Abstract

In equidistant infinite chain of metallic nanospheres the collective mode of surface plasmons propagates without radiative losses, i.e., the Lorentz friction losses in each nanosphere are compensated by energy income in near-, medium- and far-field from the rest of the chain. Within an approximate approach including numerical studies in Green function framework it has been indicated superluminal propagation of some plasmon-polariton modes. By the exact solution of the nonlinear dynamic equation we demonstrate that the superluminal modes were an artifact of the perturbation solution type and we show that the group velocities for both polarizations are limited by light velocity, though vary in large range depending on chain parameters and are typically one order lower than the light velocity.

© 2014 Optical Society of America

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  1. D. S. Citrin, “Plasmon polaritons in finite-length metal-nanoparticle chains: The role of chain length unravelled,” Nano Lett. 5, 985–989 (2005).
    [CrossRef] [PubMed]
  2. L. L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
    [CrossRef]
  3. S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
    [CrossRef] [PubMed]
  4. J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
    [CrossRef]
  5. 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, R16356 (2000).
    [CrossRef]
  6. S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, “Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy,” Phys. Rev. B 65, 193408 (2002).
    [CrossRef]
  7. 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]
  8. S. A. Maier, P. G. Kik, L. A. Sweatlock, H. A. Atwater, J. J. Penninkhof, A. Polman, S. Meltzer, E. Harel, A. Requicha, and B. E. Koel, “Energy transport in metal nanoparticle plasmon waveguides,” Mat. Res. Soc. Symp. Proc.777, T7.1.1 (2003).
  9. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit inmetal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
    [CrossRef] [PubMed]
  10. S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
    [CrossRef]
  11. I. L. Rasskazov, S. V. Karpov, and V. A. Markel, “Nondecaying surface plasmon polaritons in linear chains of silver nanospheroids,” Opt. Lett. 38, 4743–4746 (2013).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. Y. Hadad and B. Z. Steinberg, “Greens function theory for infinite and semi-infinite particle chains,” Phys. Rev. B 84, 125402 (2011).
    [CrossRef]
  14. V. A. Markel and A. K. Sarychev, “Comment on Greens function theory for infinite and semi-infinite particle chains,” Phys. Rev. B 86, 037401 (2012).
    [CrossRef]
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    [CrossRef] [PubMed]
  18. W. A. Jacak, “On plasmon polariton propagation along metallic nano-chain,” Plasmonics 8, 1317–1333 (2013).
    [CrossRef] [PubMed]
  19. C. Yannouleas, R. A. Broglia, M. Brack, and P. F. Bortignon, “Fragmentation of the photoabsorption strength in neutral and charged metal microclusters,” Phys. Rev. Lett. 63, 255–258 (1989).
    [CrossRef] [PubMed]
  20. W. Ekardt, “Anomalous inelastic electron scattering from small metal particles,” Phys. Rev. B 33, 8803–8805 (1986).
    [CrossRef]
  21. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products (Academic Press, Inc., 1994).
  22. V. A. Markel and A. K. Sarychev, “Propagation of surface plasmons in ordered and disordered chains of metal nanospheres,” Phys. Rev. B 75, 085426 (2007).
    [CrossRef]
  23. W. Jacak, J. Krasnyj, J. Jacak, R. Gonczarek, A. Chepok, L. Jacak, D. Hu, and D. Schaadt, “Radius dependent shift in surface plasmon frequency in large metallic nanospheres: Theory and experiment,” J. Appl. Phys. 107, 124317 (2010).
    [CrossRef]
  24. T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
    [CrossRef]
  25. E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B 85, 165419 (2012).
    [CrossRef]

2013

2012

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B 85, 165419 (2012).
[CrossRef]

V. A. Markel and A. K. Sarychev, “Comment on Greens function theory for infinite and semi-infinite particle chains,” Phys. Rev. B 86, 037401 (2012).
[CrossRef]

2011

Y. Hadad and B. Z. Steinberg, “Greens function theory for infinite and semi-infinite particle chains,” Phys. Rev. B 84, 125402 (2011).
[CrossRef]

2010

W. Jacak, J. Krasnyj, J. Jacak, R. Gonczarek, A. Chepok, L. Jacak, D. Hu, and D. Schaadt, “Radius dependent shift in surface plasmon frequency in large metallic nanospheres: Theory and experiment,” J. Appl. Phys. 107, 124317 (2010).
[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]

2007

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

2006

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

2005

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

D. S. Citrin, “Plasmon polaritons in finite-length metal-nanoparticle chains: The role of chain length unravelled,” Nano Lett. 5, 985–989 (2005).
[CrossRef] [PubMed]

