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研究生： 丘瑞安
Chiu, Rui-An
論文名稱： 水滴陣列之電磁波吸收特性研究
Study on Absorptance of Electromagnetic Wave by Water Droplet Array
指導教授： 鄭金祥
Cheng, Chin-Hsiang
學位類別： 碩士
Master
系所名稱： 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年： 2019
畢業學年度： 107
語文別： 中文
論文頁數： 112
中文關鍵詞： 超材料 、電磁波 、吸收特性 、Ｓ參數 、匿蹤技術
外文關鍵詞： Metamaterials, Water droplet array, Electromagnetic wave, Absorption, Numerical simulation, Experiment
相關次數： 點閱：90  下載：4 
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    • 本研究探討了一種水滴陣列超材料結構（MMT），其在寬頻帶內具有高電磁波（EMW）吸收。該材料可應用於隱形匿蹤技術，以減少雷達橫截面積，或用作飛機和船舶的電磁波吸收器。
    　　本文探討了使用ITO玻璃作為超材料的介電基板，於基板上方製造出不同水滴直徑、不同水滴間距的水滴陣列圖樣，在各參數組合下電磁波於S、C、X、Ku及K頻段(2~20 GHz)的微尺寸水滴陣列之吸收率。
    　　首先利用商業軟件COMSOL Multiphysics對水滴陣列的電磁波吸收行為進行數值模擬。預測正常入射電磁波的吸收率，工作頻率和Ｓ參數（S11、S21），評估基板厚度、水滴尺寸、水滴間距在特定頻率範圍內所產生的影響，此外可以基於模擬所獲得的結果來理解新型態水基超材料結構設計的吸收機制之物理現象，同時，也規劃實驗系統，針對水滴陣列超材料的電磁波吸收性能進行量測。
    　　最終，提出於2~20 GHz頻率範圍內，可滿足高吸收率及大頻寬的水基超材料配置。

    Study on Absorption of Electromagnetic Wave by Water Droplet Array

    Rui-An Chiu
    Chin-Hsiang Cheng
    Department of Aeronautics and Astronautics, National Cheng Kung University

    SUMMARY
    This study is concerned with a water droplet array metamaterial structure (MMT) that yields high electromagnetic wave (EMW) absorption over a wide frequency band. The material can be applied to stealth technology to reduce radar cross-sectional area or as an electromagnetic wave absorber for aircraft and ships. In this study, the dielectric substrate using ITO glass as metamaterial is investigated. The water droplet array pattern with different water droplet diameters and different water droplet spacing is placed on the substrate. The electromagnetic wave is within the S, C, X, Ku and K bands (2~20 GHz). Firstly, the commercial software COMSOL Multiphysics is used to numerically simulate the electromagnetic wave absorption behavior of the water droplet array. The absorption rate of normal incident electromagnetic waves is predicted. Operating frequency and S-parameters (S11, S21) are calculated, and the influence of substrate thickness, water droplet size, and water droplet spacing in a specific frequency range is evaluated. The numerical model can be used to investigate the physical phenomenon and the absorption mechanism of the water-based metamaterial structure design. On the other hand, experimental system is also built to measure the electromagnetic wave absorption performance of the water droplet array. Eventually, an optimal combination of the design parameters that yields high electromagnetic wave absorption in a wide frequency band is proposed.

    Keywords: Metamaterials, Water droplet array, Electromagnetic wave, Absorption, Numerical simulation, Experiment.

    INTRODUCTION
    In recent years, investigators found that the dielectric metamaterials have the advantage of wider bandwidth than the metal resonance structure metamaterials with medium dispersion characteristics. Among those selected dielectric metamaterials, water is considered to be a ubiquitous dielectric material in the world, and it demonstrates some unique properties that are suitable to develop metamaterial devices. Besides, the use of water as the primary resonant component in the design of electromagnetic wave absorbers will greatly reduce commercial costs.
    For water, as the frequency increases, the real part of the water dielectric constant decreases rapidly, while the loss tangent of the microwave region increases significantly. The loss tangent is used to indicate the ability of a material to be couple with a microwave. The greater the loss tangent, the stronger the ability of the material to couple with the microwave. At the same time, water is in liquid phase at room temperature, which makes its layout more flexible. By controlling the volume or temperature of the water, their electromagnetic characteristics can be adjusted.
    This study aims to develop a new water-based metamaterial with high electromagnetic wave absorption over a wide frequency band. This metamaterial can be applied to stealth technology to reduce the cross-sectional area of the radared objects or used as an electromagnetic wave absorber of energy devices. This study adopts the ITO glass substrate on which water droplets are formed of different diameters (8, 10, 12, 14 mm), different water droplet heights (0.5, 1, 1.5, 2, 2.5 mm), and different water droplet spacings (2, 4, 6, 8, 10 mm). The frequency range considered in this study is within the S, C, X, Ku and K bands of the radar wave, which is 2~20 GHz. The absorption rates of water-based metamaterials under different parameter combinations are predicited. A configuration that achieves an absorption rate higher than 90% within a bandwidth of 5.5 GHz. This meets the criterion of broadband absorbor that the ratio ∆f / fo needs to exceed 69% in defintion.

