A general power-series expansion method for exact analysis of the guided modes in an optical fiber

A power-series expansion method for rigorous analysis of the guided modes in a cylindrical, radially inhomogeneous, dielectric waveguide is presented. The method is developed for an arbitrary piece-wise polynomial permittivity profile. The field solutions of the inhomogeneous core are constructed by a sequence of power-series expansions. Convergence is ensured and accuracy maintained by regulating the distance between successive expansion points. The characteristic equation and the cutoff conditions are expressed in a unified manner as a set of functions. The method presented is competitive in terms of accuracy achieved and computing time required.