Abstract

We study the propagation characteristics of optical signals in waveguides composed of a double chain of metallic nanoparticles embedded in a dielectric host. We find that the complex Bloch band diagram for the guided modes, derived by the Mie scattering theory including material losses, exhibits strong differences with respect to the previously studied single chain. The results of the model are validated through the finite element solution of the Maxwell equations.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
    [CrossRef] [PubMed]
  2. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  3. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
    [CrossRef]
  4. G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
    [CrossRef]
  5. E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
    [CrossRef] [PubMed]
  6. E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. 31, 3447–3449 (2006).
    [CrossRef] [PubMed]
  7. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. 23, 1331–1333 (1998).
    [CrossRef]
  8. M. L. Brongesma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356(2000).
    [CrossRef]
  9. S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67, 205402 (2003).
    [CrossRef]
  10. W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70, 125429 (2004).
    [CrossRef]
  11. D. S. Citrin, “Coherent excitation transport in metal-nanoparticle chains,” Nano Lett. 4, 1561–1565 (2004).
    [CrossRef]
  12. R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41, 578–580 (2005).
    [CrossRef]
  13. C. R. Simovsky, A. J. Viitanen, and S. A. Tretyakov, “Resonator mode in chains of silver nanoparticles and its possible application,” Phys. Rev. E 72, 066606 (2005).
    [CrossRef]
  14. D. S. Citrin, “Plasmon-polariton transport in metal-nanoparticle chains embedded in a gain medium,” Opt. Lett. 31, 98–100(2006).
    [CrossRef] [PubMed]
  15. A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).
    [CrossRef]
  16. A. Alú and N. Engheta, “Theory of linear chains of metamaterial/plasmonic nanoparticles as a subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436 (2006).
    [CrossRef]
  17. V. A. Markel and A. K. Sarychev, “Propagation of surface plasmons in ordered and disordered chains of nanoparticles,” Phys. Rev. B 75, 085426 (2007).
    [CrossRef]
  18. A. A. Govyadinov and V. A. Markel, “From slow to superluminal propagation: dispersive properties of surface plasmon polaritons in linear chains of metallic nanospheroids,” Phys. Rev. B 78, 035403 (2008).
    [CrossRef]
  19. M. Conforti and M. Guasoni, “Dispersive properties of linear chains of lossy metal nanoparticles,” J. Opt. Soc. Am. B 27, 1576–1582 (2010).
    [CrossRef]
  20. H. Chu, W. Ewe, E. Li, and R. Vahldieck, “Analysis of sub-wavelength light propagation through long double-chain nanowires with funnel feeding,” Opt. Express 15, 4216–4223(2007).
    [CrossRef] [PubMed]
  21. A. Alú, P. A. Belov, and N. Engehta, “Parallel-chain optical transmission line for a low-loss ultraconfined light beam,” Phys. Rev. B 80, 113101 (2009).
    [CrossRef]
  22. J. M. Gerardy and M. Ausloos, “Absorption spectrum of spheres from the general solution of Maxwell’s equations. II. optical properties of aggregated metal spheres,” Phys. Rev. B 25, 4204–4229 (1982).
    [CrossRef]
  23. Y.-l. Xu, “Fast evaluation of the Gaunt coefficients,” Math. Comput. 65, 1601–1612 (1996).
    [CrossRef]
  24. A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions (Krieger, 1981), Vol.  1.
  25. F. Xu, K. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz–Mie theory for an arbitrarily oriented, located, and shaped beam scattered by a homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119–131 (2007).
    [CrossRef]
  26. S. Asano and G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975).
    [CrossRef] [PubMed]
  27. P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]

2010

2009

A. Alú, P. A. Belov, and N. Engehta, “Parallel-chain optical transmission line for a low-loss ultraconfined light beam,” Phys. Rev. B 80, 113101 (2009).
[CrossRef]

2008

A. A. Govyadinov and V. A. Markel, “From slow to superluminal propagation: dispersive properties of surface plasmon polaritons in linear chains of metallic nanospheroids,” Phys. Rev. B 78, 035403 (2008).
[CrossRef]

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

2007

2006

D. S. Citrin, “Plasmon-polariton transport in metal-nanoparticle chains embedded in a gain medium,” Opt. Lett. 31, 98–100(2006).
[CrossRef] [PubMed]

