SPECKLE STATISTICS IN THE PHOTON LOCALIZATION TRANSITION

We review the statistics of speckle in the Anderson localization transition for classical waves. Probability distributions of local and integrated transmission and of the evolution of the structure of the speckle pattern are related to their corresponding correlation functions. Steady state and pulse transport can be described in terms of modes whose speckle patterns are obtained by decomposing the frequency variation of the transmitted field. At the same time, transmission can be purposefully manipulated by adjusting the incident field and the eigenchannels of the transmission matrix can be found by analyzing sets of speckle patterns for different inputs. The many aspects of steady state propagation are reflected in diverse, but simply related, parameters so that a single localization parameter encapsulates the character of transport on both sides of the divide separating localized from diffusive waves.