## 2 The Influence of the Driving Conditions on the Performance of a Phase-Only OASLM
The resistance of the BSO under-uniform illumination level \(\phi\) is \(R_{\phi}\). The value of \(R_{1}C_{1}\) is inversely proportional to the illumination level \(\phi\). Similar models have been introduced in our previous work in Reference [19]. With the input voltage \(V_{AC}=V_{0}cos\omega t\), the voltage drop across the LC layer, \(V_{LC}\), can be calculated using the following equation. \[V_{LC}=V_{AC}\times\frac{\frac{1}{R_{0}}+\frac{1}{R_{\phi}}+j\omega C_{BSO}+ \frac{j\omega C_{1}}{1+j\omega R_{1}C_{1}}}{\frac{1}{R_{0}}+\frac{1}{R_{\phi} }+j\omega C_{BSO}+\frac{j\omega C_{1}}{1+j\omega R_{1}C_{1}}+\frac{1}{R_{LC}} +j\omega C_{LC}} \tag{3}\]  
These \(V_{LC}\) values as a function of the frequency of the \(V_{AC}\), when the OALCLV is illuminated with different write-light irradiances, are shown in Figure 2b, and are solved using Equation (3) with an root mean square (RMS) value of \(V_{AC}=3.5\) V. Several physical parameters have been used in the model as follows [20]: \(\rho_{LC}=10^{10}\)\(\Omega\cdot\)cm and \(\varepsilon_{LC}=10\) are the density and relative dielectric constant of the LC, respectively, and \(\sigma_{0}=10^{-14}\)\(\Omega^{-1}\)cm\({}^{-1}\) is the dark BSO crystal conductivity. The dotted line indicates \(V_{thr}\). These marked points correspond to the experimental values, which are basically consistent with the simulated values and confirm the validity of Equation (3). From the figure we can see that \(V_{LC}\) decreases with increase in frequency when the OALCLV is under the same write-light irradiance. Meanwhile, \(V_{LC}\) increases with increase in write-light irradiance when the OALCLV is under the same driving voltage frequency. The \(V_{LC}\) of the OALCLV must be greater than \(V_{thr}\) to ensure the voltage response and the maximum value of \(V_{LC}\) directly determines the PV value of the phase change, that is the phase modulation ability of the OASLM. However, \(V_{LC}\) on the LC layer of the OALCLV is difficult to measure directly in the experiment, so we have experimentally verified the effect of four write-light irradiances and four kinds of frequencies of \(V_{AC}\) on the phase change ability, and simulated these results using Equation (3), which are depicted in Figure 3.  
In Figure 3a, the solid lines show the relation between the phase change and \(V_{AC}\) at 200 Hz when the OASLM is subjected to four different write-light irradiances of 3.25 mW/cm\({}^{2}\), 5.75 mW/cm\({}^{2}\), 7.75 mW/cm\({}^{2}\), and 9.5 mW/cm\({}^{2}\). The dashed line shows the simulated phase-change relation deduced from the voltage response of the LC and Equation (3). The average error-rate between the simulated and experimental values is 3.5%. The figure illustrates that as the write-light irradiance decreases in the range of 9.5-3.25 mW/cm\({}^{2}\), the reduction of \(V_{LC}\) being approximately 1 V in Figure 2b, which results in a decrease in phase-change PV value of 0.4\(\lambda\). In Figure 3b, the solid lines show the relation between the phase change and \(V_{AC}\) at four different driving frequencies, namely 50 Hz, 100 Hz, 150 Hz, and 200 Hz when the OALCLV is uniformly illuminated with the write-light of irradiance 9.6 mW/cm\({}^{2}\). The dashed line shows the simulated phase-change relation. The average error-rate between the simulated and experimental values is 2%. Figure 3: (**a**) Phase change varies with \(V_{AC}\) at 200 Hz when the OALCLV is illuminated by the different write light, the \(V_{rms}\) is the RMS value of the \(V_{AC}\). (**b**) Phase change varies with \(V_{AC}\) when the OALCLV is at the different drive frequencies and the write-light irradiance is 9.6 mW/cm\({}^{2}\). Figure 2: (**a**) Equivalent circuit of the OALCLV. (**b**) The voltage values on the LC layer of the OALCLV at the applied voltage of 3.5 V, experimental points and theoretical curves according to Equation (3), for different frequencies of the applied voltage.