    NUMERICAL SIMULATION
    This study uses COMSOL Multiphysics to numerically simulate the water-based metamaterials with different combinations of parameters. The absorbance, operating frequency and S-parameters of the incident electromagnetic waves (S parameters, S11 and S21) are predicted. Among them, S11 and S21 represent a reflection coefficient and a transmission coefficient, respectively. The model uses PML to simulate the outer boundary and absorb all electromagnetic waves at the top boundary. The water-based metamaterial structure is located in an infinite space. PEC is a non-destructive surface that reflects 100% incident waves. The PEC cuts off the calculation area. Port 1 is the electromagnetic wave transmitting port and also the receiving port. The peripheral boundary limits the characteristics of its periodic array with Floquet periodic boundary conditions. The three-dimensional electromagnetic wave model and boundary conditions are shown in Figure 1.
    The simulation is to seek the solutions of the electromagnetic equations, the Maxwell equations. The calculated electric field is used to determine S11 and S21 as

    S_11=(∫▒〖Port1((E_c-E_1 ).E_1^* )dA_1 〗)/(∫▒Port1(E_1.E_1^* ) dA_1 ) (1)


    S_21=(∫▒〖Port2(E_c.E_2^* )dA_2 〗)/(∫▒Port1(E_2.E_2^* ) dA_2 ) (2)

    Figure 1. Three-dimensional electromagnetic wave model and boundary conditions.

    where E_c is the calculated electric field, and E_1 and E_2 are the electric fields on Port 1 and Port 2, respectively.
    According to Kirchhoff’s law of radiation, in this case the absorbance can be determined by the reflection and transmission coefficients:

    |A(ω)|=1-|S_11 |^2-|S_21 |^2 (3)
    In experiments, S11 and S21 can be measured by using the network analyzer to verify the results of the numerical simulation.
    Figure 2 illustrates the schematic of the water-based metamaterial structure of this study. The geometrical parameters of this study include the water droplet radius (R), water droplet spacing (d), water droplet height (h), substrate thickness (t). Effects of these geometrical parameters are investigated by changing different parameters.


    (a) (b)

    Figure 2. Dimensions of water droplet.
    Glass is used as the substrate, and ITO is the grounding surface. The water droplets are dropped on the ITO glass treated with the hydrophilic and hydrophobic surface by a micropipette to form a pattern of water droplet arrays above the ITO glass. The real part of the dielectric constant of the glass, water and air, the real part of the dielectric constant, the magnetic permeability, and the electrical conductivity are input to computation software. The true imaginary part of the dielectric constant of water varies with frequency. The real imaginary part function of the dielectric constant used in this study is obtained by the curve fitting method.
    EXPERIMENT
    The experimental system of this research consists of vector network analyzer, coaxial cable and canned antenna. Figure 3 shows the schematic diagram of the experimental system. One end of the coaxial cable is connected to the vector network analyzer Port 1 and Port 2, and the other end is connected to the canned antenna, where Port 1 is the transmitting and the receiving port, and Port 2 is the receiving port. Port 1 converts the voltage signal into electromagnetic wave through the vector network analyzer to radiate electromagnetic waves passing through the antenna. The water-based metamaterial test sample is placed between the antennas. The electromagnetic field in the space is received by Port 2, and the electromagnetic wave is converted back to the voltage signal to obtain the values of S parameters.

    Figure 3. Experimental erection diagram.

    The reflection coefficient R and transmission coefficient T of the water-based metamaterial are determined by
    T=(S_11+S_21-R)/(1-(S_11+S_21)R) (4)
    R=x±√(x^2-1) (5)
    where
    x=(〖S_11〗^2+〖S_21〗^2+1)/〖2S〗_11 (6)
    The signs (+ or –) in Equation (5) is selected in accordance with 0 < R < 1. By substituting S11 and S21 measured by the vector network analyzer, the transmission coefficient and reflection coefficient of the water-based metamaterial can be obtained. According to Kirchoff's law of radiation, the absorption rate can be obtained from the reflection coefficient and the transmission coefficient.

