"Partial control of information and correlations in scattering media"
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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.