image: (a) Complex wavelength plane illustration of the frequency response of acoustic materials. Target response and excessive response are associated with the absorption-dominated and reflection-dominated spectra in (b) respectively. (b) Absorption spectra relating to different response functions. view more
Credit: ©Science China Press
Recently, a joint team of researchers from Yong Li’s group in Tongji University (China) and Jie Zhu’s group in Hong Kong Polytechnic University presents the concepts of “over-damped” and “reduced excessive response” impedance modulation. It’s demonstrated that they are the crux in broadband efficient impedance matching at low frequency regime. Based on these concepts, the team designed a metamaterial that has realized efficient impedance modulation from 320 Hz to 6400 Hz, exhibiting broadband sound absorption performance with an average absorption coefficient of 0.93. With a thickness of 10 cm, it approaches the minimum thickness required by the causality constraint. This research has explored the over-damped nature of optimal impedance matching and revealed the significance of near-field non-locality in impedance modulation. The results entitled “Broadband impedance modulation via non-local acoustic metamaterials” have been published in National Science Review on September 11th.
In wave physics, one can rein the energy flow by accurately modulating the material’s surface impedance. When it equals the characteristic impedance of the medium, the so-called “impedance matching” is realized. In this case, energy flow carried by the incident wave is fully absorbed by the material, establishing a zero-reflection boundary at the medium-material interface. This principle is widely applied in ultrasonics study, electromagnetic cloaking, and noise control.
Under the constraint of causality, frequency response of a material must lag behind the incident waves. This constraint restricts the impedance modulating ability of a material with specific thickness, which can be mathematically proved to confine the impedance matching to a finite bandwidth. In other words, the realization of impedance matching in a specific band corresponds to a minimum thickness requirement set by the causality. This brings great challenge to broadband impedance matching in electromagnetic wave and acoustic wave systems. For instance, limited by the impedance modulating mechanism, traditional porous materials can hardly approach the minimum thickness in low frequency regime. The coupled resonant materials can realize broadband impedance matching in low frequency regime. With the bandwidth broadening, however, antiresonances between two local resonances may lead to rapid oscillation of the impedance, breaking the impedance matching condition and lowering the efficiency dramatically.
Starting from system response, the researchers explored the intrinsic connection between frequency response and the material’s absorption spectra. It is presented that the frequency response should be divided into two parts (Figure 1a). While the target response within the semi-circle, corresponding to the absorption-dominated spectra above ωc (Figure 1b)，is directly related to the impedance matching. The excessive response corresponding to the reflection-dominated spectra below ωc has no contribution. From this perspective, better broadband impedance matching can be realized by suppressing the excessive response.
In addition, damping state of the system approaching the causality limit was revealed. The researchers calculated the redundant thickness (difference between the geometry thickness and the causality limit thickness), acoustic resistance, and compared the complex frequency response of two structures with nearly identical absorption spectra (Figure 2). It is found that damping manifests an over-damped state where the causality limit is approached. Consequently, a significant conclusion was drawn: an over-damped modulation is beneficial in approaching the causality limit, which is the crux in efficient broadband impedance matching.
Based on the presented concepts, the researchers constructed a metamaterial absorber in Figure 3a with 36 units to suppress the excessive response. Harnessing near-continuous resonance modes (Figure 3b) and their non-local coupling, the surface impedance is modulated to satisfy the over-damped condition (resistance slightly exceeds 1). As a result, the metamaterial realizes ultra-broadband impedance matching from 320 Hz to 6400 Hz with an average absorption coefficient of 0.93 (Figure 3c-d). More importantly, the excellent impedance modulating ability has been proved to profit from the near-field strong nonlocality. Strong energy exchange among adjacent units in the near field can be observed (Figure 3e). This effect significantly suppresses the anti-resonance and prevents the impedance from oscillating.
See the article:
Broadband impedance modulation via non-local acoustic metamaterials
https://doi.org/10.1093/nsr/nwab171
Journal
National Science Review