    RESULTS AND DISCUSSION
    Figures 4 and 5 show the results of effects of the radius of the water droplets. It can be seen that as the radius of the water droplets is smaller, the point at which the absorption reaching the peak value also moves toward the high frequency. This phenomenon is called blue shift, and the absorption rate is mainly composed of two high points. The part of the second high point usually achieves the effect of wide frequency. When the water droplet radius is 7 mm or 6 mm, the second high point width is wider as compared to other radii.


    Figure 4. Effects of radius of water droplets, at h=2 mm, t=2 mm, and d=6 mm.


    Figure 5. Effects of radius of water droplets, at h=2 mm, t=2 mm, and d= 4 mm.

    Figure 6 displays the effects of spacing between the water droplets. As the distance between the water droplets is large, the overall absorption rate is decreased, and the absorption rate of the second highest point reaching 90% or more is narrowed. When the water droplet spacing is 10 mm, the absorption effects could not reach the demand of this study.


    Figure 6. Effects of spacing between water droplets, at h=2 mm, t=1.8 mm, and R=6 mm.

    Figure 7 shows the current density distribution associated with each high absorption point of h = 0.5 mm, t=1.8 mm, R=6 mm, and d=4 mm.


    (a) 15.5 GHz (98.43 %) (b) 16 GHz (99.92 %)


    (c) 18 GHz (99.05 %) (d) 18.5 GHz (99.01 %)
    t=1.8 mm、R=6 mm、d=4 mm，h=0.5 mm
    Figure 7. High absorption point current density distribution, at t=1.8 mm, R=6 mm, d=4 mm, h=0.5 mm.

    Experimental data of effects of water droplet radius and water droplet spacing are provided in Figures 8 and 9, respectively. As shown in these figures, the water droplet array can indeed lead to high absorption rates over a relatively wide frequency range. As the droplet radius becomes smaller or the water droplet spacing becomes larger, the absorption rate decreases.


    Figure 8. Experimental data of effects of water droplet radius.


    Figure 9. Experimental data of effects of water droplet spacing.

    CONCLUSIONS
    According to experimental measurements, the results of the absorptivity of the metamaterials using the water droplet array show that the water-based metamaterials can indeed lead to high absorption rates over a relatively wide frequency range.
    The optimal configuration of water-based metamaterial found in this study is:
    - substrate thickness 1.8 mm
    - water droplet radius 6 mm
    - water droplet spacing 4 to 6 mm
    - water droplet height 0.5 to 2.5 mm.
    In this configuration, an absorption rate higher than 90% is obtained and the bandwidth of frequency is wider than 5.5 GHz.

