Numerical Analysis of Optical Waveguides

A numerical procedure for calculating both the propagation constant and the field of modes of planar or channel waveguides with arbitrary refractive index profile is described. The procedure is based on the well-known variational expression for the propagation constant and uses as trial field an expansion in terms of Hermite-Gauss functions. The field parameters, i.e. the expansion coefficients and the spot-size of the Gaussian functions, are evaluated by numerically solving two generalized eigenvalue problems and two nonlinear equations respectively. We analyze a step-index planar waveguide and a channel waveguide with refractive index profile described by an error function in the two normal directions of the cross section. Results show that our procedure is quickly convergent and accurate