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Appl Opt. 1975 Nov 1;14(11):2578-84. doi: 10.1364/AO.14.002578.

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.

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