Abstract

We show that the effects of a nearby surface on the plasmon resonance of a metallic nanoparticle of finite size can be modeled by expanding the secondary local field at the particle position in terms of an integral expansion of elementary waves that has the form of a Sommerfeld integral. In this way it is a straightforward matter to apply the Fresnel reflection coefficients of the surface to the secondary field and thus derive a corrected expression for the effective polarizability of the particle. We apply our theoretical result to particles near metal-clad and multilayer-dielectric waveguides and show that a substantial amount of the light scattered by a particle can propagate radially outward confined to the guided modes of the substrate.

© 2002 Optical Society of America

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  1. K. Drexhage, “Interaction of light with monomolecular dye layers,” in Progress in Optics XII, E. Wolf, ed. (North Holland, Amsterdam, 1974), pp. 163–232.
  2. W. R. Holland and D. G. Hall, “Frequency shifts of an electric-dipole resonance near a conducting surface,” Phys. Rev. Lett. 52, 1041–1044 (1984).
    [CrossRef]
  3. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  4. W. R. Holland and D. G. Hall, “Surface-plasmon dispersion relation: shifts induced by the interaction with localized plasma resonances,” Phys. Rev. B 27, 7765–7768 (1983).
    [CrossRef]
  5. M. J. Bloemer, J. G. Mantovani, J. P. Goudonnet, D. R. James, R. J. Warmack, and T. L. Ferrell, “Observation of driven surface-plasmon modes in metal particulates above tunnel junctions,” Phys. Rev. B 35, 5947–5954 (1987).
    [CrossRef]
  6. H. G. Bingler, H. Brunner, M. Klenke, A. Leitner, F. R. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
    [CrossRef]
  7. F. R. Aussenegg, A. Leitner, and H. Gold, “Optical second-harmonic generation of metal-island films,” Appl. Phys. A A60, 97–101 (1995).
    [CrossRef]
  8. G. S. Agarwal and S. D. Gupta, “Interaction between surface plasmons and localized plasmons,” Phys. Rev. B 32, 3607–3611 (1985).
    [CrossRef]
  9. K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
    [CrossRef]
  10. S. Nie and S. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
    [CrossRef] [PubMed]
  11. S. Emory, W. E. Haskins, and S. Nie, “Direct observation of size-dependent optical enhancement in single metal nanoparticles,” J. Am. Chem. Soc. 120, 8009–8010 (1998).
    [CrossRef]
  12. M. Meier and A. Wokaun, “Enhanced fields on large metal particles: dynamic depolarization,” Opt. Lett. 8, 581–583 (1983).
    [CrossRef] [PubMed]
  13. H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69, 2327–2329 (1996).
    [CrossRef]
  14. H. R. Stuart and D. G. Hall, “Enhanced dipole-dipole interaction between elementary radiators near a surface,” Phys. Rev. Lett. 80, 5663–5666 (1998).
    [CrossRef]
  15. R. R. Chance, A. Prock, and R. U. Silbey, “Frequency shifts of an electric-dipole transition near a partially reflecting surface,” Phys. Rev. A 12, 1448–1452 (1975).
    [CrossRef]
  16. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
    [CrossRef]
  17. C. F. Bohren and D. R. Huffman, in Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chaps. 5 and 12.
  18. The term depolarization field is often used in the literature, and we adopt its use here. We point out, however, that this contribution to the total field can also be polarizing as opposed to depolarizing. In the language of scattering, the depolarization field is the scattered field.
  19. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, New York, 1980).
  20. M. Meier, A. Wokaun, and P. F. Liao, “Enhanced fields on rough surfaces: dipolar interactions among particles of sizes exceeding the Rayleigh limit,” Phys. Rev. B 54, 10335–10338 (1996).
  21. E. J. Zeman and G. C. Schatz, “An accurate electromagnetic theory of surface enhancement factors for Ag, Au, Cu, Li, Al, Ga, In, Zn, and Cd,” J. Phys. Chem. 91, 634–643 (1987).
    [CrossRef]
  22. T. Takemori, M. Inoue, and K. Ohtaka, “Optical response of a sphere coupled to a metal substrate,” J. Phys. Soc. Jpn. 56, 1587–1602 (1987).
    [CrossRef]
  23. M. Wind, P. Bobbert, J. Vlieger, and D. Bedeaux, “Optical properties of 2D-systems of small particles on a substrate,” Physica A 157, 269–278 (1989).
    [CrossRef]
  24. M. Wind, P. Bobbert, J. Vlieger, and D. Bedeaux, “The polarizability of truncated spheres and oblate spheroids on a substrate: comparison with experimental results,” Thin Solid Films 164, 57–62 (1988).
    [CrossRef]
  25. P. Bobbert and J. Vlieger, “The polarizability of a spheroidal particle on a substrate,” Physica A 147A, 115–141 (1987).
    [CrossRef]
  26. P. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137A, 209–242 (1986).
    [CrossRef]
  27. G. Videen, M. Turner, V. Iafelice, W. Bickel, and W. Wolfe, “Scattering from a small sphere near a surface,” J. Opt. Soc. Am. A 10, 118–126 (1993).
    [CrossRef]
  28. G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489 (1991); errata, J. Opt. Soc. Am. A 9, 844–845 (1992).
    [CrossRef]
  29. E. Fucile, P. Denti, F. Borghese, R. Saija, and O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
    [CrossRef]
  30. M. Taubenblatt and T. Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method,” J. Opt. Soc. Am. A 10, 912–919 (1993).
    [CrossRef]
  31. B. Johnson, “Light scattering from a spherical particle on a conducting plane: I. Normal incidence,” J. Opt. Soc. Am. A 9, 1341–1351 (1992); erratum, J. Opt. Soc. Am. A 10, 766 (1993).
    [CrossRef]
  32. B. Johnson, “Calculation of light scattering from a spherical particle on a surface by the multipole expansion method,” J. Opt. Soc. Am. A 13, 326–337 (1996).
    [CrossRef]
  33. T. Wriedt and A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
    [CrossRef]
  34. I. Simonsen, R. Lazzari, J. Jupille, and S. Roux, “Numerical modeling of the optical response of supported metallic particles,” Phys. Rev. B 61, 7722–7733 (2000).
    [CrossRef]
  35. R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978).
  36. W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990), p. 65.
  37. A. Sommerfeld, “Ber die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. (Leipzig) 28, 665–737 (1909).
    [CrossRef]
  38. In the absence of the surface, the induced polarization is entirely in the direction of the polarization of the incident field. However, an electric point dipole situated horizontally over a surface is described by a vector potential that has components in both the horizontal (z⁁) and the vertical (x⁁) directions.
  39. W. H. Weber and C. F. Eagen, “Energy transfer from an excited dye molecule to the surface plasmons of an adjacent metal,” Opt. Lett. 4, 236–238 (1979).
    [CrossRef] [PubMed]
  40. G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
    [CrossRef]
  41. For an excellent introduction to surface plasmons, see, for example, H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Vol. III of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1988).
  42. Assuming homogeneous polarization throughout the particle volume allows us to extract the polarization term from the integrand as a constant.
  43. We have recently observed enhancement factors of greater than 25.

