Study of the band-structure and the uncoupled modes in two-dimensional phononic crystals with the multiple-scattering theory

The multi-scattering theory (MST) method is applied to study the band structure of the two-dimensional phononic band-gap material. A comprehensive study is performed for the coupling between various order components of the cylindrical scattered wave. It has been found that there are decoupling effects at the edge of the band gap. Therefore, a self-contained self-consistent multiple scattering model of the zeroth-order scattered wave is obtained at the edge of the first band gap. A Mie scattering factor and a lattice structure factor are introduced to give a physical insight into the variation of the gap's starting frequency by graphic analytic method.