Three-dimensionnal acoustic lensing with a bubbly diamond

A sound wave travelling in water is multiply scattered by a periodic assembly of air bubbles. The local structure impacts the propagation even in the low frequency regime. For instance, when the bubbles are arranged within a Face Centered Cubic (FCC) lattice, a total band gap is observed close to the Minnaert resonant frequency, as the effective wavelength in the crystal matches the Bragg condition. For a diamond lattice, which one obtains by simply adding a second bubble in the unit cell, we report an additional negative branch. At 2929~Hz, by analogy with optics the medium can be described by a refractive index of exactly $n=-1$. We show that a slab of this material can be used to design a three dimensional flat lens. We also report super-resolution in the near field of the slab.