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The origin of magnetic polarizability in metamaterials at optical frequencies - an electrodynamic approach

Carsten Rockstuhl, Thomas Zentgraf, Ekaterina Pshenay-Severin, Jörg Petschulat, Arkadi Chipouline, Jürgen Kuhl, Thomas Pertsch, Harald Giessen, and Falk Lederer

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Abstract

We explain the origin of the electric and particular the magnetic polarizabiltiy of metamaterials employing a fully electromagnetic plasmonic picture. As example we study an U-shaped split-ring resonator based metamaterial at optical frequencies. The relevance of the split-ring resonator orientation relative to the illuminating field for obtaining a strong magnetic response is outlined. We reveal higher-order magnetic resonances and explain their origin on the basis of higher-order plasmonic eigenmodes caused by an appropriate current flow in the split-ring resonator. Finally, the conditions required for obtaining a negative index at optical frequencies in a metamaterial consisting of split-ring resonators and wires are investigated.

©2007 Optical Society of America

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Figures (7)
Fig. 1.
Fig. 1. Spectral response (R-reflectance, T -transmittance) of an array of SRRs as described in the text for an electric field polarization parallel (a) and perpendicular to the gap (c). The corresponding excitation geometry is schematically shown in (b) and (d), respectively. The geometrical details of a single SRR are shown in (e).

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Fig. 2.
Fig. 2. (a) Transmittance and reflectance for the two cases shown in (b). Retrieved effective refractive index (b), effective permittivity (c), and effective permeability (d) for the two possible orientations of the SRR at parallel incidence and an electric field polarized parallel to the gap. The geometry of the two configurations is shown on top of the figure.

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Fig. 3.
Fig. 3. (a) Transmittance and reflectance for the geometry shown in (b). Retrieved effective permittivity (c) and effective permeability (d) for the orientation of the SRR at parallel incidence and an electric field polarized perpendicularly to the gap.

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Fig. 4.
Fig. 4. Amplitude of the electric field component perpendicularly to the SRR surface at the three different resonance frequencies indicated in the figures. The illuminating plane wave is x -polarized and propagates in the positive z-direction. The arrows indicate the direction of current flow in the structure. Please note that this represents a snapshot. The direction will reverse with the frequency of the illumination. The direction of the currents flowing in the SRR was deduced from the FDTD simulations.

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Fig. 5.
Fig. 5. Diffraction efficiencies and retrieved effective material parameters for a medium made of SRRs (blue solid line), of thin metallic wires (red dashed line), and a combination of both (green dashed-dotted line). (a) shows the transmitted and (b) the reflected diffraction efficiency. In (c, d) the effective permittivities and in (e,f) the effective permeabilities are shown, respectively. The corresponding effective refractive indices for these values are shown in (g, h).

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Fig. 6.
Fig. 6. Transmission (a), real part of the effective permittivity (b), the permeability (c), and the refractive index (d) for a medium comprising SRRs and metallic wires as a function of the height h of the wires.

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Fig. 7.
Fig. 7. Real part of the effective refractive index if the SRR and the wire with a height of h = 80 nm in different dielectric environments. The blue solid curve shows the structure completely surrounded by air. The green dashed curve shows the structure as deposited on a substrate with n = 1.5. The red solid-dashed curve shows the real part of the effective refractive index if the background medium in the unit cell is a dielectric medium with n = 1.5 instead of air but the unit cell itself is yet surrounded by air. Finally the black dotted solid curve shows the effective index if this structure is finally deposited on a substrate. The latter structure is the structure which is technological feasible to fabricate.

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