Impacts of uniaxial elongation on the bandstructures of two-dimensional sonic crystals and associated applications

Influences of uniaxial elongation along the direction of triangular and direction of square sonic crystals under the constraint of conserved unit cell area are investigated by examining band structures and equi-frequency contours. Lowest-lying band gap of the triangular lattice observed at high filling fractions diminishes for negative elongation (compression), whereas another band gap develops at lower frequencies whose width reaches appreciable values for moderate elongation. The band gap of the square lattice, which appears at high filling fractions, is modified slightly with elongation. Frequency ranges of the bands, and thus the group velocities along the high-symmetry directions, vary with elongation which may be useful in applications like slow sound propagation. Elongation is observed to modify the equi-frequency contours significantly through reducing the lattice symmetry. The most prominent impact is the transformation of closed contours into open ones, whereas the rest are stretched either along or normal to the elongation axis of the 1st Brillouin Zone. This observation is utilized to implement wide-band all-angle self-collimation and superprism effect, which are demonstrated through Finite-Element computations.