Propagation et retournement temporel des ondes dans des guides d'ondes aléatoires.

摘要

This thesis concerns wave propagation and time reversal of waves in randomly perturbed waveguides. The study of wave propagation phenomena in random waveguides is an interesting subject with numerous domains of applications: for instance in telecommunication, underwater acoustics and geophysics. This thesis is composed of three chapters. In a first Chapter, we are interested in wave propagation in inhomogeneous oceanic waveguides, and we derive effective equations which model wave propagation in such media. These equations describe the role of the propagating, radiating, and evanescent modes, and allow us to quantify the radiative loss of energy in the ocean bottom during the propagation. In a second chapter we study pulse propagation and time-reversal refocusing in the perturbed waveguide model introduced in the first chapter. We get a description of the refocused wave which takes into account the radiative loss in the ocean bottom, and the evolution of the random fluctuations of the medium between the two steps of the time-reversal experiment. In a last chapter, we study time-reversal refocusing in a simple waveguide model. In this model we get superresolution phenomena by inserting a random section with low speed of propagation in the vicinity of the source, that is, we get more concentrated focal spots than in the homogeneous waveguides.