Abstract

External optical coupling into and out of semi-infinite chains of noncontacting noble-metal nanoparticles is found to be highly directional. While strong coupling of external radiation into and out of low-attenuation surface plasmon polaritons (PPs) in semi-infinite nanoparticle chains is predicted, the radiation patterns are quite complex indicating possible challenges in mode matching. We show that a treatment that neglects end effects provides an entirely inadequate description of both the PPs on the chain and of the scattered electromagnetic radiation.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Quinten, A. Leitner, J. R. Kren, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticle,” Opt. Lett. 23, 1331-1333 (1998).
    [CrossRef]
  2. S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: estimation of waveguide loss,” Appl. Phys. Lett. 81, 1714-1716 (2002).
    [CrossRef]
  3. S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, “Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy,” Phys. Rev. B 65, 193408 (2002).
    [CrossRef]
  4. V. A. Markel, “Coupled-dipole approach to scattering of light from a one-dimensional periodic dipole structure,” J. Mod. Opt. 40, 2281-2291 (1993).
    [CrossRef]
  5. D. S. Citrin, “Coherent excitation transport in metal-nanoparticle chains,” Nano Lett. 4, 1561-1565 (2004).
    [CrossRef]
  6. R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41, 13-14 (2005).
    [CrossRef]
  7. S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering lineshapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606-12612 (2005).
    [CrossRef]
  8. A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 33402-33405 (2006).
    [CrossRef]
  9. A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436-205453 (2006).
    [CrossRef]
  10. E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
    [CrossRef]
  11. S. Zou and G. C. Schatz, “Metal nanoparticle array waveguides: proposed structures for subwavelength devices,” Phys. Rev. B 74, 125111 (2006).
    [CrossRef]
  12. D. S. Citrin, “Plasmon polaritons in finite-length metal-nanoparticle chains: the role of chain length unravelled,” Nano Lett. 5, 985-989 (2005).
    [CrossRef] [PubMed]
  13. 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]
  14. P. Ghenuche, R. Quidant, and G. Badenes, “Cumulative plasmon field enhancement in finite metal particle chains,” Opt. Lett. 30, 1882-1884 (2005).
    [CrossRef] [PubMed]
  15. S. Y. Park and D. G. Stroud, “Surface plasmon dispersion relations in chains of metallic nanoparticles: exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
    [CrossRef]
  16. S. Zou, N. Janet, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871-10875 (2004).
    [CrossRef] [PubMed]
  17. C. M. Linton and P. A. Martin, “Semi-infinite arrays of isotropic point scatterers. A unified approach,” SIAM J. Appl. Math. 64, 1035-1056 (2004).
    [CrossRef]
  18. D. S. Citrin, “Plasmon-polariton transport in metal-nanoparticle chains embedded in a gain medium,” Opt. Lett. 31, 98-100 (2006).
    [CrossRef] [PubMed]
  19. J. B. Tatum, available at orca.phys.uvic.ca/~tatum/stellatm/atm10.pdf.
  20. The Lerch ζ function can be written in terms of the Lerch transcendent Φ(z,s,a) as L(x,a,s)=Φ(z,s,a), where z=exp(2πix).
  21. D. S. Citrin, “Coherent transport of excitons in quantum-dot chains: role of retardation,” Opt. Lett. 20, 901-903 (1995).
    [CrossRef] [PubMed]
  22. V. M. Agranovich and O. A. Dubovskii, “Effect of retarded interaction on the exciton spectrum in one-dimensional and two-dimensional crystals,” JETP Lett. 3, 223-226 (1966).
  23. D. S. Citrin, “Long intrinsic radiative lifetimes of excitons in quantum wires,” Phys. Rev. Lett. 69, 3393-3396 (1992).
    [CrossRef] [PubMed]
  24. F. Tassone and F. Bassani, “Quantum wire polaritons,” Nuovo Cimento Soc. Ital. Fis., D 14D, 1241-1254 (1992).
    [CrossRef]
  25. S. Jorda, “Fine structure of excitons and polariton dispersion in quantum wires,” Solid State Commun. 87, 439-444 (1993).
    [CrossRef]
  26. Equation can be formally exactly solved by means of the Wiener-Hopf technique . The evaluation of the requisite contour integrals, however, eludes the authors who suspect that they are indeed intractable. In passing, it is conjectured that a closed-form solution is indeed attainable in the long-wavelength limit κd, kzd≪1. This is left as an exercise for the interested reader. While such a result is likely to be of limited quantitative utility for practical NPCs, it may provide deeper physical insight into the details of coupling to the semi-infinite structures.
  27. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. B 11, 1491-1499 (1994).
    [CrossRef]
  28. W. Wasylkiwskyj, “Mutual coupling effects in semi-infinite arrays,” IEEE Trans. Antennas Propag. AP-21, 277-285 (1973).
    [CrossRef]

