Level repulsions of bulk acoustic waves in composite materials

Level repulsions of bulk acoustic waves in two-dimensional composite materials and phononic crystals are analyzed in this paper. Detail dispersion curves and displacement fields (polarizations) of bulk acoustic modes in the k (wave vector) space around the region of level repulsion are calculated and discussed. We show that some cross points of the modes that appear in the dispersion curves in the literature are not true intersections. Those cross points due to the level repulsions in the dispersion curves imply mode anticrossing. The displacement fields of the two modes around the cross points interchange with each other abruptly. On the other hand, the other cross points appearing in the dispersion curves are true intersections which implies that the couplings between the modes are vanishingly small. The continuous displacements of the two wave modes around the cross points provide the continuous dispersion curves. The polarizations of the different modes could be used as the criterion of real or apparent cross points in the dispersion curves.