Microwave localization by two-dimensional random scattering

Abstract

WAVEFUNCTIONS of electrons or photons in a strongly scattering random medium may become localized owing to the underlying wave nature of the particles1,2. Particularly surprising and counterintuitive is the prediction that, under appropriate conditions, scatterers placed randomly in space will always produce fully localized states—that is, an energy distribution of the normal modes whose envelope decays exponentially in all directions. In consequence, energy at the resonant frequency of a localized mode, injected into that mode's region of space, cannot diffuse away, but remains trapped until dissipated. Here we report measurements of the electric-field energy density for microwave radiation localized in essentially two-dimensional space by scattering from a random array of dielectric cylinders placed between a pair of parallel conducting plates. We detect regions of high energy density representing the signature of localized modes. The available range of measured variables, scattering materials and cylinder configurations offer the opportunity to provide quantitative answers to important general questions about strong localization. In particular, a better understanding of two-dimensional localization raises the possibility of using localized-mode resonances as a diagnostic tool for situations in which localization phenomenon may occur naturally3—for example, in investigations of the internal distribution of media and defects in geological strata, under-ocean topology or electronic thin films, all of which may exhibit pseudo-two-dimensional characteristics.