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SIAM J. APPL. MATH. c 2007 Society for Industrial and Applied Mathematics
Vol. 68, No. 2, pp. 523543
A DIFFUSION ANALYSIS APPROACH TO TE MODE
PROPAGATION IN RANDOMLY PERTURBED OPTICAL
EMMANUEL PERREY-DEBAIN AND I. DAVID ABRAHAMS
Abstract. 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.
Key words. random waveguide, modal diffusion, optical fiber
AMS subject classifications. 78A45, 78A48, 78A50