Superprism effect in a deformed triangular sonic crystal

The superprism effect in a two-dimensional sonic crystal composed of lead cylinders in water aligned on a lattice obtained by varying the angle between the primitive vectors of triangular lattice is numerically investigated. Symmetry breaking influences the equi-frequency contours to reflect the lattice symmetry, so that compression along a direction leads to smaller critical angles of incidence. The whole 0°-90° range is spanned by the refracted waves at the water/sonic crystal interface for frequencies between 165 and 183 kHz, in the third band, and angles of incidence between 0° and 15°. The studied superprism behaviour can be used to achieve both spectral and angular resolution. The refraction angle varies linearly for small angles of incidence below 3° at a constant frequency, while its frequency dependence at a given angle of incidence is quadratic for small frequencies. Finite-element computations reveal that waves are refracted into the angles calculated from the equi-frequency contours with small beam divergence at any frequencies and angles of incidence.