Abstract

Surface modes in nanostructured metallic metamaterial films are reported showing larger confinement than plasmons in metallic waveguides of similar dimensions, but in contrast to plasmons, the new modes have TE polarization. The metamaterial, formed by planar arrays of nearly-touching metallic nanoparticles, behaves as a high-index dielectric for the noted polarization, thus yielding well confined guided modes. Our results for silver particles in silica support a new paradigm for TE surface-wave guiding in unconnected nanostructured metallic systems complementary to TM plasmon waves in continuous metal surfaces.

© 2008 Optical Society of America

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References

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  1. G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (Wiley, New York, 2004).
    [CrossRef]
  2. D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
    [CrossRef]
  3. P. Berini, Phys. Rev. B 61, 10484 (2000); 63, 125417 (2001).
    [CrossRef]
  4. H. T. Miyazaki and Y. Kurokawa, "Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity," Phys. Rev. Lett. 96, 097,401 (2006).
    [CrossRef]
  5. R. Ulrich and M. Tacke, "Submillimeter waveguiding on periodic metal structure," Appl. Phys. Lett. 22, 251-253 (1972).
    [CrossRef]
  6. A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
    [CrossRef] [PubMed]
  7. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
    [CrossRef] [PubMed]
  8. F. J. Garcia de Abajo and J. J. Saenz, "Electromagnetic surface modes in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233,901 (2005).
  9. F. J. Garcia de Abajo, "Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
    [CrossRef]
  10. In virtue of Babinet’s principle, the modes of an array of perfectly-conducting coplanar disks have rigorously the same dispersion relation as the modes of the complementary hole array.
  11. N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 113, 49 (1998); 132, 189 (2000).
    [CrossRef]
  12. D. R. McKenzie and R. C. McPhedran, "Exact modelling of cubic lattice permittivity and conductivity," Nature 265, 128-129 (1977).
    [CrossRef]
  13. J. T. Shen, P. B. Catrysse, and S. Fan, "Mechanism for designing metallic metamaterials with a high index of refraction," Phys. Rev. Lett. 94, 197,401 (2005).
    [CrossRef]
  14. S. Riikonen, I. Romero, and F. J. Garcia de Abajo, "Plasmon tunability in metallodielectric metamaterials," Phys. Rev. B 71, 235,104 (2005).
    [CrossRef]
  15. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  16. I. Romero, J. Aizpurua, G. W. Bryant, and F. J. Garcia de Abajo, "Plasmons in nearly touching metallic nanoparticles: Singular response in the limit of touching dimers," Opt. Express 14, 9988-9999 (2006).
    [CrossRef] [PubMed]
  17. 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]
  18. 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 in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
    [CrossRef] [PubMed]
  19. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: The next chip-scale technology," Mater. Today 9, 20-27 (2006).
    [CrossRef]
  20. To a first-order approximation, the trapping coefficients of Figs. 1(b) and 1(f) can be added to describe particle arrays lying on a plasmon-supporting metal rather than a perfect conductor.

2007 (1)

F. J. Garcia de Abajo, "Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

2006 (3)

H. T. Miyazaki and Y. Kurokawa, "Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity," Phys. Rev. Lett. 96, 097,401 (2006).
[CrossRef]

I. Romero, J. Aizpurua, G. W. Bryant, and F. J. Garcia de Abajo, "Plasmons in nearly touching metallic nanoparticles: Singular response in the limit of touching dimers," Opt. Express 14, 9988-9999 (2006).
[CrossRef] [PubMed]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: The next chip-scale technology," Mater. Today 9, 20-27 (2006).
[CrossRef]

2005 (4)

J. T. Shen, P. B. Catrysse, and S. Fan, "Mechanism for designing metallic metamaterials with a high index of refraction," Phys. Rev. Lett. 94, 197,401 (2005).
[CrossRef]

S. Riikonen, I. Romero, and F. J. Garcia de Abajo, "Plasmon tunability in metallodielectric metamaterials," Phys. Rev. B 71, 235,104 (2005).
[CrossRef]

A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

F. J. Garcia de Abajo and J. J. Saenz, "Electromagnetic surface modes in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233,901 (2005).

