Analysis of elastic waves transmitted through a 2-D phononic crystal exhibiting negative refraction

A two-dimensional phononic crystal (PC) made of a square lattice of air holes in an aluminum matrix is studied. The band structure calculated in the irreducible Brillouin zone of the PC exhibits a branch with a negative slope that allows negative refraction. This phenomenon has been numerically verified using a prism-shaped PC for plane waves entering the PC with two different incidences. A detailed study of the waves at the exit of the PC shows that the plane wave is reconstructed after several wavelengths. Finally, the description of the refracted waves is interpreted using a point source array, giving information about the angular spreading and the relative amplitude of each refracted beam.