Abstract

We applied a multiple-multipole method to calculate the field enhancement of discrete metal nanosphere assemblies due to plasma resonance, thus performing the first full electromagnetic simulation of a variety of nanoparticle assemblies for efficient field focusing, including the self-similar geometric series of spheres first proposed by Li, Stockman and Bergman. Our study captures electromagnetic resonance effects important for optimizing nanoparticle assemblies to achieve maximum electric field focusing. We predict optical frequency electric fields can be enhanced in gold nanoparticle assemblies in aqueous solution by the order of ~450, within a factor of 2 of that achievable in silver nanostructures. We find that both absorption and far-field scattering resonances of nanoparticle assemblies must be carefully interpreted when inferring near-field focusing properties.

© 2008 Optical Society of America

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  1. L. Novotny and B. Hecht, Principles of Nano-Optics (University Press, Cambridge, 2006).
  2. K. Kneipp, M. Moskovits, and H. Kneipp, Surface-Enhanced Raman Scattering: Physics and Applications (Springer, Berlin, 2006).
    [Crossref]
  3. L. A. Sweatlock, S. A. Maier, and H. A. Atwater, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
    [Crossref]
  4. K. Li., M. I. Stockman, and D. J. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett. 91, 227402 (2003).
    [Crossref] [PubMed]
  5. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
    [Crossref] [PubMed]
  6. J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257–259 (2003).
    [Crossref]
  7. B. M. Reinhard, M. Siu, H. Argarwal, A. P. Alivisatos, and J. Liphardt, “Calibration of dynamic molecular rulers based on plasmon coupling between gold nanoparticles,” Nano Lett. 5, 2246–2252 (2005).
    [Crossref] [PubMed]
  8. F. Aldaye and H. F. Sleiman, “Dynamic DNA templates for discrete gold nanoparticles assemblies: Control of geometry, modularity, write/erase and structural switching,” J. Am. Chem. Soc. 129, 4130–4131 (2007).
    [Crossref] [PubMed]
  9. Y. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. 34, 4573–4588 (1995).
    [Crossref] [PubMed]
  10. D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc. R. Soc. London Ser. A 433, 599–614 (1991).
    [Crossref]
  11. J. H. Bruning and Y. T. Lo, “Multiple scattering of EM waves by spheres Part I – Multipole Expansion and Ray-Optical Solutions,” IEEE Tran. Antennas Propag.AP-19, 378–390 (1971).
    [Crossref]
  12. Y. Xu, “Calculation of the addition coefficients in electromagnetic multisphere-scattering theory,” J. Comput. Phys. 127, 285–298 (1996).
    [Crossref]
  13. F. J. Garcia de Abajo, “Multiple scattering of radiation in clusters of dielectrics,” Phys. Rev. B 60, 6086–6102 (1999).
    [Crossref]
  14. G. Pellegrini, G. Mattei, V. Bello, and P. Mazzoldi, “Interacting metal nanoparticles: Optical properties from nanoparticle dimers to core-satellite systems,” Mat. Sci. Eng. C 27, 1347–1350 (2007).
    [Crossref]
  15. H. Xu, “Calculation of the near field of aggregates of arbitrary spheres,” J. Opt. Soc. Am. A 21, 804–809 (2004).
    [Crossref]
  16. R.-L. Chern, X.-X. Liu, and C.-C. Chang, “Particle plasmons of metal nanospheres: Application of multiple scattering approach,” Phys. Rev. E 76, 016609 (2007).
    [Crossref]
  17. B. Khlebtsov, A. Melnikov, V. Zharov, and N. Khlebtsov, “Absorption and scattering of light by a dimer of metal nanospheres: comparison of dipole and multipole approaches,” Nanotechnology 17, 1437–1445 (2006).
    [Crossref]
  18. H.C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  19. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  20. G. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th. ed., (Academic, Orlando, 2005).
  21. D. W. Mackowski, “Calculation of total cross sections of multiple-sphere clusters,” J. Opt. Soc. Am. A 11, 2851–2861 (1994).
    [Crossref]
  22. A. R. Edmond, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, 1957).
  23. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [Crossref]
  24. L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 266802 (2007).
    [Crossref] [PubMed]
  25. F. Wang and Y. Ron Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97, 206806 (2006).
    [Crossref] [PubMed]
  26. I. H. El-Sayed, X. Huang, and M. A. El-Sayed, “Selective laser photo-thermal therapy of epithelial carcinoma using anti-EGFR antibody conjugated gold nanoparticles,” Cancer Lett. 239, 129–135 (2006).
    [Crossref]
  27. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
    [Crossref] [PubMed]
  28. C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
    [Crossref] [PubMed]
  29. B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, “Local fields at the surface of noblemetal microspheres,” Phys. Rev. B 24, 649–657 (1981).
    [Crossref]

