Defect states of acoustic waves in a two-dimensional lattice of solid cylinders

Using the plane-wave expansion method, we study the propagation of acoustic waves through two-dimensional (2D) periodic composites consisting of solid cylinders in air. Defect in those structures create localized states inside the band gaps. We study both single and line defects. Line defects can act as a waveguide for acoustic waves while single defects can be used as acoustical filters.