Electromagnetic Waves Propagation from Moving Sources in Waveguides Filled by a Dispersive Dielectric Media

Abstract

We consider the problem of electromagnetic wave propagation in homogeneous dielectric dispersive waveguides $\Pi=\mathcal{D}\times\mathbb{R}$ where $\mathcal{D}$ is a bounded domain in $\mathbb{R}^{2},$ produced by non-uniformly moving sources of the form \begin{equation} \mathbf{j(x,}t)=\mathbf{A}(t)\delta(\mathbf{x-x}_{0}(t)) \tag{0.1} \end{equation} where $\mathbf{j(x,}t)$ is the current density, $\mathbf{A}(t)$ is a vector amplitude, $\mathbf{x=x}_{0}(t)$ is a trajectory of the source.

We consider the propagation of $TE$ and $TM$ waves in the waveguide $\Pi,$ produced by the source (0.1). As example we study the propagation of electromagnetic waves in a waveguides filled by a cold, non magnetized plasma.