2007 (4)

F. Aldaye and H. F. Sleiman, “Dynamic DNA templates for discrete gold nanoparticles assemblies: Control of geometry, modularity, write/erase and structural switching,” J. Am. Chem. Soc. 129, 4130–4131 (2007).
[Crossref] [PubMed]

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 266802 (2007).
[Crossref] [PubMed]

G. Pellegrini, G. Mattei, V. Bello, and P. Mazzoldi, “Interacting metal nanoparticles: Optical properties from nanoparticle dimers to core-satellite systems,” Mat. Sci. Eng. C 27, 1347–1350 (2007).
[Crossref]

R.-L. Chern, X.-X. Liu, and C.-C. Chang, “Particle plasmons of metal nanospheres: Application of multiple scattering approach,” Phys. Rev. E 76, 016609 (2007).
[Crossref]

2006 (3)

B. Khlebtsov, A. Melnikov, V. Zharov, and N. Khlebtsov, “Absorption and scattering of light by a dimer of metal nanospheres: comparison of dipole and multipole approaches,” Nanotechnology 17, 1437–1445 (2006).
[Crossref]

F. Wang and Y. Ron Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97, 206806 (2006).
[Crossref] [PubMed]

I. H. El-Sayed, X. Huang, and M. A. El-Sayed, “Selective laser photo-thermal therapy of epithelial carcinoma using anti-EGFR antibody conjugated gold nanoparticles,” Cancer Lett. 239, 129–135 (2006).
[Crossref]

2005 (2)

B. M. Reinhard, M. Siu, H. Argarwal, A. P. Alivisatos, and J. Liphardt, “Calibration of dynamic molecular rulers based on plasmon coupling between gold nanoparticles,” Nano Lett. 5, 2246–2252 (2005).
[Crossref] [PubMed]

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

2004 (2)

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
[Crossref] [PubMed]

H. Xu, “Calculation of the near field of aggregates of arbitrary spheres,” J. Opt. Soc. Am. A 21, 804–809 (2004).
[Crossref]

2003 (3)

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257–259 (2003).
[Crossref]

K. Li., M. I. Stockman, and D. J. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett. 91, 227402 (2003).
[Crossref] [PubMed]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[Crossref] [PubMed]

2002 (1)

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
[Crossref] [PubMed]

1999 (1)

F. J. Garcia de Abajo, “Multiple scattering of radiation in clusters of dielectrics,” Phys. Rev. B 60, 6086–6102 (1999).
[Crossref]

1996 (1)

Y. Xu, “Calculation of the addition coefficients in electromagnetic multisphere-scattering theory,” J. Comput. Phys. 127, 285–298 (1996).
[Crossref]

1995 (1)

1994 (1)

1991 (1)

D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc. R. Soc. London Ser. A 433, 599–614 (1991).
[Crossref]

1981 (1)

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, “Local fields at the surface of noblemetal microspheres,” Phys. Rev. B 24, 649–657 (1981).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Aldaye, F.

F. Aldaye and H. F. Sleiman, “Dynamic DNA templates for discrete gold nanoparticles assemblies: Control of geometry, modularity, write/erase and structural switching,” J. Am. Chem. Soc. 129, 4130–4131 (2007).
[Crossref] [PubMed]

Alivisatos, A. P.

B. M. Reinhard, M. Siu, H. Argarwal, A. P. Alivisatos, and J. Liphardt, “Calibration of dynamic molecular rulers based on plasmon coupling between gold nanoparticles,” Nano Lett. 5, 2246–2252 (2005).
[Crossref] [PubMed]

Arfken, G.

G. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th. ed., (Academic, Orlando, 2005).

Argarwal, H.

B. M. Reinhard, M. Siu, H. Argarwal, A. P. Alivisatos, and J. Liphardt, “Calibration of dynamic molecular rulers based on plasmon coupling between gold nanoparticles,” Nano Lett. 5, 2246–2252 (2005).
[Crossref] [PubMed]

Atwater, H. A.

