Supplementary material to:
Perfect absorption of low-frequency sound waves by critically coupled
subwavelength resonant system
Houyou Long1, Ying Cheng1,2*, Jiancheng Tao1, Xiaojun Liu1,2†
1
Key Laboratory of Modern Acoustics, Department of Physics and Collaborative Innovation
Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
2
State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences,
Beijing 100190, China
E-mail: * [email protected]; † [email protected]
Section 1: Macroscopic effective acoustic parameters of porous materials
As mentioned in the manuscript that the porous materials used in this work satisfy the
Johnson-Champoux-Allard model and they can be assumed as homogeneous effective fluid
with an effective mass density ρα and an effective bulk modulus κα . In the manuscript, we
have depicted the porous materials by microscopic parameters. Here, we demonstrate the
effective mass density ρα, effective bulk modulus κα , and effective wave number ke of the
porous materials S1 and S2 in Figs. S1(a)-(c), respectively. Note that the imaginary part of ke
is the key parameter to characterize the transmission loss, and it can be seen from Fig. S1(c)
that Imag(ke) of S1 is larger than that of S2. To describe the loss more intuitively, the
absorptances of S1 and S2 with a thickness of 82 mm are further presented in Fig. S1(d). The
result confirms that S1 has a larger loss factor than S2.
1
Fig. S1 Macroscopic effective acoustic parameters of S1 and S2. (a) Effective mass density
ρα , (b) effective bulk modulus κα , (c) effective wave numbers ke, (d) absorptances of S1 and
S2 with a thickness of 82 mm.
Section 2: Generality of PA with different porous materials
Although we employed specific porous material S1 and S2 for illustration in the
manuscript, the findings can enable flexible realization of acoustic PA in general material
combinations. We have tested several common porous materials with different flow resistance
σ as listed in Table S1. Figure S2 shows the absorptances of these porous materials, which
indicates that σ is the key parameter to determine the loss of porous material and the loss
−1
factor 𝑄loss
consequently. Therefore, when different porous materials are employed, we can
−1
tune the leakage factor 𝑄leak
by configuring the width d of the LRP to realize a critically
coupled system and get PA, as demonstrated in Fig. S3. Thus, the scheme proposed could
show good generality and PA can be achieved in common porous materials by carefully
decorating the geometric parameters of the system.
2
Fig. S2 Absorptances for the porous material plates with different acoustic parameters. The
thicknesses of the plates are all kept as 82 mm.
Fig. S3 Absorptances for LRPs with different porous materials.
3
Table S1 Acoustic parameters of several common porous materials1-3
ϕ
α∞
Ʌ(μm)
Ʌ'(μm)
σ(N s m-4)
S1
0.96
1.07
273
672
2843
SS1
0.99
1
88
160
7300
SS2
0.99
1
70
210
7900
SS3
0.97
1.42
180
360
8900
1
J.-P. Groby, C. Lagarrigue, B. Brouard, O. Dazel, V. Tournat, and B. Nennig, J. Acoust. Soc.
Am. 137, 273 (2015).
2
O. Doutres, N. Atalla, and H. Osman, J. Acoust. Soc. Am. 137, 3502 (2015).
3
J.-P. Groby, B. Brouard, O. Dazel, B. Nennig, and L. Kelders, J. Acoust. Soc. Am. 133, 821
(2013).
4