Interaction of four counterpropagating plane waves in a medium with an instantaneous cubic nonlinearity

A theoretical analysis is made of the energy exchange between four counterpropagating plane waves during their interaction in a medium having an instantaneous cubic reactive nonlinearity. A solution of a complete system of equations in terms of Jacobi elliptic functions is obtained. The interaction pattern is constructed using concepts of dynamic holography. It is shown that the high energy exchange efficiency of a local nonlinear response of the medium is due to a shift of a hologram with respect to the interference pattern of the diffracted waves.