This paper deals with the investigation of the ray delay in gradient waveguides with any transverse refractive profile. A perturbation method is used for the calculations. It becomes apparent that the delay differences in the pure gradient medium are very small for any decreasing profile and that they are of an order of magnitude of those found in a monomode waveguide (material dispersion). Larger delay differences do, however, occur when the ray paths are to some extent determined by an outer cladding. These influences must be eliminated to allow the excellent delay time properties of a gradient medium to really be utilized.
R. Bouillie, A. Cozannet, K.-H. Steiner, and M. Tréheux, "Ray Delay in Gradient Waveguides with Arbitrary Symmetric Refractive Profile," Appl. Opt. 13, 1045-1049 (1974)