Periodic Rectangular and Circular Profiles in the Cross Section of the Straight Waveguide Based on Laplace and Fourier Transforms and Their Inverse Transforms and Applications

Abstract

This chapter presents propagation along the straight rectangular waveguide with periodic rectangular and circular profiles in the cross section. The objectives in this study are to explore the effect of the periodic rectangular and circular profiles in the cross section of the straight waveguide on the output field and to develop the technique to calculate two kinds of the periodic profiles. The method is based on Laplace and Fourier transforms and the inverse Laplace and Fourier transforms. The contribution of the proposed technique is important to improve the method that is based on Laplace and Fourier transforms and their inverse transforms also for the discontinuous periodic rectangular and circular profiles in the cross section (and not only for the continuous profiles). The proposed technique is very effective to solve complex problems, in relation to the conventional methods, especially when we have a large numbers of dielectric profiles. The application is useful for straight waveguides in the microwave and the millimeter wave regimes, with periodic rectangular and circular profiles in the cross section of the straight waveguide.