Analyzing Wave Propagation in Helical Waveguides Using Laplace, Fourier, and Their Inverse Transforms, and Applications

Part of the book: Wave Propagation

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

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.

Part of the book: Emerging Waveguide Technology

Applications and Solving Techniques of Propagated Wave in Waveguides Filled with Inhomogeneous Dielectric Materials

This chapter presents techniques to solve problems of propagation along the straight rectangular and circular waveguides with inhomogeneous dielectric materials in the cross section. These techniques are very important to improve the methods that are based on Laplace and Fourier transforms and their inverse transforms also for the discontinuous rectangular and circular profiles in the cross section (and not only for the continuous profiles). The main objective of this chapter is to develop the techniques that enable us to solve problems with inhomogeneous dielectric materials in the cross section of the straight rectangular and circular waveguides. The second objective is to understand the influence of the inhomogeneous dielectric materials on the output fields. The method in this chapter is based on the Laplace and Fourier transforms and their inverse transforms. The proposed techniques together with the methods that are based on Laplace and Fourier transforms and their inverse transforms are important to improve the methods also for the discontinuous rectangular and circular profiles in the cross section. The applications are useful for straight waveguides in the microwave and the millimeter-wave regimes, for the straight hollow waveguide and for infrared field, also in the cases of inhomogeneous dielectric materials in the cross section.

Part of the book: Emerging Waveguide Technology

The Influence of the Dielectric Materials on the Fields in the Millimeter and Infrared Wave Regimes

This chapter presents the influence of the dielectric materials on the output field for the millimeter and infrared regimes. This chapter presents seven examples of the discontinuous problems in the cross section of the straight waveguide. Two different geometrical of the dielectric profiles in the cross section of the straight rectangular and circular waveguides will be proposed to understand the behavior of the output fields. The two different methods for rectangular and circular waveguides and the techniques to calculate any geometry in the cross section are very important to understand the influence of the dielectric materials on the output fields. The two different methods are based on Laplace and Fourier transforms and the inverse Laplace and Fourier transforms. Laplace transform on the differential wave equations is needed to obtain the wave equations and the output fields that are expressed directly as functions of the transmitted fields at the entrance of the waveguide. Thus, the Laplace transform is necessary to obtain the comfortable and simple input-output connections of the fields. The applications are useful for straight waveguides in the millimeter and infrared wave regimes.

Part of the book: Electromagnetic Materials and Devices

Techniques for Calculating Two Interesting Types of Dielectric Materials in Straight Rectangular Waveguides and their Applications

View all chaptersThis chapter presents two interesting types of dielectric materials in the straight rectangular waveguides. Five examples of the different discontinuous cross sections and complementary shapes will demonstrate. We will introduce in all case the effective technique to calculate the dielectric profile in the cross section. The first type will demonstrate where the dielectric material is located in the center of the cross section. The second type will demonstrate where the hollow core is located in the center of the cross section in the case of the hollow waveguide. The two different types are complementary shapes for two different applications. The proposed techniques relate to the method based on Laplace and Fourier transforms and the inverse Laplace and Fourier transforms. The method is based also on Fourier transform, thus we need use with the image method to calculate the dielectric profile in the cross section. The image method and periodic replication are needed for fulfilling the boundary condition of the metallic waveguide. The applications are useful for straight waveguides in millimeter regimes, in the cases where the dielectric profile is located in the center of the cross section, for cases where the hollow rectangle is located in the center of the cross section, and also for complicated and discontinuous profiles in the cross section.

Part of the book: Modern Applications of Dielectrics and Electrostatics in Engineering, Physics, Chemistry, Biology and Medicine