2004 (1)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

2003 (1)

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 in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

1999 (1)

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]

1981 (1)

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

1977 (1)

D. R. McKenzie and R. C. McPhedran, "Exact modelling of cubic lattice permittivity and conductivity," Nature 265, 128-129 (1977).
[CrossRef]

1972 (2)

R. Ulrich and M. Tacke, "Submillimeter waveguiding on periodic metal structure," Appl. Phys. Lett. 22, 251-253 (1972).
[CrossRef]

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

Aizpurua, J.

Atwater, H. A.

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 in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

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]

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]

Brongersma, M. L.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: The next chip-scale technology," Mater. Today 9, 20-27 (2006).
[CrossRef]

Bryant, G.W.

Catrysse, P. B.

J. T. Shen, P. B. Catrysse, and S. Fan, "Mechanism for designing metallic metamaterials with a high index of refraction," Phys. Rev. Lett. 94, 197,401 (2005).
[CrossRef]

Chandran, A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: The next chip-scale technology," Mater. Today 9, 20-27 (2006).
[CrossRef]

Christy, R. W.

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

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]

Evans, B. R.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

Fan, S.

J. T. Shen, P. B. Catrysse, and S. Fan, "Mechanism for designing metallic metamaterials with a high index of refraction," Phys. Rev. Lett. 94, 197,401 (2005).
[CrossRef]

Garcia de Abajo, F. J.

F. J. Garcia de Abajo, "Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

I. Romero, J. Aizpurua, G. W. Bryant, and F. J. Garcia de Abajo, "Plasmons in nearly touching metallic nanoparticles: Singular response in the limit of touching dimers," Opt. Express 14, 9988-9999 (2006).
[CrossRef] [PubMed]

S. Riikonen, I. Romero, and F. J. Garcia de Abajo, "Plasmon tunability in metallodielectric metamaterials," Phys. Rev. B 71, 235,104 (2005).
[CrossRef]

F. J. Garcia de Abajo and J. J. Saenz, "Electromagnetic surface modes in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233,901 (2005).

Garcia-Vidal, F. J.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

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]

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]

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 in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Hibbins, A. P.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

Johnson, P. B.

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

Kik, P. 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 in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

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 in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

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]

Kurokawa, Y.

H. T. Miyazaki and Y. Kurokawa, "Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity," Phys. Rev. Lett. 96, 097,401 (2006).
[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]

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]

Maier, S. A.

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 in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Martin-Moreno, L.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

McKenzie, D. R.

D. R. McKenzie and R. C. McPhedran, "Exact modelling of cubic lattice permittivity and conductivity," Nature 265, 128-129 (1977).
[CrossRef]

McPhedran, R. C.

D. R. McKenzie and R. C. McPhedran, "Exact modelling of cubic lattice permittivity and conductivity," Nature 265, 128-129 (1977).
[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 in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Miyazaki, H. T.

H. T. Miyazaki and Y. Kurokawa, "Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity," Phys. Rev. Lett. 96, 097,401 (2006).
[CrossRef]

Pendry, J. B.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

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 in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Riikonen, S.

S. Riikonen, I. Romero, and F. J. Garcia de Abajo, "Plasmon tunability in metallodielectric metamaterials," Phys. Rev. B 71, 235,104 (2005).
[CrossRef]

Romero, I.

Sambles, J. R.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

Sarid, D.

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[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]

Schuller, J. A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: The next chip-scale technology," Mater. Today 9, 20-27 (2006).
[CrossRef]

Shen, J. T.

J. T. Shen, P. B. Catrysse, and S. Fan, "Mechanism for designing metallic metamaterials with a high index of refraction," Phys. Rev. Lett. 94, 197,401 (2005).
[CrossRef]

Tacke, M.

R. Ulrich and M. Tacke, "Submillimeter waveguiding on periodic metal structure," Appl. Phys. Lett. 22, 251-253 (1972).
[CrossRef]

Ulrich, R.

