On the Probability Density Function of Inter-core Crosstalk Power in Birefringent Homogeneous Multi-core Fibers

Abstract

In this paper, the inter-core crosstalk (ICXT) of the polarization directions and the probability density functions (PDFs) of the ICXT power of the polarization directions in weakly coupled birefringent homogeneous multi-core fibers (MCFs) are studied through numerical simulation. The numerical simulator is based on the coupled local mode theory (CLMT), which is a rigorous model that has the downside of requiring long computational times to compute the ICXT field and PDFs of the ICXT power. Conversely, a dual-polarization discrete changes model (DP-DCM) that allows for much faster estimates of the ICXT field is presented. It is shown that, for perfectly homogeneous MCFs, the mean ICXT power distribution between the polarization directions is similar, despite the power distribution at the MCF input, for a mean linear birefringence parameter ranging from 10−7 (low birefringence) to 10−4 (high birefringence), and for different MCF bending radii. It is also shown that the mean ICXT power estimates obtained with the CLMT and DP-DCM are very similar. Furthermore, using the CLMT, the PDFs of the ICXT power of the polarization directions are shown to be chi-squared distributions with two degrees of freedom, and the PDF of the sum of the ICXT power of the polarizations is shown to follow a chi-squared distribution with four degrees of freedom.