Finite–element analysis of discontinuities in a dielectric slab waveguide

Abstract

AbstractFor discontinuity problems in a dielectric waveguide, a method for analysis is proposed in which a finite element technique and an analytical solution are combined. A systematic formulation is carried out for both the TE and TM modes. A hypothetical wall is provided in the region outside the waveguide so that the open region waveguide is treated as a closed system. In such a closed system, the mode spectrum becomes discrete and the analysis is simplified. However, the location of the hypothetical wall needs to be chosen carefully. The solution changes violently near the cutoff point of a higher order mode. In the present method, the location of the cutoff points of the higher order modes is calculated beforehand and the hypothetical wall is placed near the midpoint of the two adjacent cutoff points. If the hypothetical wall is placed at such locations, the solution depends much less on the locations. Hence, even if the hypothetical wall is located relatively close to the waveguide, the approximate solution is accurate. In order to demonstrate the fact that the present method can be easily applied to an arbitrary discontinuity, a complicated discontinuous structure such as the core deformation at the splicing point of fibers has been treated. The analytical results have been shown for the scattering characteristics of the TE and TM modes at such junctions.