The growth characteristics of a two-dimensional Cherenkov laser composed of a planar relativistic electron beam and a parallel plate waveguide one plate of which is loaded with a nonlinear dielectric sheet are analyzed. The permittivity of the nonlinear dielectric sheet becomes inhomogeneous due to the Kerr effect as the electromagnetic wave grows along the waveguide. For the analysis of the electromagnetic fields in the nonlinear dielectric sheet, it is replaced by a number of thin dielectric layers each of which is assumed to be homogeneous. From numerical analysis, it is found that just a few homogeneous layers for the nonlinear dielectric sheet are enough to get the same results as obtained previously by means of the finite element method. This is because the variation of the permittivity across the nonlinear dielectric sheet is as small as within 10% of the linear permittivity of the nonlinear material. Thus the multilayer approximation method is found to be more simple and more efficient for the analysis of the Cherenkov laser loaded with a Kerr-like medium than the finite element method.

We present design procedures for using conducting wires in A-sandwich junctions to achieve high transmission performance; bench-test results validate the procedures. The scattering characteristics of the junction are obtained by solving the electric field integral equation of volumetric equivalent currents. The transmission performance is evaluated by subtracting the scattered fields of the same-sized A-sandwich panel in order to offset the effect of edge diffraction. Optimum wire width is determined by examining transmission performance with different arrangements. The designed junction achieves high transmission performance. The measured scattering characteristics of a bench model demonstrate the validity of the presented method.