Abstract

Ag permittivity (dielectric function) in coupled strips is different from bulk and has been studied for strips of various dimensions and surface roughness. Arrays of such paired strips exhibit the properties of metamagnetics. The surface roughness does not affect the Ag dielectric function, although it does increase the loss at the plasmon resonances of the coupled strips. The size effect in the imaginary part of the dielectric function is significant for both polarizations of light, parallel and perpendicular to the strips with relatively large A-parameter.

© 2008 Optical Society of America

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References

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  1. A. Kawabata and R. Kubo, "Electronic properties of fine metallic particles. II. Plasma resonance absorption," J. Phys. Soc. Jpn. 21, 1765 (1966).
    [CrossRef]
  2. L. P. Gor'kov and G. M. Eliashberg, "Minute metallic particles in an electromagnetic field," Sov. Phys. JETP 21, 940 (1965).
  3. U. Kreibig and M. Vollmer, Optical properties of metal clusters, (Springer-Verlag: Berlin, Heidelberg, 1995).
  4. H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, "Width of cluster plasmon resonances: bulk dielectric functions and chemical interface damping," Phys. Rev. B 48, 18178 (1993).
    [CrossRef]
  5. A. Hilger, M. Tenfelde and U. Kreibig, "Silver nanoparticles deposited on dielectric surfaces," Appl. Phys. B 73, 361 (2001).
    [CrossRef]
  6. B. N. J. Persson, "Surface resistivity and vibrational damping in adsorbed layers," Phys. Rev. B 44, 3277 (1991).
    [CrossRef]
  7. B. N. J. Persson, "Polarizability of small spherical metal particles: influence of the matrix environment," Surface Science 281, 153 (1993).
    [CrossRef]
  8. K. Charlé, F. Frank, and W. Schulze, "The optical properties of silver microcrystallites in dependence on size and the influence of the matrix environment," Ber. Bunsenges. Phys. Chem. 88, 350 (1984).
  9. A. V. Pinchuk, U. Kreibig, and A. Hilger, "Optical properties of metallic nanoparticles: influence of interface effects and interband transitions," Surface Science 557, 269 (2004).
    [CrossRef]
  10. H.-K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, and V. M. Shalaev, "A negative permeability material at red light," Opt. Express 15, 1076 (2007).
    [CrossRef] [PubMed]
  11. W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, "Metamagnetics with rainbow colors," Opt. Express 15, 3333 (2007).
    [CrossRef] [PubMed]
  12. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  13. D. W. Lynch and W. R. Hunter, in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press: New York, 1985).
  14. M. J. Weber, Handbook of optical materials, (CRC: New York, 2003).
  15. W. A. Kraus and G. C. Schatz, "Plasmon resonance broadening in small metal particles," J. Chem. Phys. 79, 6130 (1983).
    [CrossRef]
  16. COMSOL Multiphysics. Command Reference, Comsol AB: Stockholm, Sweden, 2007.

2007 (2)

2004 (1)

A. V. Pinchuk, U. Kreibig, and A. Hilger, "Optical properties of metallic nanoparticles: influence of interface effects and interband transitions," Surface Science 557, 269 (2004).
[CrossRef]

2001 (1)

A. Hilger, M. Tenfelde and U. Kreibig, "Silver nanoparticles deposited on dielectric surfaces," Appl. Phys. B 73, 361 (2001).
[CrossRef]

1993 (2)

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, "Width of cluster plasmon resonances: bulk dielectric functions and chemical interface damping," Phys. Rev. B 48, 18178 (1993).
[CrossRef]

B. N. J. Persson, "Polarizability of small spherical metal particles: influence of the matrix environment," Surface Science 281, 153 (1993).
[CrossRef]

1991 (1)

B. N. J. Persson, "Surface resistivity and vibrational damping in adsorbed layers," Phys. Rev. B 44, 3277 (1991).
[CrossRef]

1984 (1)

K. Charlé, F. Frank, and W. Schulze, "The optical properties of silver microcrystallites in dependence on size and the influence of the matrix environment," Ber. Bunsenges. Phys. Chem. 88, 350 (1984).

1983 (1)

W. A. Kraus and G. C. Schatz, "Plasmon resonance broadening in small metal particles," J. Chem. Phys. 79, 6130 (1983).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370 (1972).
[CrossRef]

1966 (1)

A. Kawabata and R. Kubo, "Electronic properties of fine metallic particles. II. Plasma resonance absorption," J. Phys. Soc. Jpn. 21, 1765 (1966).
[CrossRef]

1965 (1)

L. P. Gor'kov and G. M. Eliashberg, "Minute metallic particles in an electromagnetic field," Sov. Phys. JETP 21, 940 (1965).

