META 2021, META'12

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Coupled resonant modes in acoustic metamaterials
Ying Cheng, Xiaojun Liu

Last modified: 2011-12-30


Abstract- Acoustic metamaterials constructed by resonant microelements in subwavelength scale were generally characterized by the effective medium approximation theory, which neglects the interaction between adjunct elements. In this paper, novel coupled resonance modes induced by the strong interaction in metamaterials composed of single-slit Helmholtz resonator arranged in two-dimensional square lattice are investigated. We rotate a portion of the resonator so that the adjacent resonator elements in ΓX direction have a twist angle φ. For the system with φ = 180°, the coupling produces the symmetric coupled mode in in-phase oscillation and the anti-symmetric coupled mode in out-of-phase oscillation. The coupled resonance further produces the “hybridization effect”. Such coupled resonance modes may have novel applications in sound wave manipulation.


The artificial acoustic metamaterials consisting of Helmholtz resonator in subwavelength scale can exhibit acoustic properties beyond those found in nature. These unique properties, such as band gap and anomalous transmission, have attracted much attention due to their potential applications in sound wave manipulation. The general case of describing an acoustic metamaterial uses the effective media approximation (EMA) theory. In EMA model, since the resonator element is much smaller in size than the working wavelength, the response of the acoustic metamaterial is treated as the averaged effects of the individual element’s resonance response. Thus the metamaterial can be characterized by the effective parameters of mass density and bulk modulus.


However, the EMA theory ignores the coupling interactions between the resonator elements, which always exist when the elements are structured into metamaterials. In this paper, we investigate the coupled resonance modes in acoustic metamaterials. The metamaterials are composed of single-slit Helmholtz resonator arranged in two-dimensional square lattice with twist angle φ between adjacent resonator elements in ΓX direction. Using the analyses of the dispersion curves and the transmission spectra, a significant modulation to the band structure is demonstrated. The strong interactions between resonator elements are not negligible when φ = 180° and could lead to novel coupled resonance modes which do not exist in uncoupled metamaterials of φ = 0°. We identify these coupled resonances through the pressure fields of the supercell’s eigenmodes. The adjunct resonator elements oscillate in-phase for the symmetric coupled mode and out-of-phase for the anti-symmetric coupled mode. These coupled resonance modes further lead to some “hybridization effect” in the transmission bands, which split the one transmission band in the uncoupled case of φ = 0° into two bands in the coupled case of φ = 180°. In addition, we find that the coupling interactions are very sensitive to the twist angle φ, which could be indispensable to practical applications such as tuning the coupled modes and band gaps. This kind of coupled resonance modes may be used to develop novel metamaterials and functional acoustic devices in the future.


acoustic metamaterials; coupled resonance mode