Abstract

We have calculated the photonic band structures of metallic inverse opals and of periodic linear chains of spherical pores in a metallic host, below a plasma frequency ωp. In both cases, we use a tight-binding approximation, assuming a Drude dielectric function for the metallic component, but without making the quasistatic approximation. The tight-binding modes are linear combinations of the single-cavity transverse magnetic (TM) modes. For the inverse-opal structures, the lowest modes are analogous to those constructed from the three degenerate atomic p-states in fcc crystals. For the linear chains, in the limit of small spheres compared to a wavelength, the results bear some qualitative resemblance to the dispersion relation for metal spheres in an insulating host, as calculated by Brongersma et al. [Phys. Rev. B 62, R16356 (2000)]. Because the electromagnetic fields of these modes decay exponentially in the metal, there are no radiative losses, in contrast to the case of arrays of metallic spheres in air. We suggest that this tight-binding approach to photonic band structures of such metallic inverse materials may be a useful approach for studying photonic crystals containing metallic components, even beyond the quasistatic approximation.

© 2013 OSA

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  1. J. Q.  Xia, Y. R.  Ying, S. H.  Foulger, “Electric-Field-Induced Rejection-Wavelength Tuning of Photonic-Bandgap Composites,” Adv. Mater. 17, 2463–2467 (2005).
    [CrossRef]
  2. Kurt  Busch, Sajeev  John, “Liquid-Crystal Photonic-Band-Gap Materials: The Tunable Electromagnetic Vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
    [CrossRef]
  3. Eli  Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  4. A.  Scherer, O.  Painter, B.  D’Urso, R.  Lee, A.  Yariv, “InGaAsP photonic band gap crystal membrane microresonators,” J. Vac. Sci. Technol. B 16, 3906 (1998).
    [CrossRef]
  5. Attila  Mekis, J. C.  Chen, I.  Kurland, Shanhui  Fan, Pierre R.  Villeneuve, J. D.  Joannopoulos, “High Transmission through Sharp Bends in Photonic Crystal Waveguides, ” Phys. Rev. Lett. 77, 3787–3790 (1996).
    [CrossRef] [PubMed]
  6. O.  Painter, R. K.  Lee, A.  Scherer, A.  Yariv, J. D.  O’Brien, P. D.  Dapkus, I.  Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
    [CrossRef] [PubMed]
  7. F.  Benabid, J. C.  Knight, G.  Antonopoulos, P. St. J.  Russell, “Stimulated Raman Scattering in Hydrogen-Filled Hollow-Core Photonic Crystal Fiber,” Science 298, 399–402 (2002).
    [CrossRef] [PubMed]
  8. Y.  Cao, J. O.  Schenk, M. A.  Fiddy, “Third order nonlinear effect near a degenerate band edge,” Opt. Photonics Lett. 1, 1–7 (2008).
    [CrossRef]
  9. Arthur R.  McGurn, Alexei A.  Maradudin, “Photonic band structures of two- and three-dimensional periodic metal or semiconductor arrays,” Phys. Rev. B 48, 17576–17579 (1993).
    [CrossRef]
  10. V.  Kuzmiak, A. A.  Maradudin, F.  Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835–16844 (1994).
    [CrossRef]
  11. V.  Kuzmiak, A. A.  Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55, 7427–7444 (1997).
    [CrossRef]
  12. I. H. H.  Zabel, D.  Stroud, “Photonic band structures of optically anisotropic periodic arrays,” Phys. Rev. B 48, 5004–5012 (1993).
    [CrossRef]
  13. Mark L.  Brongersma, John W.  Hartman, Harry A.  Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356–R16359 (2000).
    [CrossRef]
  14. Stefan A.  Maier, Pieter G.  Kik, Harry A.  Atwater, Sheffer  Meltzer, Elad  Harel, Bruce E.  Koel, Ari 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]
  15. S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics–A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
    [CrossRef]
  16. Prashant K.  Jain, Wenyu  Huang, Mostafa A.  El-Sayed, “On the Universal Scaling Behavior of the Distance Decay of Plasmon Coupling in Metal Nanoparticle Pairs: A Plasmon Ruler Equation,” Nano Lett. 7, 2080–2088 (2007).
    [CrossRef]
  17. LinLin  Zhao, K.  Lance Kelly, George 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]
  18. Q.-H.  Wei, K.-H.  Su, S.  Durant, X.  Zhang, “Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains,” Nano Lett. 4, 1067–1071 (2004).
    [CrossRef]
  19. L. A.  Sweatlock, S. A.  Maier, H. A.  Atwater, J. J.  Penninkhof, A.  Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
    [CrossRef]
  20. Shengli  Zou, George C.  Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606–12612 (2004).
    [CrossRef] [PubMed]
  21. A. F.  Koenderink, Albert  Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).
    [CrossRef]
  22. Andrea  Alù, Nader  Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436 (2006).
    [CrossRef]
  23. Alexandre  Bouhelier, Renaud  Bachelot, Jin Seo  Im, Gary P.  Wiederrecht, Gilles  Lerondel, Sergei  Kostcheev, Pascal  Royer, “Electromagnetic Interactions in Plasmonic Nanoparticle Arrays,” J. Phys. Chem. B 109, 3195–3198 (2005).
    [CrossRef]
  24. Vadim A.  Markel, Andrey K.  Sarychev, “Propagation of surface plasmons in ordered and disordered chains of metal nanospheres,” Phys. Rev. B 75, 085426 (2007).
    [CrossRef]
  25. Yu-Rong  Zhen, Kin Hung  Fung, C. T.  Chan, “Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles,” Phys. Rev. B 78, 035419 (2008).
    [CrossRef]
  26. W.  Jacak, J.  Krasnyj, J.  Jacak, A.  Chepok, L.  Jacak, W.  Donderowicz, D. Z.  Hu, D. M.  Schaadt, “Undamped collective surface plasmon oscillations along metallic nanosphere chains,” J. Appl. Phys. 108, 084304 (2010).
    [CrossRef]
  27. Matthew D.  Arnold, Martin G.  Blaber, Michael J.  Ford, Nadine  Harris, “Universal scaling of local plasmons in chains of metal spheres,” Opt. Express 18, 7528–7542 (2010).
    [CrossRef] [PubMed]
  28. Sung Yong  Park, David  Stroud, “Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
    [CrossRef]
  29. W. H.  Weber, G. W.  Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70, 125429 (2004).
    [CrossRef]
  30. D.  Gaillot, T.  Yamashita, C. J.  Summers, “Photonic band gaps in highly conformal inverse-opal based photonic crystals,” Phys. Rev. B 72, 205109 (2005).
    [CrossRef]
  31. Ali E.  Aliev, Sergey B.  Lee, Anvar A.  Zakhidov, Ray H.  Baughman, “Superconductivity in Pb inverse opal,” Physica C 453, 15–23 (2007).
    [CrossRef]
  32. G.  Gantzounis, N.  Stefanou, “Cavity-plasmon waveguides: Multiple scattering calculations of dispersion in weakly coupled dielectric nanocavities in a metallic host material,” Phys. Rev. B 74, 085102 (2006).
    [CrossRef]
  33. See, e.g.,J. D.  Jackson, “Earth and Ionosphere as a Resonant Cavity: Schumann Resonances,” in Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999), pp. 374–376.
  34. See, e.g.,N. W.  Ashcroft, N. D.  Mermin, “Problem 2. Tight-Binding p-Bands in Cubic Crystals” & “General remarks on the tight-binding method,” in Solid State Physics (Saunders College Publishing, Orlando, 1976), pp. 189–190& pp. 184–185.
  35. E.  Lidorikis, M. M.  Sigalas, E. N.  Economou, C. M.  Soukoulis, “Tight-Binding Parametrization for Photonic Band Gap Materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
    [CrossRef]
  36. N.  Stefanou, A.  Modinos, V.  Yannopapas, “Optical transparency of mesoporous metals,” Solid State Commun. 118, 69–73 (2001).
    [CrossRef]
  37. B. A.  McKinnon, T. C.  Choy, “Significance of nonorthogonality in tight-binding models,” Phys. Rev. B 52, 14531–14538 (1995).
    [CrossRef]
  38. Madhu  Menon, K. R.  Subbaswamy, “Transferable nonorthogonal tight-binding scheme for silicon,” Phys. Rev. B 50, 11577–11582 (1994).
    [CrossRef]
  39. Per-Olov  Löwdin, “On the NonOrthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals,” J. Chem. Phys. 18, 365–375 (1950).
    [CrossRef]

