TEM-wave propagation in a coaxial waveguide with impedance-matched RHM to LHM transition

In this paper, we study TEM-wave propagation inside a hollow coaxial waveguide filled with an inhomogeneous metamaterial composite, with a graded transition between a right-handed material (RHM) and an impedance-matched left-handed material (LHM). The graded transition and the TEM-wave propagation occur in the direction perpendicular to the boundary between the two media, which has been chosen to be the z-direction. The relative permittivity ɛ(ω, z) and permeability µ(ω, z) of the RHM-LHM composite vary according to hyperbolic tangent functions along the z-direction. The exact analytical solutions to Maxwell's equations are derived, and the solutions for the field components and wave behavior confirm the expected properties of impedance-matched RHM-LHM structures. Furthermore, a numerical study of the wave propagation over an impedance-matched graded RHM-LHM interface, using the COMSOL Multiphysics software, is performed. An excellent agreement between the analytical results and numerical simulations is obtained, with a relative error of less than 0.1%. The present method has the ability to model smooth realistic material transitions, and includes the abrupt transition as a limiting case. Finally, the RHM-LHM interface width is included as a parameter in the analytical and numerical solutions, allowing for an additional degree of freedom in the design of practical devices using RHM-LHM composites.