Abstract
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.
Highlights
The methods of straight waveguides have been proposed in the literature
The second objective is to understand the influence of the inhomogeneous dielectric materials on the output fields
The proposed techniques are important to improve the methods that are based on Laplace and Fourier transforms and their inverse Laplace and Fourier transforms for the discontinuous rectangular and circular profiles in the cross section
Summary
The methods of straight waveguides have been proposed in the literature. Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides with. A fundamental and accurate technique to compute the propagation constant of waves in a lossy rectangular waveguide has been proposed [12] This method is based on matching the electric and magnetic fields at the boundary and allowing the wavenumbers to take complex values. We study the electromagnetic wave propagation in a rectangular waveguide filled with an inhomogeneous dielectric material in the longitudinal direction. A transfer matrix function for the analysis of electromagnetic wave propagation along the straight dielectric waveguide with arbitrary profiles has been proposed [32]. 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 proposed techniques are important to improve the methods that are based on Laplace and Fourier transforms and their inverse Laplace and Fourier transforms for the discontinuous rectangular and circular profiles in the cross section (and for the continuous profiles)
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