  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.