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

Barber, P. W.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, “Local fields at the surface of noblemetal microspheres,” Phys. Rev. B 24, 649–657 (1981).
[Crossref]

Bello, V.

G. Pellegrini, G. Mattei, V. Bello, and P. Mazzoldi, “Interacting metal nanoparticles: Optical properties from nanoparticle dimers to core-satellite systems,” Mat. Sci. Eng. C 27, 1347–1350 (2007).
[Crossref]

Bergman, D. J.

K. Li., M. I. Stockman, and D. J. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett. 91, 227402 (2003).
[Crossref] [PubMed]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Bruning, J. H.

J. H. Bruning and Y. T. Lo, “Multiple scattering of EM waves by spheres Part I – Multipole Expansion and Ray-Optical Solutions,” IEEE Tran. Antennas Propag.AP-19, 378–390 (1971).
[Crossref]

Chang, C.-C.

R.-L. Chern, X.-X. Liu, and C.-C. Chang, “Particle plasmons of metal nanospheres: Application of multiple scattering approach,” Phys. Rev. E 76, 016609 (2007).
[Crossref]

Chang, R. K.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, “Local fields at the surface of noblemetal microspheres,” Phys. Rev. B 24, 649–657 (1981).
[Crossref]

Chern, R.-L.

R.-L. Chern, X.-X. Liu, and C.-C. Chang, “Particle plasmons of metal nanospheres: Application of multiple scattering approach,” Phys. Rev. E 76, 016609 (2007).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

de Abajo, F. J. Garcia

F. J. Garcia de Abajo, “Multiple scattering of radiation in clusters of dielectrics,” Phys. Rev. B 60, 6086–6102 (1999).
[Crossref]

Edmond, A. R.

A. R. Edmond, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, 1957).

El-Sayed, I. H.

I. H. El-Sayed, X. Huang, and M. A. El-Sayed, “Selective laser photo-thermal therapy of epithelial carcinoma using anti-EGFR antibody conjugated gold nanoparticles,” Cancer Lett. 239, 129–135 (2006).
[Crossref]

El-Sayed, M. A.

I. H. El-Sayed, X. Huang, and M. A. El-Sayed, “Selective laser photo-thermal therapy of epithelial carcinoma using anti-EGFR antibody conjugated gold nanoparticles,” Cancer Lett. 239, 129–135 (2006).
[Crossref]

Feldmann, J.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
[Crossref] [PubMed]

Franzl, T.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
[Crossref] [PubMed]

Halas, N. J.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[Crossref] [PubMed]

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257–259 (2003).
[Crossref]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (University Press, Cambridge, 2006).

Hirsch, L. R.

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257–259 (2003).
[Crossref]

Huang, X.

I. H. El-Sayed, X. Huang, and M. A. El-Sayed, “Selective laser photo-thermal therapy of epithelial carcinoma using anti-EGFR antibody conjugated gold nanoparticles,” Cancer Lett. 239, 129–135 (2006).
[Crossref]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Jackson, J. B.

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257–259 (2003).
[Crossref]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Khlebtsov, B.

B. Khlebtsov, A. Melnikov, V. Zharov, and N. Khlebtsov, “Absorption and scattering of light by a dimer of metal nanospheres: comparison of dipole and multipole approaches,” Nanotechnology 17, 1437–1445 (2006).
[Crossref]

Khlebtsov, N.

B. Khlebtsov, A. Melnikov, V. Zharov, and N. Khlebtsov, “Absorption and scattering of light by a dimer of metal nanospheres: comparison of dipole and multipole approaches,” Nanotechnology 17, 1437–1445 (2006).
[Crossref]

Kneipp, H.

K. Kneipp, M. Moskovits, and H. Kneipp, Surface-Enhanced Raman Scattering: Physics and Applications (Springer, Berlin, 2006).
[Crossref]

Kneipp, K.

K. Kneipp, M. Moskovits, and H. Kneipp, Surface-Enhanced Raman Scattering: Physics and Applications (Springer, Berlin, 2006).
[Crossref]

Li., K.

K. Li., M. I. Stockman, and D. J. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett. 91, 227402 (2003).
[Crossref] [PubMed]

Liphardt, J.

B. M. Reinhard, M. Siu, H. Argarwal, A. P. Alivisatos, and J. Liphardt, “Calibration of dynamic molecular rulers based on plasmon coupling between gold nanoparticles,” Nano Lett. 5, 2246–2252 (2005).
[Crossref] [PubMed]

Liu, X.-X.

