Propagation characteristics of single-mode optical fibers with arbitrary complex index profiles

A rapidly converging numerical technique for the evaluation mode characteristics of circularly symmetric optical fibers with an arbitrary complex refractive index profile is presented. This method is based on transmission-line principles. From Maxwell's equations, we derive a transmission-line equivalent circuit for the optical fiber refractive index profile and we demonstrate how it can be used to determine the mode effective index (normalized propagation constant) of cylindrical dielectric waveguides. To illustrate the effectiveness of the procedure, we have applied it to circularly symmetric fibers with complex step, parabolic, and segmented optical refractive index profiles. We have used this method to evaluate and manipulate the gain in a typical 980-nm pumped erbium-doped fiber as well as for calculating attenuation of optical fibers when radial loss factors are present.