Abstract

We present a 2D plasmon waveguide in the form of rows of silver nanorods in hexagonal lattice, that may be used for creating a medium with novel effective electromagnetic properties. Transport of energy due to surface plasmon coupling is investigated with Finite Difference Time Domain method for visible range wavelengths from 400 to 750 nm. For 500 to 750 nm range two-mode nature of the waveguide is shown in simulations. Attenuation factors and group velocities are calculated for transmitted modes.

© 2005 Optical Society of America

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References

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Appl. Phys. Lett.

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidj, A. Leitner, F. R. Aussenegg, and J. C. Weeber, �??Surface plasmon propagation in microscale metal stripes,�?? Appl. Phys. Lett. 79, 51�??53 (2001).
[CrossRef]

T. Yatsui, M. Kourogi, and M. Ohtsu , �??Plasmon waveguide for optical far/near-field conversion,�?? Appl. Phys. Lett. 79, 4583�??4585 (2001).
[CrossRef]

J. Microscopy

F. I. Baida, D. Van Labeke, Y. Pagani, B. Guizal, and M. Al Naboulsi, �??Waveguiding through a two-dimensional metallic photonic crystal,�?? J. Microscopy 213, 144�??148 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Nature

W. L. Barnes, A. Dereux and T. W. Ebbesen, �??Surface plasmon subwavelength optics,�?? Nature 424, 824 �??830 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Optics Letters

D. F. P. Pile, D. K. Gramotnev, �??Channel plasmon-polariton in a triangular groove on a metal surface,�?? Optics Letters 29, 1069�??1071 (2004).
[CrossRef] [PubMed]

Phys. Rev. B

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�??R16359 (2000).
[CrossRef]

G. Shvets, �??Photonic approach to making a material with a negative index of refraction,�?? Phys. Rev. B 67, 035109 (2003).
[CrossRef]

M. Notomi, �??Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,�?? Phys. Rev. B 62, 10, 696 (2000).
[CrossRef]

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn and J. P. Goudonnet, �??Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,�?? Phys. Rev. B 60, 9061�?? 9068 (1999).
[CrossRef]

P. Johnson and R. Christy, �??Optical Constants of the Noble Metals,�?? Phys. Rev. B 6, 4370�??4379 (1972).
[CrossRef]

C. T. Chan, Q. L. Yu, and K. M. Ho, �??Order-N spectral method for electromagnetic waves,�?? Phys. Rev. B 51, 16635�??16642 (1995).
[CrossRef]

Phys. Rev. Lett.

J. T. Shen, P. B. Catrysse, and S. Fan, �??Mechanism for Designing Metallic Metamaterials with a High Index of Refraction,�?? Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef] [PubMed]

Other

H. Raether, Surface Plasmons (Springer, Berlin 1988).

C. Sönnichsen, Plasmons in metal nanostructures, PhD Thesis (Ludwig-Maximilians-Universtät München, München, 2001).

S. A. Maier , Guiding of electromagnetic energy in subwavelength periodic metal structures, PhD Thesis, (California Institut of Technology, Pasadena 2003).

A.Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, MA 2000).

W. M. Saj, Application of Finite Difference Time Domain Method to Modeling of Photonic Crystal Fibers, Msc Thesis (in Polish) (Warsaw University, Warsaw 2003).

Supplementary Material (4)

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Figures (12)

Fig. 1.
Fig. 1.

Real (left) and imaginary parts (right) of the dielectric function of silver: experimental results [20] and the best fit curves for the wavelength range 0.188–1.9 µm obtained using Drude model with parameters ε∞=3.70, ωp=13673 THz and Γ=27.35 THz [5].

Fig. 2.
Fig. 2.

Computation area (a) was used to analyze modes and (b) was used to simulate propagation.

Fig. 3.
Fig. 3.

(a) Mode dispersion curves plotted on frequency values calculated using FDTD for assumed wavenumbers in the z direction. (b) Intensity distributions for modes pointed with arrows on the dispersion diagram. Pseudocolors are separately normalized to maximum values.

Fig. 4.
Fig. 4.

Intensity distributions in the waveguide with Gaussian (left) and Hermite-Gaussian (right) incident beams at 600 nm wavelength. Intensities are obtained as Poynting vector lengths averaged over 5 periods of the source.

Fig. 5.
Fig. 5.

Cross-sections of intensity distribution in the waveguide with Gaussian (left column) and Hermite-Gaussian (right column) incident beams at 600 nm wavelength. Intensities are calculated at distances z=3130, 3300 and 4000 nm from the input plane.

Fig. 6.
Fig. 6.

Magnetic field component Hy of the propagating beam (left, 1.35 MB). Flow of energy in the waveguide (right, 1.56 MB). Both animations are made for Gaussian beam illumination at 600 nm wavelength for the region 1000 nm≤z≤3000 nm and 750 nm≤x≤1750 nm.

Fig. 7.
Fig. 7.

Magnetic field component Hy of the propagating beam (left, 1.82 MB). Flow of energy in the waveguide (right, 2.45 MB). Both animations are made for Hermite-Gaussian beam illumination at 600 nm wavelength for the region 1000 nm ≤z≤3000 nm and 750 nm≤x≤ 1750 nm.

Fig. 8.
Fig. 8.

Intensity profile for off-axis illumination of the waveguide. The shift of the source is 250 nm and illumination wavelength is 600 nm.

Fig. 9.
Fig. 9.

Positions of chosen single maximum values of Poynting vectors for Gaussian (left) and Hermite-Gaussian (right) fields. Linear fits give values of group velocities calculated for 600 nm wavelength incident beam.

Fig. 10.
Fig. 10.

Plots of propagating energy for Gaussian (left) and Hermite-Gaussian (right) illuminating beams calculated for different wavelengths. Each point corresponds to integration along the x axis of the intensity (Poynting vector length averaged in time).

Fig. 11.
Fig. 11.

Attenuation factors calculated for both types of illumination and various wavelengths. Results are obtained from comparison of energy at input (z=0 nm) and output (z=4000 nm) planes.

Fig. 12.
Fig. 12.

Space frequencies of symmetric and antisymmetric fields that propagate in the waveguide and their corresponding time frequencies. Green line indicates the edge of BZ.

Equations (1)

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ε ( ω ) = ε ω p 2 [ ω ( ω + i Γ ) ] 1 .

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