# Tunable Beam Splitter Based on Acoustic Binary Metagrating
## 3 Results
The white arrows show the directions of the incident and the reflected waves. The polar plots of the normalized intensity of the scattering waves in the exterior field with the incident angle of \(\theta_{i}=~{}0^{\circ}\), \(\theta_{i}=~{}5^{\circ}\), \(\theta_{i}=~{}10^{\circ}\), \(\theta_{i}=~{}15^{\circ}\), and \(\theta_{i}=~{}20^{\circ}\) are shown in Figure 5f-j, respectively. It is noted that the beam splitting effects are obvious. For all these incident angles, when a given acoustic wave arrives at the ABM, it is split into two predesigned directions: split beam 1 (\(-x\) direction) and split beam 2 (\(+x\) direction). With the increase in the oblique incident angle, the reflected angle of the split beam 1 (\(-x\) direction) decreases gradually, while the reflected angle of the split beam 2 (\(+x\) direction) increases gradually. It should be noted that in the range of \(6.4^{\circ}~{}<~{}\theta_{i}<~{}26.4^{\circ}\), there is \(~{}-~{}1~{}<\sin\theta_{i}+nG/k_{0}<~{}1\) for \(n=-2\). In other words, in addition to the diffraction orders of \(n=0\), \(n=-1\) and \(n=1\), the diffraction order of \(n=-2\) also corresponds to the propagating waves in the case of  
Figure 4: The case of \(a~{}=~{}1.4\lambda_{0}\). The scattering pressure field distributions for the beam splitting with the incident angle of (**a**) \(\theta_{i}=~{}0^{\circ}\), (**b**) \(\theta_{i}=~{}5^{\circ}\), and (**c**) \(\theta_{i}=~{}10^{\circ}\). The white arrows show the directions of the incident and the reflected waves. The polar plots of the normalized intensity of the scattering waves in the exterior field with the incident angle of (**d**) \(\theta_{i}=~{}0^{\circ}\), (**e**) \(\theta_{i}=~{}5^{\circ}\), and (**f**) \(\theta_{i}=~{}10^{\circ}\). The lateral axes in (**d–f**) are the normalized intensity defined as \(D(\theta_{r})\). All the intensities are normalized to the maximal intensity of the scattering waves of the normal incidence. \(a\ =\ 1.8\lambda_{0}\). However, as shown in Figure 5h-j, no intensity distribution of the diffracted waves of \(n=-2\) is noted. Thus, the beam splitting occurs in the incident angle range of \(0\ <\ \theta_{i}<\ 26.4^{\circ}\). The reflected angle as a function of the incident angle is also investigated. Figure 6a shows the case of \(a=1.4\lambda_{0}\). For the split beam 1 (\(-x\) direction), the reflected angle decreases from \(45.6^{\circ}\) to \(26.0^{\circ}\) when the incident angle increases from \(0^{\circ}\) to \(16^{\circ}\). For the split beam 2 (\(+x\) direction), the reflected angle increases from \(45.6^{\circ}\) to \(81.9^{\circ}\) when the incident  
Figure 5: The case of \(a\ =\ 1.8\lambda_{0}\). The scattering pressure field distributions for the beam splitting with the incident angle of (**a**) \(\theta_{i}=\ 0^{\circ}\), (**b**) \(\theta_{i}=\ 5^{\circ}\), (**c**) \(\theta_{i}=\ 10^{\circ}\) (**d**) \(\theta_{i}=\ 15^{\circ}\), and (**e**) \(\theta_{i}=\ 20^{\circ}\). The white arrows show the directions of the incident and the reflected waves. The polar plots of the normalized intensity of the scattering waves in the exterior field with the incident angle of (**f**) \(\theta_{i}=\ 0^{\circ}\), (**g**) \(\theta_{i}=\ 5^{\circ}\), (**h**) \(\theta_{i}=\ 10^{\circ}\), (**h**) \(\theta_{i}=\ 15^{\circ}\), and (**j**) \(\theta_{i}=\ 20^{\circ}\). The lateral axes in (**f**–**j**) are the normalized intensity defined as \(D(\theta_{r})\). All the intensities are normalized to the maximal intensity of the scattering waves of the normal incidence. angle increases from \(0^{\circ}\) to \(16^{\circ}\). Figure 6b shows the case of \(a~{}=~{}1.8\lambda_{0}\). For the split beam 1 (\(-x\) direction), the reflected angle decreases from \(33.7^{\circ}\) to \(6.7^{\circ}\) when the incident angle increases from \(0^{\circ}\) to \(26^{\circ}\). For the split beam 2 (\(+x\) direction), the reflected angle increases from \(33.7^{\circ}\) to \(83.7^{\circ}\) when the incident angle increases from \(0^{\circ}\) to \(26^{\circ}\).