Four wave mixing in a waveguide — Two radiation and two guided modes interaction

The theory of nonlinear interaction between two radiation modes as a pump waves and two guided modes: the input beam and the generated backward beam, is presented. In the degenerate case, for all waves at the same frequency, we demonstrate the possibility of the input wave amplification and the phase conjugate replica generation as well as of the interaction between modes of different polarization. The nondegenerate case, with the phase matching achieved by pump waves amplitude modulation is also considered.