2000 (1)

I. Simonsen, R. Lazzari, J. Jupille, and S. Roux, “Numerical modeling of the optical response of supported metallic particles,” Phys. Rev. B 61, 7722–7733 (2000).
[CrossRef]

1998 (3)

T. Wriedt and A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
[CrossRef]

S. Emory, W. E. Haskins, and S. Nie, “Direct observation of size-dependent optical enhancement in single metal nanoparticles,” J. Am. Chem. Soc. 120, 8009–8010 (1998).
[CrossRef]

H. R. Stuart and D. G. Hall, “Enhanced dipole-dipole interaction between elementary radiators near a surface,” Phys. Rev. Lett. 80, 5663–5666 (1998).
[CrossRef]

1997 (3)

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

S. Nie and S. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[CrossRef] [PubMed]

E. Fucile, P. Denti, F. Borghese, R. Saija, and O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
[CrossRef]

1996 (3)

B. Johnson, “Calculation of light scattering from a spherical particle on a surface by the multipole expansion method,” J. Opt. Soc. Am. A 13, 326–337 (1996).
[CrossRef]

M. Meier, A. Wokaun, and P. F. Liao, “Enhanced fields on rough surfaces: dipolar interactions among particles of sizes exceeding the Rayleigh limit,” Phys. Rev. B 54, 10335–10338 (1996).

