利用含超晶格技術之平面波展開法分析聲子晶體聲波波傳之研究

ANALYSIS OF WAVE PROPAGATION IN PHONONIC CRYSTALS USING THE PLANE-WAVE EXPANSION AND SUPERCELL TECHNIQUES

黃自貴(Zi-Gui Huang)

指導教授 ： 吳政忠

國立臺灣大學/工學院/應用力學研究所/博士(2005年)

https://doi.org/10.6342/NTU.2005.01840

摘要

近年來光子晶體之研究迅速增長，今由於光子與聲子的類比性，可推斷由彈性材料組成之週期性結構，在適當調整其材料常數及排列方式後，通過之聲波亦有頻溝現象存在，而將此類結構稱為聲子晶體。聲子晶體的頻溝現象，可應用於徹體波濾波器或表面聲波濾波器，阻止特定角度與頻率入射的聲子傳遞，藉以達成濾波之效果。本論文所採用之理論分析方法，乃藉由固態物理相關定理與彈性波動方程式之結合，針對兩種彈性材料組成之週期性結構進行分析。
本研究以平面波展開法分析二維聲子晶體其徹體波與表面聲波的波傳行為及頻溝現象，並針對不同效應在調變聲波頻溝上作進一步的探討。其中，針對填充率、旋轉正方柱填充體的角度、溫度效應、中空圓柱結構及組合式聲子晶體，對聲子晶體聲波頻溝大小之影響亦有深入的探究。由於結構形狀對聲子晶體聲波頻溝有很大的影響，且材料本身的特性亦會對聲波頻溝造成相當明顯的變化，因此在適當控制溫度，或以不同結構形狀設計時，聲子晶體結構的聲波頻溝大小將可作調變與應用。當聲子晶體表面聲波與徹體波模態之頻溝可作調變時，這樣的頻溝影響效應，便可對於聲子晶體共振器或濾波器作精密的設計與控制。另一方面，本文利用含超晶格技術之平面波展開法分析缺陷式及波導型聲子晶體的波傳特性，發現含缺陷式聲子晶體之設計可以將某些頻率的波傳能量侷限在缺陷處，以達到共振的效應，此特性不僅徹體波具有，表面聲波亦有明顯的現象產生。而在波導型聲子晶體的研究上，關於單一通道、兩倍寬度通道、雙通道及三通道之波導耦合分析，發現聲波在各種波導上具有特殊的物理現象，並針對這些現象進行深入的探討。
綜言之，本文研究結果顯示此含超晶格技術之平面波展開法在聲子晶體上的波傳理論分析可成功探討聲波頻溝現象及波導研究，藉以這樣的分析模式達成設計二維聲波濾波器及相關聲波元件之目的。

關鍵字

聲子晶體 ； 平面波展開法 ； 超晶格技術 ； 表面聲波 ； 徹體波

並列摘要

Successful application of photonic crystals has led to a rapid growing interest in the analogous acoustic effects in periodic elastic structures called phononic crystals recently. The phenomenon of frequency band gap in the phononic crystal can be applied to the designs of filters for surface and bulk acoustic waves. The repetitive structures made up of different elastic materials can prevent elastic/acoustic waves from passing by at some specific angles or certain frequency bands. The analysis is carried out within the framework of the theorems in solid-state physics and wave equation of motion in inhomogeneous elastic media.
The methods employed in studying the wave motion in phononic crystals are based on the plane-wave expansion method and supercell technique. The formulations for elastic/acoustic wave propagation in phononic crystals are consisted of the materials with general anisotropy. The frequency band-gap features and wave propagation of surface and bulk acoustic waves in the two-dimensional phononic crystals with either square or hexagonal lattices are investigated. The concept of tunable frequency band gaps of the surface and bulk modes in the two-dimensional phononic crystals is introduced by changing the filling fraction, rotating square rods, hollow cylinders, and sectional phononic crystals. On the other hand, the supercell technique is adopted to calculate the defect modes and extended modes in phononic crystals. The technique is also used to analyze the propagating modes and couplings of waveguides in phononic crystals with acoustic channels.
It is worth noting that through a suitable design by using the plane-wave expansion and supercell techniques, the acoustic filters, mirrors, resonators, and waveguides are the possible applications in the two-dimensional phononic crystals.

並列關鍵字

Phononic crystal ； Plane-wave expansion ； Supercell technique ； SAW ； BAW

參考文獻

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