Boltasseva, A.

Cai, W.

Charlé, K.

K. Charlé, F. Frank, and W. Schulze, "The optical properties of silver microcrystallites in dependence on size and the influence of the matrix environment," Ber. Bunsenges. Phys. Chem. 88, 350 (1984).

Chettiar, U. K.

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370 (1972).
[CrossRef]

de Silva, V. C.

Drachev, V. P.

Eliashberg, G. M.

L. P. Gor'kov and G. M. Eliashberg, "Minute metallic particles in an electromagnetic field," Sov. Phys. JETP 21, 940 (1965).

Frank, F.

K. Charlé, F. Frank, and W. Schulze, "The optical properties of silver microcrystallites in dependence on size and the influence of the matrix environment," Ber. Bunsenges. Phys. Chem. 88, 350 (1984).

Fritz, S.

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, "Width of cluster plasmon resonances: bulk dielectric functions and chemical interface damping," Phys. Rev. B 48, 18178 (1993).
[CrossRef]

Gor'kov, L. P.

L. P. Gor'kov and G. M. Eliashberg, "Minute metallic particles in an electromagnetic field," Sov. Phys. JETP 21, 940 (1965).

Hilger, A.

A. V. Pinchuk, U. Kreibig, and A. Hilger, "Optical properties of metallic nanoparticles: influence of interface effects and interband transitions," Surface Science 557, 269 (2004).
[CrossRef]

A. Hilger, M. Tenfelde and U. Kreibig, "Silver nanoparticles deposited on dielectric surfaces," Appl. Phys. B 73, 361 (2001).
[CrossRef]

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, "Width of cluster plasmon resonances: bulk dielectric functions and chemical interface damping," Phys. Rev. B 48, 18178 (1993).
[CrossRef]

Hövel, H.

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, "Width of cluster plasmon resonances: bulk dielectric functions and chemical interface damping," Phys. Rev. B 48, 18178 (1993).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Kawabata, A.

A. Kawabata and R. Kubo, "Electronic properties of fine metallic particles. II. Plasma resonance absorption," J. Phys. Soc. Jpn. 21, 1765 (1966).
[CrossRef]

Kildishev, A. V.

Kraus, W. A.

W. A. Kraus and G. C. Schatz, "Plasmon resonance broadening in small metal particles," J. Chem. Phys. 79, 6130 (1983).
[CrossRef]

Kreibig, U.

A. V. Pinchuk, U. Kreibig, and A. Hilger, "Optical properties of metallic nanoparticles: influence of interface effects and interband transitions," Surface Science 557, 269 (2004).
[CrossRef]

A. Hilger, M. Tenfelde and U. Kreibig, "Silver nanoparticles deposited on dielectric surfaces," Appl. Phys. B 73, 361 (2001).
[CrossRef]

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, "Width of cluster plasmon resonances: bulk dielectric functions and chemical interface damping," Phys. Rev. B 48, 18178 (1993).
[CrossRef]

Kubo, R.

A. Kawabata and R. Kubo, "Electronic properties of fine metallic particles. II. Plasma resonance absorption," J. Phys. Soc. Jpn. 21, 1765 (1966).
[CrossRef]

Persson, B. N. J.

B. N. J. Persson, "Polarizability of small spherical metal particles: influence of the matrix environment," Surface Science 281, 153 (1993).
[CrossRef]

B. N. J. Persson, "Surface resistivity and vibrational damping in adsorbed layers," Phys. Rev. B 44, 3277 (1991).
[CrossRef]

Pinchuk, A. V.

A. V. Pinchuk, U. Kreibig, and A. Hilger, "Optical properties of metallic nanoparticles: influence of interface effects and interband transitions," Surface Science 557, 269 (2004).
[CrossRef]

Schatz, G. C.

W. A. Kraus and G. C. Schatz, "Plasmon resonance broadening in small metal particles," J. Chem. Phys. 79, 6130 (1983).
[CrossRef]

Schulze, W.

K. Charlé, F. Frank, and W. Schulze, "The optical properties of silver microcrystallites in dependence on size and the influence of the matrix environment," Ber. Bunsenges. Phys. Chem. 88, 350 (1984).

Shalaev, V. M.

Tenfelde, M.

A. Hilger, M. Tenfelde and U. Kreibig, "Silver nanoparticles deposited on dielectric surfaces," Appl. Phys. B 73, 361 (2001).
[CrossRef]

Vollmer, M.

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, "Width of cluster plasmon resonances: bulk dielectric functions and chemical interface damping," Phys. Rev. B 48, 18178 (1993).
[CrossRef]

Yuan, H.-K.