2010

W.  Jacak, J.  Krasnyj, J.  Jacak, A.  Chepok, L.  Jacak, W.  Donderowicz, D. Z.  Hu, D. M.  Schaadt, “Undamped collective surface plasmon oscillations along metallic nanosphere chains,” J. Appl. Phys. 108, 084304 (2010).
[CrossRef]

Matthew D.  Arnold, Martin G.  Blaber, Michael J.  Ford, Nadine  Harris, “Universal scaling of local plasmons in chains of metal spheres,” Opt. Express 18, 7528–7542 (2010).
[CrossRef] [PubMed]

2008

Yu-Rong  Zhen, Kin Hung  Fung, C. T.  Chan, “Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles,” Phys. Rev. B 78, 035419 (2008).
[CrossRef]

Y.  Cao, J. O.  Schenk, M. A.  Fiddy, “Third order nonlinear effect near a degenerate band edge,” Opt. Photonics Lett. 1, 1–7 (2008).
[CrossRef]

2007

Prashant K.  Jain, Wenyu  Huang, Mostafa A.  El-Sayed, “On the Universal Scaling Behavior of the Distance Decay of Plasmon Coupling in Metal Nanoparticle Pairs: A Plasmon Ruler Equation,” Nano Lett. 7, 2080–2088 (2007).
[CrossRef]

Ali E.  Aliev, Sergey B.  Lee, Anvar A.  Zakhidov, Ray H.  Baughman, “Superconductivity in Pb inverse opal,” Physica C 453, 15–23 (2007).
[CrossRef]

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

2006

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

Andrea  Alù, Nader  Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436 (2006).
[CrossRef]

G.  Gantzounis, N.  Stefanou, “Cavity-plasmon waveguides: Multiple scattering calculations of dispersion in weakly coupled dielectric nanocavities in a metallic host material,” Phys. Rev. B 74, 085102 (2006).
[CrossRef]

2005

D.  Gaillot, T.  Yamashita, C. J.  Summers, “Photonic band gaps in highly conformal inverse-opal based photonic crystals,” Phys. Rev. B 72, 205109 (2005).
[CrossRef]

Alexandre  Bouhelier, Renaud  Bachelot, Jin Seo  Im, Gary P.  Wiederrecht, Gilles  Lerondel, Sergei  Kostcheev, Pascal  Royer, “Electromagnetic Interactions in Plasmonic Nanoparticle Arrays,” J. Phys. Chem. B 109, 3195–3198 (2005).
[CrossRef]

L. A.  Sweatlock, S. A.  Maier, H. A.  Atwater, J. J.  Penninkhof, A.  Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
[CrossRef]

J. Q.  Xia, Y. R.  Ying, S. H.  Foulger, “Electric-Field-Induced Rejection-Wavelength Tuning of Photonic-Bandgap Composites,” Adv. Mater. 17, 2463–2467 (2005).
[CrossRef]

2004

Shengli  Zou, George C.  Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606–12612 (2004).
[CrossRef] [PubMed]

Q.-H.  Wei, K.-H.  Su, S.  Durant, X.  Zhang, “Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains,” Nano Lett. 4, 1067–1071 (2004).
[CrossRef]

Sung Yong  Park, David  Stroud, “Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
[CrossRef]

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

2003

LinLin  Zhao, K.  Lance Kelly, George 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]