    目錄 摘要 I 誌謝 X 目錄 XI 表目錄 XV 圖目錄 XVI 符號索引 XXIII 第一章 緒論 1 1.1 研究背景 1 1.1.1 超材料源起 2 1.1.2 超材料發展 7 1.2 超材料應用 7 1.3 電磁波吸收器原理 8 1.3.1 傳統電磁波吸收器原理 9 1.3.2 超材料吸收器分類與原理 9 1.4 水基超材料吸收器 10 1.5 研究動機 12 1.6 論文架構 14 第二章 超材料理論模型 16 2.1 負折射 16 2.1.1 複數介電常數 20 2.2 電磁波理論 21 2.2.1 能量流動方向 23 2.2.2 邊界條件和界面條件 24 2.3 平面電磁波 30 2.3.1 橫向電（TE）波 30 2.3.2 橫向磁（TM）波 31 2.3.3 橫向電磁（TEM）波 31 2.4 介電材料 32 2.5 DRUDE模型 34 第三章 數值模擬 37 3.1 水基超材料吸收器 37 3.1.1 模型幾何結構 37 3.1.2 材料參數設定 41 3.1.3 邊界條件設定 43 3.2 散色參數（S參數） 45 3.3 吸收率計算 46 3.4 文獻比較 47 第四章 實驗量測 51 4.1 水基超材料試片製成 51 4.2 實驗系統架設 55 4.2.1 罐頭天線 56 4.3 向量網路分析儀的S參數與吸收率計算 59 4.4 測試系統 64 4.4.1 量測環境 64 4.4.2 吸波膠片 67 第五章 結果與討論 68 5.1 數值模擬結果 68 5.1.1 改變水滴直徑 75 5.1.2 改變水滴間距 83 5.1.3 改變基板厚度 86 5.1.4 改變水滴高度 92 5.1.5 電流密度分布 93 5.2 實驗量測結果 98 5.3 數值模擬與實驗量測結果之比較 100 第六章 結論 105 文獻參考 107 表目錄 表1-1 雷達波段與頻段 13 表3-1 參數配置總覽 39 表3-2 材料參數設定 42 表5-1 水基超材料吸收率模擬彙整表 71 圖目錄 圖1-1 根據介電常數和磁導率對材料進行分類 2 圖1-2 第一塊磁導率和介電常數為負數的人工材料 [5] 4 圖1-3 開口諧振環 6 圖2-1 折射示意圖 17 圖2-2 負折射模擬 18 圖2-3 波印亭向量(S ⃑)和波向量(k ⃑)的關係表示圖 24 圖2-4 兩任意材料界面示意圖 24 圖2-5 材料界面表面電流密度示意圖 25 圖2-6 材料界面表面電荷/磁荷密度示意圖 27 圖2-7 橫向電磁波傳播 31 圖3-1 水基超材料結構示意圖 38 圖3-2 三維水基超材料示意圖 42 圖3-3 水的介電常數實部、虛部隨頻率變化圖 43 圖3-4 三維電磁波全模型和邊界條件的示意圖 44 圖3-5 三維電磁波半模型和邊界條件的示意圖 45 圖3-6 玻璃基板+水滴直徑14 mm的吸收率 47 圖3-7 水滴直徑12 mm的電流密度分布圖 48 圖3-8 玻璃基板+1 mm水層之吸收率 50 圖3-9 只有玻璃基板沒有水之吸收率 50 圖4-1 微量吸管P200L(左)及P1000L(右) 52 圖4-2 水基超材料不同水滴直徑之試片 53 圖4-3 水基超材料不同水滴間距之試片 54 圖4-4 實驗架設示意圖 55 圖4-5 向量網路分析儀 56 圖4-6 罐頭天線與其天線性能S參數 58 圖4-7 天線近場與遠場關係圖 59 圖4-8 向量網路分析儀兩端口S參數測量示意圖 61 圖4-9 無反射室外部 65 圖4-10 無反射室內部 65 圖4-11 量測實驗架設圖 66 圖4-12 高頻吸波膠片 67 圖5-1 Case 28於各頻率下電場行進方向圖 69 圖5-2 改變水滴半徑，固定水滴高度2 mm、基板厚度2 mm、水滴間距10 mm(Case 5、Case 10、Case 15、Case 20) 76 圖5-3 改變水滴半徑，固定水滴高度2 mm、基板厚度2 mm、水滴間距8 mm(Case 4、Case 9、Case 14、Case 19) 76 圖5-4 改變水滴半徑，固定水滴高度2 mm、基板厚度2 mm、水滴間距6 mm(Case 3、Case 8、Case 13、Case 18) 77 圖5-5 改變水滴半徑，固定水滴高度2 mm、基板厚度2 mm、水滴間距4 mm(Case 2、Case 7、Case 12、Case 17) 77 圖5-6 改變水滴半徑，固定水滴高度2 mm、基板厚度2 mm、水滴間距2 mm(Case 1、Case 6、Case 11、Case 16) 78 圖5-7 改變水滴半徑，固定水滴高度2 mm、基板厚度1.8 mm、水滴間距10 mm(Case 25、Case 30、Case 35、Case 40) 78 圖5-8 改變水滴半徑，固定水滴高度2 mm、基板厚度1.8 mm、水滴間距8 mm(Case 24、Case 29、Case 34、Case 39) 79 圖5-9 改變水滴半徑，固定水滴高度2 mm、基板厚度1.8 mm、水滴間距6 mm(Case 23、Case 28、Case 