Numerical analysis of mode coupling in multimode graded index optical fibers with bending

Abstract

In this paper, we present a new and more realistic theoretical framework for lightwave propagation in a multimode graded index (GRIN) optical fiber when the fundamental mode is selectively excited into the fiber with constant radius bending, causing coupling between the various modes of the fiber. First, a wave equation is formulated to represent the light behavior in the GRIN fiber and solved numerically by an eigenvalue method using a difference equation representation of the differential equation, resulting in the mode amplitudes. Next, the local normal mode fields at a succession of infinitesimal corner bends are matched to calculate the bending-induced mode coupling. Finally, the power in the fundamental mode vs the distance along the propagation direction is calculated, assuming that this is the only mode that is excited initially. For large bend diameters, the output data indicates that, when the fundamental mode is excited, the light remains in a set of low-order modes. However, for small radius bends (less than 1 cm), the oscillations become irregular and the power is not completely located in the fundamental mode when z > 0. While this is consistent with experimental observations, it contradicts the predictions of the previous oversimplified model.