Electron Beam Coupling to an NRI Transmission-Line Metamaterial

A backward-wave amplifier topology based on a coaxial negative refractive index transmission-line (NRI-TL) metamaterial is introduced. The dispersion relation of the isolated coaxial metamaterial is derived rigorously using a mode-matching technique. The structure is then homogenized to derive its effective material parameters. The electron beam is subsequently introduced by means of an anisotropic, spatially dispersive permittivity. With the electron beam present, the homogenized metamaterial is analyzed to obtain a coupled-mode dispersion relation that accounts for electron beam-metamaterial interaction. Solutions to this dispersion relation yield complex coupled modes. The analytical solutions are compared with full-wave simulation of the NRI-TL with electron beam present, and show close agreement.