Construction of glass waveguide refractive index profiles by the effective-index finite-difference method

A numerical method is applied to construct the refractive index profiles of optical waveguides from the measured effective indices (EI). The method is based on choosing a proper analytical function for the refractive index profile and searching its unknown parameters using the simplex search algorithm. Simultaneously, the finite-difference method (FDM) is used to solve the semi-vectorial Helmholtz equation for the guided modes effective indices. The method is applied successfully to two particular Ag⁺---Na⁺ ion-exchanged glass slab waveguides. The results are as accurate as those obtained from from commonly used IWKB-based method. The EI-FDM in principle can be applied to both slab and channel waveguides and does not require that the index profiles are monotonically decreasing, like most of IWKB-based methods. The relation between the induced refractive index and silver concentration profile, measured by SIMS, is found to be almost linear.