R. Ulrich and M. Tacke, "Submillimeter waveguiding on periodic metal structure," Appl. Phys. Lett. 22, 251-253 (1972).
[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]

Zia, R.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: The next chip-scale technology," Mater. Today 9, 20-27 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

R. Ulrich and M. Tacke, "Submillimeter waveguiding on periodic metal structure," Appl. Phys. Lett. 22, 251-253 (1972).
[CrossRef]

Mater. Today (1)

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: The next chip-scale technology," Mater. 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. 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]

Nature (1)

D. R. McKenzie and R. C. McPhedran, "Exact modelling of cubic lattice permittivity and conductivity," Nature 265, 128-129 (1977).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (2)

S. Riikonen, I. Romero, and F. J. Garcia de Abajo, "Plasmon tunability in metallodielectric metamaterials," Phys. Rev. B 71, 235,104 (2005).
[CrossRef]

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

Phys. Rev. Lett. (5)

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]

J. T. Shen, P. B. Catrysse, and S. Fan, "Mechanism for designing metallic metamaterials with a high index of refraction," Phys. Rev. Lett. 94, 197,401 (2005).
[CrossRef]

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, "Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity," Phys. Rev. Lett. 96, 097,401 (2006).
[CrossRef]

F. J. Garcia de Abajo and J. J. Saenz, "Electromagnetic surface modes in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233,901 (2005).

Rev. Mod. Phys. (1)

F. J. Garcia de Abajo, "Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

Science (2)

A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

Other (5)

In virtue of Babinet’s principle, the modes of an array of perfectly-conducting coplanar disks have rigorously the same dispersion relation as the modes of the complementary hole array.

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 113, 49 (1998); 132, 189 (2000).
[CrossRef]

G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (Wiley, New York, 2004).
[CrossRef]

P. Berini, Phys. Rev. B 61, 10484 (2000); 63, 125417 (2001).
[CrossRef]

To a first-order approximation, the trapping coefficients of Figs. 1(b) and 1(f) can be added to describe particle arrays lying on a plasmon-supporting metal rather than a perfect conductor.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Surface electromagnetic waves are characterized by a surface component of their wavevector (k ) exceeding the momentum in the surrounding medium (k) and they pop up evanescently away from the surface up to a distance d that decreases with increasing trapping coefficient γ. (b)–(f) Various forms of light confinement at surfaces: (b) surface-plasmon polaritons, (c) dielectric waveguides, (d) supported dielectric waveguides, (e) planar particle arrays in a symmetric environment (A is the area per particle and α the polarizability), and (f) particle arrays supported on metal. The trapping coefficient γ is given in the limit of large ε in (b), small thickness d in (c) and (d), and small particles in (e) and (f), both for TM and TE modes. Notice that α , α >0 is required in (e) and (f) for the existence of the modes [9].

Fig. 2.
Fig. 2.

(a) Effective electrostatic dielectric constant ε eff and magnetostatic magnetic permeability µ eff of a fcc array of perfect-conductor spheres as a function of the filling fraction of the metal up to the fcc nearly-touching limit. The spheres are embedded in a homogeneous host medium of permittivity εh and permeability µh . Rigorous electromagnetic calculations (solid curves) are compared to the Clausius-Mossotti relation (broken curves). (b) Vis-NIR effective permittivity of fcc arrangements of silver spheres embedded in silica for three different values of the metal filling fraction. The inset shows a magnification of the long-wavelength tails. The complex spectral dependence of the dielectric constant of silver and silica is taken from optical data [15].

Fig. 3.
Fig. 3.

(a) Dispersion relation of the TE mode of a hexagonal layer of 100-nm-diameter silver spheres embedded in silica for a separation between particle surfaces of 4.17 nm (black solid curve). The parallel momentum is directed along a nearest-neighbor vector (GK direction) and extends up to the first Brillouin zone boundary. This is compared to the TE mode of a 100-nm-thick dielectric waveguide of ε=19 material surrounded by silica (dotted curve), and to the surface plasmon polaritons (TM polarization) of a silver-silica planar interface (dashed curve). Higher-order modes of the arrays are also shown (gray solid curves). (b) Propagation distance of the particle array and the silver-silica interface considered in (a). (c) Electric-field intensity in a plane located 5 nm away from the particle surfaces at the λ=1550 nm surface mode for various orientations of the parallel momentum vector relative to the lattice (see arrows) and for k =4.83 µm-1. The intensity scale is linear and the maxima correspond to bright regions.

Fig. 4.
Fig. 4.

(a) Trapping coefficient of a hexagonal layer of 100-nm-diameter silver spheres in silica as a function of the separation between particle surfaces for a wavelength of 1550 nm. (b) Propagation distance of the modes considered in (a). The values corresponding to the planar silver-silica interface are signalled by dashed horizontal lines.

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