R.-L. Chern, X.-X. Liu, and C.-C. Chang, “Particle plasmons of metal nanospheres: Application of multiple scattering approach,” Phys. Rev. E 76, 016609 (2007).
[Crossref]

Lo, Y. T.

J. H. Bruning and Y. T. Lo, “Multiple scattering of EM waves by spheres Part I – Multipole Expansion and Ray-Optical Solutions,” IEEE Tran. Antennas Propag.AP-19, 378–390 (1971).
[Crossref]

Mackowski, D. W.

D. W. Mackowski, “Calculation of total cross sections of multiple-sphere clusters,” J. Opt. Soc. Am. A 11, 2851–2861 (1994).
[Crossref]

D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc. R. Soc. London Ser. A 433, 599–614 (1991).
[Crossref]

Maier, S. A.

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

Mattei, G.

G. Pellegrini, G. Mattei, V. Bello, and P. Mazzoldi, “Interacting metal nanoparticles: Optical properties from nanoparticle dimers to core-satellite systems,” Mat. Sci. Eng. C 27, 1347–1350 (2007).
[Crossref]

Mazzoldi, P.

G. Pellegrini, G. Mattei, V. Bello, and P. Mazzoldi, “Interacting metal nanoparticles: Optical properties from nanoparticle dimers to core-satellite systems,” Mat. Sci. Eng. C 27, 1347–1350 (2007).
[Crossref]

Melnikov, A.

B. Khlebtsov, A. Melnikov, V. Zharov, and N. Khlebtsov, “Absorption and scattering of light by a dimer of metal nanospheres: comparison of dipole and multipole approaches,” Nanotechnology 17, 1437–1445 (2006).
[Crossref]

Messinger, B. J.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, “Local fields at the surface of noblemetal microspheres,” Phys. Rev. B 24, 649–657 (1981).
[Crossref]

Moskovits, M.

K. Kneipp, M. Moskovits, and H. Kneipp, Surface-Enhanced Raman Scattering: Physics and Applications (Springer, Berlin, 2006).
[Crossref]

Nordlander, P.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[Crossref] [PubMed]

Novotny, L.

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 266802 (2007).
[Crossref] [PubMed]

L. Novotny and B. Hecht, Principles of Nano-Optics (University Press, Cambridge, 2006).

Pellegrini, G.

G. Pellegrini, G. Mattei, V. Bello, and P. Mazzoldi, “Interacting metal nanoparticles: Optical properties from nanoparticle dimers to core-satellite systems,” Mat. Sci. Eng. C 27, 1347–1350 (2007).
[Crossref]

Prodan, E.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[Crossref] [PubMed]

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[Crossref] [PubMed]

Reinhard, B. M.

B. M. Reinhard, M. Siu, H. Argarwal, A. P. Alivisatos, and J. Liphardt, “Calibration of dynamic molecular rulers based on plasmon coupling between gold nanoparticles,” Nano Lett. 5, 2246–2252 (2005).
[Crossref] [PubMed]

Shen, Y. Ron

F. Wang and Y. Ron Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97, 206806 (2006).
[Crossref] [PubMed]

Siu, M.

B. M. Reinhard, M. Siu, H. Argarwal, A. P. Alivisatos, and J. Liphardt, “Calibration of dynamic molecular rulers based on plasmon coupling between gold nanoparticles,” Nano Lett. 5, 2246–2252 (2005).
[Crossref] [PubMed]

Sleiman, H. F.

F. Aldaye and H. F. Sleiman, “Dynamic DNA templates for discrete gold nanoparticles assemblies: Control of geometry, modularity, write/erase and structural switching,” J. Am. Chem. Soc. 129, 4130–4131 (2007).
[Crossref] [PubMed]

Sönnichsen, C.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
[Crossref] [PubMed]

Stockman, M. I.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
[Crossref] [PubMed]

K. Li., M. I. Stockman, and D. J. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett. 91, 227402 (2003).
[Crossref] [PubMed]

Sweatlock, L. A.

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

van de Hulst, H.C.

H.C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

von Plessen, G.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
[Crossref] [PubMed]

von Raben, K. U.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, “Local fields at the surface of noblemetal microspheres,” Phys. Rev. B 24, 649–657 (1981).
[Crossref]

Wang, F.

