  We introduce a class of two-dimensional non-resonant single-phase phononic
materials and investigate its peculiar dispersion characteristics. The material
consists of a thin plate-like structure with an embedded periodic lattice of
Acoustic Black Holes. The use of these periodic tapers allows achieving
remarkable dispersion properties such as Zero Group Velocity in the fundamental
modes, negative group refraction index, bi-refraction, and mode anisotropy. The
dispersion properties are numerically investigated using a three-dimensional
supercell plane wave expansion method. The effect on the dispersion
characteristics of key geometric parameters of the black hole, such as the
taper profile and the residual thickness, are also explored.