H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69, 2327–2329 (1996).
[CrossRef]

1995 (1)

F. R. Aussenegg, A. Leitner, and H. Gold, “Optical second-harmonic generation of metal-island films,” Appl. Phys. A A60, 97–101 (1995).
[CrossRef]

1993 (3)

1989 (1)

M. Wind, P. Bobbert, J. Vlieger, and D. Bedeaux, “Optical properties of 2D-systems of small particles on a substrate,” Physica A 157, 269–278 (1989).
[CrossRef]

1988 (1)

M. Wind, P. Bobbert, J. Vlieger, and D. Bedeaux, “The polarizability of truncated spheres and oblate spheroids on a substrate: comparison with experimental results,” Thin Solid Films 164, 57–62 (1988).
[CrossRef]

1987 (5)

P. Bobbert and J. Vlieger, “The polarizability of a spheroidal particle on a substrate,” Physica A 147A, 115–141 (1987).
[CrossRef]

E. J. Zeman and G. C. Schatz, “An accurate electromagnetic theory of surface enhancement factors for Ag, Au, Cu, Li, Al, Ga, In, Zn, and Cd,” J. Phys. Chem. 91, 634–643 (1987).
[CrossRef]

T. Takemori, M. Inoue, and K. Ohtaka, “Optical response of a sphere coupled to a metal substrate,” J. Phys. Soc. Jpn. 56, 1587–1602 (1987).
[CrossRef]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

M. J. Bloemer, J. G. Mantovani, J. P. Goudonnet, D. R. James, R. J. Warmack, and T. L. Ferrell, “Observation of driven surface-plasmon modes in metal particulates above tunnel junctions,” Phys. Rev. B 35, 5947–5954 (1987).
[CrossRef]

1986 (1)

P. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137A, 209–242 (1986).
[CrossRef]

1985 (1)

G. S. Agarwal and S. D. Gupta, “Interaction between surface plasmons and localized plasmons,” Phys. Rev. B 32, 3607–3611 (1985).
[CrossRef]

1984 (2)

W. R. Holland and D. G. Hall, “Frequency shifts of an electric-dipole resonance near a conducting surface,” Phys. Rev. Lett. 52, 1041–1044 (1984).
[CrossRef]

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

1983 (2)

W. R. Holland and D. G. Hall, “Surface-plasmon dispersion relation: shifts induced by the interaction with localized plasma resonances,” Phys. Rev. B 27, 7765–7768 (1983).
[CrossRef]

M. Meier and A. Wokaun, “Enhanced fields on large metal particles: dynamic depolarization,” Opt. Lett. 8, 581–583 (1983).
[CrossRef] [PubMed]

1979 (1)

1978 (1)

R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978).

1975 (1)

R. R. Chance, A. Prock, and R. U. Silbey, “Frequency shifts of an electric-dipole transition near a partially reflecting surface,” Phys. Rev. A 12, 1448–1452 (1975).
[CrossRef]

1909 (1)

A. Sommerfeld, “Ber die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. (Leipzig) 28, 665–737 (1909).
[CrossRef]

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and S. D. Gupta, “Interaction between surface plasmons and localized plasmons,” Phys. Rev. B 32, 3607–3611 (1985).
[CrossRef]

Aussenegg, F. R.

F. R. Aussenegg, A. Leitner, and H. Gold, “Optical second-harmonic generation of metal-island films,” Appl. Phys. A A60, 97–101 (1995).
[CrossRef]

H. G. Bingler, H. Brunner, M. Klenke, A. Leitner, F. R. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

Bedeaux, D.

M. Wind, P. Bobbert, J. Vlieger, and D. Bedeaux, “Optical properties of 2D-systems of small particles on a substrate,” Physica A 157, 269–278 (1989).
[CrossRef]

M. Wind, P. Bobbert, J. Vlieger, and D. Bedeaux, “The polarizability of truncated spheres and oblate spheroids on a substrate: comparison with experimental results,” Thin Solid Films 164, 57–62 (1988).
[CrossRef]

Bickel, W.

Bingler, H. G.

H. G. Bingler, H. Brunner, M. Klenke, A. Leitner, F. R. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

Bloemer, M. J.

M. J. Bloemer, J. G. Mantovani, J. P. Goudonnet, D. R. James, R. J. Warmack, and T. L. Ferrell, “Observation of driven surface-plasmon modes in metal particulates above tunnel junctions,” Phys. Rev. B 35, 5947–5954 (1987).
[CrossRef]

Bobbert, P.

M. Wind, P. Bobbert, J. Vlieger, and D. Bedeaux, “Optical properties of 2D-systems of small particles on a substrate,” Physica A 157, 269–278 (1989).
[CrossRef]

M. Wind, P. Bobbert, J. Vlieger, and D. Bedeaux, “The polarizability of truncated spheres and oblate spheroids on a substrate: comparison with experimental results,” Thin Solid Films 164, 57–62 (1988).
[CrossRef]

P. Bobbert and J. Vlieger, “The polarizability of a spheroidal particle on a substrate,” Physica A 147A, 115–141 (1987).
[CrossRef]

P. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137A, 209–242 (1986).
[CrossRef]

Borghese, F.

