A Diffusion Analysis Approach to TE Mode Propagation in Randomly Perturbed Optical Waveguides

The aim of this work is to model the evolution of the modal distribution of the electromagnetic field as it propagates along a randomly deformed multimode optical waveguide. When the number of guided modes becomes large we can regard the discrete set of modes as a quasi continuum. In some cases, nearest neighbor coupling predominates over other power transfer mechanisms and the coupling process can be ideally described in terms of a diffusion equation. The theory is applied to the propagation of guided transverse electric (TE) field waves in a slab waveguide with parabolic refractive index profile. Numerical simulations are in good agreement with theoretical results, and the error is shown to behave as the inverse of the number of guided modes. The technique allows the prediction of the long-distance modal distribution for a very large number of guided modes within fixed computational resources.