Abstract

Rectangular gold and silver nano-strips embedded in glass or water are considered as optical resonators. Their scattering cross section and field enhancements in the case of p-polarized plane-wave illumination are analyzed using a surface integral equation method. Peaks in the scattering spectra are shown to be related to the resonant excitation of forward and backward travelling short-range surface plasmon polaritons in thin metal strips. The influence of angle of incidence and strip thickness on resonances is investigated. Finally, we consider the possibility of obtaining large local fields in a narrow (5nm) gap between two metal strips by taking advantage of the plasmon field distribution and boundary conditions, demonstrating the feasibility of at least 10-fold field magnitude enhancement.

© 2007 Optical Society of America

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  1. K. Imura, T. Nagahara, and H. Okamoto, "Near-field imaging of plasmon modes in gold nanorods," J. Chem. Phys. 122, 154701 (2005).
    [CrossRef] [PubMed]
  2. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, R. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators," Phys. Rev. Lett. 95, 257403 (2005).
    [CrossRef] [PubMed]
  3. T. Laroche and C. Girard, "Near-field optical properties of single plasmonic nanowires," Appl. Phys. Lett. 89, 233119 (2006).
    [CrossRef]
  4. F. Neubrech et al., "Resonances in individual metal nanowires in the infrared," Appl. Phys. Lett. 89, 253104 (2006).
    [CrossRef]
  5. H. Räther, Surface Plasmons (Springer, 1988).
  6. E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
    [CrossRef]
  7. J. K. S. Poon, L. Zhu, G. A. De Rose, and A. Yariv, "Transmission and group delay of microring coupled-resonator optical waveguides," Opt. Lett. 31, 456-458 (2006).
    [CrossRef] [PubMed]
  8. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  9. D. W. Prather, M. S. Mirotznik, and J. N. Mait, "Boundary integral methods applied to the analysis of diffractive optical elements," J. Opt. Soc. Am. A 14, 34-43 (1997).
    [CrossRef]
  10. G. Schider et al., "Plasmon dispersion relation of Au and Ag nanowires," Phys. Rev. B 68, 155427 (2003).
    [CrossRef]
  11. T. Søndergaard and S. I. Bozhevolnyi, "Slow-plasmon resonant nanostructures: scattering and field enhancements," Phys. Rev. B. 75, 073402 (2007).
    [CrossRef]
  12. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
    [CrossRef] [PubMed]

2007 (1)

T. Søndergaard and S. I. Bozhevolnyi, "Slow-plasmon resonant nanostructures: scattering and field enhancements," Phys. Rev. B. 75, 073402 (2007).
[CrossRef]

2006 (3)

T. Laroche and C. Girard, "Near-field optical properties of single plasmonic nanowires," Appl. Phys. Lett. 89, 233119 (2006).
[CrossRef]

F. Neubrech et al., "Resonances in individual metal nanowires in the infrared," Appl. Phys. Lett. 89, 253104 (2006).
[CrossRef]

J. K. S. Poon, L. Zhu, G. A. De Rose, and A. Yariv, "Transmission and group delay of microring coupled-resonator optical waveguides," Opt. Lett. 31, 456-458 (2006).
[CrossRef] [PubMed]

2005 (3)

K. Imura, T. Nagahara, and H. Okamoto, "Near-field imaging of plasmon modes in gold nanorods," J. Chem. Phys. 122, 154701 (2005).
[CrossRef] [PubMed]

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, R. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators," Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

2003 (1)

G. Schider et al., "Plasmon dispersion relation of Au and Ag nanowires," Phys. Rev. B 68, 155427 (2003).
[CrossRef]

1997 (1)

1972 (1)

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

1969 (1)

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Aussenegg, R. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, R. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators," Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

T. Søndergaard and S. I. Bozhevolnyi, "Slow-plasmon resonant nanostructures: scattering and field enhancements," Phys. Rev. B. 75, 073402 (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 Rose, G. A.

Ditlbacher, H.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, R. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators," Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Economou, E. N.

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Eisler, H.-J.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Girard, C.

T. Laroche and C. Girard, "Near-field optical properties of single plasmonic nanowires," Appl. Phys. Lett. 89, 233119 (2006).
[CrossRef]

Hecht, B.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Hofer, F.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, R. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators," Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Hohenau, A.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, R. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators," Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Imura, K.

K. Imura, T. Nagahara, and H. Okamoto, "Near-field imaging of plasmon modes in gold nanorods," J. Chem. Phys. 122, 154701 (2005).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Kreibig, U.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, R. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators," Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Krenn, J. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, R. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators," Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Laroche, T.

