Numerical investigations of transmission and waveguide properties of sonic crystals by finite-difference time-domain method

The novel properties of a "sonic crystal" are investigated and its application to a new acoustic waveguide are discussed by developing the finite-difference time-domain (FDTD) method for acoustic wave propagation in a finite-size periodic structure. A sonic crystal is formally an acoustic version of a "photonic crystal." It is not an actual crystal but an artificial one composed of a periodic array of acoustic scatterers imbedded in the host material. and expected to have acoustical band gaps where the acoustic wave cannot penetrate the crystal. These properties are numerically investigated, and sonic crystals are shown not to be acoustic replicas of photonic crystals. Interesting artificial crystals which can be realizable as sonic crystals but not as photonic crystals are realized by clarifying the correspondence relationship between the transverse-electric and transverse-magnetic waves and the longitudinal acoustic wave in the two-dimensional space. Full band-gap characteristics versus wavelength and wave propagation in acoustic waveguides are shown.