Stefan A.  Maier, Pieter G.  Kik, Harry A.  Atwater, Sheffer  Meltzer, Elad  Harel, Bruce E.  Koel, Ari 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]

2002

F.  Benabid, J. C.  Knight, G.  Antonopoulos, P. St. J.  Russell, “Stimulated Raman Scattering in Hydrogen-Filled Hollow-Core Photonic Crystal Fiber,” Science 298, 399–402 (2002).
[CrossRef] [PubMed]

2001

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics–A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

N.  Stefanou, A.  Modinos, V.  Yannopapas, “Optical transparency of mesoporous metals,” Solid State Commun. 118, 69–73 (2001).
[CrossRef]

2000

Mark L.  Brongersma, John W.  Hartman, Harry A.  Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356–R16359 (2000).
[CrossRef]

1999

O.  Painter, R. K.  Lee, A.  Scherer, A.  Yariv, J. D.  O’Brien, P. D.  Dapkus, I.  Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Kurt  Busch, Sajeev  John, “Liquid-Crystal Photonic-Band-Gap Materials: The Tunable Electromagnetic Vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[CrossRef]

1998

A.  Scherer, O.  Painter, B.  D’Urso, R.  Lee, A.  Yariv, “InGaAsP photonic band gap crystal membrane microresonators,” J. Vac. Sci. Technol. B 16, 3906 (1998).
[CrossRef]

E.  Lidorikis, M. M.  Sigalas, E. N.  Economou, C. M.  Soukoulis, “Tight-Binding Parametrization for Photonic Band Gap Materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

1997

V.  Kuzmiak, A. A.  Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55, 7427–7444 (1997).
[CrossRef]

1996

Attila  Mekis, J. C.  Chen, I.  Kurland, Shanhui  Fan, Pierre R.  Villeneuve, J. D.  Joannopoulos, “High Transmission through Sharp Bends in Photonic Crystal Waveguides, ” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

1995

B. A.  McKinnon, T. C.  Choy, “Significance of nonorthogonality in tight-binding models,” Phys. Rev. B 52, 14531–14538 (1995).
[CrossRef]

1994

Madhu  Menon, K. R.  Subbaswamy, “Transferable nonorthogonal tight-binding scheme for silicon,” Phys. Rev. B 50, 11577–11582 (1994).
[CrossRef]

V.  Kuzmiak, A. A.  Maradudin, F.  Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835–16844 (1994).
[CrossRef]

1993

I. H. H.  Zabel, D.  Stroud, “Photonic band structures of optically anisotropic periodic arrays,” Phys. Rev. B 48, 5004–5012 (1993).
[CrossRef]

Arthur R.  McGurn, Alexei A.  Maradudin, “Photonic band structures of two- and three-dimensional periodic metal or semiconductor arrays,” Phys. Rev. B 48, 17576–17579 (1993).
[CrossRef]

1987

Eli  Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

1950

Per-Olov  Löwdin, “On the NonOrthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals,” J. Chem. Phys. 18, 365–375 (1950).
[CrossRef]

Aliev, Ali E.

Ali E.  Aliev, Sergey B.  Lee, Anvar A.  Zakhidov, Ray H.  Baughman, “Superconductivity in Pb inverse opal,” Physica C 453, 15–23 (2007).
[CrossRef]

Alù, Andrea

Andrea  Alù, Nader  Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436 (2006).
[CrossRef]

Antonopoulos, G.

F.  Benabid, J. C.  Knight, G.  Antonopoulos, P. St. J.  Russell, “Stimulated Raman Scattering in Hydrogen-Filled Hollow-Core Photonic Crystal Fiber,” Science 298, 399–402 (2002).
[CrossRef] [PubMed]

Arnold, Matthew D.

Ashcroft, N. W.

See, e.g.,N. W.  Ashcroft, N. D.  Mermin, “Problem 2. Tight-Binding p-Bands in Cubic Crystals” & “General remarks on the tight-binding method,” in Solid State Physics (Saunders College Publishing, Orlando, 1976), pp. 189–190& pp. 184–185.

Atwater, H. A.

L. A.  Sweatlock, S. A.  Maier, H. A.  Atwater, J. J.  Penninkhof, A.  Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
[CrossRef]

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics–A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

Atwater, Harry A.

Stefan A.  Maier, Pieter G.  Kik, Harry A.  Atwater, Sheffer  Meltzer, Elad  Harel, Bruce E.  Koel, Ari 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]

Mark L.  Brongersma, John W.  Hartman, Harry A.  Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356–R16359 (2000).
[CrossRef]

Bachelot, Renaud

Alexandre  Bouhelier, Renaud  Bachelot, Jin Seo  Im, Gary P.  Wiederrecht, Gilles  Lerondel, Sergei  Kostcheev, Pascal  Royer, “Electromagnetic Interactions in Plasmonic Nanoparticle Arrays,” J. Phys. Chem. B 109, 3195–3198 (2005).
[CrossRef]

Baughman, Ray H.

Ali E.  Aliev, Sergey B.  Lee, Anvar A.  Zakhidov, Ray H.  Baughman, “Superconductivity in Pb inverse opal,” Physica C 453, 15–23 (2007).
[CrossRef]

Benabid, F.

F.  Benabid, J. C.  Knight, G.  Antonopoulos, P. St. J.  Russell, “Stimulated Raman Scattering in Hydrogen-Filled Hollow-Core Photonic Crystal Fiber,” Science 298, 399–402 (2002).
[CrossRef] [PubMed]

Blaber, Martin G.

Bouhelier, Alexandre

Alexandre  Bouhelier, Renaud  Bachelot, Jin Seo  Im, Gary P.  Wiederrecht, Gilles  Lerondel, Sergei  Kostcheev, Pascal  Royer, “Electromagnetic Interactions in Plasmonic Nanoparticle Arrays,” J. Phys. Chem. B 109, 3195–3198 (2005).
[CrossRef]

Brongersma, M. L.

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics–A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

Brongersma, Mark L.

