Band-gap engineering in a two-dimensional periodic system of fluids

Abstract

This work emphasizes that periodic binary systems can give rise to genuine acoustic band gaps (or stop bands) within which sound and vibrations remain forbidden. Extensive band structures for two-dimensional (2-D) periodic arrays of air cylinders in water background are computed. 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 almost exact correspondence is attributed to the low-filling fraction and the huge density contrast in air and water. It is stressed that such a simple inhomogeneous system as made up of air and water exhibits the largest stop bands ever reported for 2-D or 3-D elastic as well as dielectric (photonic crystals) composites. [Work partially supported by CONACyT Grant No. 28110E.]