E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. 31, 3447–3449 (2006).
[CrossRef] [PubMed]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).
[CrossRef]

A. Alú and N. Engheta, “Theory of linear chains of metamaterial/plasmonic nanoparticles as a subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436 (2006).
[CrossRef]

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

2005

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41, 578–580 (2005).
[CrossRef]

C. R. Simovsky, A. J. Viitanen, and S. A. Tretyakov, “Resonator mode in chains of silver nanoparticles and its possible application,” Phys. Rev. E 72, 066606 (2005).
[CrossRef]

2004

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70, 125429 (2004).
[CrossRef]

D. S. Citrin, “Coherent excitation transport in metal-nanoparticle chains,” Nano Lett. 4, 1561–1565 (2004).
[CrossRef]

2003

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67, 205402 (2003).
[CrossRef]

2000

M. L. Brongesma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356(2000).
[CrossRef]

1998

1996

Y.-l. Xu, “Fast evaluation of the Gaunt coefficients,” Math. Comput. 65, 1601–1612 (1996).
[CrossRef]

1982

J. M. Gerardy and M. Ausloos, “Absorption spectrum of spheres from the general solution of Maxwell’s equations. II. optical properties of aggregated metal spheres,” Phys. Rev. B 25, 4204–4229 (1982).
[CrossRef]

1975

1972

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1969

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

Alú, A.

A. Alú, P. A. Belov, and N. Engehta, “Parallel-chain optical transmission line for a low-loss ultraconfined light beam,” Phys. Rev. B 80, 113101 (2009).
[CrossRef]

A. Alú and N. Engheta, “Theory of linear chains of metamaterial/plasmonic nanoparticles as a subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436 (2006).
[CrossRef]

Asano, S.

Atwater, H. A.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67, 205402 (2003).
[CrossRef]

M. L. Brongesma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356(2000).
[CrossRef]

Ausloos, M.

J. M. Gerardy and M. Ausloos, “Absorption spectrum of spheres from the general solution of Maxwell’s equations. II. optical properties of aggregated metal spheres,” Phys. Rev. B 25, 4204–4229 (1982).
[CrossRef]

Aussenegg, F. R.

Belov, P. A.

A. Alú, P. A. Belov, and N. Engehta, “Parallel-chain optical transmission line for a low-loss ultraconfined light beam,” Phys. Rev. B 80, 113101 (2009).
[CrossRef]

Bozhevolnyi, S. I.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. 31, 3447–3449 (2006).
[CrossRef] [PubMed]

Brongesma, M. L.

M. L. Brongesma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356(2000).
[CrossRef]

Cai, X.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Chu, H.

Citrin, D. S.

D. S. Citrin, “Plasmon-polariton transport in metal-nanoparticle chains embedded in a gain medium,” Opt. Lett. 31, 98–100(2006).
[CrossRef] [PubMed]

D. S. Citrin, “Coherent excitation transport in metal-nanoparticle chains,” Nano Lett. 4, 1561–1565 (2004).
[CrossRef]

Conforti, M.

Economou, E. N.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

Engehta, N.

A. Alú, P. A. Belov, and N. Engehta, “Parallel-chain optical transmission line for a low-loss ultraconfined light beam,” Phys. Rev. B 80, 113101 (2009).
[CrossRef]

Engheta, N.

A. Alú and N. Engheta, “Theory of linear chains of metamaterial/plasmonic nanoparticles as a subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436 (2006).
[CrossRef]

Erdelyi, A.

A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions (Krieger, 1981), Vol.  1.

Ewe, W.

Fan, S.

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Ford, G. W.

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70, 125429 (2004).
[CrossRef]

Garcia-Vidal, F. J.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. 31, 3447–3449 (2006).
[CrossRef] [PubMed]

Gerardy, J. M.

J. M. Gerardy and M. Ausloos, “Absorption spectrum of spheres from the general solution of Maxwell’s equations. II. optical properties of aggregated metal spheres,” Phys. Rev. B 25, 4204–4229 (1982).
[CrossRef]

Gouesbet, G.

Govyadinov, A. A.

A. A. Govyadinov and V. A. Markel, “From slow to superluminal propagation: dispersive properties of surface plasmon polaritons in linear chains of metallic nanospheroids,” Phys. Rev. B 78, 035403 (2008).
[CrossRef]

Gréhan, G.

Guasoni, M.

Hartman, J. W.

