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研究生: 張瑞宇
Chang, Rui-Yu
論文名稱: 透過超穎介面來實現波傳漩渦的現象
The realization of wave vortex by metasurface
指導教授: 張怡玲
Chang, I-Ling
學位類別: 碩士
Master
系所名稱: 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年: 2021
畢業學年度: 109
語文別: 中文
論文頁數: 119
中文關鍵詞: 超穎介面赫姆霍茲共振器開放腔體負折射
外文關鍵詞: metasurface, Helmholtz resonator, open cavity, negative refraction
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  • 本研究主要透過超穎介面來組成開放腔體的裝置,提出一個以廣義司乃耳定律為理論基礎設計開放腔體的方法,針對5000Hz的頻率來設計開放腔體,藉由調整超穎介面的相位梯度、聲波的入射角以及打入聲波的頻率來探討開放腔體內的波傳行為。使用兩種方法來設計超穎介面,第一種是由多種不同的材料來組成超穎介面的單元,透過改變材料的折射率來調整超穎介面的相位梯度,第二種是透過赫姆霍茲共振器來組成超穎介面的基本單元,透過調整共振器的幾何尺寸來改變超穎介面的相位梯度,並與理論計算的結果來進行波傳行為的探討。
    模擬部分使用多重物理分析軟體(COMSOL Multiphysics)建立出開放腔體的裝置進行波傳路徑的計算,透過調整入射聲波的入射角改變對開放腔體內的波傳行為,藉由模擬的結果歸納出入射角與波傳路徑的關係,並和理論解進行比較,證明提出設計方法的正確性。整體而言,本研究歸納出超穎介面的相位梯度與入射角的大小對波傳路徑影響的關係,並且額外發現一種新的超穎介面設計方法可用於負折射波傳行為的研究。

    In this study, an open cavity device is mainly composed of metasurfaces, and a method of designing an open cavity based on the generalized Snell’s law is proposed. The open cavity is designed for frequency of 5000 Hz, and investigating the different wave propagation in the open cavity via adjusting metasurfaces’ phase gradient, the incident angle, and the frequency of the acoustical wave. Here, two methods are used to compose metasurfaces. The first is to form the unit of metasurface by variety of different materials. The phase gradient of the metasurface is adjusted by changing the refractive index of the material. The second method is using Helmholtz resonator to compose the basic unit of the metasurface, which can change the phase gradient of the metasurface by adjusting the geometric size of the resonator, and the wave propagation is discussed with the results of theoretical calculations.
    The simulation use COMSOL Multiphasic to calculate the wave propagation path in the open cavity. By adjusting the incident angle of the acoustical wave, the wave propagation in the open cavity is changed. The relationship between the incident angle and the wave propagation path is concluded by the simulation results, and compared with the theoretical solution to prove the correctness of the proposed design method. On the whole, in this study, we conclude the relationship between the phase gradient of the metasurface and the angle of incident wave, and additionally discover a new metasurface design method that can be used for the study negative refraction wave propagation.

    摘要 I Extent Abstract II 誌謝 XVI 目錄 XVII 表目錄 XIX 圖目錄 XIX 第一章 緒論 1 1.1 前言 1 1.2 文獻回顧 2 1.3 動機與目的 5 1.4 本文架構 6 第二章 基本理論 13 2.1 廣義司乃耳定律(Generalized Snell’s Law) 13 2.1.1 司乃耳定律推導 13 2.1.2 廣義司乃耳定律修正 14 2.2 由不同折射率材料所構成之超穎介面 14 2.3 由荷姆霍茲共振器所構成之超穎介面 16 2.3.1 荷姆霍茲共振器(Helmholtz resonator)等效系統 16 2.3.2 超穎介面單元 17 2.4 超穎介面的全反射現象 18 2.4.1 入射角大小對波傳現象的影響 18 2.4.2 相位梯度的大小對波傳現象的影響 20 2.5 開放式腔體 21 第三章 理論超穎介面組成之開放腔體探討 34 3.1 開放腔體相位梯度計算公式 34 3.2 超穎介面單元設計 35 3.3 開放腔體內的波傳行為 36 3.3.1 θ_a=θ_b=0.5θ_c 36 3.3.2 θ_a<θ_b 39 3.3.3 θ_a+θ_b<θ_c 40 3.3.4 θ_a+θ_b>θ_c 41 3.3.5 六邊形開放腔體 42 3.4 打入波頻率對波傳現象的影響 42 第四章 荷姆霍茲共振器超穎介面組成之開放腔體探討 70 4.1 超穎介面單元設計 70 4.2 開放腔體內的波傳行為 71 4.2.1 θ_a=θ_b=0.5θ_c 71 4.2.2 θ_a<θ_b 73 4.2.3 θ_a+θ_b<θ_c 74 4.2.4 θ_a+θ_b>θ_c 75 4.3 打入波頻率對波傳現象的影響 75 第五章 結論與未來展望 97 5.1 結論 97 5.2 未來展望 98 參考文獻 99 附錄 102

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