Nonlinear characteristics of a DBR (Distributed Bragg Reflector) Cherenkov laser are investigated with the aid of particle simulation, allowing for the nonlinear properties of the electron beam. Numerical results show that the EM power extracted from the cavity is considerably suppressed by the nonlinear effect of the electron beam. Additionally, the extracted EM power is found to be critically dependent on the reflection coefficient of the DBR at the output end. Thus the DBRs at both ends of the cavity should be carefully designed in order to extract the EM power from the cavity efficiently.

In order to enhance the energy transfer efficiency in a rectangular Cherenkov laser, we propose to vary properly the permittivity of a loaded dielectric in the transverse direction. With the aid of particle simulation, we investigate the amplification characteristics of the rectangular Cherenkov laser with a dielectric permittivity varied in the transverse direction, demonstrating the effectiveness of our proposal for efficiency enhancement.

In order to enhance the energy transfer efficiency in a Cherenkov laser, we propose to use a tapered waveguide with a dielectric thickness properly varied stepwise in the longitudinal direction. With the aid of particle simulation, we investigate the nonlinear characteristics of the Cherenkov laser with the tapered waveguide, demonstrating the effectiveness of our proposal for efficiency enhancement.

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.