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 closedform
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 paper, 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.