Wave propagation retrieval method for metamaterials: Unambiguous restoration of effective parameters

In this Brief report we propose a direct method of effective-parameters restoration that is based on the wave propagation phenomenon. It is easy in implementation, has no unambiguity in retrieving effective properties and is applicable to thick metamaterial (MTM) slabs. The method is validated on the case studies of fishnet, split cube in carcass, and Jerusalem cross MTMs. The constraints of the method are designated.

Figure 1

(Color online) Wave propagation simulation configuration.

Figure 2

(Color online) An example of (a) amplitude and (b) phase of the averaged field distribution over 20 unit cells of the split cube in carcass design for the negative refractive-index regime. Color scales used in both cases for demonstration of the averaged amplitudes and phases are not equivalent.

Figure 3

Possible problematic cases of simulated average amplitude distribution inside the MTM slab: (a) standing-wave formation due to the back interface reflection and slow wave attenuation; (b) large wave attenuation and numerical noise.

Figure 4

(Color online) Refractive index (a) and impedance (b) of the fishnet structure restored with WPRM [red (black)] and SM [green (light gray)]. Real and imaginary parts are marked with solid and dashed lines, respectively. This color and line convention will be respected in all subsequent figures.

Figure 5

(Color online) Split cube in carcass effective parameters: (a) refractive index and (b) impedance.

Figure 6

(Color online) Jerusalem crosses MTM effective parameters: (a) refractive index and (b) impedance.