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

我们已经开发了基本的技术来实现声波晶体和声波晶体波导如下。(1)我们发现了一个完全对应的笛卡尔分量的粒子速度和声压的二维声波和电磁场的TE和TM波在其归一化量。(2)我们引入了一个参数空间，这是共同的声波晶体和光子晶体。(3)我们编制了一个精确可靠的声波时域有限差分程序来分析声波的传播，同时也编制了一个弹性时域有限差分程序。完美匹配层被引入声波。从理论上和数值上分析了数值色散问题，并引入了一种实用的导引线来防止色散。计算的声波传播的电影用于更好地理解和研究晶体中的波传播。(4)我们在空气中构造了一个具有晶格常数的丙烯酸树脂圆柱体的声波晶体。 ...更多信息 nt为24.0 mm，圆柱半径为10.2 mm，观察到7.0 kHz和9.4 kHz之间的全带隙，这与理论值吻合得很好。此外，我们已经构建了一个声波晶体板组成的阵列的铝柱在平板波导在空气中，与晶格常数为12.0毫米，散射体的半径为5.0毫米，并观察到一个完整的带隙之间的14.1 kHz和18.7 kHz，这也符合理论。(5)用空气中的丙烯酸树脂圆柱体的声波晶体构造直波导和弯曲波导，并且从晶体外部的小泄漏确保了波导中的声波的良好限制。FDTD数值计算结果表明，声波在直波导和弯曲波导中传播时，沿着传播，没有实际衰减，波前宽度几乎是波导的2倍，并伴有倏逝波分量。这些现象被呈现为MPEG电影文件。(6)我们还定量地研究了在空气中的丙烯酸圆柱和在琼脂凝胶中的空气圆柱组成的声波晶体中的导波的瞬态行为。少

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