F. Wang and Y. Ron Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97, 206806 (2006).
[Crossref] [PubMed]

Weber, H. J.

G. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th. ed., (Academic, Orlando, 2005).

West, J. L.

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257–259 (2003).
[Crossref]

Westcott, S. L.

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257–259 (2003).
[Crossref]

Wilk, T.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
[Crossref] [PubMed]

Xu, H.

Xu, Y.

Y. Xu, “Calculation of the addition coefficients in electromagnetic multisphere-scattering theory,” J. Comput. Phys. 127, 285–298 (1996).
[Crossref]

Y. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. 34, 4573–4588 (1995).
[Crossref] [PubMed]

Zharov, V.

B. Khlebtsov, A. Melnikov, V. Zharov, and N. Khlebtsov, “Absorption and scattering of light by a dimer of metal nanospheres: comparison of dipole and multipole approaches,” Nanotechnology 17, 1437–1445 (2006).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257–259 (2003).
[Crossref]

Cancer Lett. (1)

I. H. El-Sayed, X. Huang, and M. A. El-Sayed, “Selective laser photo-thermal therapy of epithelial carcinoma using anti-EGFR antibody conjugated gold nanoparticles,” Cancer Lett. 239, 129–135 (2006).
[Crossref]

J. Am. Chem. Soc. (1)

F. Aldaye and H. F. Sleiman, “Dynamic DNA templates for discrete gold nanoparticles assemblies: Control of geometry, modularity, write/erase and structural switching,” J. Am. Chem. Soc. 129, 4130–4131 (2007).
[Crossref] [PubMed]

J. Comput. Phys. (1)

Y. Xu, “Calculation of the addition coefficients in electromagnetic multisphere-scattering theory,” J. Comput. Phys. 127, 285–298 (1996).
[Crossref]

J. Opt. Soc. Am. A (2)

Mat. Sci. Eng. C (1)

G. Pellegrini, G. Mattei, V. Bello, and P. Mazzoldi, “Interacting metal nanoparticles: Optical properties from nanoparticle dimers to core-satellite systems,” Mat. Sci. Eng. C 27, 1347–1350 (2007).
[Crossref]

Nano Lett. (1)

B. M. Reinhard, M. Siu, H. Argarwal, A. P. Alivisatos, and J. Liphardt, “Calibration of dynamic molecular rulers based on plasmon coupling between gold nanoparticles,” Nano Lett. 5, 2246–2252 (2005).
[Crossref] [PubMed]

Nanotechnology (1)

B. Khlebtsov, A. Melnikov, V. Zharov, and N. Khlebtsov, “Absorption and scattering of light by a dimer of metal nanospheres: comparison of dipole and multipole approaches,” Nanotechnology 17, 1437–1445 (2006).
[Crossref]

Phys. Rev. B (4)

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Figures (26)

Fig. 1.
Fig. 1.

Depiction of the general problem. Each sphere is characterized by a radius aj and refractive index mj (left). The rotation scheme of a bisphere jl to the overall coordinate system (right).

Fig. 2.
Fig. 2.

An example showing the convergence of near-field enhancement at the focal point for varying maximum degree N of spherical harmonics included in the simulation (Eqs. (4), (5) specifically). The structure employed is a self-similar series of 12 nanospheres with a geometric growth factor κ=0.831 (see section 3.3 for definition). Both the cases of gold and silver particles are illustrated.

Fig. 3.
Fig. 3.

Linear chain geometries of identical gold or silver nanospheres.

Fig. 4.
Fig. 4.

Enhancement of near-field at focal point among linear chains with varying number of gold nanospheres.

Fig. 5.
Fig. 5.

Enhancement of near-field at focal point among linear chains with varying number of silver nanospheres.

Fig. 6.
Fig. 6.

A 4-sphere with varying geometric progression growth factors κ=1, 0.5, 0.3, 0.2, 0.143 and 0.111.

Fig. 7.
Fig. 7.

A 6-sphere with varying geometric progression growth factors κ=1, 0.768, 0.558, 0.456, and 0.393.

Fig. 8.
Fig. 8.

Enhancement of near-field at focal point among various geometric progressions of 4 gold nanospheres as the geometric parameter κ is varied.

Fig. 9.
Fig. 9.

Enhancement of near-field at focal point among various geometric progressions of 4 silver nanospheres. as the geometric parameter κ is varied.

