Frequency correlation and ergodicity of mode-dependent loss and channel capacity in various mode-coupling regimes

Abstract Employing the concatenation rules and a statistical model in the density-matrix formalism, we investigate the frequency diversity of mode-dependent loss (MDL) and channel capacity in multiple-mode fibers from the weak to strong mode-coupling regimes. By in-depth numerical simulation and analysis on a randomly perturbed 6-mode fiber, we show that the frequency correlation of the MDL or channel capacity is qualitatively different in the weak and strong coupling regimes: While in the strong coupling regime the MDL at two different frequencies eventually gets uncorrelated as the separation of the frequencies is sufficiently large, in the weak coupling regime significant residual correlation remains at large frequency separation; the frequency correlation of the channel capacity follows a similar pattern as that of the MDL, only that in the strong coupling regime there also exists a small amount of residual correlation. For the frequency ergodicity, by comparing the probability distributions over the statistical ensemble and the frequency ensemble, we find that the MDL undergoes a crossover from no ergodicity to full ergodicity as the system moves from the weak to strong coupling regimes, while the channel capacity does not come close to full ergodicity in any mode-coupling regimes.