Propagation of radiation in diffusive media: modes, channels, localization

Fluctuations of parameters that are ubiquitous in any real medium have pronounced, sometimes determining effect on the transport of wave radiation and quantum particles. Commonly encountered in nature is the diffusive regime, which has been extensively investigated for a long time, and nowadays is deemed to be well understood. Theoretically, it is usually studied in the framework of diffusion equations, which have proven to be quite efficient in explaining a wide variety of phenomena and experimental results in optics, acoustics, solid state physics, astronomy, biology, financial mathematics, etc. However, the issue with those equations is that they typically deal with ensemble-averaged quantities, which often have a little to do with the observations at a single random realization. Recently, it was discovered that, contrary to the common longstanding belief, the intensity of radiation propagating in a diffusive medium is not always homogeneously distributed. Under certain conditions, it is significantly structured: localized in the transverse direction in relatively narrow separated transmission channels, which are stretched along the sample and transmit the energy almost without leakage. The transmission coefficients and the incident and outgoing waveforms of these channels are given by the singular value decomposition of the transmission matrix, which connects the normal modes at the input to those at the output of a random sample. The unique physical properties of transmission channels open up new avenues for controlling the energy transmission and distribution inside a random medium, and for using it as a useful optical element. In my talk, a brief history and the current state of art in studying of the wave transport in diffusive media will be presented.