We investigate, both experimentally and theoretically, the effect of coupling between resonant scatterers on the transmission coefficient of a model system of isotropic scatterers. The model system consists of a monodisperse layer of bubbles, which exhibit a strong monopole scattering resonance at low ultrasonic frequencies. The layer was a true 2D structure obtained by injecting very monodisperse bubbles (with radius a approximately 100 microm) into a yield-stress polymer gel. Even for a layer with a low concentration of bubbles (areal fraction, n pi a(2), of 10-20%, where n is the number of bubbles per unit area), the ultrasonic transmission was found to be significantly reduced by the presence of bubbles (-20 to -50 dB) and showed a sharp minimum at a particular frequency. Interestingly, this frequency did not correspond to the resonance frequency of the individual, isolated bubbles, but depended markedly on the concentration. This frequency shift is an indication of strong coupling between the bubbles. We propose a simple model, based on a self-consistent relation, which takes into account the coupling between the bubbles and gives good agreement with the measured transmission coefficient.
International audienceWe report the practical realization of phononic crystals with gas inclusions, using soft lithography techniques. Ultrasonic experiments from 0.3 to 5 MHz confirm the existence of deep and wide minima of transmission through the crystal. We show that the first gap is due to the combined effects of Bragg reflections and bubble resonances. We propose a simple layered model that gives a reasonable prediction of the ultrasonic transmission. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3254243
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