Multimode graded-index optical fibers: comparison of two Wentzel–Kramers–Brillouin formulations

Light propagation in graded-index optical fibers is described by two WKB methods, a classical formulation and the Langer–McKelvey approach. Explicit errors in these methods are evaluated for a fiber profile of near-parabolic shape and for one far from parabolic shape by comparing the methods with the results of evanescent wave theory that involve asymptotic error estimates. The most accurate formulation in general is the classical method, but in special cases the Langer–McKelvey approach is slightly more accurate. One example shows an inaccuracy of −672.5 to −672.1 psec/km in modal group delay for the latter method when the maximum intermodal group delay difference is 2.84 nsec/km.