Giant sonic stop bands in two-dimensional periodic system of fluids

Abstract

Periodic binary systems can give rise to genuine acoustic stop bands within which sound and vibrations remain forbidden. We compute extensive band structures for two-dimensional (2D) periodic arrays of air cylinders in water. Complete, multiple, huge stop bands are found for both square and hexagonal lattices. The lowest stop bands are largest for a range of filling fraction 10%⩽f⩽55%, with a gap/midgap ratio of 1.8. The most interesting finding of the present investigation is that the low-frequency, flat passbands for a perfectly periodic system correspond to the discrete modes of a single airy cylinder. This is attributed to the low filling fraction and huge density contrast in air and water. We stress that such a simple inhomogeneous system as made up of air and water exhibits the largest stop bands ever reported for 2D or 3D elastic as well as dielectric composites.