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Plasmon modes and negative refraction in metal nanowire composites

Viktor A. Podolskiy, Andrey K. Sarychev, and Vladimir M. Shalaev

Open Access Open Access

Abstract

Optical properties of metal nanowires and nanowire composite materials are studied. An incident electromagnetic wave can effectively couple to the propagating surface plasmon polariton (SPP) modes in metal nanowires resulting in very large local fields. The excited SPP modes depend on the structure of nanowires and their orientation with respect to incident radiation. A nanowire percolation composite is shown to have a broadband spectrum of localized plasmon modes. We also show that a composite of nanowires arranged into parallel pairs can act as a left-handed material with the effective magnetic permeability and dielectric permittivity both negative in the visible and near-infrared spectral ranges.

©2003 Optical Society of America

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Figures (9)
Fig. 1.
Fig. 1. A nanowire represented by an array of “intersecting” spheres [8]

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Fig. 2.
Fig. 2. Intensity enhancement distribution around silver nanowire excited by a plane electromagnetic wave [8]. The wavelength of incident light is 540 nm. The angle between the needle and the light wavevector is 30°, the wavevector and vector E of the incident irradiation are in the plane of the figure

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Fig. 3.
Fig. 3. Surface plasmon polariton resonance in a silver nanowire excited by a plane electromagnetic wave [8]. The intensity distribution (top panel) and simulated near-field optical microscope image (bottom panel) are shown. The wavelength of incident light is 540 nm; the angle between the nanowire and the wavevector of the incident light is 30°. The wavevector and E vector of the incident irradiation are in the plane of the figure; the needle length is 480 nm

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Fig. 4.
Fig. 4. Nanowire percolation Ag composite (left) and the field distribution over this composite for the incident wavelength of 550 nm (center) and 750 nm (right). In both figures the case of normal incidence with E‖x is considered [8]

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Fig. 5.
Fig. 5. Two parallel nanowires (a) and a layer of such pairs (b). A composite material based on such nanowire pairs may have the negative refraction index in the optical range [8]

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Fig. 6.
Fig. 6. Numerically simulated dielectric (left panels) and magnetic (right panels) moments for single nanowires (b 1=0.35µm, b 2=0.05µm) (green lines) and their pairs (d=0.15µm) (red lines) compared to the analytical Eqs. (11) (black lines). Magnetic moment of the single nanowire is multiplied by 10. The moments are normalized to the unit volume.

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Fig. 7.
Fig. 7. Dielectric moments for individual nanowires (left) and for nanowire pairs (center) and magnetic moments for nanowire pairs as functions of wavelengths. The nanowire thickness is varied for different plots: b 2=0.035µm (blue), b 2=0.05µm (red), and b 2=0.07µm (green); for all plots, b 1=0.35µm and d=0.23µm. The moments are normalized to the unit volume

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Fig. 8.
Fig. 8. Dielectric (left) and magnetic (right) moments in nanowire pairs as functions of wavelengths. The distance between the nanowires in the pairs is varied: d=0.15µm (red), d=0.23µm(blue), d=0.3µm (green), and d=0.45µm (black)); for all plots, b 1=0.35µm and b 2=0.05µm. The moments are normalized to the unit volume

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Fig. 9.
Fig. 9. Real (colored) and imaginary (black) parts of dielectric (left) and magnetic (right) moments in nanowire pair as functions of wavelengths. The system parameters: d=0.075µm, b 1=0.35µm and b 2=0.025µm. The moments are normalized to the unit volume

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Equations (14)

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d i = α 0 [ E i n c + ∑ j ≠ i N G ̂ ( r i − r j ) d j ] ,
G α β = k 3 [ A ( k r ) δ α β + B ( k r ) r α r β ] ,
A ( x ) = [ x − 1 + i x − 2 − x − 3 ] exp ( i x ) ,
B ( x ) = [ − x − 1 − 3 i x − 2 + 3 x − 3 ] exp ( i x ) ,
α 0 = α L L 1 − i ( 2 k 3 3 ) α L L
α L L = R 3 ∊ − 1 ∊ + 2 ,
a R = ( 4 π 3 ) 1 3 ≈ 1.612
A = e i k R c R [ e − i k 2 ( n · d ) ∫ − b 1 b 1 e − i k 2 ( n · ρ ) j 1 ( ρ ) d ρ + e i k 2 ( n · d ) ∫ − b 1 b 1 e − i k n · ρ j 2 ( ρ ) d ρ ] ,
A = e i k R c R [ ∫ − b 1 b 1 ( j 1 + j 2 ) d ρ − i k 2 ( n · d ) ∫ − b 1 b 1 ( j 1 − j 2 ) d ρ ] .
P = ∫ p ( r ) d r ,
A m q = − i k e i k R R [ [ n × M ] + d 2 c ∫ − b 1 b 2 ( n · ( j 1 − j 2 ) ) d ρ ] ,
M = 1 2 c ∫ [ j ( r ) × r ] d r ,
M = 2 H b 1 3 C 2 ( k d ) 2 tan ⁡ ( g b 1 ) − g b 1 ( g b 1 ) 3
P = 2 3 b 1 b 2 2 f ( Δ ) E ∊ m 1 1 + f ( Δ ) ∊ m ( b 1 b 2 ) 2 ln ⁡ ( 1 + b 1 b 2 ) cos ⁡ Ω ,
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