Effect of relaxation on the transfer of orbital angular momentum via four-wave mixing process in the four-level double lambda atomic system

In this work, we have theoretically studied the resonant four-wave mixing (FWM) in a four-level double Lambda (Λ) atomic system in connection with orbital angular momentum (OAM) transfer from probe to generated signal beam. The effect of the relaxation process is studied in the forward as well as backward FWM. Based on the semiclassical model, our analysis shows a strong dependence of conversion efficiency on spontaneous decay and decoherence rates. From the intensity and phase profile, we have confirmed the OAM nature of the generated signal beam. The physical explanation is given for the dependence of efficiency on the decay rate of the excited atomic state. We have shown that decoherence present in the system always leads to a deleterious effect on conversion efficiency. Our presentation treats forward and backward FWM in a unified way in the context of OAM transfer and sheds light on the parameter dependence of conversion efficiency.