Single-layer terahertz metamaterials with bulk optical constants

We investigate the conditions under which single layer metamaterials may be described by bulk optical constants. Terahertz time domain spectroscopy is utilized to investigate two types of geometries, both with two different sizes of embedding dielectric—cubic and tetragonal unit cells. The tetragonal metamaterials are shown to yield layer dependent optical constants, whereas the cubic metamaterials yielded layer independent optical constants. We establish guidelines for when $\epsilon$ and $\mu$ can be used as material parameters for single layer metamaterials. Experimental results at terahertz frequencies are presented and supported by full wave three-dimensional electromagnetic simulations.

Figure 1

Geometry and dimensions of (a) ERR1 and (b) ERR2. Polarization of the incident electromagnetic radiation is shown in (a) for both ERR1 and ERR2. A schematic detailing the stacking of multiple layers is shown in (c), along with the the incident polarization specified. Microscopic photographs of the fabricated samples are shown in (d).

Figure 2

Dependence of the resonant frequencies of ERR1 (blue symbols) and ERR2 (red symbols) (single layer structures) on the embedding substrate thickness.

Figure 3

Experimental and simulated transmission coefficient for type 50 metamaterials. ERR1 is shown in (a) and (c) and ERR2 in (b) and (d).

Figure 4

Experimental and simulated transmission coefficient for type 15 metamaterials. ERR1 is shown in (a) and (c) and ERR2 in (b) and (d).

Figure 5

Experimentally determined dielectric function for type 50 metamaterials for ERR1 (a) and ERR2 (b). Simulated dielectric function for type 50 results for ERR1 are shown in (c) and ERR2 in (d).

Figure 6

Experimentally determined dielectric function for type 15 metamaterials for ERR1 (a) and ERR2 (b). Simulated dielectric function for type 15 results for ERR1 are shown in (c) and ERR2 in (d).