An Economic Method for the Solution of the Scalar Wave Equation for Arbitrarily Shaped Optical Waveguides

In the method presented here, the discrete sine method, the basis functions consist of sine functions defined on a set of parallel discretization lines. The method is a combination of a scalar version of the finite difference method and the sine method. The choice of the basis set leads, for the eigenvalue equation to be solved, to a sparse matrix with a small bandwidth. As a consequence, the propagation constant of guided modes in optical waveguides may be calculated with short computation times and low storage needs. Results, obtained with the method, for three different waveguiding structures, are compared with those of other methods.