The Resonance Structure Units: Comparison
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The construction of structural units is crucial in developing acoustic metasurfaces. These units must fulfill the necessary requirements, including the 2π phase change and being as small as possible. The resonant structure unit that controls large wavelengths with a small size precisely meets this requirement.

  • acoustic wave
  • acoustic metasurfaces
  • reflection
  • transmission
  • absorptive

1. Introduction

The efficient manipulation of electromagnetic or acoustic waves is a prominent area of natural sciences. The metasurface provides a new idea for wave manipulation. In 2011, Yu et al. proposed the theory of interfacial phase discontinuity [1]. “V”-shaped microstructures can be designed in sub-wavelength materials based on the theory, and these materials, known as metasurfaces, can be controlled by geometric parameters of the structure to obtain the phase change of 0 to 2π [2], and consequently, arbitrarily regulate electromagnetic wave propagation, driving a boom in electromagnetic metasurfaces [3,4,5,6][3][4][5][6]. An electromagnetic metasurface has the advantage of a strong modulation, thin size and various production capabilities. Similar to electromagnetic waves, the concept of electromagnetic metasurfaces was quickly extended to the acoustics field. Acoustic metasurfaces can also achieve an arbitrary modulation of acoustic wave propagation. Li et al. designed a two-dimensional ultrathin acoustic metasurface with a space-coiling structure and realized arbitrary regulation of the reflected acoustic wave both theoretically and experimentally [7,8][7][8].
Space-coiling structures [9] and resonance structures are the main two types of structural units for building acoustic metasurfaces. The space-coiling structure achieves relative control of the phase shift by accumulating travel distances of acoustic waves in the coil channel. Furthermore, the resonant structure has the advantage of manipulating large wavelengths with a smaller structure, and the acoustic metasurface constructed by the resonant unit realizes anomalous reflection and focusing at deep subwavelengths. In addition, efficiency is an important issue in the design of acoustic metasurfaces. For example, perfect absorbers and bianisotropic metasurfaces were used in perfect anomalous reflection and transmission. However, it is worth noting that the functionality of these metasurfaces is fixed and they operate only at a single operating frequency or a narrow frequency range. Therefore, the design of tunable acoustic metasurfaces has become a fascinating topic. Such metasurfaces should be tuned either by the geometrical parameters of the structure unit or by external physical fields (e.g., electromagnetic or force fields).

2. The Resonance Structure Units

The construction of structural units is crucial in developing acoustic metasurfaces. These units must fulfill the necessary requirements, including the 2π phase change and being as small as possible. The resonant structure unit that controls large wavelengths with a small size precisely meets this requirement, and it is increasingly researched. These resonant units (e.g., Helmholtz resonance, thin film resonance) can induce unipolar or dipole resonance in the entire structure through various resonance mechanisms and can achieve negative effective modulus or mass density, which is a benefit for adjusting parameters such as phase and resonant frequency. The following provides a concise overview of the resonance principle and research progress on Helmholtz resonance and thin film resonance.

2.1. Helmholtz Resonance Unit

The Helmholtz resonator (HR) is a basic acoustic resonance system that features a cavity surrounded by a rigid wall and an elongated neck. According to the acoustic force analogy theory, this system can be analogized as a spring-mass system, where the cavity’s neck is viewed as a mass and the cavity as a spring. Near the resonant frequency, the incident sound wave resonates strongly in HR and the body cavity gathers a large amount of energy, causing strong vibration of the acoustic medium at the neck. The vibration intensity is much greater than the excitation intensity of incident sound waves, and the dynamic response of the material is not synchronized with the excitation of external sound waves, exhibiting opposite response patterns. That is, when external sound waves compress the medium, the acoustic medium in the material undergoes an expansion motion. When sound waves stretch the medium, it undergoes compression. Therefore, a negative dynamic response occurs and the dynamic elastic modulus of the material is negative near the resonant frequency [12,13,14,15,16,17,18][10][11][12][13][14][15][16]. HRs offer several benefits including a straightforward design, ease of assembly, and a lengthy lifespan. Depending on their structural features, these resonators can be classified into three categories: HR, HR array, and HR-like units. Long et al. present the mechanism for the asymmetric absorption of acoustic waves in a two-port transparent waveguide system by shunting detuned HR pairs in cascade. Acoustic absorption in multiple bands or broadbands is attained by placing several HRs within a waveguide. This design advances the concept of asymmetric acoustic manipulation in passive two-port systems [22,23][17][18]. An HR-like unit is constructed by inserting one or more separating plates with a small hole into the interior of an HR. The multi-order sound absorption mechanism can be achieved so that with the original absorption peak and the structural size unchanged, multiple near-perfect peaks are obtained in higher frequencies by a perforated composite Helmholtz resonator (PCHR) unit [24][19].

2.2. Membrane Resonance Unit

Thin-film acoustic metamaterials can exhibit negative mass and bulk modulus, as well as double negativity within specific frequency ranges. The thin-film unit can also be analogized as a spring-mass system [25][20], where the mass block is viewed as the mass model and the preloading of the thin film as a spring. At the non-resonant frequencies, the thin film, restricted by the acoustic wave and the mass, vibrates near the equilibrium position; that is, all the components move simultaneously, and then the effective and static mass densities become equal. At the resonant frequencies, the cavity accumulates a considerable amount of energy. This energy hinders the synchronized motion of the thin-film structure and the phase reversal of the inner mass and spring occur. When the inner mass momentum exceeds that of the outer mass, the loading force and response acceleration are in the opposite direction, resulting in a negative effective mass density. A double-layer thin-film structural unit is constructed by replacing the lower hard boundary with a thin film. This structure exhibits two dipolar modes that are comparable to those of a single thin film unit; hence, the feature of negative effective mass density is mostly retained. In addition, a new resonance mode has also emerged in the double-layer thin-film structure, and the relative vibration of compression/expansion occurs between the two membranes while the center of mass remains stationary, resulting in a negative effective bulk modulus

References

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