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The Ag dielectric function in plasmonic metamaterials

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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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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)

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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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