Complex band structure of acoustic waves in superlattices

Abstract Using a transfer matrix method, we investigate the complex band structure of acoustic waves involving one, two or three components of the displacement field. The example of an hexagonal Y-Dy superlattice and a cubic GaAsAlAs superlattice are studied. When two or three directions of vibrations are coupled together the dispersion curves may show both direct and indirect gaps appearing inside the reduced Brillouin zone. The attenuation coefficients and the behaviour of surface waves whose frequencies are situated inside the gaps are also discussed.