2004

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[CrossRef] [PubMed]

2003

L. L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[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]

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

2002

S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, “Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy,” Phys. Rev. B 65, 193408 (2002).
[CrossRef]

2000

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, R16356 (2000).
[CrossRef]

1999

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

1998

T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
[CrossRef]

1989

C. Yannouleas, R. A. Broglia, M. Brack, and P. F. Bortignon, “Fragmentation of the photoabsorption strength in neutral and charged metal microclusters,” Phys. Rev. Lett. 63, 255–258 (1989).
[CrossRef] [PubMed]

1986

W. Ekardt, “Anomalous inelastic electron scattering from small metal particles,” Phys. Rev. B 33, 8803–8805 (1986).
[CrossRef]

Andrianov, E. S.

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B 85, 165419 (2012).
[CrossRef]

Anger, P.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

Atwater, H. A.

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

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

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, M. L. Brongersma, P. G. Kik, and H. A. Atwater, “Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy,” Phys. Rev. B 65, 193408 (2002).
[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, R16356 (2000).
[CrossRef]

S. A. Maier, P. G. Kik, L. A. Sweatlock, H. A. Atwater, J. J. Penninkhof, A. Polman, S. Meltzer, E. Harel, A. Requicha, and B. E. Koel, “Energy transport in metal nanoparticle plasmon waveguides,” Mat. Res. Soc. Symp. Proc.777, T7.1.1 (2003).

Aussenegg, F. R.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

Bharadwaj, P.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

Bortignon, P. F.

C. Yannouleas, R. A. Broglia, M. Brack, and P. F. Bortignon, “Fragmentation of the photoabsorption strength in neutral and charged metal microclusters,” Phys. Rev. Lett. 63, 255–258 (1989).
[CrossRef] [PubMed]

Bourillot, E.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

Brack, M.

C. Yannouleas, R. A. Broglia, M. Brack, and P. F. Bortignon, “Fragmentation of the photoabsorption strength in neutral and charged metal microclusters,” Phys. Rev. Lett. 63, 255–258 (1989).
[CrossRef] [PubMed]

Broglia, R. A.

C. Yannouleas, R. A. Broglia, M. Brack, and P. F. Bortignon, “Fragmentation of the photoabsorption strength in neutral and charged metal microclusters,” Phys. Rev. Lett. 63, 255–258 (1989).
[CrossRef] [PubMed]

Brongersma, M. L.

S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, “Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy,” Phys. Rev. B 65, 193408 (2002).
[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, R16356 (2000).
[CrossRef]

Chepok, A.

W. Jacak, J. Krasnyj, J. Jacak, R. Gonczarek, A. Chepok, L. Jacak, D. Hu, and D. Schaadt, “Radius dependent shift in surface plasmon frequency in large metallic nanospheres: Theory and experiment,” J. Appl. Phys. 107, 124317 (2010).
[CrossRef]

Citrin, D. S.

D. S. Citrin, “Plasmon polaritons in finite-length metal-nanoparticle chains: The role of chain length unravelled,” Nano Lett. 5, 985–989 (2005).
[CrossRef] [PubMed]

Dereux, A.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

Dorofeenko, A. V.

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B 85, 165419 (2012).
[CrossRef]

Ekardt, W.

W. Ekardt, “Anomalous inelastic electron scattering from small metal particles,” Phys. Rev. B 33, 8803–8805 (1986).
[CrossRef]

Feldmann, J.

T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
[CrossRef]

Girard, C.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

Gonczarek, R.

W. Jacak, J. Krasnyj, J. Jacak, R. Gonczarek, A. Chepok, L. Jacak, D. Hu, and D. Schaadt, “Radius dependent shift in surface plasmon frequency in large metallic nanospheres: Theory and experiment,” J. Appl. Phys. 107, 124317 (2010).
[CrossRef]

Gotschy, W.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

Goudonnet, J. P.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

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]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products (Academic Press, Inc., 1994).

Grosse, S.

T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
[CrossRef]

Hadad, Y.

Y. Hadad and B. Z. Steinberg, “Greens function theory for infinite and semi-infinite particle chains,” Phys. Rev. B 84, 125402 (2011).
[CrossRef]

Harel, E.

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

S. A. Maier, P. G. Kik, L. A. Sweatlock, H. A. Atwater, J. J. Penninkhof, A. Polman, S. Meltzer, E. Harel, A. Requicha, and B. E. Koel, “Energy transport in metal nanoparticle plasmon waveguides,” Mat. Res. Soc. Symp. Proc.777, T7.1.1 (2003).