2006 (4)

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 33402-33405 (2006).
[CrossRef]

A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436-205453 (2006).
[CrossRef]

S. Zou and G. C. Schatz, “Metal nanoparticle array waveguides: proposed structures for subwavelength devices,” Phys. Rev. B 74, 125111 (2006).
[CrossRef]

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

2005 (4)

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

P. Ghenuche, R. Quidant, and G. Badenes, “Cumulative plasmon field enhancement in finite metal particle chains,” Opt. Lett. 30, 1882-1884 (2005).
[CrossRef] [PubMed]

R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41, 13-14 (2005).
[CrossRef]

S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering lineshapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606-12612 (2005).
[CrossRef]

2004 (5)

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

S. Y. Park and D. G. Stroud, “Surface plasmon dispersion relations in chains of metallic nanoparticles: exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
[CrossRef]

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

C. M. Linton and P. A. Martin, “Semi-infinite arrays of isotropic point scatterers. A unified approach,” SIAM J. Appl. Math. 64, 1035-1056 (2004).
[CrossRef]

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]

2002 (2)

S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: estimation of waveguide loss,” Appl. Phys. Lett. 81, 1714-1716 (2002).
[CrossRef]

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

1998 (1)

1995 (1)

1994 (1)

B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. B 11, 1491-1499 (1994).
[CrossRef]

1993 (2)

S. Jorda, “Fine structure of excitons and polariton dispersion in quantum wires,” Solid State Commun. 87, 439-444 (1993).
[CrossRef]

V. A. Markel, “Coupled-dipole approach to scattering of light from a one-dimensional periodic dipole structure,” J. Mod. Opt. 40, 2281-2291 (1993).
[CrossRef]

1992 (2)

D. S. Citrin, “Long intrinsic radiative lifetimes of excitons in quantum wires,” Phys. Rev. Lett. 69, 3393-3396 (1992).
[CrossRef] [PubMed]

F. Tassone and F. Bassani, “Quantum wire polaritons,” Nuovo Cimento Soc. Ital. Fis., D 14D, 1241-1254 (1992).
[CrossRef]

1973 (2)

W. Wasylkiwskyj, “Mutual coupling effects in semi-infinite arrays,” IEEE Trans. Antennas Propag. AP-21, 277-285 (1973).
[CrossRef]

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

1966 (1)

V. M. Agranovich and O. A. Dubovskii, “Effect of retarded interaction on the exciton spectrum in one-dimensional and two-dimensional crystals,” JETP Lett. 3, 223-226 (1966).

Agranovich, V. M.

V. M. Agranovich and O. A. Dubovskii, “Effect of retarded interaction on the exciton spectrum in one-dimensional and two-dimensional crystals,” JETP Lett. 3, 223-226 (1966).

Alù, A.

A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436-205453 (2006).
[CrossRef]

Atwater, H. A.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: estimation of waveguide loss,” Appl. Phys. Lett. 81, 1714-1716 (2002).
[CrossRef]

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

Aussenegg, F. R.

Badenes, G.

Bassani, F.

F. Tassone and F. Bassani, “Quantum wire polaritons,” Nuovo Cimento Soc. Ital. Fis., D 14D, 1241-1254 (1992).
[CrossRef]

Brongersma, M. L.

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

Citrin, D. S.

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

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

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

D. S. Citrin, “Coherent transport of excitons in quantum-dot chains: role of retardation,” Opt. Lett. 20, 901-903 (1995).
[CrossRef] [PubMed]

D. S. Citrin, “Long intrinsic radiative lifetimes of excitons in quantum wires,” Phys. Rev. Lett. 69, 3393-3396 (1992).
[CrossRef] [PubMed]

Draine, B. T.

