Structure of lasing modes generated as a result of a four-wave interaction with feedback

The diffraction approximation is used to determine the structure of the radiation generated as a result of a four-wave interaction with feedback and the conditions for phase conjugation are identified. Phase conjugation can be expected in the case of a signal beam with a smooth distribution of the amplitude if the transverse size of this beam decreases as a result of passing through a feedback loop. In the case of a multimode signal beam it is additionally necessary to ensure that the resonator length or the length of the nonlinear medium exceeds the spreading length of the transverse inhomogeneity of the field.