Statistics of 3rd-order modal dispersion in mode-division multiplexing optical communication systems

Based on the group-delay matrix and its frequency derivatives, we study the statistics of modal dispersion (MD) up to 3rd order in randomly perturbed fibers. Particularly, we numerically simulate and analyze the statistical properties of quantities that characterize various aspects of the MD in a randomly perturbed six-mode fiber of sufficiently large length <i>L</i>. The results show that, under proper normalization by the group-delay difference, the probability density functions (PDFs) of all 1st-, 2nd-, and 3rd-order MD are essentially independent of <i>L</i>. Furthermore, we find that the 2nd-order and 3rd-order MD effects become significant at roughly the same signal spectral width, and the frequency variation of the principal modes dominates over that of the group delays in both the 2nd- and 3rd-order MD. The correlations among MD of different orders are also investigated by simulating the bivariate joint PDFs of relevant quantities.