Transmission and dispersion relations of perfect and defect-containing waveguide structures in phononic band gap materials

By using a combination of finite difference time domain (FDTD) and plane wave expansion (PWE) methods, we study the propagation of acoustic waves through waveguide structures in phononic band gap crystals composed of solid constituents. We investigate transmission through perfect linear waveguides, waveguides containing a resonant cavity, or waveguides coupled with a side branch resonator such as a cavity or a stub. A linear guide can support one or several modes failing in the absolute band gap of the phononic crystal. It can be made monomode over a large frequency range of the band gap by varying the width of the guide. The transmission through a guide containing a cavity can be made very selective and reduced to narrow peaks associated with some of the eigenmodes of the cavity. The effect of a side branch resonator is to induce zeros of transmission in the spectrum of the perfect guide that appear as narrow dips with frequencies depending upon the shape of the resonator and its coupling with the guide. We find perfect correspondences between the peaks in the transmission spectrum of a waveguide containing a cavity and the dips in the transmission of a cavity side coupled waveguide. Finally, when a gap exists in the spectrum of the perfect guide, a stub can also permit selective transmission of frequency in this gap. The results are discussed in relation with the symmetry of the modes associated with a linear guide or with a cavity.