Statistical Distributions and Correlations of Modal Dispersion in All Mode-Coupling Regimes

While most prior studies on the statistical properties of modal dispersion (MD) in multiple-mode fibers have been primarily focused on the strong mode-coupling regime, in this paper we investigate the statistics of 1st- and 2nd-order MD across the full range of weak-, intermediate- and strong-coupling regimes. By simulating and analyzing a randomly-perturbed 6-mode fiber, we show that, under proper normalization of the MD quantities, the probability density functions (PDFs) would change significantly with the fiber length$L$in the weak coupling regime, while eventually get steady – i.e., no longer change as$L$further increases – in the strong coupling regime, and the random mode-coupling affects the 2nd-order MD on a considerably larger fiber length scale than that for the 1st-order MD. Furthermore, by calculating the joint bi-variate PDFs, the correlations among the 1st- and 2nd-order MD quantities are analyzed, which reveals that the correlation between the group-delay difference and the frequency variation of the principal modes is much stronger than the correlation between the group-delay difference and its frequency derivative.