Generalized guided-wave mode calculations in graded-index fibers

In this paper a novel approximated method is introduce to calculate guided-wave modes in graded-index fibers. Useful solutions have been obtained on the whole range of r for the corresponding scalar wave equation, using two-point quasirational approximations. This approach is better than the WKB approximation which is good only for the ray optic pictures and when the phase changes at the caustic are ignored. Here an adequate change of variables have been found that allows determine power series and asymptotic expansions suitable for application of the two-point quasi-rational approximant method. The results presented here agree very well with the numerical solutions.