Brunner, H.

H. G. Bingler, H. Brunner, M. Klenke, A. Leitner, F. R. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

Chance, R. R.

R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978).

R. R. Chance, A. Prock, and R. U. Silbey, “Frequency shifts of an electric-dipole transition near a partially reflecting surface,” Phys. Rev. A 12, 1448–1452 (1975).
[CrossRef]

Dasari, R.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Denti, P.

Doicu, A.

T. Wriedt and A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
[CrossRef]

Eagen, C. F.

Emory, S.

S. Emory, W. E. Haskins, and S. Nie, “Direct observation of size-dependent optical enhancement in single metal nanoparticles,” J. Am. Chem. Soc. 120, 8009–8010 (1998).
[CrossRef]

S. Nie and S. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[CrossRef] [PubMed]

Feld, M.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Ferrell, T. L.

M. J. Bloemer, J. G. Mantovani, J. P. Goudonnet, D. R. James, R. J. Warmack, and T. L. Ferrell, “Observation of driven surface-plasmon modes in metal particulates above tunnel junctions,” Phys. Rev. B 35, 5947–5954 (1987).
[CrossRef]

Ford, G. W.

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Fucile, E.

Gold, H.

F. R. Aussenegg, A. Leitner, and H. Gold, “Optical second-harmonic generation of metal-island films,” Appl. Phys. A A60, 97–101 (1995).
[CrossRef]

Goudonnet, J. P.

M. J. Bloemer, J. G. Mantovani, J. P. Goudonnet, D. R. James, R. J. Warmack, and T. L. Ferrell, “Observation of driven surface-plasmon modes in metal particulates above tunnel junctions,” Phys. Rev. B 35, 5947–5954 (1987).
[CrossRef]

Gupta, S. D.

G. S. Agarwal and S. D. Gupta, “Interaction between surface plasmons and localized plasmons,” Phys. Rev. B 32, 3607–3611 (1985).
[CrossRef]

Hall, D. G.

H. R. Stuart and D. G. Hall, “Enhanced dipole-dipole interaction between elementary radiators near a surface,” Phys. Rev. Lett. 80, 5663–5666 (1998).
[CrossRef]

H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69, 2327–2329 (1996).
[CrossRef]

W. R. Holland and D. G. Hall, “Frequency shifts of an electric-dipole resonance near a conducting surface,” Phys. Rev. Lett. 52, 1041–1044 (1984).
[CrossRef]

W. R. Holland and D. G. Hall, “Surface-plasmon dispersion relation: shifts induced by the interaction with localized plasma resonances,” Phys. Rev. B 27, 7765–7768 (1983).
[CrossRef]

Haskins, W. E.

S. Emory, W. E. Haskins, and S. Nie, “Direct observation of size-dependent optical enhancement in single metal nanoparticles,” J. Am. Chem. Soc. 120, 8009–8010 (1998).
[CrossRef]

Holland, W. R.

W. R. Holland and D. G. Hall, “Frequency shifts of an electric-dipole resonance near a conducting surface,” Phys. Rev. Lett. 52, 1041–1044 (1984).
[CrossRef]

W. R. Holland and D. G. Hall, “Surface-plasmon dispersion relation: shifts induced by the interaction with localized plasma resonances,” Phys. Rev. B 27, 7765–7768 (1983).
[CrossRef]

Iafelice, V.

Inoue, M.

T. Takemori, M. Inoue, and K. Ohtaka, “Optical response of a sphere coupled to a metal substrate,” J. Phys. Soc. Jpn. 56, 1587–1602 (1987).
[CrossRef]

Itzkan, I.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

James, D. R.

M. J. Bloemer, J. G. Mantovani, J. P. Goudonnet, D. R. James, R. J. Warmack, and T. L. Ferrell, “Observation of driven surface-plasmon modes in metal particulates above tunnel junctions,” Phys. Rev. B 35, 5947–5954 (1987).
[CrossRef]

Johnson, B.

Jupille, J.

I. Simonsen, R. Lazzari, J. Jupille, and S. Roux, “Numerical modeling of the optical response of supported metallic particles,” Phys. Rev. B 61, 7722–7733 (2000).
[CrossRef]

Klenke, M.

H. G. Bingler, H. Brunner, M. Klenke, A. Leitner, F. R. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

Kneipp, H.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Kneipp, K.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Lazzari, R.

I. Simonsen, R. Lazzari, J. Jupille, and S. Roux, “Numerical modeling of the optical response of supported metallic particles,” Phys. Rev. B 61, 7722–7733 (2000).
[CrossRef]

Leitner, A.

