Mode Propagation Through a Step Discontinuity in Dielectric Planar Waveguide

This paper proposes two analytical methods which are essential for dealing with the wave propagation through a dielectric step discontinuity; one is a method to accelerate the convergence rate of solutions, especially for TM-mode problems, and the other is a method to treat efficiently the waves with continuous spectrum, in case of open waveguides. It is shown with a number of numerical results that our proposals are quite powerful to the investigation of discontinuity problems.