Theory of the interaction of counterpropagating waves in a nonlinear cubic medium

A theoretical study is presented of four-photon scattering in a bounded nonlinear cubic medium with allowance for parametric interaction. It is shown that this system is unstable, and self-excitation thresholds for various modes of the system are determined. It is found that, with an increase in pumping, the frequency spectrum of generated modes is rapidly (exponentially) broadened. The analysis is based on parabolic equations, and the simple case of the equality of the amplitude of counterpropagating waves is considered.