F. R. Aussenegg, A. Leitner, and H. Gold, “Optical second-harmonic generation of metal-island films,” Appl. Phys. A A60, 97–101 (1995).
[CrossRef]

H. G. Bingler, H. Brunner, M. Klenke, A. Leitner, F. R. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

Liao, P. F.

M. Meier, A. Wokaun, and P. F. Liao, “Enhanced fields on rough surfaces: dipolar interactions among particles of sizes exceeding the Rayleigh limit,” Phys. Rev. B 54, 10335–10338 (1996).

Mantovani, J. G.

M. J. Bloemer, J. G. Mantovani, J. P. Goudonnet, D. R. James, R. J. Warmack, and T. L. Ferrell, “Observation of driven surface-plasmon modes in metal particulates above tunnel junctions,” Phys. Rev. B 35, 5947–5954 (1987).
[CrossRef]

Meier, M.

M. Meier, A. Wokaun, and P. F. Liao, “Enhanced fields on rough surfaces: dipolar interactions among particles of sizes exceeding the Rayleigh limit,” Phys. Rev. B 54, 10335–10338 (1996).

M. Meier and A. Wokaun, “Enhanced fields on large metal particles: dynamic depolarization,” Opt. Lett. 8, 581–583 (1983).
[CrossRef] [PubMed]

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Nie, S.

S. Emory, W. E. Haskins, and S. Nie, “Direct observation of size-dependent optical enhancement in single metal nanoparticles,” J. Am. Chem. Soc. 120, 8009–8010 (1998).
[CrossRef]

S. Nie and S. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[CrossRef] [PubMed]

Ohtaka, K.

T. Takemori, M. Inoue, and K. Ohtaka, “Optical response of a sphere coupled to a metal substrate,” J. Phys. Soc. Jpn. 56, 1587–1602 (1987).
[CrossRef]

Perelman, L.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Prock, A.

R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978).

R. R. Chance, A. Prock, and R. U. Silbey, “Frequency shifts of an electric-dipole transition near a partially reflecting surface,” Phys. Rev. A 12, 1448–1452 (1975).
[CrossRef]

Roux, S.

I. Simonsen, R. Lazzari, J. Jupille, and S. Roux, “Numerical modeling of the optical response of supported metallic particles,” Phys. Rev. B 61, 7722–7733 (2000).
[CrossRef]

Saija, R.

Schatz, G. C.

E. J. Zeman and G. C. Schatz, “An accurate electromagnetic theory of surface enhancement factors for Ag, Au, Cu, Li, Al, Ga, In, Zn, and Cd,” J. Phys. Chem. 91, 634–643 (1987).
[CrossRef]

Silbey, R.

R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978).

Silbey, R. U.

R. R. Chance, A. Prock, and R. U. Silbey, “Frequency shifts of an electric-dipole transition near a partially reflecting surface,” Phys. Rev. A 12, 1448–1452 (1975).
[CrossRef]

Simonsen, I.

I. Simonsen, R. Lazzari, J. Jupille, and S. Roux, “Numerical modeling of the optical response of supported metallic particles,” Phys. Rev. B 61, 7722–7733 (2000).
[CrossRef]

Sindoni, O. I.

Sommerfeld, A.

A. Sommerfeld, “Ber die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. (Leipzig) 28, 665–737 (1909).
[CrossRef]

Stuart, H. R.

H. R. Stuart and D. G. Hall, “Enhanced dipole-dipole interaction between elementary radiators near a surface,” Phys. Rev. Lett. 80, 5663–5666 (1998).
[CrossRef]

H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69, 2327–2329 (1996).
[CrossRef]

Takemori, T.

T. Takemori, M. Inoue, and K. Ohtaka, “Optical response of a sphere coupled to a metal substrate,” J. Phys. Soc. Jpn. 56, 1587–1602 (1987).
[CrossRef]

Taubenblatt, M.

Tran, T.

Turner, M.

Videen, G.

Vlieger, J.

M. Wind, P. Bobbert, J. Vlieger, and D. Bedeaux, “Optical properties of 2D-systems of small particles on a substrate,” Physica A 157, 269–278 (1989).
[CrossRef]

M. Wind, P. Bobbert, J. Vlieger, and D. Bedeaux, “The polarizability of truncated spheres and oblate spheroids on a substrate: comparison with experimental results,” Thin Solid Films 164, 57–62 (1988).
[CrossRef]

P. Bobbert and J. Vlieger, “The polarizability of a spheroidal particle on a substrate,” Physica A 147A, 115–141 (1987).
[CrossRef]

P. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137A, 209–242 (1986).
[CrossRef]

Wang, Y.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Warmack, R. J.

