Band Structure of Three-Dimensional Phononic Crystals with an Opal Structure

We made a systematic investigation on the band structure of sound waves in three-dimensional phononic crystals consisting of periodic arrays of spheres with an opal structure. The opal structure is made with close-packed solid spheres surrounded by air (or vacuum). We introduce a sintering parameter which characterizes the contact between adjacent spheres. For a proper range of parameters we find the existence of a complete band gap in the structure. We also find that several flat bands appear below the lowest eigenfrequency of vibration of the isolated sphere. To understand the vibrational motion of the modes in these flat bands, their intensity distributions are also shown.