M. L. Brongesma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356(2000).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Kik, P. G.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67, 205402 (2003).
[CrossRef]

Koenderink, A. F.

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).
[CrossRef]

Krenn, J. R.

Leitner, A.

Li, E.

Magnus, W.

A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions (Krieger, 1981), Vol.  1.

Maier, S. A.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67, 205402 (2003).
[CrossRef]

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Markel, V. A.

A. A. Govyadinov and V. A. Markel, “From slow to superluminal propagation: dispersive properties of surface plasmon polaritons in linear chains of metallic nanospheroids,” Phys. Rev. B 78, 035403 (2008).
[CrossRef]

V. A. Markel and A. K. Sarychev, “Propagation of surface plasmons in ordered and disordered chains of nanoparticles,” Phys. Rev. B 75, 085426 (2007).
[CrossRef]

Martin-Moreno, L.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. 31, 3447–3449 (2006).
[CrossRef] [PubMed]

Moreno, E.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. 31, 3447–3449 (2006).
[CrossRef] [PubMed]

Oberhettinger, F.

A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions (Krieger, 1981), Vol.  1.

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

Polman, A.

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).
[CrossRef]

Quinten, M.

Ren, K.

Rodrigo, S. G.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. 31, 3447–3449 (2006).
[CrossRef] [PubMed]

Sarychev, A. K.

V. A. Markel and A. K. Sarychev, “Propagation of surface plasmons in ordered and disordered chains of nanoparticles,” Phys. Rev. B 75, 085426 (2007).
[CrossRef]

Shore, R. A.

R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41, 578–580 (2005).
[CrossRef]

Simovsky, C. R.

C. R. Simovsky, A. J. Viitanen, and S. A. Tretyakov, “Resonator mode in chains of silver nanoparticles and its possible application,” Phys. Rev. E 72, 066606 (2005).
[CrossRef]

Tretyakov, S. A.

C. R. Simovsky, A. J. Viitanen, and S. A. Tretyakov, “Resonator mode in chains of silver nanoparticles and its possible application,” Phys. Rev. E 72, 066606 (2005).
[CrossRef]

Tricomi, F. G.

A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions (Krieger, 1981), Vol.  1.

Vahldieck, R.

Veronis, G.

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Viitanen, A. J.

C. R. Simovsky, A. J. Viitanen, and S. A. Tretyakov, “Resonator mode in chains of silver nanoparticles and its possible application,” Phys. Rev. E 72, 066606 (2005).
[CrossRef]

Weber, W. H.

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70, 125429 (2004).
[CrossRef]

Xu, F.

Xu, Y.-l.

Y.-l. Xu, “Fast evaluation of the Gaunt coefficients,” Math. Comput. 65, 1601–1612 (1996).
[CrossRef]

Yaghjian, A. D.

R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41, 578–580 (2005).
[CrossRef]

Yamamoto, G.

Appl. Opt.

Appl. Phys. Lett.

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Electron. Lett.

R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41, 578–580 (2005).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Math. Comput.

Y.-l. Xu, “Fast evaluation of the Gaunt coefficients,” Math. Comput. 65, 1601–1612 (1996).
[CrossRef]

Nano Lett.

D. S. Citrin, “Coherent excitation transport in metal-nanoparticle chains,” Nano Lett. 4, 1561–1565 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

Phys. Rev. B

M. L. Brongesma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356(2000).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67, 205402 (2003).
[CrossRef]

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70, 125429 (2004).
[CrossRef]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).
[CrossRef]

A. Alú and N. Engheta, “Theory of linear chains of metamaterial/plasmonic nanoparticles as a subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436 (2006).
[CrossRef]

V. A. Markel and A. K. Sarychev, “Propagation of surface plasmons in ordered and disordered chains of nanoparticles,” Phys. Rev. B 75, 085426 (2007).
[CrossRef]

A. A. Govyadinov and V. A. Markel, “From slow to superluminal propagation: dispersive properties of surface plasmon polaritons in linear chains of metallic nanospheroids,” Phys. Rev. B 78, 035403 (2008).
[CrossRef]

A. Alú, P. A. Belov, and N. Engehta, “Parallel-chain optical transmission line for a low-loss ultraconfined light beam,” Phys. Rev. B 80, 113101 (2009).
[CrossRef]

J. M. Gerardy and M. Ausloos, “Absorption spectrum of spheres from the general solution of Maxwell’s equations. II. optical properties of aggregated metal spheres,” Phys. Rev. B 25, 4204–4229 (1982).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Phys. Rev. E

C. R. Simovsky, A. J. Viitanen, and S. A. Tretyakov, “Resonator mode in chains of silver nanoparticles and its possible application,” Phys. Rev. E 72, 066606 (2005).
[CrossRef]

Phys. Rev. Lett.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

Science

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

Other

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions (Krieger, 1981), Vol.  1.

