In this work we study the relation between time reversal and wave transport in (mainly 2D) systems with anisotropic disorder. It is shown, in particular, that for relatively short wavelengths which are comparable to the correlation scales of the disorder, the transport properties of random media are essentially different in the directions along and across the correlation ellipse. Fast propagation is predicted in the direction across the structure where the wave is exponentially localized and tunneling of evanescent modes plays a dominant role in typical realizations. Along the structure, where the wave is channeled as in a waveguide, motion of the wave energy is relatively slow. Also, extensive numerical time reversal experiments aimed at studying the resolution in both space focusing and time compression of ultra-wideband signals have been performed. The resolution obtained is shown to depend essentially on both the propagation angle and the aspect ratio of the random structure.
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