Conditions for generation of a phase-conjugate wave in a ring resonator with a local transient nonlinear response of the medium

An approximation of a constant intensity of two counterpropagating noncollinear waves in a ring system is used to consider phase conjugation as a result of a four-beam interaction in a medium with a transient nonlinear response. An analytic solution is obtained of a system of equations for weak waves consisting of an arbitrary set of quasiplane components. It is shown that when the absolute instability threshold is exceeded by a nonlinear phase shift, the maximum increment is exhibited by those components which are inclined at a certain angle to the phase-conjugate wave. The conditions for reliable phase conjugation by introduction of a phase screen into the ring are identified.