# An Ultra-Thin Composite Metasurface with Hybrid-Damping Modes for Broadband Sound Absorption
## 1 Introduction  
As modern equipment rapidly develops toward being more heavy-duty and high-speed, there exists a large amount of low-frequency broadband noise inside, but the stringent constraints on weight and thickness impose higher requirements on the absorption structures or materials. While traditional porous materials can achieve broadband absorption [1; 2], they demonstrate poor efficiency for low-frequency noise. In recent years, the advancement of metamaterials and metasurfaces has presented novel solutions to tackle the low-frequency challenge [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15]. However, the peak remains narrow due to the inherent limitations of resonance. Therefore, it remains a significant challenge to achieve broadband absorption from a low-frequency to high-frequency regime with compact structures.  
By stimulating more absorption peaks and achieving rigorous peak couplings, the band of the current metamaterials can nearly encompass the low- and mid-frequency range below 4000 Hz [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. However, for the equipment applications, these structures are too thick, and the band is not wide enough. To expand the band into the high-frequency region, specifically up to 10,000 Hz, the most practical approach is to couple the metamaterials with porous materials [27; 28; 29; 30; 31; 32; 33; 34; 35; 36]. The composite structures can be generally divided into two categories: series or parallel arrangement. The parallel structure comprises metamaterials and porous materials arranged in parallel [27; 28; 29; 30; 31], enabling separate absorption of low- and high-frequency noise by each material. To prevent significant degradation in high-frequency absorption, it is crucial to ensure that the utilization ratio of porous materials to the whole structure remains above 70%. Owing to the limited absorption area, the metamaterials can only achieve a narrow band in the low-frequency range, thus preventing the full realization of their potential. In a series structure, the porous materials are placed in front of the metamaterial surface, and the sound waves need to pass through porous materials to reach the metamaterials [32; 33; 34; 35; 36]. To ensure continuous absorption, the porous materials must possess a specific thickness (usually above 20 mm) to achieve a lower-limit frequencythat can be extended to the upper-limit frequency of the metamaterials band. However, the 20 mm-thick porous layer is highly detrimental to the design of compact structures, which can result in a larger utilization ratio exceeding 50%. If the porous layer possesses a thinner thickness, its lower-limit frequency shifts towards higher frequencies, resulting in a discontinuity in the middle of the entire frequency band. Consequently, this significant challenge needs to be solved to achieve a broader band with a thinner metamaterial. To fully leverage the low-frequency absorption advantages of the metamaterials, it is essential to reduce the utilization ratio of porous materials to mitigate their effects; otherwise, the benefits of metamaterials will be submerged or even lost.  
In this work, an ultra-thin composite metasurface is introduced, in which a compound Helmholtz resonant (HR) structure and porous materials are integrated into a series-parallel connection. The HR structure comprises multiple compound cells with hybrid-damping modes, resulting in an excellent absorption spectrum that extends up to 3000 Hz. After incorporating the porous materials in series-parallel connection, the metasurface achieves about 85% average absorption across an ultra-broadband range of 750-10,000 Hz, while maintaining a thickness of just 31 mm. The utilization ratio of porous materials is reduced to about 35% for fully exploiting the low-frequency advantages of the metamaterial. Compared to the traditional porous materials, the metasurface exhibits a significant enhancement in low-frequency performance, particularly below 1600 Hz.