0.201 and 0.044.

Fig. 4.
Fig. 4.

Dispersion diagrams for (a) periodic chain: (b) quasi-periodic Fibonacci chain, transverse polarization; (c) quasi-periodic Fibonacci chain, longitudinal polarization.

Equations (9)

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

i , n = ω 0 2 p i , n Γ e p ˙ i , n + Γ R ω 0 2 p i , n γ i α n 2 ( p i , n 1 + p i , n + 1 )
u n + 1 = [ ω 2 ω 0 2 i ( Γ e ω Γ R ω 3 ω 0 2 ) γ i α n 2 ] u n u n 1 u n + 1
u n + 1 u n = T n u n u n 1
T n = ω 2 ω 0 2 i ( Γ e ω Γ R ω 3 ω 0 2 ) γ i α n 2 1 1 0
u N + 1 u N = T N T N 1 T N 1 T 2 T 1 u 1 u 0 = Q u 1 u 0
Q 11 ( ω ) = 0
g ( ω ) = k δ ( ω ω k )
P ( ω k ) = n e n ( ω k ) 2 N n e n ( ω k ) 4
n e n ( ω k ) 2 = 1

Metrics