Numerical Study on Light Localization in Impedance-Matched Meta-Material Random Systems

We investigate the localization properties of light propagating in two-dimensional systems with impedance-matched meta-material scatterers which are randomly positioned. Numerically, the localization length ξ versus the index of meta-material is obtained first. We find that, unlike traditional random systems, the localization length of such meta-material random systems does not depend on the total scattering cross section of scatterers, but on the back-scattering cross-section of scatterers. Furthermore, our analysis shows that there are “back-scattering paths of single scattere” in such meta-material systems, which can cause a strong localization effect. Such back-scattering paths inside single scatterers can be thought of as the supplement to the traditional back-scattering paths of multiple scatterers.