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Nat Mater. 2006 Jun;5(6):452-6. Epub 2006 Apr 30.

Ultrasonic metamaterials with negative modulus.

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Nano-scale Science and Engineering Center, 5130 Etcheverry Hall, University of California, Berkeley, California 94720-1740, USA.


The emergence of artificially designed subwavelength electromagnetic materials, denoted metamaterials, has significantly broadened the range of material responses found in nature. However, the acoustic analogue to electromagnetic metamaterials has, so far, not been investigated. We report a new class of ultrasonic metamaterials consisting of an array of subwavelength Helmholtz resonators with designed acoustic inductance and capacitance. These materials have an effective dynamic modulus with negative values near the resonance frequency. As a result, these ultrasonic metamaterials can convey acoustic waves with a group velocity antiparallel to phase velocity, as observed experimentally. On the basis of homogenized-media theory, we calculated the dispersion and transmission, which agrees well with experiments near 30 kHz. As the negative dynamic modulus leads to a richness of surface states with very large wavevectors, this new class of acoustic metamaterials may offer interesting applications, such as acoustic negative refraction and superlensing below the diffraction limit.


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