Effect of a magnetic field on polarisation of light in an optical fibre with a random distribution of linear birefringence

A numerical model is proposed to describe the evolution of polarisation of a light wave propagating through a telecommunication fibre with random linear birefringence in a magnetic field. As a result of statistical processing of a set of numerical simulation results, a convenient phenomenological formula is obtained for the first time for the dependence of the average value of the polarisation rotation angle on the magnetic field, the fibre parameters and its length. It is found that the average value of the polarisation rotation angle in a long telecommunication fibre in the representation of the Stokes vectors linearly depends on the applied longitudinal magnetic field (as in the classical Faraday effect for an isotropic medium) but is proportional to the root of the fibre length. It is theoretically shown and experimentally confirmed that the polarisation rotation angle for an extended segment of a telecommunication fibre (50 km) is two orders of magnitude less than that for an isotropic fibre of the same length and material.