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, R16356 (2000).
[CrossRef]

Hu, D.

W. Jacak, J. Krasnyj, J. Jacak, R. Gonczarek, A. Chepok, L. Jacak, D. Hu, and D. Schaadt, “Radius dependent shift in surface plasmon frequency in large metallic nanospheres: Theory and experiment,” J. Appl. Phys. 107, 124317 (2010).
[CrossRef]

Jacak, J.

W. Jacak, J. Krasnyj, J. Jacak, R. Gonczarek, A. Chepok, L. Jacak, D. Hu, and D. Schaadt, “Radius dependent shift in surface plasmon frequency in large metallic nanospheres: Theory and experiment,” J. Appl. Phys. 107, 124317 (2010).
[CrossRef]

Jacak, L.

W. Jacak, J. Krasnyj, J. Jacak, R. Gonczarek, A. Chepok, L. Jacak, D. Hu, and D. Schaadt, “Radius dependent shift in surface plasmon frequency in large metallic nanospheres: Theory and experiment,” J. Appl. Phys. 107, 124317 (2010).
[CrossRef]

Jacak, W.

W. Jacak, J. Krasnyj, J. Jacak, R. Gonczarek, A. Chepok, L. Jacak, D. Hu, and D. Schaadt, “Radius dependent shift in surface plasmon frequency in large metallic nanospheres: Theory and experiment,” J. Appl. Phys. 107, 124317 (2010).
[CrossRef]

Jacak, W. A.

W. A. Jacak, “On plasmon polariton propagation along metallic nano-chain,” Plasmonics 8, 1317–1333 (2013).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (John Willey and Sons Inc., 1998).

Janel, N.

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[CrossRef] [PubMed]

Karpov, S. V.

Kelly, K. L.

L. L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[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]

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

S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, “Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy,” Phys. Rev. B 65, 193408 (2002).
[CrossRef]

S. A. Maier, P. G. Kik, L. A. Sweatlock, H. A. Atwater, J. J. Penninkhof, A. Polman, S. Meltzer, E. Harel, A. Requicha, and B. E. Koel, “Energy transport in metal nanoparticle plasmon waveguides,” Mat. Res. Soc. Symp. Proc.777, T7.1.1 (2003).

Klar, T.

T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
[CrossRef]

Koel, B. E.

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

S. A. Maier, P. G. Kik, L. A. Sweatlock, H. A. Atwater, J. J. Penninkhof, A. Polman, S. Meltzer, E. Harel, A. Requicha, and B. E. Koel, “Energy transport in metal nanoparticle plasmon waveguides,” Mat. Res. Soc. Symp. Proc.777, T7.1.1 (2003).

Krasnyj, J.

W. Jacak, J. Krasnyj, J. Jacak, R. Gonczarek, A. Chepok, L. Jacak, D. Hu, and D. Schaadt, “Radius dependent shift in surface plasmon frequency in large metallic nanospheres: Theory and experiment,” J. Appl. Phys. 107, 124317 (2010).
[CrossRef]

Krenn, J. R.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

Lacroute, Y.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Field Theory (Nauka, 1973).

Leitner, A.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Field Theory (Nauka, 1973).

Lisyansky, A. A.

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B 85, 165419 (2012).
[CrossRef]

Maier, S. A.

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

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

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, M. L. Brongersma, P. G. Kik, and H. A. Atwater, “Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy,” Phys. Rev. B 65, 193408 (2002).
[CrossRef]

S. A. Maier, P. G. Kik, L. A. Sweatlock, H. A. Atwater, J. J. Penninkhof, A. Polman, S. Meltzer, E. Harel, A. Requicha, and B. E. Koel, “Energy transport in metal nanoparticle plasmon waveguides,” Mat. Res. Soc. Symp. Proc.777, T7.1.1 (2003).

Markel, V. A.

I. L. Rasskazov, S. V. Karpov, and V. A. Markel, “Nondecaying surface plasmon polaritons in linear chains of silver nanospheroids,” Opt. Lett. 38, 4743–4746 (2013).
[CrossRef] [PubMed]

V. A. Markel and A. K. Sarychev, “Comment on Greens function theory for infinite and semi-infinite particle chains,” Phys. Rev. B 86, 037401 (2012).
[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]

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

Meltzer, S.

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

S. A. Maier, P. G. Kik, L. A. Sweatlock, H. A. Atwater, J. J. Penninkhof, A. Polman, S. Meltzer, E. Harel, A. Requicha, and B. E. Koel, “Energy transport in metal nanoparticle plasmon waveguides,” Mat. Res. Soc. Symp. Proc.777, T7.1.1 (2003).

