Finite‐element analysis of dielectric slab waveguide with finite periodic corrugation

Abstract

AbstractTo calculate the reflection/transmission characteristics of a dielectric slab waveguide with finite periodic corrugation, a numerical approach based on the finite‐element method is proposed. Although the finite‐element method has already been applied to discontinuity problems in dielectric waveguides, it was virtually impossible from the viewpoints of computation time and computer capacity to apply the finite‐element method directly to a waveguide with many discontinuities such as a finite periodic waveguide. In the present article, a “substructure” has been introduced to the finite‐element formulation to treat a large number of discontinuities. Consequently, the interaction of surface waves and radiated waves among all discontinuities is automatically taken into account. Also, an unbounded waveguide is replaced by a corresponding bounded one; this creates a problem where an artificial boundary should be set. It was found that in a finite periodic waveguide, a good approximate solution can be obtained by choosing the position of the artificial boundary with an adequate distance from the waveguide, since the dependence of the solution on the position of the artificial boundary is not significant. The validity and usefulness of this method was confirmed by comparing the numerical results with the values obtained from other theoretical methods and the experimental values.