二維有限尺寸聲子晶體區缺陷態之遠場行為及其用於指向性聲波波源之設計

Abstract

當在一個完美周期的聲子晶體結構中，移除單一或更改局部多個散射體之幾何條件會引致局域共振模態。本文採用多重散射法(Multiple Scattering Theory)探討二維有限尺寸聲子晶體之缺陷模態現象，文中首先以單一圓柱散射體之散射矩陣（T-Matrix）與叢集散射體之自恰方程式（Self-Consistent Equation）並搭配布拉格定理（Bloch theorem）進行聲子晶體散射總場、穿射率、散射截面與頻散曲線之分析。次，針對二維有限尺寸聲子晶體缺陷模態與遠場行為散射截面之關係，由散射頻譜可對應出聲子晶體頻溝之現象，並測定缺陷模態之特徵頻率，其結果與現有其他方法之分析相符。此外，基於對局域共振模態之研究，本文亦提出以聲子晶體點共振腔結構產生具放大效果之指向性聲波波源，其中指出共振腔尺寸及局域共振模態之發生頻率為聲波波源指向性效果及放大倍率之關鍵。文對聲子晶體局域共振模態的研究結果及聲子晶體共振腔結構概念的提出，對於水下聲納系統、指向性麥克風或壓電換能器之前瞻研發，可有相當助益。

In this thesis, we present a comprehensive analysis of localized defect modes in two-dimensional finite-size phononic crystals by means of the multiple scattering theory (MST). Based on the theory, we calculate the dispersion diagram, the transmission coefficients, the scattering cross sections, and the elastic field distribution. We find that the far-field analysis based on the scattering cross section can show resonance peaks owing to the resonant tunneling through the defect. Further more, the appearance of a flat plateau feature in the scattering spectra coheres well with the band gap phenomenon. Based on the MST analysis, we also propose a directional enhanced acoustic source by introducing a tunable defect mode. A simple geometrical construction gives a very comprehensive guideline to obtain an enhanced emission with angular confinement from the phononic crystals. We demonstrate that the operating frequency of defect modes and the number of surrounding layers of the cavity are the key factors to the directivity and the amplification ratio of the directional enhanced acoustic source.