Mode properties and dispersion for two optical fiber-index profiles by the propagating beam method

The propagating beam method generates solutions for the electric field in a graded-index optical fiber that emphasize beam characteristics rather than modal properties. Through Fourier analysis with respect to axial distance z, these solutions can be made to yield such mode properties as the propagation constants beta(n), the mode group delays partial differentialbeta(n)/ partial differentialomega, and the mode eigenfunctions. The propagating beam method has been applied to a detailed study of two index profiles with finite thickness cladding: an axisymmetric power-law (alpha = 1.85) profile both without and with an on-axis dip. In nine successive computer runs, eighty-five and eighty-four bound or guided modes were excited and characterized for the two respective profiles. The mode group delays near cutoff for both profiles show large deviation from those derived with the WKB method. In addition, sets of almost degenerate modes near cutoff show large differences in group delay. Modes with low azimuthal quantum number are strongly perturbed by the central dip. It is found that rms pulse dispersion is quite sensitive to the inclusion or exclusion of modes near cutoff, but that frequency response bandwidth is not. This leads to the conclusion that fiber bandwidth cannot be accurately inferred from rms pulse dispersion and may explain why broadband multimode fibers exist dispite strong perturbation of the modes near cutoff.