New Expression for Evaluating the Mean Crosstalk Power in Weakly-Coupled Multi-Core Fibers

A closed-form expression is proposed for evaluating the mean inter-core crosstalk (ICXT) power in weakly-coupled multi-core fibers (WC-MCFs), with cores' propagation constants perturbed by bending, twist, and random structure fluctuations. This expression generalizes the expression proposed by Koshiba et al. by taking the dependence of the propagation constants on the longitudinal coordinate of the fiber (induced by constant bending and twist along the MCF) into account in a more rigorous way. We provide a physical interpretation of the proposed expression as the convolution of the spectrum of the z-dependent component of the propagation constant induced by the bending and the spectrum of the perturbation induced by the structure fluctuation. The accuracy of the proposed closed-form expression is assessed by comparing simulation results of the coupled-mode equations with the theoretical predictions from the proposed expression. Very good agreement of the mean ICXT power estimates is shown in the whole range of tested bending radius, difference of intrinsic effective refractive indexes of cores, twisting period and correlation length, for fiber lengths longer than one half of the twisting period and five times the correlation length. We show that the proposed expression enables evaluating the mean ICXT power in WC-MCFs with improved accuracy relative to Koshiba's expression: remarkable differences of mean ICXT power, that may exceed 6 dB, can occur between the estimates provided by the Koshiba's expression and the closed-form expression derived in this article, particularly for high correlation length and twisting rate. Differently from the expression proposed by Koshiba et al., the proposed closed-form expression predicts that the twisting period may have a significant influence on the mean ICXT power, in qualitative agreement with experimental results reported by other authors.