33、Case 38) 79 圖5-10 改變水滴半徑，固定水滴高度2 mm、基板厚度1.8 mm、水滴間距4 mm(Case 22、Case 27、Case 32、Case 37) 80 圖5-11 改變水滴半徑，固定水滴高度2 mm、基板厚度1.8 mm、水滴間距2 mm(Case 21、Case 26、Case 31、Case 36) 80 圖5-12 改變水滴半徑，固定水滴高度2 mm、基板厚度1.1 mm、水滴間距10 mm(Case 45、Case 50、Case 55、Case 60) 81 圖5-13 改變水滴半徑，固定水滴高度2 mm、基板厚度1.1 mm、水滴間距8 mm(Case 44、Case 49、Case 54、Case 59) 81 圖5-14 改變水滴半徑，固定水滴高度2 mm、基板厚度1.1 mm、水滴間距6 mm(Case 43、Case 48、Case 53、Case 58) 82 圖5-15 改變水滴半徑，固定水滴高度2 mm、基板厚度1.1 mm、水滴間距4 mm(Case 42、Case 47、Case 52、Case 57) 82 圖5-16 改變水滴半徑，固定水滴高度2 mm、基板厚度1.1 mm、水滴間距2 mm(Case 41、Case 46、Case 51、Case 56) 83 圖5-17 改變水滴間距，固定水滴高度2 mm、基板厚度1.8 mm、水滴半徑7 mm(Case 21~Case 25) 84 圖5-18 改變水滴間距，固定水滴高度2 mm、基板厚度1.8 mm、水滴半徑6 mm(Case 26~Case 30) 84 圖5-19 改變水滴間距，固定水滴高度2 mm、基板厚度1.8 mm、水滴半徑5 mm(Case 31~Case 35) 85 圖5-20 改變水滴間距，固定水滴高度2 mm、基板厚度1.8 mm、水滴半徑4 mm(Case 36~Case 40) 85 圖5-21 改變基板厚度，固定水滴高度2 mm、水滴半徑6 mm、水滴間距10 mm(Case 10、Case 30、Case 50) 86 圖5-22 改變基板厚度，固定水滴高度2 mm、水滴半徑6 mm、水滴間距8 mm(Case 9、Case 29、Case 49) 87 圖5-23 改變基板厚度，固定水滴高度2 mm、水滴半徑6 mm、水滴間距6 mm(Case 8、Case 28、Case 48) 87 圖5-24 改變基板厚度，固定水滴高度2 mm、水滴半徑6 mm、水滴間距4 mm(Case 7、Case 27、Case 47) 88 圖5-25 改變基板厚度，固定水滴高度2 mm、水滴半徑6 mm、水滴間距2 mm(Case 6、Case 26、Case 46) 88 圖5-26 改變基板厚度，固定水滴高度2 mm、水滴半徑4 mm、水滴間距10 mm(Case20 、Case40 、Case60 ) 89 圖5-27 改變基板厚度，固定水滴高度2 mm、水滴半徑4 mm、水滴間距8 mm(Case19 、Case39 、Case59 ) 90 圖5-28 改變基板厚度，固定水滴高度2 mm、水滴半徑4 mm、水滴間距6 mm(Case18 、Case38 、Case58 ) 90 圖5-29 改變基板厚度，固定水滴高度2 mm、水滴半徑4 mm、水滴間距4 mm(Case17 、Case37 、Case57 ) 91 圖5-30 改變基板厚度，固定水滴高度2 mm、水滴半徑4 mm、水滴間距2 mm(Case16 、Case36 、Case56 ) 91 圖5-31 改變水滴高度，固定基板厚度1.8 mm、水滴半徑6 mm、水滴間距6 mm(Case 61~Case 64、Case 28) 92 圖5-32 改變水滴高度，固定基板厚度1.8 mm、水滴半徑6 mm、水滴間距4 mm(Case 65~Case 68、Case 27) 93 圖5-33 Case 27的高點電流密度分布圖 94 圖5-34 Case 28的高點電流密度分布圖 95 圖5-35 Case 64的高點電流密度分布圖 96 圖5-36 Case 65的高點電流密度分布圖 97 圖5-37 改變水滴半徑實驗值(Case 23、Case 38) 99 圖5-38 改變水滴間距實驗值(Case 26、Case 30) 99 圖5-39 Case 23實驗與模擬吸收率比較圖 100 圖5-40 Case 28實驗與模擬吸收率比較圖 101 圖5-41 Case 26實驗與模擬吸收率比較圖 101 圖5-42 Case 27實驗與模擬吸收率比較圖 102 圖5-43 Case 29實驗與模擬吸收率比較圖 102 圖5-44 Case 30實驗與模擬吸收率比較圖 103 圖5-45 Case 46實驗與模擬吸收率比較圖 103 圖5-46 Case 47實驗與模擬吸收率比較圖 104 圖5-47 Case 48實驗與模擬吸收率比較圖 104

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