Sub-wavelength focusing of acoustic waves in bubbly media

The purpose of this paper is to investigate acoustic wave scattering by a large number of bubbles in a liquid at frequencies near the Minnaert resonance frequency. This bubbly media has been exploited in practice to obtain super-focusing of acoustic waves. Using layer potential techniques, we derive the scattering function for a single spherical bubble excited by an incident wave in the low frequency regime. We then propose a point scatterer approximation for N bubbles, and describe several numerical simulations based on this approximation, that demonstrate the possibility of achieving super-focusing using bubbly media.