Theory of phase-conjugation by four-wave mixing in a waveguide

It is shown that it is possible to generate the time-reverse replica of an 'input' monochromatic, image-bearing beam by coupling it into a waveguide where it interacts with counterpropagating multimode 'pump' waves of the same frequency. The nonlinear electric polarization density that is third order in the propagating electric fields in the guide medium generates the replica by the process of four-wave mixing. A phase conjugate (or time-reversed replica) beam can be generated that is either at the same frequency as the input beam being conjugated or not, depending on the values of the pump frequencies. It is shown how the frequency dependence of the replication process can be used to realize a narrowband optical filter with a large solid angle of acceptance.