# Tunable Beam Splitter Based on Acoustic Binary Metagrating
## 4 Discussion  
In this paper, we demonstrate the beam splitter based on the ABM, which is constructed by etching a straight-walled groove per period on the planar hard surface. This is in contrast to the typical design of the subwavelength unit cells on the acoustic meta-surfaces, which are usually constructed by the multi-folded channels or multi-connected cavities of a deep subwavelength scale. The structure of the ABM in our proposal gives rise to the reduced intrinsic loss and the easy fabrication. The diffraction orders in the proposed ABM take a value of \(n=-1\) (split beam \(1\), \(-x\) direction) and \(n=1\) (split beam \(2\), \(+x\) direction), and hence, the beam splitting occurs. In other words, when a given acoustic wave arrives at the ABM, it is split into two predesigned directions. In our design, the broad region of the incident angle reported here distinguishes our splitter from previous splitters using acoustic metagrating, which are designed only for the normal incidence [8]. The reflected angles of the two split beams are affected by the incident angle. Thus, the directions of the split beams can be readily controlled by setting a proper incident angle. Theoretical analysis of a general grating theory is provided here to demonstrate the physical mechanism underlying the beam splitting. Numerical simulations are provided to give the proof of concept for the proposed acoustic beam splitter. Throughout the paper, the full wave simulations based on the finite-element analysis were performed using COMSOL Multiphysics. In addition to the pressure acoustics module, the electromagnetic waves module was also used. Here, equivalence between acoustics and electromagnetics (TM polarization) in the two-dimensional systems is used. The parameters of density \(\rho\), bulk modulus \(B\), and pressure \(P\) in acoustics are equivalent to the parameters of permittivity \(\varepsilon\), reciprocal permeability \(\mu^{-1}\), and magnetic field component \(H_{y}\) in electromagnetics (TM polarization), respectively. In the proposed ABM, the beam splitting occurs when the period length \(a\) is in the range of \(\lambda_{0}<~{}a~{}<~{}2\lambda_{0}\) and the incident angle \(\theta_{i}\) is in the range of \(0~{}<~{}\sin\theta_{i}<~{}1~{}-~{}\lambda_{0}/a\). Here, the operating wavelength is set as \(\lambda_{0}=~{}100\) mm. Thus, the beam splitting occurs when the period length \(a\) is in the range of \(100\) mm \(<~{}a~{}<~{}200\) mm. In the case of \(a~{}=~{}1.4\lambda_{0}=~{}140\) mm, the beam splitting occurs when the incident angle \(\theta_{i}\) is in the range of \(0~{}<~{}\theta_{i}<~{}16.6^{\circ}\). In the case of \(a~{}=~{}1.8\lambda_{0}=~{}180\) mm, the beam splitting occurs when the incident angle \(\theta_{i}\) is in the range of \(0~{}<~{}\theta_{i}<~{}26.4^{\circ}\). We envision that the proposed beam splitter based on the ABM has potential applications in information processing and biomedical diagnostics. Our beam splitter may be applied in information processing where two positions should be provided with the sound information. For example, considering a scenario in an open and multi-functional conference room, when two regions are the listening regions, our proposed beam splitter can reflect sound along the predesigned routings and enable listening in the two regions without any disturbance in the other regions. In addition, this design may have potential applications in biomedical diagnostics involving two image targets.