Analytical Expression of Average Power-Coupling Coefficients for Estimating Intercore Crosstalk in Multicore Fibers

Abstract

In order to realize fast and accurate estimation of intercore crosstalk in bent multicore fibers (MCFs), an analytical expression of the average power-coupling coefficient (PCC) based on an exponential autocorrelation function is, for the first time, derived, resulting in no need for heavy numerical computations. It is revealed that, when the bending radius is large and the correlation length is large, the average PCC is inversely proportional to the correlation length and to the square of the propagation constant difference Δβ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mn</sub> between core m and core n, and when the bending radius is small and the correlation length is large, the average PCC is proportional to the bending radius and is independent of the correlation length. When the correlation length is small, on the other hand, the average PCC is proportional to the correlation length and is independent of the bending radius. For homogeneous MCFs (Δβ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mn</sub> = 0) with small bending radius, the average PCC coincides with the mean crosstalk increase per unit length derived from the coupled-mode theory of Hayashi et al. that is proportional to the bending radius. Average crosstalk values calculated by using the analytical expression derived here are in excellent agreement with those of numerical solutions of coupled-power equations, irrespective of the values of bending radius and correlation length.