An asymptotic expansion approach for variable refractive index optical fibers (in weak guidance case)

Abstract

To study the propagation of guided modes in an optical fiber under weak guidance assumptions, we usually use a scalar approximation of the Maxwell’s system which generally leads to the Helmholtz equations. Most of works in the literature treat optical fibers where the refractive index is constant in the core. In this work, we give more detailed calculations and expend the study to the case where the index of refraction is variable in the core of the fiber. The technique of calculation we propose is based on a formal asymptotic expansion that allows us to derive the equation and the transmission conditions of the scalar eigenvalue problem from Maxwell’s equations in the vectorial case. In the case where the refractive index is variable, which is the main contribution of this work, we carry out asymptotic expansions of lower order and higher order leading to a scalar eigenvalue problem.