Impact of Longitudinal Variation of the Coupling Coefficient Due to Bending and Twisting on Inter-Core Crosstalk in Weakly-Coupled MCFs

Abstract

A novel analytical discrete changes model (DCM) of inter-core crosstalk (ICXT) in weakly-coupled multi-core fibers (MCFs) that considers the inter-core coupling coefficient (ICCC) variation, induced by bending and twisting effects along the longitudinal direction of propagation, is proposed. An approximated closed-form expression of the ICCC is proposed for step-index MCFs and validated by comparison with the rigorous ICCC expression, solved numerically. The linearization of the ICCC, in a logarithmic scale, around the intrinsic ICCC, is proposed to simplify the derivation of the novel analytical DCM. The novel DCM is validated by comparison of the mean ICXT power estimates obtained analytically, which are very quick to estimate, with the ones obtained by solving the coupled-mode equations numerically, which are much more computationally demanding. It is shown that, in the range of tested MCF parameters, the proposed model allows for an improvement of the mean ICXT power estimates reaching 4.5 dB, compared to the estimates obtained without considering the longitudinal variation of the ICCC, depending on the fiber parameters. The improvement of the mean ICXT power estimates was assessed for MCFs between 100 m and 10 km long, core pitches between 30 $\mu$ m and 50 $\mu$ m, and normalized difference between the refractive index of the cores between $-0.028\%$ and $0.028\%$ , typical of weakly-coupled real homogeneous MCFs. The largest improvements of mean ICXT power estimates tend to occur for larger core pitches and for larger differences between the refractive index of the cores. Accurate mean ICXT power estimates obtained with the novel DCM for MCFs with typical fiber birefringence parameters are also reported.