## 3 Results and Discussion
### Two-Wavelength Coupling Experiment  
In this experiment, variable-valence Fe\({}^{3+}\) and Cu\({}^{2+}\) ions were incorporated into the crystal lattice as photorefractive centers. Specifically, Fe\({}^{2+}\) and Cu\({}^{+}\) acted as donor levels, while Fe\({}^{3+}\) and Cu\({}^{2+}\) ions served as acceptor levels. These two ions play a crucial role as the sensitive centers for photorefraction and significantly influence the photorefractive properties of the crystal, thereby having a substantial impact on its holographic storage performance. The Zn\({}^{2+}\) ion remains in a stable univalent state within the crystal, thereby abstaining from participating in both the charge transport and grating formation processes. The carrier transport model of Zn:Cu:Fe:LiNbO\({}_{\rm 3}\) crystal is illustrated in Figure 6, where the conduction band edge is represented by the 4d orbital of the Nb\({}^{5+}\) ion, and the valence band edge is represented by the 2p orbital of the O\({}^{2-}\) ion. The iron exists as Fe\({}^{3+}\) and Fe\({}^{2+}\) ions, serving as shallow central levels, while the copper exists as Cu\({}^{2+}\) and Cu\({}^{+}\) ions, acting as deep central levels. The deep-level carriers of the Cu\({}^{+}\) and Fe\({}^{2+}\) ions are excited through energy absorption under illumination conditions, thereby complementing each other by facilitating energy transfer and modifying the ionization cross-section as well as capturing the cross-section. The enhancement in the photorefractive properties can be attributed to the utilization of double photorefractive ions in LiNbO\({}_{\rm 3}\) crystals. The Fe\({}^{3+}\) and Cu\({}^{2+}\) ions undergo electron acquisition to form Fe\({}^{2+}\) and Cu\({}^{+}\) ions, thereby initiating a continuous release of electrons. Subsequently, these released electrons are captured by migrating Fe\({}^{3+}\) and Cu\({}^{2+}\) ions, thus completing the transportation process. The process can be represented as follows:  
\[\rm{Fe}^{2+}+hv\to Fe^{3+}+e \tag{15}\]  
\[\rm{Fe}^{3+}+e\to Fe^{2+} \tag{16}\]  
\[\rm{Cu}^{+}+hv\to Cu^{2+}+e \tag{17}\]  
\[\rm{Cu}^{2+}+e\to Cu^{+} \tag{18}\]The presence of doped Zn\({}^{2+}\) ions directly influences the occupancy of ions and the types of defects in Zn:Cu:Fe:LiNbO\({}_{3}\) crystals, subsequently leading to changes in their internal structure and defect type, which in turn affect the photoconductivity of the crystal and consequently its photorefractive effect. Figure 7 illustrates the readout curves of the nonvolatile two-wavelength holographic recording. Table 2 presents the holographic storage parameters of Zn:Cu:Fe:LiNbO\({}_{3}\) crystals, which were determined through a two-wavelength coupling experiment. It is evident that the diffraction efficiency of the crystal exhibits a gradual increase as the concentration of Zn\({}^{2+}\) ions rises. When the doping concentration of Zn\({}^{2+}\) ions is below 7 mol%, they preferentially replace the Nb\({}_{\text{Li}}^{4+}\) in the lattice, which reduces the intrinsic defect concentration and then increases the crystal conductivity. The writing time \(\tau_{w}\) can be expressed as follows [41]:  
\[\tau_{w}\approx\frac{\varepsilon\varepsilon_{0}}{4\pi\sigma_{ph}} \tag{19}\]  
Figure 6: The model of carrier transport in double photorefractive centers. Figure 7: Time dependence of diffraction efficiency during two-wavelength holographic recording for samples. where \(\varepsilon\) represents the dielectric constant; its specific value is 2.8 \(\times\) 10\({}^{-11}\) and does not change due to doping ions. \(\varepsilon_{0}\) is the dielectric constant in free space, and its specific value is 8.9 \(\times\) 10\({}^{-12}\). The writing time \(\tau_{w}\) exhibits a negative correlation with the photoconductance \(\sigma_{ph}\). As the concentration of Zn\({}^{2+}\) ions increases, the defect concentration of Nb\({}_{\rm Li}^{4+}\) decreases, thereby enhancing the photoconductivity \(\sigma_{ph}\) of the crystal and reducing the writing time \(\tau_{w}\).