Design of an Artificial Three-Dimensional Composite Metamaterial with Magnetic Resonances in the Visible Range of the Electromagnetic Spectrum

We propose an artificial three-dimensional material that exhibits a strong resonance in the effective permeability in the visible spectral domain. This material may be implemented in a two-step procedure. First, a metamaterial made of densely packed metallic nanoparticles is fabricated that shows a Lorentz-type resonance in the permittivity at the collective plasmon frequency. Second, spheres are formed out of this material and arranged in a cubic lattice. This meta-metamaterial exhibits a strong resonance in the permeability which is caused by a Mie resonance associated with the magnetic mode of a single metamaterial sphere. Realization of this material based on self-organization in liquid crystals and the limitations of the approach are discussed.

Figure 1

Conceptual sketch of the various levels used for constructing a MMM. Noble metals as in (a) are used to form NPs as shown in (b) that support plasmonic resonances. A MM as in (c) made of these NPs shows a strong dispersion in the permittivity. If this MM attains a spherical shape as in (d), strong Mie resonances of the magnetic mode may occur. By ultimately densely packing these spheres in (e), we arrive at a medium with a negative effective permeability in the spectral domain of the Mie resonance.

Figure 2

Transmission or reflection spectrum of (a) MM slab made of densely packed Ag NPs for two different periods of the cubic lattice. The effective material properties of this MM are shown in (b), (c), and (d).

Figure 3

Effective material parameters of a MMM that consists of spheres ($R^{\mathrm{MM}}=22.5\mathrm{nm}$) arranged in a cubic lattice ($a^{\mathrm{MM}}=50\mathrm{nm}$). The material properties of the spheres are those shown in Fig. 2 with a period of $a=6\mathrm{nm}$. Calculations were performed with the KKR method and effective medium theory.

Figure 4

Amplitude of the $y$ component of the $\mathbf{H}$ field in the $x\mathrm{\text{−}}z$ plane at $y=0\mathrm{nm}$ of a MMM sphere. The illuminating plane wave propagates in the $z$ direction and the $\mathbf{E}$- field is $x$ polarized. (a) Mie theory for a single homogenous sphere made of a medium with the effective parameters of the MM consisting of Ag NPs; (b) FDTD calculation for periodically arranged NPs building the same sphere.

Figure 5

Effective permeability of a MMM as a function of the MM sphere’s radius. The MM spheres are arranged in a cubic lattice with $R^{\mathrm{MM}}=0.45a^{\mathrm{MM}}$ and have the effective material properties shown in Fig. 2 ($a=6\mathrm{nm}$).