The Investigation Of Four-Wave Mixing In Multi-level Atomic Systems

Four-wave mixing, a very important nonlinear optical effect, has attracted people's attention from the time when Franken firstly discovered it. Scientists have carried on a lot of deep researches in the theoretical and experimental aspects. In recent years, people will apply electromagnetically induced transparency to four-wave mixing and find that electromagnetically induced transparency effect can dramatically decrease linear susceptibilities of the medium and resonantly increase non-linear susceptibilities of the medium,thereby improving the conversion efficiency of four-wave mixing. The discovery will push the research on the four-wave mixing effect toward another climax.The article, taking use of the principle of electromagnetically induced transparency in the interaction picture, theoretically researches on the four-wave mixing effects in the four-level ladder-type atomic system and five-level atomic system. The research work is as follows:Firstly, we study the four-wave mixing effect in the four-level ladder-type atomic system. We firstly give out the expression of the Hamiltonian in the interaction picture according to the physical model and work out the analytical expressions of the intensities of the generated four-wave mixing signal fields by use of the density matrix method. Then, we will make the analyses of the influence of different physical parameters(for example: the detuning of probe field?the intensity of coupling field) on the intensities of the generated four-wave signal mixing fields by numerical simulation.Secondly, we mainly study the four-wave mixing effect in the five-level atomic system. Here, we consider the case of the re-absorption of the generated four-wave mixing signal fields. We firstly work out the corresponding density matrix elements,which are related to the generated four-wave mixing signal fields in the atomic system, by use of density matrix method and perturbation theory. In addition, we will also combine it with the Maxwell equations, and give out the analytical expressions of the signal efficiency of dual-channel four-wave mixing by use of Laplace transform. Finally, by numerical simulation we find that the signal efficiency of dual-channel four-wave mixing can be controlled by changing the intensity of coupling field or the decay rate of energy level.