B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. B 11, 1491-1499 (1994).
[CrossRef]

Dubovskii, O. A.

V. M. Agranovich and O. A. Dubovskii, “Effect of retarded interaction on the exciton spectrum in one-dimensional and two-dimensional crystals,” JETP Lett. 3, 223-226 (1966).

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]

Engheta, N.

A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436-205453 (2006).
[CrossRef]

Flatau, P. J.

B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. B 11, 1491-1499 (1994).
[CrossRef]

Ghenuche, P.

Janet, N.

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

Jorda, S.

S. Jorda, “Fine structure of excitons and polariton dispersion in quantum wires,” Solid State Commun. 87, 439-444 (1993).
[CrossRef]

Kik, P. G.

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

S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: estimation of waveguide loss,” Appl. Phys. Lett. 81, 1714-1716 (2002).
[CrossRef]

Koenderink, A. F.

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 33402-33405 (2006).
[CrossRef]

Kren, J. R.

Leitner, A.

Linton, C. M.

C. M. Linton and P. A. Martin, “Semi-infinite arrays of isotropic point scatterers. A unified approach,” SIAM J. Appl. Math. 64, 1035-1056 (2004).
[CrossRef]

Maier, S. A.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: estimation of waveguide loss,” Appl. Phys. Lett. 81, 1714-1716 (2002).
[CrossRef]

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

Markel, V. A.

V. A. Markel, “Coupled-dipole approach to scattering of light from a one-dimensional periodic dipole structure,” J. Mod. Opt. 40, 2281-2291 (1993).
[CrossRef]

Martin, P. A.

C. M. Linton and P. A. Martin, “Semi-infinite arrays of isotropic point scatterers. A unified approach,” SIAM J. Appl. Math. 64, 1035-1056 (2004).
[CrossRef]

Park, S. Y.

S. Y. Park and D. G. Stroud, “Surface plasmon dispersion relations in chains of metallic nanoparticles: exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
[CrossRef]

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Polman, A.

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 33402-33405 (2006).
[CrossRef]

Purcell, E. M.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Quidant, R.

Quinten, M.

Schatz, G. C.

S. Zou and G. C. Schatz, “Metal nanoparticle array waveguides: proposed structures for subwavelength devices,” Phys. Rev. B 74, 125111 (2006).
[CrossRef]

S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering lineshapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606-12612 (2005).
[CrossRef]

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

Shore, R. A.

R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41, 13-14 (2005).
[CrossRef]

Stroud, D. G.

S. Y. Park and D. G. Stroud, “Surface plasmon dispersion relations in chains of metallic nanoparticles: 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]

Tassone, F.

F. Tassone and F. Bassani, “Quantum wire polaritons,” Nuovo Cimento Soc. Ital. Fis., D 14D, 1241-1254 (1992).
[CrossRef]

Tatum, J. B.

J. B. Tatum, available at orca.phys.uvic.ca/~tatum/stellatm/atm10.pdf.

Wasylkiwskyj, W.

W. Wasylkiwskyj, “Mutual coupling effects in semi-infinite arrays,” IEEE Trans. Antennas Propag. AP-21, 277-285 (1973).
[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]

Yaghjian, A. D.

R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41, 13-14 (2005).
[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]

Zou, S.

S. Zou and G. C. Schatz, “Metal nanoparticle array waveguides: proposed structures for subwavelength devices,” Phys. Rev. B 74, 125111 (2006).
[CrossRef]

S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering lineshapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606-12612 (2005).
[CrossRef]

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

Appl. Phys. Lett. (1)

S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: estimation of waveguide loss,” Appl. Phys. Lett. 81, 1714-1716 (2002).
[CrossRef]

Astrophys. J. (1)

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Electron. Lett. (1)

R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41, 13-14 (2005).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

W. Wasylkiwskyj, “Mutual coupling effects in semi-infinite arrays,” IEEE Trans. Antennas Propag. AP-21, 277-285 (1973).
[CrossRef]

J. Chem. Phys. (2)

S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering lineshapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606-12612 (2005).
[CrossRef]

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

J. Mod. Opt. (1)

V. A. Markel, “Coupled-dipole approach to scattering of light from a one-dimensional periodic dipole structure,” J. Mod. Opt. 40, 2281-2291 (1993).
[CrossRef]

J. Opt. Soc. Am. B (1)

B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. B 11, 1491-1499 (1994).
[CrossRef]

JETP Lett. (1)

V. M. Agranovich and O. A. Dubovskii, “Effect of retarded interaction on the exciton spectrum in one-dimensional and two-dimensional crystals,” JETP Lett. 3, 223-226 (1966).

