Mesoscopic phenomena in disordered media

Probability density distribution of Anderson localized modes.

Generally, when radiation is transported through matter, it suffers from dissipation due to the natural absorptive properties of the material. In a scattering medium, some very exotic behaviour can be expected due to the interplay of scattering of waves and their interference. However, the presence of absorption inhibits the observation of this behaviour. So when samples are created such that they are smaller than the absorption length-scales, and yet scattering, then we can see the manifestation of interference. Such small scales are the mesoscopic scales, and the phenomena are called mesoscopic. With light, we have an advantage of designing our media such that absorption length-scales become rather large, and such phenomena become measurable. As examples, conductance fluctuations, coherent backscattering of light, or Anderson localization of light are direct consequences of interference of waves in disorder. Experiments in the lab are aimed to observe these, and similar, mesoscopic effects.

The figure shows calculated intensity distribution of light in a two-dimensional localizing medium. Two localized states are observed, that are spatially separated from each other. The intensity decays exponentially outwards from the maximum. Localization occurs only after a critical disorder in three dimensional systems, while in lower dimensional systems, all states are localized, and the size of the sample determines the probability of observing them.