| This dissertation describes a theoretical analysis for optical propagation in a multimode graded-index (GRIN) fiber when the lowest-order mode is selectively excited and the fiber is bent around a constant radius mandrel. The bending causes coupling between the various modes of the fiber.; First we formulate the wave equation that represents light behavior in the GRIN fiber. We solve this equation numerically by an eigenvalue method using a difference equation representation of the differential equation and obtain mode amplitudes. The modes are classified according to integers m (= 0, ±1, ±2, …), which gives the electric field angular (&thetas;) dependence, and l (= 0, 1, 2, 3, …) which gives the number of zero crossings in the amplitude as a function of r, the radial distance from the fiber axis. Then, we match local normal mode fields at a succession of infinitesimal corner bends to calculate mode coupling induced by the constant radius bending. Finally we compute power in the fundamental mode vs. distance along the propagation direction, assuming that this is the only mode which is excited initially.; The output data indicates that, when the fundamental mode is excited, the light remains in a set of low-order modes for small bend diameters. This is consistent with previously published experimental results which show that in graded-index multimode fiber subject to constant diameter bending, the light tends to oscillate between low order modes and remain trapped therein rather than diffuse to high-order modes.; For small radius bends, on the other hand, the oscillations become irregular and all of the power is not found in the fundamental mode for any z > 0. This is also consistent with observation, but contrasts with predictions of a previous oversimplified model.; Implications for an intrusion-resistant communication system using multimode graded-index optical fiber are also discussed. |
