Propagation of electromagnetic waves in elliptical waveguides made of materials with anisotropic Hermitian dielectric tensors

Abstract

This paper studies the generalized equations of electromagnetic fields and their solutions in long waveguides with several regions made of materials with Hermitian dielectric tensors and elliptical cross-sections. The special conditions under which the quadratic homogeneous equations of the hybrid modes can be reduced to second-order equations are presented. IntroductionIt is well known that the dispersion relation of electromagnetic waves in a waveguide essentially depends on its geometrical dimensions, and the dielectric permittivity and permeability coefficients of its materials [1-3]. There are waveguides with different cross-sections, made of different materials and different configurations. Many years ago these instruments with elliptical cross-sections were used as accelerators of charged particles [4], were used for microwave heating [5], and were also used as transmission lines [6]. Recently an elliptical waveguide made of metamaterials in which the phase velocity and energy flow of an electromagnetic wave can be antiparallel has also been investigated [7]. In [4][5][6][7], it was assumed that the waveguides were made of solid materials with isotropic scaler dielectric permittivity and permeability. The propagation characteristics of ferrite-filled elliptical waveguides have been investigated as an anisotropic problem only in [8,9], where the anisotropic properties refer to the permeability tensor. Recently, ideal stability of an elliptical plasma column [10] and propagation of charge-space and slow waves in elliptical waveguides [11,12] have been investigated. Furthermore, the theory of the equilibrium and stability of a high-intensity beam and the attenuation characteristics of elliptic waveguides have been analysed in [13] and [14], respectively. In the other words, plasma waveguides with elliptical cross-section are a new application of elliptic waveguides. Generally, there are two methods for investigating wave propagation in a material. In the first method, the perturbed values of the macroscopic quantities of the system are matched with the governing fundamental electromagnetic equations of the system [15]. In the second method, the perturbed values of the microscopic

Terahertz electromagnetic wave generation and amplification by an electron beam in the elliptical plasma waveguides with dielectric rod

“…The elliptical representation of Maxwell's equations shows that the field components are strongly coupled. 41 On the other hand, existence of an external infinitely strong magnetic field results that the equations can be separated. Under these conditions, there is an independent wave equation for both electric and magnetic fields.…”