Differential group delay estimation of bent two-core fibers using an approximate solution

In coupled multi-core fibers (MCFs), the differential group delay (DGD) between cores is reduced due to random coupling. We propose what we believe to be a novel analytic approach to interpret the phenomenon using an approximate solution of the two-core coupled mode equations for bent and twisted fibers, taking into account fluctuations due to the non-uniformity of the bending radius and manufacturing errors. As the input pulse wave propagates, it transforms into multiple pulse waves with varying amplitudes and group delay times. We derive distribution functions from the group delay times of these waves, allowing for the numerical calculation of DGD and pulse width as weighted averages. The results show that when distribution functions rapidly approach their final state, DGD remains small, while pulse width increases with the square root of distance. Conversely, if not fully evolved, DGD increases linearly, and pulse width grows convexly. The numerical findings obtained using the distribution functions align with the simulation results.