Preprint A198/2003
Time reversal for dispersive waves in random media
Andre Nachbin | Fouque, Jean-Pierre | Garnier, Josselin
Keywords: dispersive waves | inhomogeneous media | asymptotic theory | time reversal
Refocusing for time reversed waves propagating in disordered media has recently been observed experimentally and studied mathematically. This surprising effect has a great potential of applications in domains such as medical imaging, underwater acoustics, wireless communications among others. 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 reversing the incoherent transmitted wave still enables refocusing.