Fig. 10.
Fig. 10.

Enhancement of nearfield at focal point among various geometric progressions of 6 gold nanospheres as the geometric growth parameter κ is varied.

Fig. 11.
Fig. 11.

Enhancement of nearfield at focal point among various geometric progressions of 6 silver nanospheres as the geometric growth parameter κ is varied.

Fig. 12.
Fig. 12.

Geometric progression of nanospheres in self-similar structures whose total lengths are fixed to that of a 16-sphere linear chain (167.5nm).

Fig. 13.
Fig. 13.

Focal point electric fieldenhancement for gold self-similar structures equal in length to a 16-sphere linear chain (167.5nm).

Fig. 14.
Fig. 14.

Focal point electric fieldenhancement for silver selfsimilar structures equal in length to a 16-sphere linear chain (167.5nm).

Fig. 15.
Fig. 15.

Focal point electric fieldenhancement for gold self-similar structures equal in length to a 20-sphere linear chain (209.5nm).

Fig. 16.
Fig. 16.

Focal point electric fieldenhancement for silver selfsimilar structures equal in length to a 20-sphere linear chain (209.5nm).

Fig. 17.
Fig. 17.

The electric field enhancement in the xz-plane for self-similar gold assemblies of length 167.5nm.

Fig. 18.
Fig. 18.

The electric field enhancement in the xy-plane for self-similar gold assemblies of length 167.5nm.

Fig. 19.
Fig. 19.

The time-average Poynting vector magnitude in the xz-plane for self-similar gold assemblies of length 167.5nm. The reference incident power is situated at -2.58=log (1/η).

Fig. 20.
Fig. 20.

Electric field enhancement in the xz-plane for the silver Ns =8-self-similar structure at three different wavelengths. a) 542nm, b) 474nm c) 440nm.

Fig. 21.
Fig. 21.

Absorption efficiency among various geometric progressions of gold nanospheres whose lengths are fixed to that of a 16-sphere linear chain.

Fig. 22.
Fig. 22.

Absorption efficiency among various geometric progressions of silver nanospheres whose lengths are fixed to that of a 16-sphere linear chain.

Fig. 23.
Fig. 23.

Scattering efficiency among various geometric progressions of gold nanospheres whose lengths are fixed to that of a 16-sphere linear chain.

Fig. 24.
Fig. 24.

Scattering efficiency among various geometric progressions of silver nanospheres whose lengths are fixed to that of a 16-sphere linear chain.

Fig. 29.
Fig. 29.

Discrete approximation of a) cone, b) pyramid and c) triangular truss.

Fig. 30.
Fig. 30.

Enhancement of nearfield at focal point among the cone, pyramid and truss geometries.

Tables (1)

Tables Icon

Table 1: Summary of resonance peaks for self-similar structures of length 167.5nm taken from data plotted in Figs. 13,14,21,22. Near-field distributions are plotted at near-field enhancement peaks.

Equations (36)

