在早期聲子晶體的研究與探討主要是集中於能隙的應用與計算，如濾波器、波導或共振腔的設計。而近年來研究發現在其傳導區擁有異常之頻散現象，發現聲子晶體具有負折射特性，使得該方面之研究更成為最近學術界的熱門話題。
本文以平面波展開法求得二維聲子晶體的等頻圖，並利用等頻圖判斷出會產生負折射的入射角度與頻率，預測其負折射角度，分析其頻散現象。再利用有限元素法模擬負折射現象。
為了主動調變聲波的傳遞方向，我們用溫度的變化來改變背景的密度與波速，進而控制聲子晶體的折射方向，用以控制聲波聚焦的距離，並可以藉此設計出以溫度調變的可調式平面聲波透鏡。除此之外，我們將聲子晶體之填充物以橢圓柱取代圓柱後，橢圓柱之幾何非等向性明顯使其等頻圖產生改變，使得垂直入射的聲波即可發生折射，分析橢圓柱不同的旋轉角，來獲得不同的折射角度，與不同方向的晶格排列之頻散現象，進而控制聲波傳遞的方向，可利用橢圓柱聲子晶體的概念可設計出可調式聲波導、聲波開關與可調式分波器，且經過適當旋轉角配置之橢圓柱聲子晶體，也可藉此設計出使平面入射的聲波聚焦的聲波聚焦透鏡。最後，以實驗來證明聲子晶體的負折射現象，並與有限元素法之模擬結果做比對。這些聲子晶體聲波元件可應用在未來的生醫科技與機械領域上。

Dispersion characteristics of negative refraction sonic crystals are investigated, of which the anomalous refractive properties (especially negative refraction) have become hot topics of scientific research over the past few years. Scope of the investigation is not limited to the band gap region. The plane wave expansion method is used to obtain the equifrequency surface. The anomalous refractive properties of sonic crystals are analyzed and predicted by using the equifrequency surface. Then we employ the finite element method to simulate the acoustic wave propagation within sonic crystals, and the obtained refractive direction is compared with that predicted by the equifrequency surface.
The temperature tunable dispersion characteristics of sonic crystals are observed. By controlling the temperature, we can tune the refractive direction and adjust the location of focus, and then the tunable acoustic superlenses can be designed. The dispersion characteristics of the two-dimension sonic crystals of elliptic rods are also studies. Due to the large anisotropy of elliptic rods, we can rotate the elliptic rods to obtain different structure factors. The anisotropic property can then be used to tune the refraction direction and the dispersion characteristics. The obtained results can be applied to develop various sonic crystal devices, such as tunable acoustic waveguides, acoustic switches and tunable acoustic splitters. In addition, we design an acoustic focusing superlens made of a two-dimension elliptic rod sonic crystal that will cause an incident plane wave to be converted to a point source. Finally, we work on the negative refraction phenomena experiments of sonic crystals and compare the results of experiments with simulation results of finite element method. The novel sonic crystal devices may provide applications in biomedical and mechanical technology

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