Communications in Mathematical Sciences

Volume 18 (2020)

Number 4

Intensity fluctuations in random waveguides

Pages: 947 – 971



Josselin Garnier (Centre de Mathématiques Appliquées (CMAP), CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France)


An asymptotic analysis of wave propagation in randomly perturbed waveguides is carried out in order to identify the effective Markovian dynamics of the guided mode powers. The main result consists in a quantification of the fluctuations of the mode powers and wave intensities that increase exponentially with the propagation distance. The exponential growth rate is studied in detail so as to determine its dependence with respect to the waveguide geometry, the statistics of the random perturbations, and the operating wavelength.


waveguide, wave propagation in random media, diffusion approximation

2010 Mathematics Subject Classification

35L05, 35Q60, 35Q99, 35R60, 60F05

Received 16 June 2019

Accepted 2 January 2020

Published 28 July 2020