Novotny, L.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

Penninkhof, J. J.

S. A. Maier, P. G. Kik, L. A. Sweatlock, H. A. Atwater, J. J. Penninkhof, A. Polman, S. Meltzer, E. Harel, A. Requicha, and B. E. Koel, “Energy transport in metal nanoparticle plasmon waveguides,” Mat. Res. Soc. Symp. Proc.777, T7.1.1 (2003).

Perner, M.

T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
[CrossRef]

Polman, A.

S. A. Maier, P. G. Kik, L. A. Sweatlock, H. A. Atwater, J. J. Penninkhof, A. Polman, S. Meltzer, E. Harel, A. Requicha, and B. E. Koel, “Energy transport in metal nanoparticle plasmon waveguides,” Mat. Res. Soc. Symp. Proc.777, T7.1.1 (2003).

Pukhov, A. A.

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B 85, 165419 (2012).
[CrossRef]

Rasskazov, I. L.

Requicha, A.

S. A. Maier, P. G. Kik, L. A. Sweatlock, H. A. Atwater, J. J. Penninkhof, A. Polman, S. Meltzer, E. Harel, A. Requicha, and B. E. Koel, “Energy transport in metal nanoparticle plasmon waveguides,” Mat. Res. Soc. Symp. Proc.777, T7.1.1 (2003).

Requicha, A. A. G.

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

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products (Academic Press, Inc., 1994).

Sarychev, A. K.

V. A. Markel and A. K. Sarychev, “Comment on Greens function theory for infinite and semi-infinite particle chains,” Phys. Rev. B 86, 037401 (2012).
[CrossRef]

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

Schaadt, D.

W. Jacak, J. Krasnyj, J. Jacak, R. Gonczarek, A. Chepok, L. Jacak, D. Hu, and D. Schaadt, “Radius dependent shift in surface plasmon frequency in large metallic nanospheres: Theory and experiment,” J. Appl. Phys. 107, 124317 (2010).
[CrossRef]

Schatz, G. C.

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[CrossRef] [PubMed]

L. L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

Schider, G.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

Spirkl, W.

T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
[CrossRef]

Steinberg, B. Z.

Y. Hadad and B. Z. Steinberg, “Greens function theory for infinite and semi-infinite particle chains,” Phys. Rev. B 84, 125402 (2011).
[CrossRef]

Sweatlock, L. A.

S. A. Maier, P. G. Kik, L. A. Sweatlock, H. A. Atwater, J. J. Penninkhof, A. Polman, S. Meltzer, E. Harel, A. Requicha, and B. E. Koel, “Energy transport in metal nanoparticle plasmon waveguides,” Mat. Res. Soc. Symp. Proc.777, T7.1.1 (2003).

Vinogradov, A. P.

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B 85, 165419 (2012).
[CrossRef]

von Plessen, G.

T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
[CrossRef]

Weeber, J. C.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

Yannouleas, C.

C. Yannouleas, R. A. Broglia, M. Brack, and P. F. Bortignon, “Fragmentation of the photoabsorption strength in neutral and charged metal microclusters,” Phys. Rev. Lett. 63, 255–258 (1989).
[CrossRef] [PubMed]

Zhao, L. L.

L. L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

Zou, S.

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[CrossRef] [PubMed]

J. Appl. Phys.

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

W. Jacak, J. Krasnyj, J. Jacak, R. Gonczarek, A. Chepok, L. Jacak, D. Hu, and D. Schaadt, “Radius dependent shift in surface plasmon frequency in large metallic nanospheres: Theory and experiment,” J. Appl. Phys. 107, 124317 (2010).
[CrossRef]

J. Chem. Phys.

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[CrossRef] [PubMed]

J. Phys. Chem. B

L. L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

Nano Lett.

D. S. Citrin, “Plasmon polaritons in finite-length metal-nanoparticle chains: The role of chain length unravelled,” Nano Lett. 5, 985–989 (2005).
[CrossRef] [PubMed]

Nat. Mater.

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

Opt. Lett.