M. J. Bloemer, J. G. Mantovani, J. P. Goudonnet, D. R. James, R. J. Warmack, and T. L. Ferrell, “Observation of driven surface-plasmon modes in metal particulates above tunnel junctions,” Phys. Rev. B 35, 5947–5954 (1987).
[CrossRef]

Weber, W. H.

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

W. H. Weber and C. F. Eagen, “Energy transfer from an excited dye molecule to the surface plasmons of an adjacent metal,” Opt. Lett. 4, 236–238 (1979).
[CrossRef] [PubMed]

Wind, M.

M. Wind, P. Bobbert, J. Vlieger, and D. Bedeaux, “Optical properties of 2D-systems of small particles on a substrate,” Physica A 157, 269–278 (1989).
[CrossRef]

M. Wind, P. Bobbert, J. Vlieger, and D. Bedeaux, “The polarizability of truncated spheres and oblate spheroids on a substrate: comparison with experimental results,” Thin Solid Films 164, 57–62 (1988).
[CrossRef]

Wokaun, A.

M. Meier, A. Wokaun, and P. F. Liao, “Enhanced fields on rough surfaces: dipolar interactions among particles of sizes exceeding the Rayleigh limit,” Phys. Rev. B 54, 10335–10338 (1996).

H. G. Bingler, H. Brunner, M. Klenke, A. Leitner, F. R. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

M. Meier and A. Wokaun, “Enhanced fields on large metal particles: dynamic depolarization,” Opt. Lett. 8, 581–583 (1983).
[CrossRef] [PubMed]

Wolfe, W.

Wriedt, T.

T. Wriedt and A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Zeman, E. J.

E. J. Zeman and G. C. Schatz, “An accurate electromagnetic theory of surface enhancement factors for Ag, Au, Cu, Li, Al, Ga, In, Zn, and Cd,” J. Phys. Chem. 91, 634–643 (1987).
[CrossRef]

Adv. Chem. Phys. (1)

R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978).

Ann. Phys. (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Ann. Phys. (Leipzig) (1)

A. Sommerfeld, “Ber die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. (Leipzig) 28, 665–737 (1909).
[CrossRef]

Appl. Phys. A (1)

F. R. Aussenegg, A. Leitner, and H. Gold, “Optical second-harmonic generation of metal-island films,” Appl. Phys. A A60, 97–101 (1995).
[CrossRef]

Appl. Phys. Lett. (1)

H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69, 2327–2329 (1996).
[CrossRef]

J. Am. Chem. Soc. (1)

S. Emory, W. E. Haskins, and S. Nie, “Direct observation of size-dependent optical enhancement in single metal nanoparticles,” J. Am. Chem. Soc. 120, 8009–8010 (1998).
[CrossRef]

J. Chem. Phys. (1)

H. G. Bingler, H. Brunner, M. Klenke, A. Leitner, F. R. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

J. Opt. Soc. Am. A (4)

J. Phys. Chem. (1)

E. J. Zeman and G. C. Schatz, “An accurate electromagnetic theory of surface enhancement factors for Ag, Au, Cu, Li, Al, Ga, In, Zn, and Cd,” J. Phys. Chem. 91, 634–643 (1987).
[CrossRef]

J. Phys. Soc. Jpn. (1)

T. Takemori, M. Inoue, and K. Ohtaka, “Optical response of a sphere coupled to a metal substrate,” J. Phys. Soc. Jpn. 56, 1587–1602 (1987).
[CrossRef]

Opt. Commun. (1)

T. Wriedt and A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
[CrossRef]

Opt. Lett. (2)

Phys. Rep. (1)

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Phys. Rev. A (1)

R. R. Chance, A. Prock, and R. U. Silbey, “Frequency shifts of an electric-dipole transition near a partially reflecting surface,” Phys. Rev. A 12, 1448–1452 (1975).
[CrossRef]

Phys. Rev. B (5)

M. Meier, A. Wokaun, and P. F. Liao, “Enhanced fields on rough surfaces: dipolar interactions among particles of sizes exceeding the Rayleigh limit,” Phys. Rev. B 54, 10335–10338 (1996).

