ANALYSIS OF A CHERENKOV LASER LOADED WITH A KERR-LIKE MEDIUM BY MULTILAYER APPROXIMATION METHOD

The growth characteristics of a two-dimensional Cherenkov laser compos ed of a planar relativistic electron beam and a parallel plate wavegui de one plate of which is loaded with a nonlinear dielectric sheet are analyzed. The permittivity of the nonlinear dielectric sheet becomes i nhomogeneous 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 di electric layers each of which is assumed to be homogeneous. From numer ical analysis, it is found that just a few homogeneous layers for the nonlinear dielectric sheet are enough to get the same results as obtai ned previously by means of the finite element method. This is because the variation of the permittivity across the nonlinear dielectric shee t is as small as within 10% of the linear permittivity of the nonlinea r material. Thus the multilayer approximation method is found to be mo re simple and more efficient for the analysis of the Cherenkov laser l oaded with a Kerr-like medium than the finite element method.