Mark L.  Brongersma, John W.  Hartman, Harry A.  Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356–R16359 (2000).
[CrossRef]

Busch, Kurt

Kurt  Busch, Sajeev  John, “Liquid-Crystal Photonic-Band-Gap Materials: The Tunable Electromagnetic Vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[CrossRef]

Cao, Y.

Y.  Cao, J. O.  Schenk, M. A.  Fiddy, “Third order nonlinear effect near a degenerate band edge,” Opt. Photonics Lett. 1, 1–7 (2008).
[CrossRef]

Chan, C. T.

Yu-Rong  Zhen, Kin Hung  Fung, C. T.  Chan, “Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles,” Phys. Rev. B 78, 035419 (2008).
[CrossRef]

Chen, J. C.

Attila  Mekis, J. C.  Chen, I.  Kurland, Shanhui  Fan, Pierre R.  Villeneuve, J. D.  Joannopoulos, “High Transmission through Sharp Bends in Photonic Crystal Waveguides, ” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Chepok, A.

W.  Jacak, J.  Krasnyj, J.  Jacak, A.  Chepok, L.  Jacak, W.  Donderowicz, D. Z.  Hu, D. M.  Schaadt, “Undamped collective surface plasmon oscillations along metallic nanosphere chains,” J. Appl. Phys. 108, 084304 (2010).
[CrossRef]

Choy, T. C.

B. A.  McKinnon, T. C.  Choy, “Significance of nonorthogonality in tight-binding models,” Phys. Rev. B 52, 14531–14538 (1995).
[CrossRef]

D’Urso, B.

A.  Scherer, O.  Painter, B.  D’Urso, R.  Lee, A.  Yariv, “InGaAsP photonic band gap crystal membrane microresonators,” J. Vac. Sci. Technol. B 16, 3906 (1998).
[CrossRef]

Dapkus, P. D.

O.  Painter, R. K.  Lee, A.  Scherer, A.  Yariv, J. D.  O’Brien, P. D.  Dapkus, I.  Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Donderowicz, W.

W.  Jacak, J.  Krasnyj, J.  Jacak, A.  Chepok, L.  Jacak, W.  Donderowicz, D. Z.  Hu, D. M.  Schaadt, “Undamped collective surface plasmon oscillations along metallic nanosphere chains,” J. Appl. Phys. 108, 084304 (2010).
[CrossRef]

Durant, S.

Q.-H.  Wei, K.-H.  Su, S.  Durant, X.  Zhang, “Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains,” Nano Lett. 4, 1067–1071 (2004).
[CrossRef]

Economou, E. N.

E.  Lidorikis, M. M.  Sigalas, E. N.  Economou, C. M.  Soukoulis, “Tight-Binding Parametrization for Photonic Band Gap Materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

El-Sayed, Mostafa A.

Prashant K.  Jain, Wenyu  Huang, Mostafa A.  El-Sayed, “On the Universal Scaling Behavior of the Distance Decay of Plasmon Coupling in Metal Nanoparticle Pairs: A Plasmon Ruler Equation,” Nano Lett. 7, 2080–2088 (2007).
[CrossRef]

Engheta, Nader

Andrea  Alù, Nader  Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436 (2006).
[CrossRef]

Fan, Shanhui

Attila  Mekis, J. C.  Chen, I.  Kurland, Shanhui  Fan, Pierre R.  Villeneuve, J. D.  Joannopoulos, “High Transmission through Sharp Bends in Photonic Crystal Waveguides, ” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Fiddy, M. A.

Y.  Cao, J. O.  Schenk, M. A.  Fiddy, “Third order nonlinear effect near a degenerate band edge,” Opt. Photonics Lett. 1, 1–7 (2008).
[CrossRef]

Ford, G. W.

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

Ford, Michael J.

Foulger, S. H.

J. Q.  Xia, Y. R.  Ying, S. H.  Foulger, “Electric-Field-Induced Rejection-Wavelength Tuning of Photonic-Bandgap Composites,” Adv. Mater. 17, 2463–2467 (2005).
[CrossRef]

Fung, Kin Hung

Yu-Rong  Zhen, Kin Hung  Fung, C. T.  Chan, “Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles,” Phys. Rev. B 78, 035419 (2008).
[CrossRef]

Gaillot, D.

D.  Gaillot, T.  Yamashita, C. J.  Summers, “Photonic band gaps in highly conformal inverse-opal based photonic crystals,” Phys. Rev. B 72, 205109 (2005).
[CrossRef]

Gantzounis, G.

G.  Gantzounis, N.  Stefanou, “Cavity-plasmon waveguides: Multiple scattering calculations of dispersion in weakly coupled dielectric nanocavities in a metallic host material,” Phys. Rev. B 74, 085102 (2006).
[CrossRef]

Harel, Elad

Stefan A.  Maier, Pieter G.  Kik, Harry A.  Atwater, Sheffer  Meltzer, Elad  Harel, Bruce E.  Koel, Ari 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]

Harris, Nadine

Hartman, John W.

Mark L.  Brongersma, John W.  Hartman, Harry A.  Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356–R16359 (2000).
[CrossRef]

Hu, D. Z.

W.  Jacak, J.  Krasnyj, J.  Jacak, A.  Chepok, L.  Jacak, W.  Donderowicz, D. Z.  Hu, D. M.  Schaadt, “Undamped collective surface plasmon oscillations along metallic nanosphere chains,” J. Appl. Phys. 108, 084304 (2010).
[CrossRef]

Huang, Wenyu

Prashant K.  Jain, Wenyu  Huang, Mostafa A.  El-Sayed, “On the Universal Scaling Behavior of the Distance Decay of Plasmon Coupling in Metal Nanoparticle Pairs: A Plasmon Ruler Equation,” Nano Lett. 7, 2080–2088 (2007).
[CrossRef]

Im, Jin Seo

Alexandre  Bouhelier, Renaud  Bachelot, Jin Seo  Im, Gary P.  Wiederrecht, Gilles  Lerondel, Sergei  Kostcheev, Pascal  Royer, “Electromagnetic Interactions in Plasmonic Nanoparticle Arrays,” J. Phys. Chem. B 109, 3195–3198 (2005).
[CrossRef]

Jacak, J.

