Eigenvalues for a trapezoidal waveguide

The egienvalue solution for modes propagating in a trappezoidal waveguide is derived using Schwarz´s iterative method of overlapping regions. The technique involves matching the field expansion of each two overlapping regions on one boundary of the overlapping region and using field continuity on the other boundary to couple the successive iterations. The method is efficient and provides accurate results for the eigenvalues of the dominant and first few higher order modes. Numerical results are presented for the isosceles trapezoidal waveguide case, where the solution is simplified by making use of symmetry planes.