Appl. Phys. B (1)

A. Hilger, M. Tenfelde and U. Kreibig, "Silver nanoparticles deposited on dielectric surfaces," Appl. Phys. B 73, 361 (2001).
[CrossRef]

Ber. Bunsenges. Phys. Chem. (1)

K. Charlé, F. Frank, and W. Schulze, "The optical properties of silver microcrystallites in dependence on size and the influence of the matrix environment," Ber. Bunsenges. Phys. Chem. 88, 350 (1984).

J. Chem. Phys. (1)

W. A. Kraus and G. C. Schatz, "Plasmon resonance broadening in small metal particles," J. Chem. Phys. 79, 6130 (1983).
[CrossRef]

J. Phys. Soc. Jpn. (1)

A. Kawabata and R. Kubo, "Electronic properties of fine metallic particles. II. Plasma resonance absorption," J. Phys. Soc. Jpn. 21, 1765 (1966).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (3)

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370 (1972).
[CrossRef]

B. N. J. Persson, "Surface resistivity and vibrational damping in adsorbed layers," Phys. Rev. B 44, 3277 (1991).
[CrossRef]

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, "Width of cluster plasmon resonances: bulk dielectric functions and chemical interface damping," Phys. Rev. B 48, 18178 (1993).
[CrossRef]

Sov. Phys. JETP (1)

L. P. Gor'kov and G. M. Eliashberg, "Minute metallic particles in an electromagnetic field," Sov. Phys. JETP 21, 940 (1965).

Surface Science (2)

B. N. J. Persson, "Polarizability of small spherical metal particles: influence of the matrix environment," Surface Science 281, 153 (1993).
[CrossRef]

A. V. Pinchuk, U. Kreibig, and A. Hilger, "Optical properties of metallic nanoparticles: influence of interface effects and interband transitions," Surface Science 557, 269 (2004).
[CrossRef]

Other (4)

COMSOL Multiphysics. Command Reference, Comsol AB: Stockholm, Sweden, 2007.

U. Kreibig and M. Vollmer, Optical properties of metal clusters, (Springer-Verlag: Berlin, Heidelberg, 1995).

D. W. Lynch and W. R. Hunter, in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press: New York, 1985).

M. J. Weber, Handbook of optical materials, (CRC: New York, 2003).

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Figures (6)

Fig. 1.
Fig. 1.

(a) and (b): Real part and imaginary part of the dielectric function of bulk silver from various sources in the literature, J&C [12], L&H [13], and Weber [14]; (c) The same as (b) but only the visible range; (d) Imaginary part of the bulk Ag dielectric function: experiment Ref. [12] (red crosses), Drude-Lorentz approximation (dashed orange line), Drude term (blue solid line).

Fig. 2.
Fig. 2.

Paired strips geometry with different roughness. (a) Ideal structure, δ=0, (b) δ=1.5nm, and (c) δ=2.0nm.

Fig. 3.
Fig. 3.

Example of field emission scanning electron microscope and atomic force microscope images (sample #2).

Fig. 4.
Fig. 4.

TM polarization spectra (a)–(c): (a) simulated (dashed lines) spectra of transmission (blue), reflection (red), and absorption (orange) for one of the samples (sample #4) calculated with different the RMS surface roughness vs. the experimental data (solid lines); (b) simulated effective optical density D obtained for the RMS surface roughness (orange, δ=1.7 nm, purple, δ=2.3 nm, and blue, δ=2.9 nm) vs. the experimental data (red). (c) simulated effective optical density D obtained for the RMS surface roughness (orange, δ=1.7, blue, δ=2.3, and purple, δ=2.9). TE polarization spectra (d): experimental (solid lines) and simulated (dashed lines) spectra of transmission (blue), reflection (red), and effective optical density (orange).

Fig. 5.
Fig. 5.

The experimental spectra of the imaginary part of the Ag dielectric function in the coupled strips for five samples in comparison with the bulk dielectric function from two sources J&C, Ref. [12] and L&H, Ref. [13] for TE (a) and TM (b) polarizations.

Fig. 6.
Fig. 6.

(a) Size dependent term of the relaxation rate (eV) versus the inverse effective width of the strips for TM (blue squares) and TE (red circles) polarizations. (b) the real part of effective permeability vs. the RMS of surface roughness.

Tables (1)

Tables Icon

Table 1. Parameters of the samples.

Equations (5)

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ε m ( ω ) = 1 ω p 2 ω ( ω + i γ ) + 4 π χ ib ,
γ ( R ) = γ + A V F R ,
γ size = 3 2 ( 3 π ) 1 3 V F L x .
ε m ( ω , α , β ) = 1 ω p 2 ω ( ω i α γ ) + f ω L 2 ω L 2 ω 2 + i β Γ L ω ,
γ size = 1.5 V F L x .

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