Abstract
This chapter presents wave propagation along a straight rectangular waveguide for practical applications where there are two complementary shapes of the dielectric profile in the cross section. In the first case, the cross section consists of circular dielectric material in the center of the cross section. In the second case, the cross section consists of a circular hollow core in the center of the cross section. These examples show two discontinuous cross sections and complementary shapes that cannot be solved by analytical methods. We will explain in detail the special technique for calculating the dielectric profile for all cases. The method is based on Laplace and Fourier transforms and inverse Laplace and Fourier transform. In order to solve any inhomogeneous problem in the cross section, more than one technique can be proposed for the same mode-model method. We will explain in detail how and where the technique can be integrated into the proposed mode-model. The image method and periodic replication are needed for fulfilling the boundary condition of the metallic waveguide. The applications are useful for straight rectangular waveguides in millimeter regimes, where the circular dielectric material is located in the center of the cross section, and also for hollow waveguides, where the circular hollow core is located in the center of the cross section.