Phys. Rev. B

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

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B 85, 165419 (2012).
[CrossRef]

W. Ekardt, “Anomalous inelastic electron scattering from small metal particles,” Phys. Rev. B 33, 8803–8805 (1986).
[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]

Y. Hadad and B. Z. Steinberg, “Greens function theory for infinite and semi-infinite particle chains,” Phys. Rev. B 84, 125402 (2011).
[CrossRef]

V. A. Markel and A. K. Sarychev, “Comment on Greens function theory for infinite and semi-infinite particle chains,” Phys. Rev. B 86, 037401 (2012).
[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, R16356 (2000).
[CrossRef]

S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, “Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy,” Phys. Rev. B 65, 193408 (2002).
[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]

Phys. Rev. Lett.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

C. Yannouleas, R. A. Broglia, M. Brack, and P. F. Bortignon, “Fragmentation of the photoabsorption strength in neutral and charged metal microclusters,” Phys. Rev. Lett. 63, 255–258 (1989).
[CrossRef] [PubMed]

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
[CrossRef]

Plasmonics

W. A. Jacak, “On plasmon polariton propagation along metallic nano-chain,” Plasmonics 8, 1317–1333 (2013).
[CrossRef] [PubMed]

Other

L. D. Landau and E. M. Lifshitz, Field Theory (Nauka, 1973).

J. D. Jackson, Classical Electrodynamics (John Willey and Sons Inc., 1998).

S. A. Maier, P. G. Kik, L. A. Sweatlock, H. A. Atwater, J. J. Penninkhof, A. Polman, S. Meltzer, E. Harel, A. Requicha, and B. E. Koel, “Energy transport in metal nanoparticle plasmon waveguides,” Mat. Res. Soc. Symp. Proc.777, T7.1.1 (2003).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products (Academic Press, Inc., 1994).

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Figures (3)

Fig. 1
Fig. 1

Exact solution for self-frequency and damping rate of transversally (upper) and longitudinally (lower) polarized modes of plasmon-polariton in the nano-chain (ω in ω1 units)–there is presented solution of Eq. (3) in 1000 points on the sector kd ∈ [0, 2π); in plot for self-frequency of transversal mode a truncated logarithmic-type singularity of self-energy is marked; for longitudinal polarization the almost vertical local slop of self-frequency is marked

Fig. 2
Fig. 2

Exact solution for the group velocity of transversal mode of plasmon-polariton in the nano-chain for a = 10 nm and d = 4a; solution of nonlinear Eq. (3) removes the logarithmic singularity–the remaining local very narrow extremes are truncated exactly at value of c; in close vicinity of the singular point the solution was found in more than 1000 values for kd (in bottom: scale-magnification of marked fragments in upper panels); asymmetry in singular points is caused by imposition of hyperbolic and logarithmic truncated singularities of group velocity for the transversally polarized mode

Fig. 3
Fig. 3

Exact solution for the group velocity of longitudinally polarized mode of plasmon-polariton in the nano-chain for a = 10 nm and d = 3a; almost vertical slope of self-frequency (right panels) is limited by light velocity (in bottom: scale-magnification of fragments marked in upper panels)

Equations (6)

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E ( r , r 0 , t ) = 1 ε ( 2 v 2 t 2 1 r 0 v t 1 r 0 2 1 r 0 3 ) D ( r , t r 0 / v ) + 1 ε ( 2 v 2 t 2 1 r 0 + v t 3 r 0 2 + 3 r 0 3 ) n 0 ( n 0 D ( r , t r 0 / v ) ) ,
D α ( ld , t ) = D α ( k , t ) e i k l d , 0 k 2 π d
( ω 2 i 2 τ 0 ω + ω 1 2 ) D α ( k , ω ) = ω 1 2 a 3 d 3 F α ( k , ω ) D α ( k , ω ) ,
F z ( k , ω ) = 4 m = 1 ( cos ( m k d ) m 3 cos ( m ω d / v ) + ω d / v cos ( m k d ) m 2 sin ( m ω d / v ) ) + 2 i [ 1 3 ( ω d / v ) 3 + 2 m = 1 ( cos ( m k d ) m 3 sin ( m ω d / v ) ω d / v cos ( m k d ) m 2 cos ( m ω d / v ) ) ] , F x ( y ) ( k , ω ) = 2 m = 1 ( cos ( m k d ) m 3 cos ( m ω d / v ) + ω d / v cos ( m k d ) m 2 sin ( m ω d / v ) ( ω d / v ) 2 cos ( m k d ) m cos ( m ω d / v ) ) i [ 2 3 ( ω d / v ) 3 + 2 m = 1 ( cos ( m k d ) m 3 sin ( m ω d / v ) + ω d / v cos ( m k d ) m 2 cos ( m ω d / v ) ( ω d / v ) 2 cos ( m k d ) m sin ( m ω d / v ) ) ] .
1 τ 0 v F 2 λ b + C v F 2 a ,
m = 1 cos ( m ( k d + ω d / v ) ) + cos ( m ( k d ω d / v ) ) m = 1 2 ln [ ( 2 2 cos ( k d + ω d / v ) ) ( 2 2 cos ( k d ω d / v ) ) ] ,

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