Evidence of Fano-Like Interference Phenomena in Locally Resonant Materials

Goffaux, Cécile; Sánchez‐Dehesa, José; Yeyati, A. Levy; Lambin, Ph.; Khelif, Abdelkrim; Vasseur, J. O.; Djafari‐Rouhani, Bahram

doi:10.1103/physrevlett.88.225502

Cited by 345 publications

(186 citation statements)

References 18 publications

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“…In the second implementation, the ventilated composite absorber, we place a DMR in the center of a hollow tube and mount a HMR on the sidewall to generate monopolar resonance. When the HMR resonates at the same frequency of the DMR's Fano resonance [7,[23][24][25], perfect absorption has also been found while the air can freely flow through the tube.The basis of understanding the perfect absorption by this type of degenerate resonators is that, for a resonator in a planar array with sub-wavelength dimension, only its surfaceaveraged displacement W over the unit cell, i.e., piston-like motion component, couples to radiative modes in air. Here, W denotes the resonator's displacement normal to the plane and the brackets denote surface averaging.…”

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confidence: 99%

Subwavelength total acoustic absorption with degenerate resonators

Yang

Meng

et al. 2015

Applied Physics Letters

241

117

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We report the experimental realization of perfect sound absorption by sub-wavelength monopole and dipole resonators that exhibit degenerate resonant frequencies. This is achieved through the destructive interference of two resonators' transmission responses, while the matching of their averaged impedances to that of air implies no backscattering, thereby leading to total absorption. Two examples, both using decorated membrane resonators (DMRs) as the basic units, are presented. The first is a flat panel comprising a DMR and a pair of coupled DMRs, while the second one is a ventilated short tube containing a DMR in conjunction with a sidewall DMR backed by a cavity. In both examples, near perfect absorption, up to 99.7%, has been observed with the airborne wavelength up to 1.2 m, which is at least an order of magnitude larger than the composite absorber. Excellent agreement between theory and experiment is obtained.Total absorption of sound using subwavelength structures or materials has always been a challenge, since the linear dynamics of dissipative systems dictates the fractional power to be linearly proportional to the elastic deformation energy [1], which is negligible in the sub-wavelength scale. To enhance the dissipation, it is usually necessary to increase the energy density, for example, through resonances. However, in an open system, radiation coupling to resonances is an alternative that can be effective in reducing dissipation. In previous studies, by utilizing localized subwavelength resonances, membrane-type metamaterial [2][3][4][5][6][7], containing decorated membrane resonator (DMR) with tunable weights, has shown efficient and flexible capability in low frequency sound absorption [8]. A balance between dissipation and scattering at resonance has been found for optimum absorption [9]. More recently, a perfect absorber has been realized by hybridizing DMR's two resonances through coupling via a thin gas layer. Through interference, waves reflected from such DMR have been shown to completely cancel that from a reflective wall placed a short distance (about 1/133 of airborne wavelength) behind the DMR [9,10]. Meanwhile, the coherent perfect absorber (CPA) in optics shows that the scattering waves at resonance can be cancelled when another counterpropagating coherent light wave, with specific phase and intensity, interferes with the incident beam, thereby leading to total absorption [11][12][13][14][15][16]. Recent efforts have also been made for its analogy in acoustics [17][18][19][20]. However, except for some theoretical attempts in acoustic [21] and numerical studies in optics [22], up to now no perfect absorber has been experimentally realized that intrinsically eliminates all the scattered waves, thereby realizing total absorption regardless of the incident direction, and with no need for a control wave.In this article, we advance the idea of creating a total acoustic absorption unit comprising a monopole (symmetric under mirror reflection) and a dipole (anti-symmetric) resonator that are re...

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confidence: 99%

Subwavelength total acoustic absorption with degenerate resonators

Yang

Meng

et al. 2015

Applied Physics Letters

241

117

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“…2 Similar results were reported for a three-component two-dimensional (2D) system: resonance-induced band gap was observed for rubber-coated lead cylinders embedded in an epoxy matrix. 3 For 2D structures formed with rubber-coated square lead rods embedded in an epoxy matrix, numerical simulations indicate that the transmission coefficient show dips at resonant frequencies. Dips in transmission loss spectra of stiff structures containing local resonant units can be modeled by simple onedimensional harmonic oscillators with frequency-dependent effective complex mass.…”

Section: Introductionmentioning

confidence: 99%

Analytic model of phononic crystals with local resonances

2005

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A simple analytic model is presented to describe the low-frequency effective mass densities of threecomponent phononic crystals with local resonances. We show that the effective mass densities can turn negative close to the local resonances. Expressions for the effective mass densities are derived for both threedimensional systems with coated spheres embedded in a host matrix, and two-dimensional systems with coated cylinders embedded in a host matrix.

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“…These values have been used not only to represent experimental phononic band diagrams 4,6,7 but also to perform theoretical calculations of phononic structures. [9][10][11][12] Owing to the presence of cross links, this silicone rubber is reported to possess a small but finite shear modulus G = 40 kPa. 8 Hence, the longitudinal sound velocity c l = (M/ρ) 1/2 ≈ 23 m/s is beyond any physically meaningful value in polymer science; for a low molecular weight (i.e., liquid) PDMS, c l = 1050 m/s and G is zero because shear waves cannot be supported.…”

Section: Introductionmentioning

confidence: 99%

Soft silicone rubber in phononic structures: Correct elastic moduli

et al. 2013

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We report on a combination of experiments to determine the elastic moduli of a soft poly (dimethylsiloxane) rubber that was utilized in a smart experiment on resonant phononic modes [Liu et al., Science 289, 1734(2000] and whose reported moduli became widely used as a model system in theoretical calculations of phononic materials. We found that the most peculiar hallmark of these values, an extremely low longitudinal sound velocity, is not supported by our experiments. Anyhow, performing theoretical band structure calculations, we can reproduce the surprising experimental findings of Liu et al. even utilizing the correct mechanical parameters. Thus, the physical conclusions derived in the theoretical works do not require the use of an extremely low longitudinal velocity, but can be reproduced assuming only a low value of the shear modulus, in agreement with our experiments.

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Evidence of Fano-Like Interference Phenomena in Locally Resonant Materials

Cited by 345 publications

References 18 publications

Subwavelength total acoustic absorption with degenerate resonators

Subwavelength total acoustic absorption with degenerate resonators

Analytic model of phononic crystals with local resonances

Soft silicone rubber in phononic structures: Correct elastic moduli

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