Time reversal for dispersive waves in random media

Refocusing for time reversed waves propagating in disordered media has recently been observed experimentally and studied mathematically. This surprising effect has many potential applications in domains such as medical imaging, underwater acoustics, and wireless communications. Time refocusing for one-dimensional acoustic waves is now mathematically well understood. In this paper the important case of one-dimensional dispersive waves is addressed. Time reversal is studied in reflection and in transmission. In both cases we derive the self-averaging properties of time reversed refocused pulses. An asymptotic analysis allows us to derive a precise description of the combined effects of randomness and dispersion. In particular, we study an important regime in transmission, where the coherent front wave is destroyed while time reversal of the incoherent transmitted wave still enables refocusing.