Nano Lett. (3)

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

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

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]

Nuovo Cimento Soc. Ital. Fis., D (1)

F. Tassone and F. Bassani, “Quantum wire polaritons,” Nuovo Cimento Soc. Ital. Fis., D 14D, 1241-1254 (1992).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. B (5)

S. Y. Park and D. G. Stroud, “Surface plasmon dispersion relations in chains of metallic nanoparticles: exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
[CrossRef]

S. Zou and G. C. Schatz, “Metal nanoparticle array waveguides: proposed structures for subwavelength devices,” Phys. Rev. B 74, 125111 (2006).
[CrossRef]

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

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 33402-33405 (2006).
[CrossRef]

A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436-205453 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

D. S. Citrin, “Long intrinsic radiative lifetimes of excitons in quantum wires,” Phys. Rev. Lett. 69, 3393-3396 (1992).
[CrossRef] [PubMed]

SIAM J. Appl. Math. (1)

C. M. Linton and P. A. Martin, “Semi-infinite arrays of isotropic point scatterers. A unified approach,” SIAM J. Appl. Math. 64, 1035-1056 (2004).
[CrossRef]

Solid State Commun. (1)

S. Jorda, “Fine structure of excitons and polariton dispersion in quantum wires,” Solid State Commun. 87, 439-444 (1993).
[CrossRef]

Other (3)

Equation can be formally exactly solved by means of the Wiener-Hopf technique . The evaluation of the requisite contour integrals, however, eludes the authors who suspect that they are indeed intractable. In passing, it is conjectured that a closed-form solution is indeed attainable in the long-wavelength limit κd, kzd≪1. This is left as an exercise for the interested reader. While such a result is likely to be of limited quantitative utility for practical NPCs, it may provide deeper physical insight into the details of coupling to the semi-infinite structures.

J. B. Tatum, available at orca.phys.uvic.ca/~tatum/stellatm/atm10.pdf.

The Lerch ζ function can be written in terms of the Lerch transcendent Φ(z,s,a) as L(x,a,s)=Φ(z,s,a), where z=exp(2πix).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Schematic of the semi-infinite nanoparticle chain. The z axis is parallel to the chain while the x y plane is perpendicular to the chain. The azimuthal angle measured from the z axis is θ and the angle in the x y plane measured from the x axis is ϕ. For longitudinally ( L ) polarized PPs, the nanoparticle SP dipole moment is parallel to the z axis while for the two degenerate transversely ( T ) polarized PPs the dipole moment is in the x or y directions.

Fig. 2
Fig. 2

Correction ξ n to the Kirchhoff solution for dipole moments on a nanoparticle chain excited by resonant light with k z d = 1.5 and κ d = 1.25 . Left panels, L mode; right panels, T modes. Re [ 1 + exp ( i n k z d ) ξ n ] (top); Im [ 1 + exp ( i n k z d ) ξ n ] (bottom).

Fig. 3
Fig. 3

Far-field angular θ distribution of radiation for the same parameters as in Fig. 2, k z d = 1.5 , κ d = 1.25 . (a) L mode; (b) T-modes, ϕ = 0 ; (c) T modes, ϕ = π 2 . Dashed curves [see insets in (b) and (c)] show the Kirchhoff solution; solid curves show full solution. Note that (b) and (c) have different horizontal and vertical scales to emphasize detail.

Fig. 4
Fig. 4

Correction ξ n to the Kirchhoff solution for dipole moments on the nanoparticle chain excited by resonant light with k z d = 1.5 and κ d = 1.25 . Left panels, L mode; right panels, T modes. Re [ 1 + exp ( i n k z d ) ξ n ] (top); Im [ 1 + exp ( i n k z d ) ξ n ] (bottom).

