Fundamental Experiment and Analysis by FDTD Method on Two-Dimensional Acoustic Artificial Crystals and Acoustic Wave Guide Made of A Periodic Structure

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We have developed fundamental techniques to realize sonic crystals and sonic crystal wave-guides as follows.(1) We found a complete correspondence between the Cartesian components of the particle velocity and sound pressure of two-dimensional sound waves and the electro-magnetic fields of TE and TM waves in their normalized quantities.(2) We introduced a parameter space which is common with sonic crystals and photonic crystals.(3) We constructed an accurate and reliable sonic FDTD program to analyze sound wave propagation, and also an elastic FDTD program. Perfect matched layers are introduced for sound waves. The numerical dispersion problem was theoretically and numerically examined and a practical guide-line was introduced to prevent the dispersion. Movies of the calculated sound-wave propagation are used for a better understanding and investigation of the wave propagation in the crystals.(4) We have constructed a sonic crystal of acrylic-resin cylinders in air with a lattice consta … More nt of 24.0 mm and a radius of the cylinder of 10.2 mm, and observed a full band-gap between 7.0 kHz and 9.4 kHz, which agrees well with theoretical one. Also, we have constructed a sonic crystal slab composed of an array of aluminum cylinders in a slab wave-guide in air, with a lattice constant of 12.0 mm and a scatterer's radius of 5.0 mm, and observed a full band-gap between 14.1 kHz and 18.7 kHz, which also agrees well with theoretical one.(5) Straight and bending wave guides were constructed with the sonic crystals of acrylic-resin cylinders in air, and a good confinement of the sound waves in the wave-guide was assured from the small leakage outside of the crystal. FDTD numerical calculations showed that the sound waves propagate along the straight and bending wave-guides with no practical attenuation with a wide wave-front of almost two times the wave-guide accompanying the evanescent-wave components. These phenomena are presented as MPEG movie files.(6) We have also investigated quantitatively the transient behavior of the guided sound waves in the wave-guides constructed in both sonic crystals composed of acrylic cylinders in air and of air cylinders in agar-gel. Less