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 (7)

Fig. 1
Fig. 1

The system analyzed in this paper consists of two chains of spheres over the x y plane. The chains have distance L, displacement s along the x axis, and the spheres (of radius R) in the chains have a center-to-center distance d. Odd spheres stay in the left chain, and even spheres stay in the right chain. Note as an example, the angle β ( 1 ) between the spheres 0 and 3.

Fig. 2
Fig. 2

General view of the real and imaginary part of k ( ω ) for the theoretically predicted modes in the double chain: bold black dashed curve, mode T 1 i ; bold black curve, T 2 i L a ; thin black curve, T 1 a ; thin black dashed curve, T 2 a L i together with L i T 2 a ; black dotted curve, L a T 2 i . The real part represents the dispersion curve of the mode; the imaginary part represents its losses.

Fig. 3
Fig. 3

Real and imaginary part of k ( ω ) for the mode T 1 i (thin black curve, theoretical results; triangles, FEM results) and T 2 i L a (bold black curve, theoretical results; circles, FEM results). The black dashed–dotted curve is relative to modes T 1 and T 2 in the single chain.

Fig. 4
Fig. 4

Real and imaginary part of k ( ω ) for the mode T 1 a (bold black curve, theoretical results; circles, FEM results). The black dashed–dotted curve is relative to modes T 1 and T 2 in the single chain.

Fig. 5
Fig. 5

Real and imaginary part of k ( ω ) for the mode T 2 a L i and L i T 2 a (thin black curve, theoretical results; triangles, FEM results) and L a T 2 i (bold black curve, theoretical results; circles, FEM results). The black dashed–dotted curve is relative to mode L in the single chain. The curve relative to T 2 a L i flows into that of L i T 2 a starting from ω d 1.72 .

Fig. 6
Fig. 6

Field H x of modes T 1 in the single chain (a,  ω d = 1.50 ) and of modes T 1 i (b,  ω d = 1.50 ) and T 1 a in the double chain (c,  ω d = 1.59 ).

Fig. 7
Fig. 7

Fields H x , H y and H z of modes T 2 (a,  ω d = 1.50 ) and L (b,  ω d = 1.70 ) in the single chain and of modes T 2 i L a (c,  ω d = 1.34 ), T 2 a L i (d,  ω d = 1.70 ) and L i T 2 a (e,  ω d = 1.76 ) in the double chain.

Equations (19)

