A backward wave amplifier based on an NRI transmission-line metamaterial

Analysis of the coupling between an electron beam and a coaxial negative-refractive-index transmission-line metamaterial is presented. The electron beam is modeled as a spatially dispersive anisotropic permittivity, and the coaxial metamaterial is homogenized to derive its effective material parameters. The homogenized problem lends itself to an analytic coupled-mode dispersion relation. Solutions are obtained for both complex frequency and complex wavenumber, and all analytic results are verified through full-wave simulation. The work will find application in the design of backward wave amplifiers (BWA).