Iterative simplex-finite difference method for the characterization of optical waveguides

A new method is presented for reconstructing smooth refractive index profiles of optical waveguides from measured effective indexes. It is based on the semivectorial finite difference method to solve the polarized wave equation for a given refractive index profile. An iterative simplex algorithm is used to find the best refractive index parameters that give, as a solution, effective indexes close to the measured ones. The method is applied successfully to Ag⁺-Na ⁺ ion-exchanged glass slab waveguides and to diffused Mg/Ti:LiNbO₃ slab waveguides. Dopant concentration profiles are obtained by using secondary ion mass spectrometry. The relationship between the refractive index change and the dopant concentration is determined for both cases. The iterative simplex algorithm-finite difference method (ISA-FDM) is compared to other index profile reconstruction methods, and the advantages with respect to WKB-based methods are pointed out