"Partial control of information and correlations in scattering media"

Random matrix theory as well as microscopic theory predict that the transmission eigenvalues of a disordered dielectric material have, in the diffusive regime, a bimodal distribution peaked around 0 and 1 that gives rise to the concept of closed and open eigenchannels. However, in a typical optical experiment where only a small fraction of the channels are excited or measured, the distribution of the transmission eigenvalues is not the bimodal but the Marchenko-Pastur law. We propose an analytical theory that quantitatively describes the transition between these two distributions. In particular, we show that the reduction of the number of controlled input/output channels abruptly suppresses the open eigenchannels and then gradually yields to an effective loss of the correlations contained in the scattering matrix. This effect is illustrated with the study of the information capacity of a disordered waveguide. Finally, we show how the abrupt loss of the open eigenchannels can dramatically reduce the effect of coherent enhancement of absorption.