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Recently, Lemoult et al. [Phys. Rev. Lett. 107, 064301 (2011)] used timereversal to focus sound above an array of soda cans into a spot much smallerthan the acoustic wavelength in air. In this study, we show that equally sharpfocusing can be achieved without time reversal, by arranging transducers arounda nearly circular array of soda cans. The size of the focal spot at the centerof the array is made progressively smaller as the frequency approaches theHelmholtz resonance frequency of a can from below, and, near the resonance,becomes smaller than the size of a single can. We show that the locallyresonant metamaterial formed by soda cans supports a guided wave at frequenciesbelow the Helmholtz resonance frequency. The small focal spot results from asmall wavelength of this guided wave near the resonance in combination with anear field effect making the acoustic field concentrate at the opening of acan. The focusing is achieved with propagating rather than evanescent waves. Nosub-diffraction-limited focusing is observed if the diffraction limit isdefined with respect to the wavelength of the guided mode in the metamaterialmedium rather than the wavelength of the bulk wave in air.

Extraordinary focusing of sound above a soda can array without time reversal