Numerical analysis of the discontinuities in slab dielectric waveguides

We propose an approximate method, of general applicability, for analyzing the discontinuities in slab dielectric waveguides. The method is based on replacing the unbounded configuration by a corresponding periodic multilayer structure. Hence the entire spectrum becomes discrete, and this makes the problem easier. The characteristic equation for the modal solution in a periodical multilayer dielectric waveguide is expressed in a matrix form which can be readily solved with a computer. In order to solve the discontinuity problems of slab waveguides, we expressed the reflected and transmitted fields by truncated modal expansions. The unknown amplitudes of the reflected and transmitted modes are determined by the boundary conditions. Numerical results are graphically shown including the cases which have been difficult to analyze by other methods. The accuracy of our results is checked by evaluating the relative errors and comparing with other available results.