Phase grating in a doubly degenerate four-level system

In this paper, we suggest a doubly degenerate four-level system, in which the transition takes place between the hyperfine energy 5²S_1/2 F = 1 and 5²P_3/2 F = 2 in rubidium 87 D₂ line, for studying atomic phase grating based on the cross-Kerr and phase conjugation effects. The phase grating with high efficiency can be obtained by tuning phase shift Φ between the coupling and probe field, when the coupling intensity is much stronger than the strength of probe field. Under different coupling intensities, a high diffraction efficiency can be maintained. A new and simple way of implementing phase grating is presented. However, in such an atomic system, two main limitations must be taken into account. First, the independence between steady state probe susceptibility and the coupling intensity, when the population decay rate is larger than the Rabi frequency of the coupling field, cannot result in diffraction grating; second, the sample to be prepared should not be too long.