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, and S. H. Foulger, “Electric-Field-Induced Rejection-Wavelength Tuning of Photonic-Bandgap Composites,” Adv. Mater. 17, 2463–2467 (2005).
    [CrossRef]
  2. Kurt Busch and 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, and 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, and 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, and 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, and 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, and M. A. Fiddy, “Third order nonlinear effect near a degenerate band edge,” Opt. Photonics Lett. 1, 1–7 (2008).
    [CrossRef]
  9. Arthur R. McGurn and 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, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835–16844 (1994).
    [CrossRef]
  11. V. Kuzmiak and 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 and 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, and 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, and 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, and H. A. Atwater, “Plasmonics–A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
    [CrossRef]
  16. Prashant K. Jain, Wenyu Huang, and 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, and 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, and 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, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
    [CrossRef]
  20. Shengli Zou and 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 and Albert Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).
    [CrossRef]
  22. Andrea Alù and 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, and Pascal Royer, “Electromagnetic Interactions in Plasmonic Nanoparticle Arrays,” J. Phys. Chem. B 109, 3195–3198 (2005).
    [CrossRef]
  24. Vadim A. Markel and 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, and 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, and 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, and Nadine Harris, “Universal scaling of local plasmons in chains of metal spheres,” Opt. Express 18, 7528–7542 (2010).
    [CrossRef] [PubMed]
  28. Sung Yong Park and 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 and 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, and 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, and Ray H. Baughman, “Superconductivity in Pb inverse opal,” Physica C 453, 15–23 (2007).
    [CrossRef]
  32. G. Gantzounis and 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 and 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, and C. M. Soukoulis, “Tight-Binding Parametrization for Photonic Band Gap Materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
    [CrossRef]
  36. N. Stefanou, A. Modinos, and V. Yannopapas, “Optical transparency of mesoporous metals,” Solid State Commun. 118, 69–73 (2001).
    [CrossRef]
  37. B. A. McKinnon and T. C. Choy, “Significance of nonorthogonality in tight-binding models,” Phys. Rev. B 52, 14531–14538 (1995).
    [CrossRef]
  38. Madhu Menon and 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 (2)

W. Jacak, J. Krasnyj, J. Jacak, A. Chepok, L. Jacak, W. Donderowicz, D. Z. Hu, and 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, and Nadine Harris, “Universal scaling of local plasmons in chains of metal spheres,” Opt. Express 18, 7528–7542 (2010).
[CrossRef] [PubMed]

2008 (2)

Yu-Rong Zhen, Kin Hung Fung, and 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, and M. A. Fiddy, “Third order nonlinear effect near a degenerate band edge,” Opt. Photonics Lett. 1, 1–7 (2008).
[CrossRef]

2007 (3)

Prashant K. Jain, Wenyu Huang, and 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, and Ray H. Baughman, “Superconductivity in Pb inverse opal,” Physica C 453, 15–23 (2007).
[CrossRef]

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

2006 (3)

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

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

G. Gantzounis and 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 (4)

D. Gaillot, T. Yamashita, and 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, and 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, and 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, and S. H. Foulger, “Electric-Field-Induced Rejection-Wavelength Tuning of Photonic-Bandgap Composites,” Adv. Mater. 17, 2463–2467 (2005).
[CrossRef]

2004 (4)

Shengli Zou and 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, and X. Zhang, “Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains,” Nano Lett. 4, 1067–1071 (2004).
[CrossRef]

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

2003 (2)

LinLin Zhao, K. Lance Kelly, and 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, and 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 (1)

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

2001 (2)

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

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

2000 (1)

Mark L. Brongersma, John W. Hartman, and 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 (2)

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

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

1998 (2)

A. Scherer, O. Painter, B. D’Urso, R. Lee, and 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, and C. M. Soukoulis, “Tight-Binding Parametrization for Photonic Band Gap Materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

1997 (1)

V. Kuzmiak and 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 (1)

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

1995 (1)

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

1994 (2)

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

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

1993 (2)

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

Arthur R. McGurn and 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 (1)

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

1950 (1)

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, and Ray H. Baughman, “Superconductivity in Pb inverse opal,” Physica C 453, 15–23 (2007).
[CrossRef]

Alù, Andrea

Andrea Alù and 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, and 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 and 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, and 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, and 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, and 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, and 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, and 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, and Ray H. Baughman, “Superconductivity in Pb inverse opal,” Physica C 453, 15–23 (2007).
[CrossRef]

Benabid, F.

F. Benabid, J. C. Knight, G. Antonopoulos, and 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, and 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, and 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, and 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 and 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, and 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, and 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, and 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, and 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 and 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, and 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, and 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, and 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, and 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, and 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, and 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 and 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, and 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, and 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 and 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, and 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, and 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, and 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 and 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, and 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, and 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, and 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, and 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, and 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, and 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, and 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, and 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, and 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, and 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 and 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, and 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, and 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, and 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, and 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, and 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 and 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, and 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, and 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, and 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 and 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, and 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, and 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, and 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, and 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, and 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, and 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, and 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, and 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, and 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, and 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 and 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, and 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 and 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 and 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 and 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 and 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, and 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, and 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, and 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 and 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 and 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, and 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, and 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, and 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, and A. Yariv, “InGaAsP photonic band gap crystal membrane microresonators,” J. Vac. Sci. Technol. B 16, 3906 (1998).
[CrossRef]

Park, Sung Yong

Sung Yong Park and 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, and 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, and 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, and 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 and 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, and 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, and 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, and 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, and 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 and 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, and D. M. Schaadt, “Undamped collective surface plasmon oscillations along metallic nanosphere chains,” J. Appl. Phys. 108, 084304 (2010).
[CrossRef]

Schatz, George C.

Shengli Zou and 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, and 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, and 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, and 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, and 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, and 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, and C. M. Soukoulis, “Tight-Binding Parametrization for Photonic Band Gap Materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

Stefanou, N.

G. Gantzounis and 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, and V. Yannopapas, “Optical transparency of mesoporous metals,” Solid State Commun. 118, 69–73 (2001).
[CrossRef]

Stroud, D.

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

Stroud, David

Sung Yong Park and 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, and X. Zhang, “Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains,” Nano Lett. 4, 1067–1071 (2004).
[CrossRef]

Subbaswamy, K. R.

Madhu Menon and 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, and 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, and 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, and 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 and 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, and 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, and 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, and 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, and 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, and 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, and 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, and 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, and 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 and 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, and 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, and 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, and 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, and 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 and 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. (2)

J. Q. Xia, Y. R. Ying, and 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, and H. A. Atwater, “Plasmonics–A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

J. Appl. Phys. (1)

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

J. Chem. Phys. (2)

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 and 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 (2)

LinLin Zhao, K. Lance Kelly, and 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, and Pascal Royer, “Electromagnetic Interactions in Plasmonic Nanoparticle Arrays,” J. Phys. Chem. B 109, 3195–3198 (2005).
[CrossRef]

J. Vac. Sci. Technol. B (1)

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

Nano Lett. (2)

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

Prashant K. Jain, Wenyu Huang, and 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]

Nat. Mater. (1)

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

Opt. Express (1)

Opt. Photonics Lett. (1)

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

Phys. Rev. B (16)

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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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