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Applied Math Seminar
Pulse propagation and time reversal in random waveguides
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We consider pulse propagation in a random waveguide and we perform an asymptotic analysis based on separation of scales, when the propagation distance is large compared to the size of the random inhomogeneities, which have small variance. We derive an asymptotic deterministic system of time-frequency transport equations for the mode amplitudes and we quantify the effective pulse spreading. We next analyze time-reversal in a random waveguide. We show that randomness enhances spatial refocusing and that diffraction-limited focal spots can be obtained even with small-size time reversal mirrors. However, statistical stability for narrowband refocused fields is achieved only for large-size time reversal mirrors. The mechanisms responsible for statistically stable refocusing in a random waveguide are clarified. |