Abstract

The boundary-element method is applied to the interaction of light with resonant metallic nanoparticles. At a certain wavelength, excitation of a surface plasmon takes place, which leads to a resonantly enhanced near-field amplitude and a large scattering cross section. The resonance wavelength for different scatterer geometries is determined. Alteration of the scattering properties in the presence of other metallic nanoparticles is discussed. To treat this problem, a novel formulation of the boundary-element method is presented that solves the interaction problem for all the coupled particles.

© 2003 Optical Society of America

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  1. M. Scharte, R. Porath, T. Ohms, M. Aeschlimann, J. R. Krenn, H. Ditlbacher, F. R. Aussenegg, A. Liebisch, “Do Mie plasmons have a longer lifetime on resonance than off resonance?” Appl. Phys. B 73, 305–310 (2001).
    [CrossRef]
  2. D. Wang, S. Guo, H. Ren, S. Yin, “Optical characteristics of silver-doped polarizing glass,” Opt. Lett. 27, 992–994 (2002).
    [CrossRef]
  3. C. F. Bohren, D. R. Huffmann, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  4. E. Moreno, D. E. Erni, C. Hafner, R. Vahldieck, “Multiple multipole method with automatic multipole setting applied to the simulation of surface plasmons in metallic nanostructures,” J. Opt. Soc. Am. A 19, 101–111 (2002).
    [CrossRef]
  5. W. H. Yang, G. C. Schatz, R. P. Van Duyne, “Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitary shape,” J. Chem. Phys. 103, 869–875 (1995).
    [CrossRef]
  6. J. P. Kottmann, O. J. F. Martin, “Accurate solution of the volume integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48, 1719–1726 (2000).
    [CrossRef]
  7. J. P. Kottmann, O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon-resonance spectrum of silver nanowires,” Appl. Phys. B 73, 299–304 (2001).
    [CrossRef]
  8. L. C. Wrobel, M. Aliabadi, The Boundary Element Method (Wiley, New York, 2002).
  9. J. M. Bendickson, E. Glytsis, T. K. Gaylord, “Focusing diffractive cylindrical mirrors: rigorous evaluation of various design methods,” J. Opt. Soc. Am. A 18, 1487–1494 (2001).
    [CrossRef]
  10. M. K. Choi, “Numerical calculation of light scattering from a layered sphere by the boundary-element method,” J. Opt. Soc. Am. A 18, 577–583 (2001).
    [CrossRef]
  11. J. Liu, B.-Y. Gu, B.-Z. Dong, G.-Z. Yang, “Interference effect of dual diffractive cylindrical microlenses analyzed by rigorous electromagnetic theory,” J. Opt. Soc. Am. A 18, 526–536 (2001).
    [CrossRef]
  12. D. W. Prather, M. S. Mirotznik, J. N. Mait, “Boundary integral method applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34–43 (1997).
    [CrossRef]
  13. D. W. Prather, J. N. Mait, M. S. Mirotznik, J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A 15, 1599–1607 (1998).
    [CrossRef]
  14. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999).
  15. M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–825 (1985).
    [CrossRef]
  16. H. Xu, E. J. Bjernfeld, M. Käll, L. Börjesen, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
    [CrossRef]
  17. P. B. Johnson, R. W. Christy, “Optical constants of the Nobel metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]

2002 (2)

2001 (5)

J. Liu, B.-Y. Gu, B.-Z. Dong, G.-Z. Yang, “Interference effect of dual diffractive cylindrical microlenses analyzed by rigorous electromagnetic theory,” J. Opt. Soc. Am. A 18, 526–536 (2001).
[CrossRef]

M. K. Choi, “Numerical calculation of light scattering from a layered sphere by the boundary-element method,” J. Opt. Soc. Am. A 18, 577–583 (2001).
[CrossRef]

J. M. Bendickson, E. Glytsis, T. K. Gaylord, “Focusing diffractive cylindrical mirrors: rigorous evaluation of various design methods,” J. Opt. Soc. Am. A 18, 1487–1494 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon-resonance spectrum of silver nanowires,” Appl. Phys. B 73, 299–304 (2001).
[CrossRef]

M. Scharte, R. Porath, T. Ohms, M. Aeschlimann, J. R. Krenn, H. Ditlbacher, F. R. Aussenegg, A. Liebisch, “Do Mie plasmons have a longer lifetime on resonance than off resonance?” Appl. Phys. B 73, 305–310 (2001).
[CrossRef]

2000 (1)

J. P. Kottmann, O. J. F. Martin, “Accurate solution of the volume integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48, 1719–1726 (2000).
[CrossRef]

1999 (1)

H. Xu, E. J. Bjernfeld, M. Käll, L. Börjesen, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

1998 (1)

1997 (1)

1995 (1)

W. H. Yang, G. C. Schatz, R. P. Van Duyne, “Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitary shape,” J. Chem. Phys. 103, 869–875 (1995).
[CrossRef]

1985 (1)

M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–825 (1985).
[CrossRef]

1972 (1)

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

Aeschlimann, M.