I. Simonsen, R. Lazzari, J. Jupille, and S. Roux, “Numerical modeling of the optical response of supported metallic particles,” Phys. Rev. B 61, 7722–7733 (2000).
[CrossRef]

G. S. Agarwal and S. D. Gupta, “Interaction between surface plasmons and localized plasmons,” Phys. Rev. B 32, 3607–3611 (1985).
[CrossRef]

W. R. Holland and D. G. Hall, “Surface-plasmon dispersion relation: shifts induced by the interaction with localized plasma resonances,” Phys. Rev. B 27, 7765–7768 (1983).
[CrossRef]

M. J. Bloemer, J. G. Mantovani, J. P. Goudonnet, D. R. James, R. J. Warmack, and T. L. Ferrell, “Observation of driven surface-plasmon modes in metal particulates above tunnel junctions,” Phys. Rev. B 35, 5947–5954 (1987).
[CrossRef]

Phys. Rev. Lett. (4)

W. R. Holland and D. G. Hall, “Frequency shifts of an electric-dipole resonance near a conducting surface,” Phys. Rev. Lett. 52, 1041–1044 (1984).
[CrossRef]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

H. R. Stuart and D. G. Hall, “Enhanced dipole-dipole interaction between elementary radiators near a surface,” Phys. Rev. Lett. 80, 5663–5666 (1998).
[CrossRef]

Physica A (3)

M. Wind, P. Bobbert, J. Vlieger, and D. Bedeaux, “Optical properties of 2D-systems of small particles on a substrate,” Physica A 157, 269–278 (1989).
[CrossRef]

P. Bobbert and J. Vlieger, “The polarizability of a spheroidal particle on a substrate,” Physica A 147A, 115–141 (1987).
[CrossRef]

P. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137A, 209–242 (1986).
[CrossRef]

Science (1)

S. Nie and S. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[CrossRef] [PubMed]

Thin Solid Films (1)

M. Wind, P. Bobbert, J. Vlieger, and D. Bedeaux, “The polarizability of truncated spheres and oblate spheroids on a substrate: comparison with experimental results,” Thin Solid Films 164, 57–62 (1988).
[CrossRef]

Other (11)

G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489 (1991); errata, J. Opt. Soc. Am. A 9, 844–845 (1992).
[CrossRef]

B. Johnson, “Light scattering from a spherical particle on a conducting plane: I. Normal incidence,” J. Opt. Soc. Am. A 9, 1341–1351 (1992); erratum, J. Opt. Soc. Am. A 10, 766 (1993).
[CrossRef]

K. Drexhage, “Interaction of light with monomolecular dye layers,” in Progress in Optics XII, E. Wolf, ed. (North Holland, Amsterdam, 1974), pp. 163–232.

C. F. Bohren and D. R. Huffman, in Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chaps. 5 and 12.

The term depolarization field is often used in the literature, and we adopt its use here. We point out, however, that this contribution to the total field can also be polarizing as opposed to depolarizing. In the language of scattering, the depolarization field is the scattered field.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, New York, 1980).

For an excellent introduction to surface plasmons, see, for example, H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Vol. III of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1988).

Assuming homogeneous polarization throughout the particle volume allows us to extract the polarization term from the integrand as a constant.

We have recently observed enhancement factors of greater than 25.

In the absence of the surface, the induced polarization is entirely in the direction of the polarization of the incident field. However, an electric point dipole situated horizontally over a surface is described by a vector potential that has components in both the horizontal (z⁁) and the vertical (x⁁) directions.

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990), p. 65.

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Figures (6)

Fig. 1
Fig. 1

Geometry and coordinate system referred to throughout this paper. The particle is shown situated above a two-layered surface for simplicity.

Fig. 2
Fig. 2

Modulus squared of the free-space polarizability per unit volume of a Ag sphere in the electrostatic limit, 50-nm-radius sphere, 2:1:1 ellipsoid along the major (60-nm) axis, and 2:1:1 ellipsoid along the minor (30-nm) axis.

Fig. 3
Fig. 3

Modulus squared of the polarizability per unit volume (in the plane of the surface) of a small Ag sphere and a 2:1:1 ellipsoid separated tens of nanometers from a plane Ag surface; d is the distance from the bottom of the particle to the Ag surface. The radius of the sphere is 50 nm, and the 2:1:1 ellipsoid is of 60-30-30 nm semi-axes. The calculation for the ellipsoid was done for illumination polarization along the 60-nm axis.

Fig. 4
Fig. 4

Modulus squared of the polarizability per unit volume (in the plane of the surface) of a 30-nm Ag sphere in (solid curve) free space and (dashed curve) separated ten nanometers from a plane silver surface; d is the distance from the bottom of the particle to the Ag surface.

