The role of evanescent modes in randomly perturbed single-mode waveguides

Pages: 455 - 472, Volume 8, Issue 2, September 2007

doi:10.3934/dcdsb.2007.8.455       Abstract        Full Text (228.7K)       Related Articles

Josselin Garnier - Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris VII, 2 Place Jussieu, 75251 Paris Cedex 5, France (email)

Abstract: Pulse propagation in randomly perturbed single-mode waveguides is considered. By an asymptotic analysis the pulse front propagation is reduced to an effective equation with diffusion and dispersion. Apart from a random time shift due to a random total travel time, two main phenomena can be distinguished. First, coupling and energy conversion between forward- and backward-propagating modes is responsible for an effective diffusion of the pulse front. This attenuation and spreading is somewhat similar to the one-dimensional case addressed by the O'Doherty-Anstey theory. Second, coupling between the forward-propagating mode and the evanescent modes results in an effective dispersion. In the case of small-scale random fluctuations we show that the second mechanism is dominant.

Keywords:  Acoustic waves, random media, asymptotic theory.
Mathematics Subject Classification:  Primary: 35L05, 35R60; Secondary: 76Q05, 60F15.

Received: October 2006;      Revised: March 2007;      Published: June 2007.