M. Scharte, R. Porath, T. Ohms, M. Aeschlimann, J. R. Krenn, H. Ditlbacher, F. R. Aussenegg, A. Liebisch, “Do Mie plasmons have a longer lifetime on resonance than off resonance?” Appl. Phys. B 73, 305–310 (2001).
[CrossRef]

Aliabadi, M.

L. C. Wrobel, M. Aliabadi, The Boundary Element Method (Wiley, New York, 2002).

Aussenegg, F. R.

M. Scharte, R. Porath, T. Ohms, M. Aeschlimann, J. R. Krenn, H. Ditlbacher, F. R. Aussenegg, A. Liebisch, “Do Mie plasmons have a longer lifetime on resonance than off resonance?” Appl. Phys. B 73, 305–310 (2001).
[CrossRef]

Bendickson, J. M.

Bjernfeld, E. J.

H. Xu, E. J. Bjernfeld, M. Käll, L. Börjesen, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Bohren, C. F.

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

Börjesen, L.

H. Xu, E. J. Bjernfeld, M. Käll, L. Börjesen, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999).

Choi, M. K.

Christy, R. W.

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

Collins, J. P.

Ditlbacher, H.

M. Scharte, R. Porath, T. Ohms, M. Aeschlimann, J. R. Krenn, H. Ditlbacher, F. R. Aussenegg, A. Liebisch, “Do Mie plasmons have a longer lifetime on resonance than off resonance?” Appl. Phys. B 73, 305–310 (2001).
[CrossRef]

Dong, B.-Z.

Erni, D. E.

Gaylord, T. K.

Glytsis, E.

Gu, B.-Y.

Guo, S.

Hafner, C.

Huffmann, D. R.

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

Johnson, P. B.

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

Käll, M.

H. Xu, E. J. Bjernfeld, M. Käll, L. Börjesen, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Kottmann, J. P.

J. P. Kottmann, O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon-resonance spectrum of silver nanowires,” Appl. Phys. B 73, 299–304 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, “Accurate solution of the volume integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48, 1719–1726 (2000).
[CrossRef]

Krenn, J. R.

M. Scharte, R. Porath, T. Ohms, M. Aeschlimann, J. R. Krenn, H. Ditlbacher, F. R. Aussenegg, A. Liebisch, “Do Mie plasmons have a longer lifetime on resonance than off resonance?” Appl. Phys. B 73, 305–310 (2001).
[CrossRef]

Liebisch, A.

M. Scharte, R. Porath, T. Ohms, M. Aeschlimann, J. R. Krenn, H. Ditlbacher, F. R. Aussenegg, A. Liebisch, “Do Mie plasmons have a longer lifetime on resonance than off resonance?” Appl. Phys. B 73, 305–310 (2001).
[CrossRef]

Liu, J.

Mait, J. N.

Martin, O. J. F.

J. P. Kottmann, O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon-resonance spectrum of silver nanowires,” Appl. Phys. B 73, 299–304 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, “Accurate solution of the volume integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48, 1719–1726 (2000).
[CrossRef]

Mirotznik, M. S.

Moreno, E.

Moskovits, M.

M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–825 (1985).
[CrossRef]

Ohms, T.

M. Scharte, R. Porath, T. Ohms, M. Aeschlimann, J. R. Krenn, H. Ditlbacher, F. R. Aussenegg, A. Liebisch, “Do Mie plasmons have a longer lifetime on resonance than off resonance?” Appl. Phys. B 73, 305–310 (2001).
[CrossRef]

Porath, R.

M. Scharte, R. Porath, T. Ohms, M. Aeschlimann, J. R. Krenn, H. Ditlbacher, F. R. Aussenegg, A. Liebisch, “Do Mie plasmons have a longer lifetime on resonance than off resonance?” Appl. Phys. B 73, 305–310 (2001).
[CrossRef]

Prather, D. W.

Ren, H.

Scharte, M.

