Nonlinear gain and threshold current variations in a periodically corrugated waveguide

A rectangular periodically corrugated waveguide is considered in the exponential gain regime. In general, gain obeys a nonlinear cubic equation. In this paper it is solved numerically. Also the behavior of gain diagrams versus beam velocities for various parameters of the problem is surveyed. Furthermore, in the context of a slow-wave periodic structure oscillator, the threshold current which cause the system to be self-sustained, is obtained from a nonlinear cubic equation similar to the one obtained for gain, and the variation of its diagrams with other parameters is also considered.