Nonreciprocity of a six-wave mixing light droplet by a moving electromagnetically induced grating

For the first time, we investigate the nonreciprocal generation of six-wave mixing (SWM) in an inverted-Y type four-level system with spatially uniform distribution of atoms. The nonreciprocity results from a moving electromagnetically induced grating (EIG) which is formed by two coupling beams with different frequencies. We demonstrate that the nonreciprocity can be controlled by the frequencies of the coupling fields and the powers of the dressing beams. As the distribution of atoms is uniform, the atomic density cannot affect the nonreciprocity, but it will affect the formation of the photonic band gap structure of the moving EIG. This research can be used to make optical diodes or optical isolators, because the moving EIG, the speed of which is related to the frequency difference of the two coupling beams, can break time-reversal symmetry. We also demonstrate that the nonreciprocal SWM can form a nonreciprocal light droplet when it propagates in atomic vapors with third- and fifth-order nonlinear susceptibilities.