Abstract:
Measurements of microwave and optical transmission though random media in the crossover to Anderson localization will be described from two different but complete perspectives: Quasi-normal modes (modes) of excitation within the medium and eigenchannels of the transmission matrix (channels). Because modes do not mix as they decay, they afford a natural framework for describing transmission in the time domain and near-threshold lasing from localized states. At the same time, since the sum of eigenvalues of orthogonal channels is equal to the transmittance or “optical” conductance, they are useful in understanding the statistics of steady-state transmission for a single incident channel, “optical” conductance, and focusing in single samples and in random ensembles. We determine the individual eigenvalues of the transmission matrix and achieve nearly complete transmission in ordinarily opaque diffusive samples. The change in the statistics of the transmittance in the Anderson transition is shown to emerge from the joint distribution of the transmission eigenvalues and the transmittance. We demonstrate the power of the Coulomb model that associates transmission eigenvalues with the positions of charges and their images in this model. The relationship between the mode and channel descriptions will be seen in the determination of the density of states in random samples using these approaches.

In collaboration with Zhou Shi, Jing Wang and Matthieu Davy