## 4 Coherent Manipulation on Light Fields via Atomic Coherence Gratings
### Nondegenerate Phase-Conjugate Wave  
The phase aberration induced by spatial inhomogeneities during the propagation of light is a severe problem in coherent imaging systems [64; 65], which causes the image to be blurred or distorted, therefore losing accurate information. Apart from all other correction algorithms, one of the phase aberration correction methods, which is simple in principle, is to use the phase-conjugate wave [66]. The phase aberration can be removed by letting the aberrated phase-conjugate wave pass in the reverse direction through the same phase aberration medium; therefore, the phase-conjugate wave is also called the time-reversal wave. An optical phase-conjugate wave can be generated through various nonlinear optical processes, for instance, three-wave mixing [67; 68], four-wave mixing [69; 70; 71; 72], photorefractive wave-mixing [73], backward stimulated scatterring and emission [74; 75; 76; 77] and photon-echo process in a resonant medium [78; 79]. In general, the key to generate phase-conjugate waves is to form a holographic grating, through which the reversal wave front with identical transverse distribution is restored. We note that atomic coherence grating is induced during the light pulse storage based on the EIT effect; therefore, it is possible, in principle, to generate phase-conjugate waves based on the EIT-induced atomic coherence grating. [PERSON] et al. [80] reported the generation of phase-conjugate waves in Pr:YSO  
Figure 4: (**a**) is the schematic diagram of the angular multiplexing storage of light pulses in Pr:YSO crystal based on the EIT effect. Here, \(\theta\) is the angular distance between two neighboring channels; \(E_{\mathrm{C1}}\), \(E_{\mathrm{S1}}\) and \(E_{\mathrm{C2}}\), \(E_{\mathrm{S2}}\) represent the coupling and the signal pulses for channel 1 and channel 2, respectively. (**b**) demonstrates the angularly addressable two-channel optical buffer memory based on the angular multiplexing light pulse storage technique in Pr:YSO crystal under the EIT condition. The angular distance between two channels was set to be \(\theta=3.9^{o}\), which is much larger than the angular resolution of the atomic coherence gratings recorded in a 3-mm Pr:YSO crystal. Note that the strength of the retrieved signal pulses in both channels has been multiplied by a factor of 3 for clarity. Figure 4b was adapted from reference [24]. crystal based on the EIT effect in a four-wave mixing configuration, in which the EIT effect was proved to significantly enhance the conversion efficiency of the phase-conjugate wave. In addition, in a coherently prepared atomic vapor, [PERSON] et al. [81] proposed and realized the transportation and time reversal of light pulses between different spatial and temporal points via atomic coherence. We demonstrated a nondegenerate phase-conjugate wave in Pr:YSO crystal through the EIT-based light pulse storage and retrieval technique. Figure 5a shows the experimental configuration used to generate the phase-conjugate wave. Here, we first stored a phase-distorted signal pulse, \(E_{S}\), in Pr:YSO crystal based on the EIT effect by adiabatically switching off the coupling beam, \(E_{C}\). Then, we launched a readout beam, \(E_{R}\), propagating in the opposite direction with respect to the coupling beam to re-accelerate the atomic coherence grating, and a new field, \(E_{S^{\prime}}\), which was the phase-conjugate wave of the stored signal pulse with distorted phase distribution, was generated.