T. Laroche and C. Girard, "Near-field optical properties of single plasmonic nanowires," Appl. Phys. Lett. 89, 233119 (2006).
[CrossRef]

Mait, J. N.

Martin, O. J. F.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Mirotznik, M. S.

Mühlschlegel, P.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Nagahara, T.

K. Imura, T. Nagahara, and H. Okamoto, "Near-field imaging of plasmon modes in gold nanorods," J. Chem. Phys. 122, 154701 (2005).
[CrossRef] [PubMed]

Neubrech, F.

F. Neubrech et al., "Resonances in individual metal nanowires in the infrared," Appl. Phys. Lett. 89, 253104 (2006).
[CrossRef]

Okamoto, H.

K. Imura, T. Nagahara, and H. Okamoto, "Near-field imaging of plasmon modes in gold nanorods," J. Chem. Phys. 122, 154701 (2005).
[CrossRef] [PubMed]

Pohl, D. W.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Poon, J. K. S.

Prather, D. W.

Rogers, M.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, R. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators," Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Schider, G.

G. Schider et al., "Plasmon dispersion relation of Au and Ag nanowires," Phys. Rev. B 68, 155427 (2003).
[CrossRef]

Søndergaard, T.

T. Søndergaard and S. I. Bozhevolnyi, "Slow-plasmon resonant nanostructures: scattering and field enhancements," Phys. Rev. B. 75, 073402 (2007).
[CrossRef]

Wagner, D.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, R. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators," Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Yariv, A.

Zhu, L.

Appl. Phys. Lett. (2)

T. Laroche and C. Girard, "Near-field optical properties of single plasmonic nanowires," Appl. Phys. Lett. 89, 233119 (2006).
[CrossRef]

F. Neubrech et al., "Resonances in individual metal nanowires in the infrared," Appl. Phys. Lett. 89, 253104 (2006).
[CrossRef]

J. Chem. Phys. (1)

K. Imura, T. Nagahara, and H. Okamoto, "Near-field imaging of plasmon modes in gold nanorods," J. Chem. Phys. 122, 154701 (2005).
[CrossRef] [PubMed]

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

Opt. Lett. (1)

Phys. Rev. (1)

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Phys. Rev. B (2)

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

G. Schider et al., "Plasmon dispersion relation of Au and Ag nanowires," Phys. Rev. B 68, 155427 (2003).
[CrossRef]

Phys. Rev. B. (1)

T. Søndergaard and S. I. Bozhevolnyi, "Slow-plasmon resonant nanostructures: scattering and field enhancements," Phys. Rev. B. 75, 073402 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, R. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators," Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Science (1)

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Other (1)

H. Räther, Surface Plasmons (Springer, 1988).

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Figures (6)

Fig. 1.
Fig. 1.

(a). Normalized scattering cross section vs wavelength for 10-nm-thin silver strips of widths w embedded in glass or water. The angle of incidence is θ=45° with respect to the x-axis. (b). Electric field magnitude along the centre line of the silver strip in water at resonance for the widths w=96nm (λ=672nm, θ=90°), w=244nm (λ=680nm, θ=41°) and w=392nm (λ=684nm, θ=90°).

Fig. 2.
Fig. 2.

Normalized scattering cross section vs wavelength for 10-nm-thin gold strips of widths w embedded in glass or water. The angle of incidence is θ=45° with respect to the x-axis. (b) Electric field magnitude along the centre line of the gold strip in water at resonance for the widths w=75nm (λ=684nm, θ=90°), w=194nm (λ=688nm, θ=41°) and w=313nm (λ=688nm, (θ=90°).

Fig. 3.
Fig. 3.

Normalized scattering cross section vs angle of incidence θ of the plane wave with respect to the x-axis for 10nm-high gold or silver strips. The strip widths correspond to the 1st or 2nd-order resonances for standing SR-SPP waves.

Fig. 4.
Fig. 4.

Normalized scattering cross section vs wavelength for metal strips made of (a) silver and (b) gold of different thickness h and widths w.

Fig. 5.
Fig. 5.

(a). Normalized scattering cross section vs wavelength for a structure consisting of two 10-nm-thick silver (Ag) or gold (Au) strips of widths w separated by the distance δ. (b). The corresponding field magnitude distributions (marked with the same colours) along the strip centre line at resonance.

Fig. 6.
Fig. 6.

Field magnitude distributions for 10-nm-thin silver strips embedded in water for the angle of incidence θ=90°. (a) Single strip with w=96nm, λ=672nm and (b) two strips with w=48nm separated by a 5-nm-wide gap, λ=580nm.

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