Fluctuation of Gaussian beams propagating through a light-focusing glass fibre

The mean-square fluctuations of log-amplitude and phase are studied theoretically for Gaussian beams propagating through a light-focusing glass fibre having a Gaussian covariance of the refractive-index inhomogeneities. The study is based on a method of the Rytov approximation which has been mainly employed for an analysis of the beam fluctuations in an atmosphere. The results show that the mean-square fluctuations increase proportionally to the propagation distance for gz>1,g andz being the focusing coefficient of a fibre and the actual propagation distance, and also increase monotonically as the beam spot size becomes larger. It is also shown that the fluctuations increase significantly in the radial direction of the beam from the centre and that the on-axis fluctuations of log-amplitude and phase depend greatly on the beam spot size.