聲子晶體與聲學超穎介質之聲學特性研究

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姓名

江鎮余(Chen-yu Chiang) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

聲子晶體與聲學超穎介質之聲學特性研究
(The acoustic properties of phonotic crystals and acoustic metamaterials)

相關論文

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★ 光子晶體異常折射之研究	★ 光子晶體傳導帶與介電質柱波導之研究
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★ 新式光子晶體波導濾波器之研究	★ 廣義非均向性介質的光傳播研究
★ 光子晶體耦合濾波器之研究	★ 聲子晶體傳導帶與週期性彈性柱波導之研究
★ 對稱與非對稱波導光柵之特性研究	★ 雙曲透鏡之研究
★ 電磁波與聲波隱形斗篷之研究	★ 一維光子晶體等效非均向介值之研究

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摘要(中)

本篇論文主要探討聲波在超穎材料介質 (metamaterial media) 中的波傳特性。我們首先回顧超穎材料發展史及介紹超穎材料各項熱門研究主題，接下來介紹在本論文研究中會使用到的各項理論模擬計算方法以及算式的推演，包括：平面波展開法、Dirichlet to Neumann 法、多重散射法、聲波電路圖以及有限時域差分法 (使用Z transformation)。此篇論文的研究主題包括：探討不同晶格排列的光子晶體平板對點波源聚焦點像的影響、聲子晶體平板負折射、聲子晶體波導耦合條件限制，以及管中聲波能量的傳遞特性及分佈之探討。最後總結此篇論文的主要結論以及探討未來的展望。

摘要(英)

In this thesis we discuss the properties of acoustic wave in metamaterial media. We first review the history of metamaterials and introduce activity topics of metamaterial research. The numerical methods are introduced and relevant formulas are derived in chapter 2. These numerical methods include: Plane wave expansion method, Dirichlet to Neumann method, Multiple scattering method, Effective circuit diagram of acoustic system, and Finite difference time domain (FDTD) method based on Z transforms. Four topics are included in this thesis: the stability of subwavelength imaging of a photonic crystal slab, the off-plane shear waves focusing of a phononic crystal slab, phononic crystal waveguide of array cylinders, and acoustic field propagation in a dispersive medium. Finally, we summarized the main conclusions and discuss the future work.

關鍵字(中)

★ 聲學超穎介質
★ 聲子晶體

關鍵字(英)

★ acoustic metamaterials
★ phononic crystals

論文目次

摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 VI
表目錄 X
第一章簡介 1
1-1 光子晶體 (photonic crystals) 2
1-2 完美透鏡 (Perfect lens) 4
1-3 雙曲透鏡 (Hyperlens) 6
1-4 人工電磁黑洞 (Artificial EM-wave black hole) 8
1-5 隱形斗篷 (Invisibility cloak) 10
1-6 幻象光學 (Illusion optics) 12
1-7 聲波超穎材料 (Acoustic metamaterials) 13
第二章理論及計算方法 18
2-1 平面波展開法 (Plane wave expansion) 18
2-1-1 電磁波能帶計算 18
2-1-2 彈性波頻帶計算 21
2-1-3 彈性波頻帶計算—二維系統 25
2-2 Dirichlet to Neumann method (DtN) 28
2-2-1 電磁波能帶計算—二維系統 28
2-2-2 正方晶格 29
2-2-3 三角晶格 33
2-2-4 超晶胞 (Supercell) 與波導模態計算 38
2-2-5 DtN應用於彈性波方程式 41
2-3 多重散射 (Multiple scattering method) 46
2-3-1 能流分析 49
2-4 聲學系統對應的電路系統 51
2-4-1 能流分析 (暫態和穩態) 55
2-5 FDTD-Z-transform 58
第三章分析及模擬 64
3-1 光子晶體平板成像穩定 64
3-2 純剪波聲子晶體平板成聚焦點 71
3-3 柱波導型的聲子晶體波導 76
3-4 聲學負折射系統的動態波場分析 88
第四章結論及展望 93
參考文獻 96

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指導教授

欒丕綱(Pi-Gang Luan)

審核日期

2011-7-11

推文