Statistics of the Kerr-nonlinearities and linear mode coupling interaction in the few mode fiber optical communications

In this paper we study statistical properties of nonlinear impairments enhancement due to linear mode coupling in few mode optical fibers. Previously we have shown that strong linear mode coupling leads to the enlargement of nonlinear distortions, but in the case of the weak linear mode coupling this phenomenon shows itself in the stochastic manner. Therefore we use simulations based on numerical solving of the generalized coupled nonlinear Schrödinger equations to plot distribution histograms of the difference between rms of nonlinear impairments in the case of presence and in the case of absence of the weak linear mode coupling for different mean lengths of coupling fiber sections, different values of signal power, and modulation formats. Presented results show that distribution plotted for the fundamental mode has higher dispersion than the same one for the first- or second-order modes. In mode division multiplexed systems it means that channel using fundamental mode as a carrier is more affected to nonlinear impairments enhancement than mode channels of higher orders. Nonlinear impairments may sufficiently decrease the effectiveness of linear coupling compensation for all the mode channels.