W.  Jacak, J.  Krasnyj, J.  Jacak, A.  Chepok, L.  Jacak, W.  Donderowicz, D. Z.  Hu, D. M.  Schaadt, “Undamped collective surface plasmon oscillations along metallic nanosphere chains,” J. Appl. Phys. 108, 084304 (2010).
[CrossRef]

Jacak, L.

W.  Jacak, J.  Krasnyj, J.  Jacak, A.  Chepok, L.  Jacak, W.  Donderowicz, D. Z.  Hu, D. M.  Schaadt, “Undamped collective surface plasmon oscillations along metallic nanosphere chains,” J. Appl. Phys. 108, 084304 (2010).
[CrossRef]

Jacak, W.

W.  Jacak, J.  Krasnyj, J.  Jacak, A.  Chepok, L.  Jacak, W.  Donderowicz, D. Z.  Hu, D. M.  Schaadt, “Undamped collective surface plasmon oscillations along metallic nanosphere chains,” J. Appl. Phys. 108, 084304 (2010).
[CrossRef]

Jackson, J. D.

See, e.g.,J. D.  Jackson, “Earth and Ionosphere as a Resonant Cavity: Schumann Resonances,” in Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999), pp. 374–376.

Jain, Prashant K.

Prashant K.  Jain, Wenyu  Huang, Mostafa A.  El-Sayed, “On the Universal Scaling Behavior of the Distance Decay of Plasmon Coupling in Metal Nanoparticle Pairs: A Plasmon Ruler Equation,” Nano Lett. 7, 2080–2088 (2007).
[CrossRef]

Joannopoulos, J. D.

Attila  Mekis, J. C.  Chen, I.  Kurland, Shanhui  Fan, Pierre R.  Villeneuve, J. D.  Joannopoulos, “High Transmission through Sharp Bends in Photonic Crystal Waveguides, ” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

John, Sajeev

Kurt  Busch, Sajeev  John, “Liquid-Crystal Photonic-Band-Gap Materials: The Tunable Electromagnetic Vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[CrossRef]

Kik, P. G.

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics–A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

Kik, Pieter G.

Stefan A.  Maier, Pieter G.  Kik, Harry A.  Atwater, Sheffer  Meltzer, Elad  Harel, Bruce E.  Koel, Ari 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]

Kim, I.

O.  Painter, R. K.  Lee, A.  Scherer, A.  Yariv, J. D.  O’Brien, P. D.  Dapkus, I.  Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Knight, J. C.

F.  Benabid, J. C.  Knight, G.  Antonopoulos, P. St. J.  Russell, “Stimulated Raman Scattering in Hydrogen-Filled Hollow-Core Photonic Crystal Fiber,” Science 298, 399–402 (2002).
[CrossRef] [PubMed]

Koel, Bruce E.

Stefan A.  Maier, Pieter G.  Kik, Harry A.  Atwater, Sheffer  Meltzer, Elad  Harel, Bruce E.  Koel, Ari 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]

Koenderink, A. F.

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

Kostcheev, Sergei

Alexandre  Bouhelier, Renaud  Bachelot, Jin Seo  Im, Gary P.  Wiederrecht, Gilles  Lerondel, Sergei  Kostcheev, Pascal  Royer, “Electromagnetic Interactions in Plasmonic Nanoparticle Arrays,” J. Phys. Chem. B 109, 3195–3198 (2005).
[CrossRef]

Krasnyj, J.

W.  Jacak, J.  Krasnyj, J.  Jacak, A.  Chepok, L.  Jacak, W.  Donderowicz, D. Z.  Hu, D. M.  Schaadt, “Undamped collective surface plasmon oscillations along metallic nanosphere chains,” J. Appl. Phys. 108, 084304 (2010).
[CrossRef]

Kurland, I.

Attila  Mekis, J. C.  Chen, I.  Kurland, Shanhui  Fan, Pierre R.  Villeneuve, J. D.  Joannopoulos, “High Transmission through Sharp Bends in Photonic Crystal Waveguides, ” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Kuzmiak, V.

V.  Kuzmiak, A. A.  Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55, 7427–7444 (1997).
[CrossRef]

V.  Kuzmiak, A. A.  Maradudin, F.  Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835–16844 (1994).
[CrossRef]

Lance Kelly, K.

LinLin  Zhao, K.  Lance Kelly, George 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]

Lee, R.

A.  Scherer, O.  Painter, B.  D’Urso, R.  Lee, A.  Yariv, “InGaAsP photonic band gap crystal membrane microresonators,” J. Vac. Sci. Technol. B 16, 3906 (1998).
[CrossRef]

Lee, R. K.

O.  Painter, R. K.  Lee, A.  Scherer, A.  Yariv, J. D.  O’Brien, P. D.  Dapkus, I.  Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Lee, Sergey B.

Ali E.  Aliev, Sergey B.  Lee, Anvar A.  Zakhidov, Ray H.  Baughman, “Superconductivity in Pb inverse opal,” Physica C 453, 15–23 (2007).
[CrossRef]

Lerondel, Gilles

Alexandre  Bouhelier, Renaud  Bachelot, Jin Seo  Im, Gary P.  Wiederrecht, Gilles  Lerondel, Sergei  Kostcheev, Pascal  Royer, “Electromagnetic Interactions in Plasmonic Nanoparticle Arrays,” J. Phys. Chem. B 109, 3195–3198 (2005).
[CrossRef]

Lidorikis, E.

E.  Lidorikis, M. M.  Sigalas, E. N.  Economou, C. M.  Soukoulis, “Tight-Binding Parametrization for Photonic Band Gap Materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

Löwdin, Per-Olov

Per-Olov  Löwdin, “On the NonOrthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals,” J. Chem. Phys. 18, 365–375 (1950).
[CrossRef]

Maier, S. A.

