Study of the maximum conversion efficiency of the four-wave mixing process based on the Hamiltonian approach

In the four-wave mixing process, since the intensity of the generated coherence field is related closely to the third-order nonlinear susceptibility. With the help of a Hamiltonian approach, we obtain the expression of third-order nonlinear susceptibility χ(3), and the special relation between χ(3) and the nonlinear conversion coefficient. They are very useful to analyze the phase mismatch due to the Kerr effect and linear refraction contributions, which affect the maximum conversion efficiency under the condition taking account into pump field depletion. The investigative results show that energy conversion efficiency from the weak idler field to the generated field may exceed 100% when the phase mismatch induced by linear refraction is compensated, though the phase mismatch contribution from the Kerr effect can not be compensated simultaneously. Moreover, the conversion efficiency of the photon numbers fast reaches a plateau value.