A continuous model for mode mixing in graded-index multimode fibres with random imperfections

This article investigates the evolution of the distribution of propagating modes in a graded-index multimode fibre with random imperfections. These perturbations may be microscopic random bends and ellipticity, or an index of refraction fluctuations, introduced during manufacture. For large-diameter fibres (with respect to a typical electromagnetic wavelength), the number of guided modes becomes large, and so we can regard the discrete set as a continuum in which the mode number is treated as a continuous variable. The theory is applied to the propagation of guided optical modes in round fibres with a parabolic refractive index profile. This continuous model offers the great advantage of elucidating the relevant physical parameters that participate in the mode mixing dynamics, and leads to a numerically tractable problem. Numerical results are presented for the specific problem of random micro-bends, demonstrating that the theoretically predicted behaviour is achieved.