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Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks

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Abstract

Numerical simulations of a near-infrared negative-index metama-terial (NIM) slab consisting of multiple layers of perforated metal-dielectric stacks exhibiting a small imaginary part of the index over the wavelength range for negative refraction are presented. A consistent effective index is obtained using both scattering matrix and modal analysis approaches. Backward phase propagation is verified by calculation of fields inside the metamaterial. The NIM figure of merit, [-Re(n)/Im(n)], for these structures is improved by ~ 10× compared with previous reports, establishing a new approach to thick, low-loss metamaterials at infrared and optical frequencies.

©2006 Optical Society of America

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Figures (7)

Fig. 1.
Fig. 1. Schematic of a metamaterial consisting of multiple unit cells. The geometric parameters are: 801-nm pitch along orthogonal in-plane directions and a linewidth of the metal gratings along the direction of magnetic field of 500 nm and that along the electrical field of 200 nm. The thickness of the air/Au/dielectric/Au/air unit cell is 5/30/60/30/5 nm.
Fig. 2.
Fig. 2. Schematic of forward and backward propagating beams before and after a single unit cell. (2N+1) diffraction orders are kept for both in-plane directions.
Fig. 3.
Fig. 3. The magnitude of the transmission (a), (c) and reflectance (b), (d) for slabs consisting of 1, 2, 5, 6 and 10, 100 and 200 unit cells along the propagation direction.
Fig. 4.
Fig. 4. Refractive index extracted from the complex coefficient of transmission and reflectance for different numbers of unit cells. The unfilled square, triangle, black, red and blue symbols represent the effective index extracted from slabs consisting of 1, 2, 5, 6 and 10 unit cells, respectively.
Fig. 5.
Fig. 5. (a) The effective indices of the two modes with the lowest decay rates. For wavelengths below ~ 2 μm mode 1 has the lowest loss and dominates the response. At longer wavelengths, mode 2 has a lower loss and becomes dominant. (b) The ratio of the real part to the imaginary part of effective index in the negative index region.
Fig. 6.
Fig. 6. (a) Evolution of the phase of the average electric field along the propagation direction across a unit cell. (b), (c) Electric field amplitude and phase plots (λ = 1.7 μm) at the center of the cell (z = 65 nm) across a unit cell in the transverse plane. The white frames represent the location of the open aperture.
Fig. 7.
Fig. 7. The magnitude and phase of the magnetic field for a three-layer structure across one transverse unit cell atthe middle of the structure (indicated by the dashed line) for wavelengths of 1.5, 1.7 and 2.1 μm.

Equations (4)

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E A , i , σ = m , n A mn , i , σ f mn ( x , y ) g imn ( z ) e imn , σ
f mn ( x , y ) = exp [ j ( α m x + β n y ) ] and g imn ( z ) = exp ( j Λ imn z )
[ A mn , 0 , σ B mn , 0 , σ ] = M ̿ [ A mn , l , σ B mn , l , σ ]
n′ = Im [ log ( γ ) ] ( k o d ) and n″ = log ( γ ) ( k o d )
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