Pulsed signal propagation on a one-dimensional random waveguide—A numerical simulation

Abstract

A numerical simulation of the following experimental scenario is accomplished. A pulse, narrow in space/time, is incident upon a spatially irregular, piecewise-homogeneous transition interval of finite length in an otherwise homogeneous waveguide of unbounded length. The characterization narrow implies an extent that is small when compared to the lengths/transit times for the homogeneous segments. One, of several, result of interest is a demonstration that an ensemble averaged, or mean, field description of this experiment should accommodate two pulsed coherent signals to exit the transition layer. The first signal ‘‘propagates’’ with a velocity that can be identified with an averaged wave speed. This signal decays rapidly with increasing length of the transition interval as a result of scattering, and spreads, in general, due to variation in propagation speed across an ensemble of transition intervals. The genesis of this first pulse is the ‘‘primitive’’ pulse that transmits every interface in the transition interval. The second mean-field pulse propagates with an ‘‘effective,’’ or composite material, wave speed. The genesis of this second pulse are a large number of primitive pulses, all of which have suffered a large number of reflections at the internal interfaces of the transition interval.