L. A.  Sweatlock, S. A.  Maier, H. A.  Atwater, J. J.  Penninkhof, A.  Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
[CrossRef]

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics–A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

Maier, Stefan A.

Stefan A.  Maier, Pieter G.  Kik, Harry A.  Atwater, Sheffer  Meltzer, Elad  Harel, Bruce E.  Koel, Ari 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]

Maradudin, A. A.

V.  Kuzmiak, A. A.  Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55, 7427–7444 (1997).
[CrossRef]

V.  Kuzmiak, A. A.  Maradudin, F.  Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835–16844 (1994).
[CrossRef]

Maradudin, Alexei A.

Arthur R.  McGurn, Alexei A.  Maradudin, “Photonic band structures of two- and three-dimensional periodic metal or semiconductor arrays,” Phys. Rev. B 48, 17576–17579 (1993).
[CrossRef]

Markel, Vadim A.

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

McGurn, Arthur R.

Arthur R.  McGurn, Alexei A.  Maradudin, “Photonic band structures of two- and three-dimensional periodic metal or semiconductor arrays,” Phys. Rev. B 48, 17576–17579 (1993).
[CrossRef]

McKinnon, B. A.

B. A.  McKinnon, T. C.  Choy, “Significance of nonorthogonality in tight-binding models,” Phys. Rev. B 52, 14531–14538 (1995).
[CrossRef]

Mekis, Attila

Attila  Mekis, J. C.  Chen, I.  Kurland, Shanhui  Fan, Pierre R.  Villeneuve, J. D.  Joannopoulos, “High Transmission through Sharp Bends in Photonic Crystal Waveguides, ” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Meltzer, S.

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics–A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

Meltzer, Sheffer

Stefan A.  Maier, Pieter G.  Kik, Harry A.  Atwater, Sheffer  Meltzer, Elad  Harel, Bruce E.  Koel, Ari 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]

Menon, Madhu

Madhu  Menon, K. R.  Subbaswamy, “Transferable nonorthogonal tight-binding scheme for silicon,” Phys. Rev. B 50, 11577–11582 (1994).
[CrossRef]

Mermin, N. D.

See, e.g.,N. W.  Ashcroft, N. D.  Mermin, “Problem 2. Tight-Binding p-Bands in Cubic Crystals” & “General remarks on the tight-binding method,” in Solid State Physics (Saunders College Publishing, Orlando, 1976), pp. 189–190& pp. 184–185.

Modinos, A.

N.  Stefanou, A.  Modinos, V.  Yannopapas, “Optical transparency of mesoporous metals,” Solid State Commun. 118, 69–73 (2001).
[CrossRef]

O’Brien, J. D.

O.  Painter, R. K.  Lee, A.  Scherer, A.  Yariv, J. D.  O’Brien, P. D.  Dapkus, I.  Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Painter, O.

O.  Painter, R. K.  Lee, A.  Scherer, A.  Yariv, J. D.  O’Brien, P. D.  Dapkus, I.  Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

A.  Scherer, O.  Painter, B.  D’Urso, R.  Lee, A.  Yariv, “InGaAsP photonic band gap crystal membrane microresonators,” J. Vac. Sci. Technol. B 16, 3906 (1998).
[CrossRef]

Park, Sung Yong

Sung Yong  Park, David  Stroud, “Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
[CrossRef]

Penninkhof, J. J.

L. A.  Sweatlock, S. A.  Maier, H. A.  Atwater, J. J.  Penninkhof, A.  Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
[CrossRef]

Pincemin, F.

V.  Kuzmiak, A. A.  Maradudin, F.  Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835–16844 (1994).
[CrossRef]

Polman, A.

L. A.  Sweatlock, S. A.  Maier, H. A.  Atwater, J. J.  Penninkhof, A.  Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
[CrossRef]

Polman, Albert

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

Requicha, A. A. G.

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics–A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

Requicha, Ari A.G.

Stefan A.  Maier, Pieter G.  Kik, Harry A.  Atwater, Sheffer  Meltzer, Elad  Harel, Bruce E.  Koel, Ari 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]

Royer, Pascal

Alexandre  Bouhelier, Renaud  Bachelot, Jin Seo  Im, Gary P.  Wiederrecht, Gilles  Lerondel, Sergei  Kostcheev, Pascal  Royer, “Electromagnetic Interactions in Plasmonic Nanoparticle Arrays,” J. Phys. Chem. B 109, 3195–3198 (2005).
[CrossRef]

Russell, P. St. J.

F.  Benabid, J. C.  Knight, G.  Antonopoulos, P. St. J.  Russell, “Stimulated Raman Scattering in Hydrogen-Filled Hollow-Core Photonic Crystal Fiber,” Science 298, 399–402 (2002).
[CrossRef] [PubMed]

Sarychev, Andrey K.

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

Schaadt, D. M.

W.  Jacak, J.  Krasnyj, J.  Jacak, A.  Chepok, L.  Jacak, W.  Donderowicz, D. Z.  Hu, D. M.  Schaadt, “Undamped collective surface plasmon oscillations along metallic nanosphere chains,” J. Appl. Phys. 108, 084304 (2010).
[CrossRef]

Schatz, George C.

Shengli  Zou, George C.  Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606–12612 (2004).
[CrossRef] [PubMed]

LinLin  Zhao, K.  Lance Kelly, George 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]

Schenk, J. O.

Y.  Cao, J. O.  Schenk, M. A.  Fiddy, “Third order nonlinear effect near a degenerate band edge,” Opt. Photonics Lett. 1, 1–7 (2008).
[CrossRef]

Scherer, A.

O.  Painter, R. K.  Lee, A.  Scherer, A.  Yariv, J. D.  O’Brien, P. D.  Dapkus, I.  Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

A.  Scherer, O.  Painter, B.  D’Urso, R.  Lee, A.  Yariv, “InGaAsP photonic band gap crystal membrane microresonators,” J. Vac. Sci. Technol. B 16, 3906 (1998).
[CrossRef]

Sigalas, M. M.

