# Tunable Beam Splitter Based on Acoustic Binary Metagrating
## 3 Results
In the two cases, it is noted that the reflected angle is affected by the incident angle. Thus, the directions of the split beams can be readily controlled by setting a proper incident angle. The intensity distributions of the diffracted waves of different diffraction orders as a function of the incident angle were also calculated using the COMSOL Multiphysics electromagnetic waves module. It can be derived from Equation (1) that when \(a~{}=~{}1.4\lambda_{0}\) and the incident angle is in the range of \(0~{}<~{}\theta_{i}<~{}16.6^{\circ}\), only the diffraction waves of \(n=0\), \(n=-1\) and \(n=1\) give rise to the propagating waves. Figure 7a shows the normalized intensity of the corresponding diffraction orders as a function of the incident angle. All the intensities are normalized to the intensity of the split beam 1 at normal incidence. It is noted that the intensity of the split beam 1 (\(n=-1\)) gradually increases when the incident angle increases from \(0^{\circ}\) to \(16^{\circ}\). The intensity of the specular reflected beam (\(n=0\)) is extremely small compared to the two split beams (\(n=-1\) and \(n=1\)). Consequently, the beam splitting occurs. It can be derived from Equation (1) that when \(a~{}=~{}1.8\lambda_{0}\) and the incident angle is in the range of \(0~{}<~{}\theta_{i}<~{}26.4^{\circ}\), only the diffracted waves of \(n=0\), \(n=-1\), \(n=-2\) and \(n=1\) give rise to the propagating waves. Figure 7b shows the normalized intensity of the corresponding diffraction orders as a function of the incident angle. All the intensities are normalized to the intensity of the split beam 1 at normal incidence. It is noted that the intensity of the diffracted waves of the high diffraction order (\(n=-2\)) and the specular reflected beam (\(n=0\)) is extremely small compared to the two split beams (\(n=-1\) and \(n=1\)). Consequently, the beam splitting occurs. Figure 6: Analytical and simulated results of the reflected angle \(\theta_{i}\) at different incident angles (**a**) in the case of \(a~{}=~{}1.4\lambda_{0}\) and (**b**) in the case of \(a~{}=~{}1.8\lambda_{0}\). Figure 7: Simulated results of the normalized intensity of the reflected waves at different incident angles (**a**) in the case of \(a~{}=~{}1.4\lambda_{0}\) and (**b**) in the case of \(a~{}=~{}1.8\lambda_{0}\). All the intensities are normalized to the intensity of the split beam 1 at normal incidence. To further investigate the intensity distribution of the diffracted waves of different diffraction orders, a series of numerical simulations were performed to calculate the reflection as a function of the incident angle \(\theta_{i}\) and the period length \(a\) using the COMSOL Multiphysics electromagnetic waves module. It can be derived from Equation (1) that when the period length \(a\) is in range of \(\lambda_{0}<\ a<\ 2\lambda_{0}\) and the incident angle \(\theta_{i}\) is in range of \(0\ <\ \theta_{i}<\ 30^{\circ}\), only the diffraction waves of \(n=0\), \(n=-1\), \(n=-2\), and \(n=1\) give rise to the propagating waves. The reflection of the diffracted waves of \(n=0\), \(n=-1\), \(n=-2\), and \(n=1\) were calculated and are shown in Figure 8a-d, respectively. It is noted that in range of \(0\ <\ \sin\theta_{i}<\ 1\ -\ \lambda_{0}/a\), corresponding to the left part of the orange lines, the reflection of the diffracted waves of the high diffraction order (\(n=-2\)) and the specular reflected wave (\(n=0\)) are extremely small compared to the two split beams (\(n=-1\) and \(n=1\)). In other words, in the proposed ABM, the beam splitting occurs when the period length \(a\) is in range of \(\lambda_{0}<\ a<\ 2\lambda_{0}\) and the incident angle \(\theta_{i}\) is in range of \(0\ <\ \sin\theta_{i}<\ 1\ -\ \lambda_{0}/a\).