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P S ( v S ) E focal 4 E 0 4
E sca j = n = 1 m = n n i E mn [ a mn j N mn ( 3 ) ( j ) + b mn j M mn ( 3 ) ( j ) ]
E inc j = n = 1 m = n n i E mn [ p mn j N mn ( 1 ) ( j ) + q mn j M mn ( 1 ) ( j ) ]
E int j = n = 1 m = n n i E mn [ d mn j N mn ( 1 ) ( j ) + c mn j M mn ( 1 ) ( j ) ]
H sca j = 1 η n = 1 m = n n E mn [ b mn j N mn ( 3 ) ( j ) + a mn j M mn ( 3 ) ( j ) ]
H inc j = 1 η n = 1 m = n n E mn [ q mn j N mn ( 1 ) ( j ) + p mn j M mn ( 1 ) ( j ) ]
H int j = 1 η j n = 1 m = n n E mn [ c mn j N mn ( 1 ) ( j ) + d mn j M mn ( 1 ) ( j ) ]
E sca = i N s E sca j .
p 1 n 0 = q 1 n 0 = exp ( i Z j ) 2 , p 1 n 0 = q 1 n 0 = exp ( i Z j ) 2 n ( n + 1 )
a mn j = α n j ( p mn j j = 1 j l N s v = 1 μ = v v E μ v E m n [ a μ v l A mn μ v ( R jl ) + b μ v l B mn μ v ( R jl ) ] )
b mn j = β n j ( q mn j j = 1 j l N s v = 1 μ = v v E μ v E m n [ a μ v l B mn μ v ( R jl ) + b μ v l A mn μ v ( R jl ) ] )
a j + i = 1 i j N s T ji a i = p j or ( 1 + T ) a = p
α n j = m j ψ n ( x j ) ψ n ( m j x j ) ψ n ( x j ) ψ n ( m j x j ) m j ξ n ( x j ) ψ n ( m j x j ) ξ n ( x j ) ψ n ( m j x j )
β n j = ψ n ( x j ) ψ n ( m j x j ) m j ψ n ( x j ) ψ n ( m j x j ) ξ n ( x j ) ψ n ( m j x j ) m j ξ n ( x j ) ψ n ( m j x j )
M mn ( 3 ) ( j ) = v = 1 μ = v v [ A μ v mn ( R jl ) M μ v ( 1 ) ( l ) + B μ v mn ( R jl ) N μ v ( 1 ) ( l ) ]
N mn ( 3 ) ( j ) = v = 1 μ = v v [ B μ v mn ( R jl ) M μ v ( 1 ) ( l ) + A μ v mn ( R jl ) N μ v ( 1 ) ( l ) ] .
A μ v mn ( R jl ) ( R μ m ( n ) ) 1 A μ v mn ( 0 , 0 , R jl ) R μ m ( n )
B μ v mn ( R jl ) ( R μ m ( n ) ) 1 B μ v mn ( 0 , 0 , R jl ) R μ m ( n )
R μ m ( n ) ( α , β , γ ) = E mn E μ n F μ n F mn D μ m ( n ) ( α , β , γ )
E mn = E 0 i n ( 2 n + 1 ) ( n m ) ! ( n + m ) !
F mn = ( 1 ) m ( 2 n + 1 ) ( n m ) ! ( 4 π ( n + m ) ! )
D μ m ( n ) ( α , β , γ ) = e ik γ d μ m ( n ) ( β ) e im α
d μ m ( n ) ( β ) = [ ( n + μ ) ! ( n μ ) ! ( n + m ) ! ( n m ) ! ] 1 2 ( cos β 2 ) μ + m ( sin β 2 ) μ m P n μ ( μ m , μ + m ) ( cos β )
P n ( α , β ) ( x ) = 2 n v = 0 n ( n + α v ) ( n + β n v ) ( x 1 ) n v ( x + 1 ) v .
A mn mv = ( 1 ) m + n 2 n + 1 2 n ( n + 1 ) p = n v n + v ( 1 ) q [ n ( n + 1 ) + v ( v + 1 ) p ( p + 1 ) ] a ( m , n , m , v , p ) h p ( 1 ) ( R jl )
B mn mv = ( 1 ) m + n 2 n + 1 2 n ( n + 1 ) 2 im R jl p = n v n + v ( 1 ) q a ( m , n , m , v , p ) h p ( 1 ) ( R jl )
q = ( n + v p ) 2
α p 3 a p 4 ( α p 2 + α p 1 4 m 2 ) a p 2 + α p a p = 0
α p = [ ( n + v + 1 ) 2 p 2 ] [ p 2 ( n v ) 2 ] 4 p 2 1
a n + v = ( 2 n 1 ) ! ! ( 2 v 1 ) ! ! ( 2 n + 2 v 1 ) ! ! ( n + v ) ! ( n m ) ! ( v + m ) !
a n + v 2 = ( 2 n + 2 v 3 ) ( 2 n 1 ) ( 2 v 1 ) ( n + v ) [ n v m 2 ( 2 n + 2 v 1 ) ] a n + v
Q sca = 4 π G k 2 n = 1 m = n n n ( n + 1 ) ( 2 n + 1 ) ( n m ) ! ( n + m ) ! ( a mn T 2 + b mn T 2 )
Q ext = 4 π G k 2 n = 1 m = n n n ( n + 1 ) ( 2 n + 1 ) ( n m ) ! ( n + m ) ! Re { p mn 0 * a mn T + q mn 0 * b mn T }
Q abs = Q ext Q sca
a mn T = j = 1 N s v = 1 μ = v v [ A mn μ v ( R jl ) a μ v j + B mn μ v ( R jl ) b μ v j ]
b mn T = j = 1 N s v = 1 μ = v v [ A mn μ v ( R jl ) b μ v j + B mn μ v ( R jl ) a μ v j ] .

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