E.  Lidorikis, M. M.  Sigalas, E. N.  Economou, C. M.  Soukoulis, “Tight-Binding Parametrization for Photonic Band Gap Materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

Soukoulis, C. M.

E.  Lidorikis, M. M.  Sigalas, E. N.  Economou, C. M.  Soukoulis, “Tight-Binding Parametrization for Photonic Band Gap Materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

Stefanou, N.

G.  Gantzounis, N.  Stefanou, “Cavity-plasmon waveguides: Multiple scattering calculations of dispersion in weakly coupled dielectric nanocavities in a metallic host material,” Phys. Rev. B 74, 085102 (2006).
[CrossRef]

N.  Stefanou, A.  Modinos, V.  Yannopapas, “Optical transparency of mesoporous metals,” Solid State Commun. 118, 69–73 (2001).
[CrossRef]

Stroud, D.

I. H. H.  Zabel, D.  Stroud, “Photonic band structures of optically anisotropic periodic arrays,” Phys. Rev. B 48, 5004–5012 (1993).
[CrossRef]

Stroud, David

Sung Yong  Park, David  Stroud, “Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
[CrossRef]

Su, K.-H.

Q.-H.  Wei, K.-H.  Su, S.  Durant, X.  Zhang, “Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains,” Nano Lett. 4, 1067–1071 (2004).
[CrossRef]

Subbaswamy, K. R.

Madhu  Menon, K. R.  Subbaswamy, “Transferable nonorthogonal tight-binding scheme for silicon,” Phys. Rev. B 50, 11577–11582 (1994).
[CrossRef]

Summers, C. J.

D.  Gaillot, T.  Yamashita, C. J.  Summers, “Photonic band gaps in highly conformal inverse-opal based photonic crystals,” Phys. Rev. B 72, 205109 (2005).
[CrossRef]

Sweatlock, L. A.

L. A.  Sweatlock, S. A.  Maier, H. A.  Atwater, J. J.  Penninkhof, A.  Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
[CrossRef]

Villeneuve, Pierre R.

Attila  Mekis, J. C.  Chen, I.  Kurland, Shanhui  Fan, Pierre R.  Villeneuve, J. D.  Joannopoulos, “High Transmission through Sharp Bends in Photonic Crystal Waveguides, ” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Weber, W. H.

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

Wei, Q.-H.

Q.-H.  Wei, K.-H.  Su, S.  Durant, X.  Zhang, “Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains,” Nano Lett. 4, 1067–1071 (2004).
[CrossRef]

Wiederrecht, Gary P.

Alexandre  Bouhelier, Renaud  Bachelot, Jin Seo  Im, Gary P.  Wiederrecht, Gilles  Lerondel, Sergei  Kostcheev, Pascal  Royer, “Electromagnetic Interactions in Plasmonic Nanoparticle Arrays,” J. Phys. Chem. B 109, 3195–3198 (2005).
[CrossRef]

Xia, J. Q.

J. Q.  Xia, Y. R.  Ying, S. H.  Foulger, “Electric-Field-Induced Rejection-Wavelength Tuning of Photonic-Bandgap Composites,” Adv. Mater. 17, 2463–2467 (2005).
[CrossRef]

Yablonovitch, Eli

Eli  Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Yamashita, T.

D.  Gaillot, T.  Yamashita, C. J.  Summers, “Photonic band gaps in highly conformal inverse-opal based photonic crystals,” Phys. Rev. B 72, 205109 (2005).
[CrossRef]

Yannopapas, V.

N.  Stefanou, A.  Modinos, V.  Yannopapas, “Optical transparency of mesoporous metals,” Solid State Commun. 118, 69–73 (2001).
[CrossRef]

Yariv, A.

O.  Painter, R. K.  Lee, A.  Scherer, A.  Yariv, J. D.  O’Brien, P. D.  Dapkus, I.  Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

A.  Scherer, O.  Painter, B.  D’Urso, R.  Lee, A.  Yariv, “InGaAsP photonic band gap crystal membrane microresonators,” J. Vac. Sci. Technol. B 16, 3906 (1998).
[CrossRef]

Ying, Y. R.

J. Q.  Xia, Y. R.  Ying, S. H.  Foulger, “Electric-Field-Induced Rejection-Wavelength Tuning of Photonic-Bandgap Composites,” Adv. Mater. 17, 2463–2467 (2005).
[CrossRef]

Zabel, I. H. H.

I. H. H.  Zabel, D.  Stroud, “Photonic band structures of optically anisotropic periodic arrays,” Phys. Rev. B 48, 5004–5012 (1993).
[CrossRef]

Zakhidov, Anvar A.

Ali E.  Aliev, Sergey B.  Lee, Anvar A.  Zakhidov, Ray H.  Baughman, “Superconductivity in Pb inverse opal,” Physica C 453, 15–23 (2007).
[CrossRef]

Zhang, X.

Q.-H.  Wei, K.-H.  Su, S.  Durant, X.  Zhang, “Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains,” Nano Lett. 4, 1067–1071 (2004).
[CrossRef]

Zhao, LinLin

LinLin  Zhao, K.  Lance Kelly, George 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]

Zhen, Yu-Rong

Yu-Rong  Zhen, Kin Hung  Fung, C. T.  Chan, “Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles,” Phys. Rev. B 78, 035419 (2008).
[CrossRef]

Zou, Shengli

Shengli  Zou, George C.  Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606–12612 (2004).
[CrossRef] [PubMed]

Adv. Mater.

