Abstract

A self–consistent model based on the classical field-susceptibilities formalism has been developed to simulate recent experiments where metallic particle chain waveguides are addressed locally by the tip of a Scanning Near-Field Optical Microscope (SNOM) [1]. This approach which accounts for the actual optical response of the particles leads to a reliable description of both near–field transmittances and losses of this kind of integrated devices.

© 2004 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. J. R. Krenn, J. C. Weeber, E. Bourillot, J. P. Goudonnet, B. Schider, A. Leitner, F. R. Aussenegg, and Ch. Girard, ???Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,??? Phys. Rev. Lett. 82, 2590 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  12. C. Girard and X. Bouju, ???Coupled electromagnetic modes between a corrugated surface and a thin probe tip,??? J. Chem. Phys. 95, 2056 (1991).
    [CrossRef]
  13. O. J. F. Martin, C. Girard, and A. Dereux, ???Generalized field propagator for electromagnetic scattering and light confinement,??? Phys. Rev. Lett. 74, 526 (1995).
    [CrossRef] [PubMed]
  14. E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, CA, 1985).
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    [CrossRef]

Europhys Lett.

M. Brun, A. Drezet, H. Mariette, N. Chevalier, J. C. Woehl, and S., ???Remote optical addressing of single nanoobjects,??? Europhys Lett. 64, 634 (2003).
[CrossRef]

J. Chem. Phys.

C. Girard and X. Bouju, ???Coupled electromagnetic modes between a corrugated surface and a thin probe tip,??? J. Chem. Phys. 95, 2056 (1991).
[CrossRef]

J. Opt. Soc. Am. B

Nanotechnology

G. Colas des Francs and C. Girard, ???Coplanar devices for optical addressing of single molecules,??? Nanotechnology 12, 75 (2001).
[CrossRef]

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, ???Surface Plasmon subwavelength optics,??? Nature 424, 824 (2003).
[CrossRef] [PubMed]

Nature Materials

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, ???Local detection of electromagnetic energy transport below the diffraction limit inmetal nanoparticle plasmon waveguides,??? Nature Materials 2, 229 (2003).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. B

S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, ???Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy,??? Phys. Rev. B 65, 193408 (2002).
[CrossRef]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, ???Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,??? Phys. Rev. B 62, R16356 (2000).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, ???Optical pulse propagation in metal nanoparticle chain waveguides,??? Phys. Rev. B 67, 205402 (2003).
[CrossRef]

Phys. Rev. E

C. Girard, A. Dereux and C. Joachim, ???Resonant optical tunnel effect through dielectric structures of subwavelength cross-sections,??? Phys. Rev. E 59 6097 (1999)
[CrossRef]

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, C. Girard and Y. Chen, ???Spatially resolved energy transfer through mesoscopic heterowires,??? Phys. Rev. E 65 036616 (2002).
[CrossRef]

Phys. Rev. Lett.

O. J. F. Martin, C. Girard, and A. Dereux, ???Generalized field propagator for electromagnetic scattering and light confinement,??? Phys. Rev. Lett. 74, 526 (1995).
[CrossRef] [PubMed]

J. R. Krenn, J. C. Weeber, E. Bourillot, J. P. Goudonnet, B. Schider, A. Leitner, F. R. Aussenegg, and Ch. Girard, ???Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,??? Phys. Rev. Lett. 82, 2590 (1999).
[CrossRef]

Other

E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, CA, 1985).

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Figures (3)

Fig. 1.
Fig. 1.

(A) Perspective view of a periodic and linear chain of metal particles optically addressed by the extremity of a SNOM tip. (B) Top view of the cartesian frame we used to perform the numerical simulations. The arrow inside the dashed circle schematizes the SNOM tip dipole and the (OZ) axis is perpendicular to the figure.

Fig. 2.
Fig. 2.

(A–B) Transmittance of metal particle chains computed by increasing the number N of particles. The arrow inside the inset frame schematizes the SNOM tip dipole. (A) The tip dipole is along the longitudinal axis (LM); (B) The tip dipole is perpendicular to the chain (TM). (C) Decay of the near–field intensity at the exit of particle chain wave guides versus the number of gold pads. The intensities computed at the resonance have been normalized with respect to the intensity computed at the exit of a five particles linear chain. (D) same as (B) but with truncated cylinders of same height (40 nm) and 100 nm in diameter.

Fig. 3.
Fig. 3.

Near–field optical images of a gold particle chain wave guide calculated for two different excitation wavelengths (N=17). The SNOM tip is polarized along the OY axis (TM). (A) λ 0=692 nm; (B) λ 0=670 nm.

Equations (14)

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m ( t ) = u m cos ( ω 0 t ) .
𝓔 0 ( r , t ) = 𝓔 0 ( r , ω ) exp ( i ω t ) d ω ,
𝓔 0 ( r , ω 0 ) = S ( r , r tip , ω ) · m ( ω ) ,
S α , β 0 ( r , r tip , ω ) = A α , β exp ( i k 0 R ) ,
A α , β = { k 0 2 R 3 ( R α R β R 2 δ α , β ) + ( 1 R 5 i k 0 R 4 ) ( 3 R α R β R 2 δ α , β ) } ,
𝓔 ( r , t ) = exp ( i ω t ) dt v d r 𝓚 ( r , r , ω ) · 𝓔 0 ( r , ω ) ,
𝓚 ( r , r , ω ) = 𝓘 δ ( r r ) + 𝓢 ( r , r , ω ) · χ ( ω ) ,
𝓢 ( r , r , ω ) = S 0 ( r , r , ω ) + S surf ( r , r , ω )
+ v d r [ S 0 ( r , r , ω ) + S surf ( r , r , ω ) ] · χ ( ω ) · 𝓢 ( r , r , ω ) ,
𝓔 α ( r , t ) = E α ( r , ω 0 ) cos ( ω 0 t + Φ α ( r , ω 0 ) ) ,
E α ( r , ω 0 ) = m { 2 ( v d r 𝓚 α , β ( r , r ω 0 ) S β , γ ( r , r tip , ω 0 ) ) u γ
+ 2 ( v d r 𝓚 α , β ( r , r , ω 0 ) S β , γ ( r , r tip , ω 0 ) ) u γ } 1 2 ,
Φ α ( r , ω 0 ) = arctan { ( v d r 𝓚 α , β ( r , r , ω 0 ) S β , γ ( r , r tip , ω 0 ) u γ ) ( v d r 𝓚 α , β ( r , r , ω 0 ) S β , γ ( r , r tip , ω 0 ) u γ ) } .
Int ( r , ω 0 ) = 1 2 E ( r , ω 0 ) 2 .

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