Multimode theory of graded-core fibers

New technologies of fiber manufacture and a demand for unusual fiber qualities in communication systems have intensified the interest in a comprehensive theory of multimode fibers with nonuniform index distributions. This paper deals with a general class of circular symmetric profiles which comprise the parabolic distribution and the abrupt core-cladding index step as special cases. We obtain general results of useful simplicity for the impulse response, the mode volume, and the near- and far-field power distributions. We suggest a modified parabolic distribution for best equalization of mode delay differences. The effective width of the resulting impulse is more than four times smaller than that produced by the parabolic profile. Of course, practical manufacturing tolerances are likely to influence this distribution. A relation is derived between the maximum index error and the impulse response.