J. Q.  Xia, Y. R.  Ying, S. H.  Foulger, “Electric-Field-Induced Rejection-Wavelength Tuning of Photonic-Bandgap Composites,” Adv. Mater. 17, 2463–2467 (2005).
[CrossRef]

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics–A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

J. Appl. Phys.

W.  Jacak, J.  Krasnyj, J.  Jacak, A.  Chepok, L.  Jacak, W.  Donderowicz, D. Z.  Hu, D. M.  Schaadt, “Undamped collective surface plasmon oscillations along metallic nanosphere chains,” J. Appl. Phys. 108, 084304 (2010).
[CrossRef]

J. Chem. Phys.

Per-Olov  Löwdin, “On the NonOrthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals,” J. Chem. Phys. 18, 365–375 (1950).
[CrossRef]

Shengli  Zou, George C.  Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606–12612 (2004).
[CrossRef] [PubMed]

J. Phys. Chem. B

LinLin  Zhao, K.  Lance Kelly, George 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]

Alexandre  Bouhelier, Renaud  Bachelot, Jin Seo  Im, Gary P.  Wiederrecht, Gilles  Lerondel, Sergei  Kostcheev, Pascal  Royer, “Electromagnetic Interactions in Plasmonic Nanoparticle Arrays,” J. Phys. Chem. B 109, 3195–3198 (2005).
[CrossRef]

J. Vac. Sci. Technol. B

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram for (a) an inverse opal structure with a lattice constant d and a void sphere radius R; (b) a linear chain of nanopores with a pore separation d and a nanopore radius R.

Fig. 2
Fig. 2

Tight-binding inverse opal band structure for ω < ωp with R / d = 3 / ( 10 2 ) and ωpd/c = 1.0, using ωatd/(2πc) = 0.1296 (ωat = 0.8143ωp) for = 1 in an infinite medium. The horizontal dotted line represents the “atomic” level.

Fig. 3
Fig. 3

Dependence of the triply degenerate frequency at Γ on the number of nearest neighbor shells included in the tight-binding calculation, for the inverse-opal calculation shown in Fig. 2. Up to seven shells are included.

Fig. 4
Fig. 4

Tight-binding results of a periodic chain of nanopores in a Drude metal host, for ω < ωp. We take R/d = 1/3 and ωpd/c = 0.35, using ωatd/(2πc) = 0.0454 (ωat = 0.8150ωp) for = 1 in an infinite medium. The horizontal dotted line represents the “atomic” level. Three different numbers of neighbors are included: nearest-neighbors (nn’s), next-nearest-neighbors (nnn’s), and fifth-nearest-neighbors (5nn’s). In this and the following two plots, “L” and “T” denote the longitudinal and transverse branches, respectively.

Fig. 5
Fig. 5

Same as Fig. 4, except ωpd/c = 5.0 and ωatd/(2πc) = 0.5691 (ωat = 0.7152ωp).

Fig. 6
Fig. 6

Plotting together three different results for ω < ωp, all with ωpd/c = 0.35, but with different (R/d)’s: R/d = 0.25 and ωatd/(2πc) = 0.04546 (ωat = 0.8161ωp); R/d = 0.33 and ωatd/(2πc) = 0.04544 (ωat = 0.8157ωp); R/d = 0.40 and ωatd/(2πc) = 0.04543 (ωat = 0.8156ωp), with inclusion of up to the fifth nearest-neighbors. For the larger values of R/d, it may be necessary to include more than just = 1.

Tables (1)

Tables Icon

Table 1 TM mode frequencies ω′ = ωd/(2πc), where ω < ωp and ωpd/c = 1, calculated for an isolated spherical cavity (“Infinite medium”) and those when both kR ≪ 1 and k′R ≪ 1. The (modified) spherical Bessel functions are extremely close to the ω′ axis for > 5, so that it is difficult to get eigenfrequencies for > 5 in the isolated spherical cavity. However this does not happen when kR ≪ 1 and k′R ≪ 1.

Equations (21)

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[ ω 2 ω p 2 ( 1 θ ( x ) ) ] × ( × B ) = ω 2 c 2 ( ω 2 ω p 2 ) B .
k 2 [ j ( k R ) + k R j ( k R ) ] = k 2 j ( k R ) k ( k R ) [ k ( k R ) + k R k ( k R ) ] ,
ω 2 = + 1 2 + 1 ω p 2 .
j ( k R ) + k R j ( k R ) = j ( k R ) k ( k R ) [ k ( k R ) + k R k ( k R ) ] .
× ( × E λ ( x ) ) + ω p 2 θ ( x ) c 2 E λ ( x ) 𝒪 E λ ( x ) = ω λ 2 c 2 E λ ( x ) ,
E λ * ( x ) E μ ( x ) d x = δ λ , μ .
M α , β ( R ) = E α * ( x ) 𝒪 E β ( x R ) d x ,
E λ * ( x R ) E μ ( x R ) d x = δ λ , μ δ R , R .
E k , λ ( x ) = N 1 / 2 R e i k R E λ ( x R ) ,
M λ , μ ( k ) = R e i k R M λ , μ ( R ) .
det | M λ , μ ( k ) ( ω 2 ( k ) c 2 ω at 2 c 2 ) δ λ , μ | = 0 ,
𝒪 R E β ( x R ) = ω at 2 c 2 E β ( x R ) ,
M α , β ( R ) = E α ( x ) 𝒪 E β ( x R ) d x .
𝒪 = ω p 2 c 2 R θ R ( x ) ,
θ R ( x ) = θ ( x R ) ,
M α , β ( R ) ~ ω p 2 c 2 E α ( x ) E β ( x R ) d x ,
M α , β ( R ) ~ ω p 2 c 2 E β ( R ) E α ( x ) d x ,
ε ( ω ) = 1 ω p 2 ω 2 ,
k R = ω c R < ω p c R = ω p d c R d = 3 10 2 = 0.2121 , k R = ω p 2 ω 2 c R = ( ω p R c ) 2 ( ω R 2 ) 2 = ( ω p d c R d ) 2 ( k R ) 2 = ( 3 10 2 ) 2 ( k R ) 2 = 0.045 ( k R ) 2 < 0.045 = 0.2121 .
S λ μ ( R ) = E λ * ( x ) E μ ( x R ) d x
H = ( I + S ) 1 / 2 ( I + S ) 1 / 2 ,

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