Analysis of dispersion characteristics of phononic structures

A general theory for calculating the dispersion of bulk acoustic waves in 3D and 2D phononic crystals made of anisotropic materials is presented, which is based on the plane-wave expansion method. Two approaches to separating acoustic modes in the dispersion diagrams are proposed. The pattern of the acoustic field distribution is studied as depending on the wavevector direction for various types of modes. Degeneracy of acoustic modes in directions different from the axes of symmetry of the phononic crystal is demonstrated. Possibilities of the proposed method are illustrated by the application to 3D and 2D silicon-based phononic crystal structures.