Modal dispersion in multimode graded-index fibers

A complete analysis of the propagation characteristics of a ray through an axially symmetric graded-index medium is carried out in the geometrical optics approximation. First, two constants of the motion are shown to exist for a ray propagating in an infinite medium. Secondly, these constants of the motion are shown to be invariant when reflection occurs on the core-cladding interface of cladded graded index fibers. This conservation law allows the study of the propagation characteristics of a ray through a fiber even though its trajectory may be discontinuous because of reflection at the core-cladding interface. The temporal behavior of various cladded parabolic-index fibers is given by their impulse responses when excited uniformly by parallel beams under different input angles. Rays are shown to propagate in two different ways: a reflected type of propagation takes place through reflections on the core-cladding interface, and a selfocusing type of propagation where rays go through the fiber core without touching the cladding.