The statistics of polarization-dependent loss in a recirculating loop

In this paper, we study the statistical distribution of the accumulated polarization-dependent loss (PDL) in a recirculating loop. The distribution is studied both via numerical simulations and with analytical theory and very good agreement is found between the two. In addition, we have experimentally obtained the probability density distribution for the PDL and, even in this case, we find good agreement with the predicted one. The mean accumulated PDL is found to grow linearly with the number of circulations N in contraposition to a straight-line system. Moreover, the statistical distribution tends to become uniformly distributed as N is increasing. Finally, the statistics of the PDL for a recirculating loop, when considering small values of PDL, is found to be equal to the statistics of the differential group delay for recirculating loops.