Equivalent modeling of micro-bending in MMF with parabolic index profile using discrete coupling points

Multimode fibers (MMF) have attracted much attention recently because of its potential of increasing the transmission capacity by the number of guided modes. Because of this, it is necessary to develop fast and simple methods to estimate transmission effects like mode coupling along the MMF and the losses induced by it. Mode coupling theory provides a possibility for describing amplitude and phase effects but the MMF has to be divided into many sections, making its evaluation lengthy. The results presented in give insight on the differential group delay (DGD) reduction induced by mode coupling in presence of micro-bendings, but neglect the induced losses. Here this model is expanded, by including the losses induced by mode coupling using the quasi-mode approach, extended here to use for MMF. The DGD, computed using the imaginary part of the eigenvalues of the group delay operator G(u) = θ_ωT(ω)·T(ω)-¹, is shown in Fig. 1 (a) for a MMF guiding 10 modes (4 mode groups). T(w) is the transmission matrix of the MMF modeled using the methods mentioned above. The narrowing behavior of the DGD as the std. dev σ_1/R of the micro-bending curvature increases, matches the results presented in [2]. Additionally it shows in the lower frame axis the losses induced by the mode mixing effect. To validate these results, we propose an alternative model in which a bending is transformed into a splice mismatch.