Fig. 5
Fig. 5

Per unit volume power-spectra calculated for Ag spheres of radii, a, 10 nm; b, 30 nm; c, 50 nm in free space 50 nm above a Ag surface at λ=500 nm, illuminated at normal incidence. These spectra are calculated from the imaginary part of Eq. (29) and are a function of the normalized transverse wave number kρ/k, where k=2π/λ. Values of kρ<1 represent waves that propagate in the half-space above the surface, and values kρ>1 represent waves that are evanescent in that space. The strong feature at kρ/k=1.3 corresponds to the excitation of the surface plasmon of the Ag–dielectric interface by the Ag nanoparticle resonance.

Fig. 6
Fig. 6

Per-unit-volume power spectra calculated for Ag spheres of radii 10, 30, and 50 nm in free space 50 nm above a dielectric waveguide defined by a 165-nm-thick layer of Si separated from an infinitely thick Si substrate by a 200-nm-thick layer of SiO2 (SOI) at λ=800 nm. The TE and TM designations refer to guided waves excited in the upper Si layer by the Ag nanoparticle resonance. Note the logarithmic scale.

Equations (38)

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p¨i+b0p˙i+ω02pi=q2m(eˆi·ER),
ER=E0 exp(-iΩt),p=p0 exp(-iΩt),
bb0=1+q2mωp0b0Im(eˆi·ER),
ω2-ω02=b24-bb02-q2mp0Re(eˆi·ER).
dp=α0Eloc,α0=dV[(ω)-1],
Ei=1i[ki2Πi+(·Πi)],
Πi=p4π0exp(iki|r-r0|)|r-r0|
ΠV(r)=1VS SΠpt(r-r0)dV,
Edep=1[k2ΠV+(·ΠV)].
Edep=ξdep(x, y, z)p,
p=V[(ω)-1][Einc+ξ(0)p],
pi=V(ω)-11-V[(ω)-1]ξii(0)Ei
=V(ω)-11+[(ω)-1]LeffEi
=αeff,i(ω)Ei,
Leff=-Vξii(0)
p=4πr3{[(ω)-1]/[(ω)+2]}Einc,
αeff=4πr3-13+(-1)[1-(kr)2-23i(kr)3],
ΠV(r)=1VS SΠpt(r-r0)dV,
dΠV(x-x0; y, z)=dx0VS -dydzΠpt(x-x0; y-y, z-z)×S(x0; y, z)
=dx0VS Πpt(x-x0; y, z)  S(x0; y, z),
exp(ikr)r=i2π0dkρkρkx02πdθ×exp[ikρρ cos(θ-φ)+ikx|x|],
J0(kρρ)=12π02πdθ exp[ikρρ cos(θ-φ)],
Π(r-r0)pt=ip4π00dkρkρkxJ0(kρ(ρ-ρ0))×exp(ikx|x-x0|).
Πpt=ip4π0zˆ0dkρkρkxJ0(kρρ){exp(ikx|x-d|)+rs exp[ikx(x+d)]}-xˆ cos φ0dkρkρkxJ1(kρρ)×(rp+rs)exp[ikx(x+d)],
zˆ·Esurf=1k2Πz,vol+2z2Πz,vol+2xzΠx,volsurf,
zˆ·Esurf(ρ, φ, x)=ikp4πε0VS SdV×k0dkρkρkxrs exp[ikx(x+x)]J0(kρ(ρ-ρ))+0dkρkxk12kx2rs+rp×exp[ikx(x+x)]C(kρ(ρ-ρ)),
C(kρρ)=kρ2cos2 φ[J0(kρρ)-J2(kρρ)]-sin2 φJ0(kρρ)ρ.
P=-12 V Re(J*·E)dV=ω2V V Im(p*·E)dV,
J=tP=-iωpV.
P=ω2VIm(p*·VEdV)
=ω2Im[p*·(Edep+Esurf)]
=ω2Im[p*·(ξdepp+ξsurfp)]
=ω|pz|22Im[(ξdep+ξsurf)zz].
(ξtot)zz=ik2Vs0dkρkρkx[A-(ρ, x; kρ)+kρk2B-(ρ, x; kρ)]+kρkxrsA+(ρ, z; kρ)+kxk2kx2rs+rpB+(ρ, x; kρ),
A±(ρ, x; kρ)=Sexp(ikx|x±x|)×J0(kρ(ρ-ρ))dV,
B±(ρ, x; kρ)=Sexp(ikx|x±x|)×C(kρ(ρ-ρ))dV.
P=0dPdkρdkρ=0S(kρ)dkρ,
Πpt=ip4πε0 xˆ0dkρkρkxJ0(kρρ)×{exp(ikx|x-d|)-rp exp[ikx(x+d)]}.

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