Simple Approach to Calculate the Refractive Index Profile of Ion-Exchanged Waveguides

Abstract

In graded-index glass waveguides a key factor for the design of components and devices is usually the accurate determination of the refractive index profile as a function of depth. The problem of reconstructing the index profile using the measured effective refractive indices has been faced by several authors.Here we suggest a new expression, linear combination of two analytical functions, which is able to provide a good approximation of the solution of the differential equation that rules the thermal diffusion process. The use of this equation, in connection with the general approach of inverting the Wentzel-Kramer-Bruilloin (WKB) eigenvalue equation, leads to a simple, fast, and accurate computation of the refractive index profile obtained by ion exchange. The application of the method to various Ag-exchanged waveguides in different glass matrices, with better accuracy than most of the usual procedures, has been demonstrated.