## 2 Materials and Methods
### Characterization of Two-Wavelength Coupling Experiment  
The holographic storage properties of ZnCu:Fe:LiNbO\({}_{3}\) crystals were investigated using a two-wavelength coupling experiment [31; 32]. This technique is employed to study the interaction between two light waves in nonlinear optical materials, enabling the observation and analysis of phenomena such as energy transfer and phase modulation between light waves. Consequently, it provides insights into the nonlinear optical properties of the materials. The experimental setup is illustrated in Figure 2. A Kr\({}^{+}\) laser operating at a wavelength of 476 nm and a He-Ne laser operating at a wavelength of 633 nm were used to generate the recording and readout beams, respectively. The recording beam was split into two beams, \(I_{s}\) and \(I_{r}\), of equal intensity (120 mW/cm\({}^{2}\)) using a continuously adjustable beam splitter. These beams were polarized in the incidence plane and directed toward the crystal at the corresponding Bragg angle of 16\({}^{\circ}\), intersecting symmetrically inside the crystal to form a grating vector along the c-axis. The beams were precisely controlled by electronic shutters placed in the object light, reference light, and detection light paths, separating the holographic storage into different storage processes. During grating recording, the shutters in the object light and reference light paths were simultaneously opened to record the refractive index grating, while the probe light was activated to detect the diffraction grating in real time. During grating  
Figure 1: Experimental setup of light-induced scattering measurement. reading, only the shutter in the probe light path was opened, allowing the shallow-level grating to be erased while the deep-level grating was fixed, enabling nonvolatile reading. This process, known as the erasure process, involves eliminating the grating recorded in the shallow layer and fixing the grating recorded in the deep center. The variation in the diffracted light intensity over time was measured using a precision power meter. In the two-wavelength coupling experiment, several parameters, including diffraction efficiency (\(\eta\)), sensitivity (\(S\)), and dynamic range (\(M\)/\(\#\)), were used to evaluate the holographic storage performance of the materials. Diffraction efficiency is a critical indicator for assessing the performance of holographic storage systems, as it directly reflects the efficiency of information recording and reading. Holographic storage records information in materials through interference patterns, and the diffraction efficiency indicates the material's response capability to these patterns. High diffraction efficiency implies that the material can efficiently record interference patterns, thereby storing more information. The diffraction efficiency is defined as the ratio of the intensity of the diffracted light (\(I_{d}\)) to that of the transmitted light (\(I_{t}\)):  
\[\eta=\frac{I_{d}}{I_{t}}\times 100\% \tag{7}\]  
The writing time, or response time, is a crucial parameter in holographic storage, reflecting the dynamic formation of gratings. The formation of a refractive index grating through a dynamic time process can be described by  
\[\sqrt{\eta}=\sqrt{\eta_{sat}}(1-\exp(-t/\tau_{w})) \tag{8}\]  
Here, \(\tau_{w}\) represents the writing time, which determines the speed of recording, and \(\eta_{sat}\) is the saturation diffraction efficiency during recording, a fixed parameter determined by the material's properties. The process of eliminating the refractive index grating can be described by  
\[\sqrt{\eta}=\sqrt{\eta_{sat}}(1-\exp(-t/\tau_{c})) \tag{9}\]  
In this equation, \(\tau_{e}\) represents the time constant for erasing, which characterizes the rate at which the grating is eliminated [33].