Fig. 5
Fig. 5

Far-field angular θ distribution of radiation for the same parameters as in Fig. 2, k z d = 1.5 , κ d = 1.25 . (a) L mode; (b) T modes, ϕ = 0 ; (c) T modes, ϕ = π 2 . Dashed curves show the Kirchhoff solution; solid curves show full solution. Note that (b) and (c) have different horizontal and vertical scales to emphasize detail.

Equations (26)

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

d n = α ( E n ( inc ) + j E n ( j ) ) ,
E n ( j ) = α 1 χ Σ n j d j ,
d n = α E n ( inc ) + χ j Σ n j d j ,
Σ n j = { 2 3 i γ r δ n j + γ r ( 1 δ n j ) [ 1 ( κ d ) 3 n j 3 i ( κ d ) 2 ( n j ) 2 1 κ d n j ] e i κ d n j , T 2 3 i γ r δ n j 2 γ r ( 1 δ n j ) [ 1 ( κ d ) 3 n j 3 i ( κ d ) 2 ( n j ) 2 ] e i κ d n j , L ]
χ = 2 ε 0 ε 2 ε 0 2 + 2 i ε 0 γ n r .
2 γ r = q 2 ε 0 2 n emb 12 π ϵ 0 2 m c 3
b = 2 q 2 2 ε 0 m = 6 π ϵ 0 ( c ) 3 n emb ε 0 3 ( 2 γ r ) .
χ 1 d ¯ 0 d ¯ 0 j Σ n j e i k z d ( j n ) = b E 0 .
χ 1 d ¯ 0 d ¯ 0 Σ k z = b E 0 ,
Σ k z ( κ ) = { 2 3 γ r + γ r [ β 1 ( k z , κ ) + β 2 ( k z , κ ) ] , T 2 3 γ r 2 γ r β 1 ( k z , κ ) , L
β 1 ( k z , κ ) = 1 ( κ d ) 3 { Li 3 [ e i ( κ k z ) d ] + Li 3 [ e i ( κ + k z ) d ] } i ( κ d ) 2 { Li 2 [ e i ( κ k z ) d ] + Li 2 [ e i ( κ + k z ) d ] } ,
β 2 ( k z , κ ) = 1 κ d Ln [ 2 e i κ d ( cos κ d cos k z d ) ] ,
η n χ j > 0 Σ n j η j = χ d ¯ 0 Σ n , k z
= b E 0 χ χ 1 Σ k z Σ n , k z , n + ,
Σ n , k z = j 0 Σ n j e i j k z d .
Σ n , k z ( κ ) = { γ r [ β n , 1 ( k z , κ ) + β n , 2 ( k z , κ ) ] , T 2 γ r β n , 1 ( k z , κ ) , L ,
β n , 1 ( k z , κ ) = e i n κ d [ 1 ( κ d ) 3 L ( ( κ k z ) d 2 π , n , 3 ) i ( κ d ) 2 L ( ( κ k z ) d 2 π , n , 2 ) ] ,
β n , 2 ( k z , κ ) = e i n κ d 1 κ d L ( ( κ k z ) d 2 π , n , 1 ) .
ξ n j > 0 Ξ n j , k z ξ j = Ξ n , k z , n + .
E ( sc ) ( r ) = κ 2 d ¯ 0 4 π ϵ 0 u sc ,
u sc = n = 0 ( d ¯ n d ¯ 0 + ξ n ) [ 1 ̱ ( r r n ) ( r r n ) r r n 2 ] e i κ r r n r r n .
u sc = e i κ r r n = 0 ( e i n k z d d ¯ ̂ 0 + ξ n ) ( 1 ̱ r ̂ r ̂ ) e i n κ d cos θ ,
u sc = { e i κ r r ( z ̂ r ̂ cos θ ) ( Γ ( K ) + Γ ( C ) ) , L mode , e i κ r r ( x ̂ r ̂ sin θ cos ϕ ) ( Γ ( K ) + Γ ( C ) ) , T modes
Γ ( K ) = n = 0 e i n k z d e i n κ d cos θ = 1 1 e i ( k z d κ d cos θ ) ,
Γ ( C ) = n = 0 ξ n e i n κ d cos θ .
u sc ( j ) = { e i κ r r ( z ̂ r ̂ cos θ ) Γ ( j ) , L mode , e i κ r r ( x ̂ r ̂ sin θ cos ϕ ) Γ ( j ) , T modes

Metrics