## 3 Numerical Simulations and Experiment
and the sub-region lookup table method further drastically reduces the time. According to the trend, it can be seen that the proposed method will be more significant as the sampling spacing decreases and the number of sampling points becomes larger. It is worth discussing the trade-off between the storage size of the lookup table and the computation time. The advantage of the ALUT method is that it requires a smaller lookup table to be stored, while the advantage of the ASLUT method is that it takes less time to compute. Figure 6: (a) Structure of acoustic-optic modulator. (b) The electrode shape of the Ultrasonic transducer. Figure 8: Comparison of the time spent by the point source method, the traditional lookup table method, and the sub-region lookup table method (three forms) for different computational volumes. Figure 7: (**a**) Comparison of the acoustic field distribution calculated by the four methods. (**b**) Comparison of the time taken to calculate the acoustic field distribution by the four methods. (**c**) Root mean square error of angular spectrum method and point source method along the propagation direction. To verify the effectiveness of these two methods for planar radiation sources in practical applications, the point source method, the ALUT method and the ASLUT method are calculated for four different radiation sources. These four sources of radiation are applied in their respective fields. The diamond-shaped and Gaussian-shaped ultrasonic transducers are applied in acousto-optic tunable filters [6]. Ultrasonic transducers with random Gaussian distribution are an improvement of Gaussian-shaped transducers [37]. Segmented transducers are used in acousto-optical devices with large bandwidth requirements and phased arrays [38; 39]. Except for the shape of the transducer, the conditions were the same as in the first experiment. As shown in Figure 9, the ASLUT which stores a single point source and 3 \(\times\) 3 point source array (labeled N3) takes the shortest time to calculate, the ALUT method (labeled \(N2\)) takes the next shortest time and the point source method (labeled \(N1\)) is the slowest. This result is consistent with the theoretical ranking of the three methods of calculating time. It can be seen that any shape of planar radiation source can be reduced by the ALUT and ASLUT methods. It is worth noting that the greater the number of sub-regions that can be separated, the more significant the acceleration effect of the ASLUT method. Finally, the internal acoustic field of the acousto-optic modulator with rectangular electrodes was tested using a digital holographic interferometer and compared with simulation results to verify the computational accuracy of the proposed algorithms. The length and width of the electrodes are 29 mm and 1.5 mm respectively. The propagation distance in the simulation is 12 mm. The propagation distance of the acoustic waves in the real object is slightly shorter and the remaining acoustic waves are deflected by the wedge structure, which does not affect the waveform of the main beam. The rest of the conditions remain the same as in the previous simulation. As shown in Figure 10, the simulation results of the acoustic field distribution after superimposition along the length direction (Y-axis) are approximately the same as those measured by holographic interferometry along the same direction. The results demonstrate that our proposed method can be utilized by industries involved in planar radiation sources which contributes to accurate calculations and reducing time costs. Figure 9: (**a**) Diamond-shaped transducer and acoustic intensity interface at Y = 5 mm. (**b**) Segmented transducer and acoustic intensity interface at Y = 5 mm. (**c**) Gaussian-shaped transducer and acoustic intensity interface at Y = 5 mm. (**d**) random Gaussian-shaped transducer and acoustic intensity interface at Y = 5 mm. (**e**) comparison of three methods to calculate the time of different shapes of electrodes.