Calculation of Modes in an Optical Fiber Using the Finite Element Method and EISPACK

Abstract

This paper presents a method for computing the propagation modes of a circular optical fiber. Finite element analysis reduces Maxwell's equations to standard eigenvalue equations involving symmetric tridiagonal matrices. Routines from the Eigensystem Package (EISPACK) compute their eigenvalues and eigenvectors, and from these the waveforms, propagation constants, and delays (per unit length) of the modes are obtained. An extension allows loss of leaky modes to be calculated. Examples indicate that the method is reliable, economical, and comprehensive, applying to both single and multimode fibers.