Asymptotic eigenvalues of vector wave equation for guided modes in graded-index fibre

Abstract

Asymptotic eigenvalues of the vector wave equation—a system of coupled second-order differential equations—are calculated by the perturbation method in which we use the exact solutions of the scalar wave equation as the unperturbed term. We examine a graded-index fibre with a polynomial profile core and obtain the propagation constants of the vector modes in analytic form. The results coincide with those found by a sophisticated method.