Low-Frequency Low-Reflection Bidirectional Sound Insulation Tunnel with Ultrathin Lossy Metasurfaces  
[PERSON]  
1 Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang 212013, China; [EMAIL_ADDRESS] (Y-J.G. ); [EMAIL_ADDRESS] (Y-WX.J. ); [EMAIL_ADDRESS] (Y.G.) [PERSON]  
1 Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang 212013, China; [EMAIL_ADDRESS] (Y-J.G. ); [EMAIL_ADDRESS] (Y-WX.J. ); [EMAIL_ADDRESS] (Y.G.) [PERSON]  
1 Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang 212013, China; [EMAIL_ADDRESS] (Y-J.G. ); [EMAIL_ADDRESS] (Y-WX.J. ); [EMAIL_ADDRESS] (Y.G.) [PERSON]  
1 Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang 212013, China; [EMAIL_ADDRESS] (Y-J.G. ); [EMAIL_ADDRESS] (Y-WX.J. ); [EMAIL_ADDRESS] (Y.G.) [PERSON]  
1 Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang 212013, China; [EMAIL_ADDRESS] (Y.-J.G. ); [EMAIL_ADDRESS] (Y.-WX.J. ); [EMAIL_ADDRESS] (Y.G.) [PERSON]  
2 Key Laboratory of Modern Acoustics, National Laboratory of Solid State Microstructures, Department of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China 23 State Key Laboratory of Acousticsof two reverse ellipse-shaped split tubes [37]. The systems designed by these types of unit cells have the advantages of subwavelength thickness and high-performance sound insulation or absorption. However, most of them have been designed to be closed, and it is therefore difficult to apply them to ventilation structures. To overcome this, a variety of open structures with sound insulation or absorption based on different mechanisms have previously been proposed, including open sound barriers based on resonance coupling [38], coherent interference [39] and artificial Mie resonances [40], and ventilation tunnels based on Helmholtz resonances [41], destructive interference [42] and asymmetric multiple scatterings [43]. In these demonstrated structures, the sound insulation or absorption with ventilation can be shown theoretically and experimentally, but the relatively large thickness and narrow ventilation width restrict their practical applications. Recently, a class of ultrathin structures called acoustic metasurfaces (AMs), which have sound modulation based on the generalized Snell's law [44], have attracted more and more attention due to their wide potential application. By setting desired gradient-phase profiles, the AMs can be applied to the design of metacages [45], open tunnels [46] and windows [47; 48], achieving sound insulation and ventilation simultaneously. However, the working bands of these structures are generally higher than 1000 Hz, and few of them are applied in the low-frequency region. Beyond that, the success of sound insulation is mainly determined by sound reflections created by the AMs, but in some practical scenarios, it is also necessary to create low reflection of sound through open structures. Thus, the design of low-frequency low-reflection open structures with sound insulation based on the sound modulations of AMs has become an urgent problem to be solved. In this work, we propose a type of low-frequency low-reflection bidirectional sound insulation (BSI) tunnel, which is constructed from a pair of lossy AMs with six ultrathin coiled unit cells attached on both sides. Based on the generalized Snell's law and phase modulations by both AMs, we achieved a low-frequency BSI in the tunnel, which arose from the sound reflections and acoustic blind areas created by the AMs. The low-frequency BSI of the tunnel existed in the range 337-356 Hz, and the simulated and measured results were consistent with each other.