Pulse broadening caused by deviations from the optimal index profile.

The excess pulse broadening caused by deviations from the optimal index profile is analyzed for multimode optical fibers. First-order perturbation theory is used to evaluate the effects of arbitrary index perturbations having longitudinal spatial frequencies which are too low to cause mode coupling. A simplified expression is found for the excess pulse broadening in terms of a double integral over a weighting function. Weighting functions are evaluated and used to calculate the effects of two kinds of circularly symmetric perturbations, a Gaussian-shaped bump or dip in the index profile and an oscillating perturbation. These perturbations are found to affect the pulse broadening significantly according to the position and width of the bump and the transverse spatial frequency of the oscillating perturbation. The more narrow bumps and those located at larger core radii are found to have the greatest effect. For a typical multimode fiber, perturbations making 2-18 oscillations along the radius are found to cause significant increases in pulse broadening, while more rapid oscillations are found to have negligible effect. These results indicate the type and degree of index profile control required to keep the pulse broadening below a specified level.