M. Scharte, R. Porath, T. Ohms, M. Aeschlimann, J. R. Krenn, H. Ditlbacher, F. R. Aussenegg, A. Liebisch, “Do Mie plasmons have a longer lifetime on resonance than off resonance?” Appl. Phys. B 73, 305–310 (2001).
[CrossRef]

Schatz, G. C.

W. H. Yang, G. C. Schatz, R. P. Van Duyne, “Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitary shape,” J. Chem. Phys. 103, 869–875 (1995).
[CrossRef]

Vahldieck, R.

Van Duyne, R. P.

W. H. Yang, G. C. Schatz, R. P. Van Duyne, “Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitary shape,” J. Chem. Phys. 103, 869–875 (1995).
[CrossRef]

Wang, D.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999).

Wrobel, L. C.

L. C. Wrobel, M. Aliabadi, The Boundary Element Method (Wiley, New York, 2002).

Xu, H.

H. Xu, E. J. Bjernfeld, M. Käll, L. Börjesen, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Yang, G.-Z.

Yang, W. H.

W. H. Yang, G. C. Schatz, R. P. Van Duyne, “Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitary shape,” J. Chem. Phys. 103, 869–875 (1995).
[CrossRef]

Yin, S.

Appl. Phys. B (2)

M. Scharte, R. Porath, T. Ohms, M. Aeschlimann, J. R. Krenn, H. Ditlbacher, F. R. Aussenegg, A. Liebisch, “Do Mie plasmons have a longer lifetime on resonance than off resonance?” Appl. Phys. B 73, 305–310 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon-resonance spectrum of silver nanowires,” Appl. Phys. B 73, 299–304 (2001).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

J. P. Kottmann, O. J. F. Martin, “Accurate solution of the volume integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48, 1719–1726 (2000).
[CrossRef]

J. Chem. Phys. (1)

W. H. Yang, G. C. Schatz, R. P. Van Duyne, “Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitary shape,” J. Chem. Phys. 103, 869–875 (1995).
[CrossRef]

J. Opt. Soc. Am. A (6)

Opt. Lett. (1)

Phys. Rev. B (1)

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

Phys. Rev. Lett. (1)

H. Xu, E. J. Bjernfeld, M. Käll, L. Börjesen, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Rev. Mod. Phys. (1)

M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–825 (1985).
[CrossRef]

Other (3)

L. C. Wrobel, M. Aliabadi, The Boundary Element Method (Wiley, New York, 2002).

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999).

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

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Figures (7)

Fig. 1
Fig. 1

SCS of a silver circular cylinder (r=25 nm), assuming a Drude model.

Fig. 2
Fig. 2

Near-field amplitude for the excited plasmons (dipole and quadrupole).

Fig. 3
Fig. 3

SCS of a silver elliptical cylinder (r1=10 nm, r2=20 nm) assuming a Drude model.

Fig. 4
Fig. 4

Near field for various plasmons of a Drude–silver elliptical cylinder (r1=10 nm, r2=20 nm) at different wavelengths and illumination angles.

Fig. 5
Fig. 5

SCS for two coupled silver circular cylinders (r=25 nm) that have a surface separation of d=5 nm, assuming a Drude model.

Fig. 6
Fig. 6

Near-field amplitude after illumination of two coupled silver circular cylinders (r=25 nm, d=5 nm) from above at λ1=303 nm and λ2=209 nm.

Fig. 7
Fig. 7

SCS (divided by two) for two coupled silver circular cylinders (r=25 nm, d=75 nm) compared with that for a single cylinder.

Equations (5)

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

0=2uItot(ρ)+kI2uItot(ρ)for ρI, -f(ρ)=2uOtot(ρ)+kO2uOtot(ρ)for ρO,
0=usc(ρ)+Cusc(ρ) GI(ρ, ρ)nˆI-pIGI(ρ, ρ)vsc(ρ)dl+uinc(ρ)+Cuinc(ρ) GI(ρ, ρ)nˆI-pIGI(ρ, ρ)vinc(ρ)dlfor ρI,0=usc(ρ)+CpOGO(ρ, ρ)vsc(ρ)+usc(ρ) GO(ρ, ρ)nˆOdlfor ρO,
usc(ρ)=Cusc(ρ) GO(ρ,ρ)nˆI-pOGO(ρ, ρ)vsc(ρ)dl.
uminc(ρm)=u0inc(ρm)+nmCunsc(ρn) GO(ρm, ρn)nˆI-pOGO(ρm, ρn)vnsc(ρn)dl,
Ag(ν)=1+iτωp22πν(1-i2πτν),

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