Differential group delay analytical estimation of bent 2-Core fibers introducing the continuous approximations

We have already demonstrated the reduction of the differential group delay (DGD) in coupled multi-core fibers (MCFs). Based on these results, we introduced the distribution functions in coupled MCFs for calculating the DGD and pulse width. However, it takes a considerable amount of time to compute these physical quantities over long distances because the distribution functions are discrete quantities. In this report, we approximate these functions as continuous quantities to resolve this issue. The distribution functions exhibit different properties over short and long distances. For short distances, the Poisson distribution should be used. On the other hand, the Gaussian distribution should be used for long distances. With these approximations, it is found that the pulse width evolves with the square root of the distance over long distances, while it evolves with the three-halves power of the distance over short distances.