A method based on ray-optics techniques is used to evaluate the dispersion characteristics of a symmetrical-slab waveguide with an index distribution that varies from a quasi-parabolic to the quasi-step profile. The validity and accuracy of the method are checked by comparison with results that can be obtained by different methods, either for the cases of a particular graded index or for a step-index profile.
A. M. Scheggi, P. F. Checcacci, and R. Falciai, "Dispersion characteristics in quasi-step and graded-index slab waveguides by ray-tracing technique," J. Opt. Soc. Am. 65, 1022-1026 (1975)