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

b i , 1 m ( n ) = Δ 1 1 d 1 m ( n ) v n q = 1 1 T 1 q 1 m ( v , n ) d 1 q ( v ) ,
b i , 10 ( 2 n ) = Δ 1 1 d 10 ( 2 n ) v n T 1010 ( 2 v , 2 n ) d 10 ( 2 v ) v T 1010 ( 2 v + 1 , 2 n ) d 10 ( 2 v + 1 ) ,
b i , 10 ( 2 n + 1 ) = Δ 1 1 d 10 ( 2 n + 1 ) v T 1010 ( 2 v , 2 n + 1 ) d 10 ( 2 v ) v n T 1010 ( 2 v + 1 , 2 n + 1 ) d 10 ( 2 v + 1 ) .
b i , 10 E ( n ) = Δ 1 1 d 10 E ( n ) + v n U 1010 ( v n ) d 10 E ( v ) ++ v E 1010 ( v n ) d 10 O ( v ) ,
b i , 10 O ( n ) = Δ 1 1 d 10 O ( n ) + v O 1010 ( v n ) d 10 E ( v ) ++ v n U 1010 ( v n ) d 10 O ( v ) .
b i , 10 E ( n ) = U 1010 ( n ) * d 10 E ( n ) + E 1010 ( n ) * d 10 O ( n ) ,
b i , 10 O ( n ) = O 1010 ( n ) * d 10 E ( n ) + U 1010 ( n ) * d 10 O ( n ) .
M A [ d ^ 10 E ( k ) d ^ 10 O ( k ) ] = [ b ^ i , 10 E ( k ) b ^ i , 10 O ( k ) ] ,
M A = [ U ^ 1010 ( k ) E ^ 1010 ( k ) O ^ 1010 ( k ) U ^ 1010 ( k ) ] ,
M B [ d ^ 11 E ( k ) d ^ 1 1 E ( k ) d ^ 11 O ( k ) d ^ 1 1 O ( k ) ] = [ b ^ i , 11 E ( k ) b ^ i , 1 1 E ( k ) b ^ i , 11 O ( k ) b ^ i , 1 1 O ( k ) ] ,
M B = [ U ^ 1111 ( k ) U ^ 1 111 ( k ) E ^ 1111 ( k ) E ^ 1 111 ( k ) U ^ 111 1 ( k ) U ^ 1 11 1 ( k ) E ^ 111 1 ( k ) E ^ 1 11 1 ( k ) O ^ 1111 ( k ) O ^ 1 111 ( k ) U ^ 1111 ( k ) U ^ 1 111 ( k ) O ^ 111 1 ( k ) O ^ 1 11 1 ( k ) U ^ 111 1 ( k ) U ^ 1 11 1 ( k ) ] .
U 1010 ( n ) = i 3 2 e i d U ( n ) d U ( n ) 3 2 e i d U ( n ) d U ( n ) 2 i 3 2 e i d U ( n ) d U ( n ) 3 , n 0 U 1111 ( n ) = i 3 4 e i d U ( n ) d U ( n ) + 3 4 e i d U ( n ) d U ( n ) 2 + i 3 4 e i d U ( n ) d U ( n ) 3 , n 0 U 1 111 ( n ) = i 3 4 e i d U ( n ) d U ( n ) + 9 4 e i d U ( n ) d U ( n ) 2 + i 9 4 e i d U ( n ) d U ( n ) 3 , n 0 E 1010 ( n ) = i 3 2 e i d E ( n ) d E ( n ) 3 2 e i d E ( n ) d E ( n ) 2 i 3 2 e i d E ( n ) d E ( n ) 3 , E 1111 ( n ) = i 3 4 e i d E ( n ) d E ( n ) + 3 4 e i d E ( n ) d E ( n ) 2 + i 3 4 e i d E ( n ) d E ( n ) 3 , E 1 111 ( n ) = i 3 4 e i d E ( n ) d E ( n ) + 9 4 e i d E ( n ) d E ( n ) 2 + i 9 4 e i d E ( n ) d E ( n ) 3 , E 111 1 ( n ) = i 3 4 e i d E ( n ) d E ( n ) + 9 4 e i d E ( n ) d E ( n ) 2 + i 9 4 e i d E ( n ) d E ( n ) 3 ,
E ^ 1010 ( k ) = E 1010 ( 0 ) + v = 1 3 a v [ n = 1 e i k M ( d n + s ) i k n k M v ( d n + s ) v + n = 1 e i k M ( d n s ) + i k n k M v ( d n s ) v ] ,
n = 1 e i k M ( d n s ) ± i k n k M v ( d n s ) v = ( k M d ) v e i k M ( d s ) ± i k Lerch ( e i k M d ± i k , v , 1 ( s / d ) ) .
f ( n ) = e i k M L 2 + ( d n s ) 2 ± i k n / [ k M v L 2 + ( d n s ) 2 ] v ,
n = 1 f ( n ) = n = 1 N 1 f ( n ) + n = N f ( n ) n = 1 N 1 f ( n ) + n = N f T ( n ) == n = 1 f T ( n ) + n = 1 N 1 ( f ( n ) f T ( n ) ) ,
[ a , b , b , a ] = ( a / 2 + b / 2 ) [ 1 , 1 , 1 , 1 ] + ( a / 2 b / 2 ) [ 1 , 1 , 1 , 1 ] ,
n a + b 2 [ n 11 3 ( n ) + n 1 1 3 ( n ) ] e i k n + n a b 2 [ n 11 3 ( n ) n 1 1 3 ( n ) ] e i k n ,
n a + b 2 [ n 11 3 ( n ) + n 1 1 3 ( n ) ] e i k n n a b 2 [ n 11 3 ( n ) n 1 1 3 ( n ) ] e i k n .

Metrics