Wave localization in one-dimensional random structures composed of single-negative metamaterials

By using the transfer-matrix method, we study the Anderson localization behavior in one-dimensional random systems composed of two different single-negative (SNG) metamaterials, in which either the permittivity or the permeability is negative. Both nondispersive and dispersive models have been adopted in this study. We find that when both the averaged permittivity and the averaged permeability are negative, or effectively a negative refractive index, the localization behavior in the long-wavelength limit is found to be similar to that of the traditional random systems made of double-positive (DP) materials, i.e., positive permittivity and positive permeability, and can be described by the standard localization theory developed for DP materials, although the wave transport mechanism of such systems is very different from that of DP materials. In the case of a dispersive model, a different localization behavior has been found inside a gap created around a particular frequency at which the sum of the impedances of the two SNG metamaterials vanishes. For example, the frequency dependence of the localization length can exhibit a sharp peak inside the gap, and the localization length is found to be smaller than the decay length of the corresponding periodic structure. The latter is opposite to the well-known localization behavior found in DP materials, where the localization length is, in general, larger than the decay length. Various wave propagation properties associated with this gap have been obtained. Some analytical results based on transfer matrices and long-wavelength limit description have been used to explain the simulation results.