Three-Dimensional Metamaterials with an Ultrahigh Effective Refractive Index over a Broad Bandwidth

The authors introduce a general mechanism, based on electrostatic and magnetostatic considerations, for designing three-dimensional isotropic metamaterials that possess an enhanced refractive index over an extremely large frequency range. The mechanism allows nearly independent control of effective electric permittivity and magnetic permeability without the use of resonant elements.

Figure 1

Electromagnetic responses of metamaterials consisting of a cubic lattice of metallic objects. In all three structures, the outer dimension of the metallic objects is $19a/20$, where $a$ is the lattice constant. In (a)–(c), the top panels show the object and the bottom panels are the corresponding transmission spectra through a slab of such metamaterial with a thickness of $10a$. The dots are from FDTD simulation and the lines are the response of a corresponding uniform medium with an effective $\epsilon$ and $\mu$ indicated. (a) Metallic cube. The left and right insets in the bottom panel show a structure with $3\times 3\times 3$ unit cells, and a transmission spectrum over broader frequency range, respectively. (b) A cube with connected metal plates. (c) Similar to (b), except that each plate now has slits.

Figure 2

Electromagnetic response of metallic objects to externally applied electric and magnetic fields along the $z$-direction. The top panel in (a)–(c) shows the object, the colors indicate the charge distribution when the electric field is applied. The middle panel in (a)–(c) shows the current distribution when the magnetic field is applied. The bottom panels show the distribution and the direction of the total magnetic field on a slice as indicated in the middle panels. Gray lines indicate the boundaries of the metallic region. (a) A metallic cube. (b) Two metallic plates connected by a metal-wire. (c) Similar to (b), except that each plate now has slits.

Figure 3

Numerical results of (a) relative permittivity and (b) relative permeability as a function of $a-b$ in structures similar to Fig. 1c, where $b$ is the outer dimension of the metallic object, and $a$ is the periodicity. The solid line is a theoretical prediction.

Figure 4

Effective index of refraction when the loss of the metal (gold) is considered. The structure is the same as in Fig. 1b. The real part of the index and the ratio of the real and imaginary parts (figure of merit) are shown.