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September  2007, 8(2): 455-472. doi: 10.3934/dcdsb.2007.8.455

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

Josselin Garnier 1,

1. 

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

Received  October 2006 Revised  March 2007 Published  June 2007

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, 60F1.
Citation: Josselin Garnier. The role of evanescent modes in randomly perturbed single-mode waveguides. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 455-472. doi: 10.3934/dcdsb.2007.8.455
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