Comprehensive theory of dispersion in graded-index optical fibers

This paper presents a theoretical investigation on the dispersion in graded-index silica glass fibers under overfilled launching with equal excitation of modes. This theory incorporates both chromatic effect and modal contribution which takes not only the modal delay into account but also the distributed loss and mode-coupling. Random microbends are considered to be the most dominant source of coupling. All index perturbations and intrinsic core diameter variations are assumed to be negligible, but they could readily be included without changing the basic structure of the model. The 3-dB bandwidth is analyzed through the study of the fiber transfer function which introduces the wavelength and modal effects as two separate filter functions. The formal derivation of the chromatic transfer function is analytical. On the other hand, the modal transfer function is obtained by numerically solving the power flow equation in the frequency domain using Crank-Nicholson method. As an application, the results are illustrated showing, in particular, the influence of the fiber core/outside diameters, for the first time.