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研究生: 黃柏鈞
Huang, Bo-Jyun
論文名稱: 負折射率超穎材料的光學微影
Optical lithography of the structure of metamaterials with negative refractive index
指導教授: 張世慧
Chang, Shih-Hui
學位類別: 碩士
Master
系所名稱: 理學院 - 光電科學與工程學系
Department of Photonics
論文出版年: 2021
畢業學年度: 109
語文別: 中文
論文頁數: 69
中文關鍵詞: 負折射率 、有限時域差分法 、色散關係 、超穎結構 、表面電漿子
外文關鍵詞: negative refractive index, FDTD, dispersion relation, hyperbolic metamaterials, surface plasmons
相關次數: 點閱:169  下載:1 
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  • 光學微影技術能投射的最小線寬P_min=2k_1 λ/NA (P_min為圖案線寬,k_1為製成參數,NA為數值孔徑,?為光波長) ,因為繞射極限的限制,需要不斷的縮小光波長才能達到提高光學微影技術的解析度,若能在可見光波段達到突破繞射極限的效果,就可以大幅降低昂貴光源的成本。
    我們利用Hyperbolic Metamaterials的超穎介質作為負折射率材料,其構成的完美透鏡可以達到突破繞射極限的聚焦效果,接著透過分析光線在三層、五層、無限層完美透鏡中的色散關係,找到符合負折射率的波長,最後取適合的光波長,藉由FDTD模擬聚焦成像的結果驗證,進一步探討此技術的可行性。

    The minimum line width that optical lithography technology can project P_min=2k_1 λ/(N.A.) (P_min is the pattern line width, k_1 is the manufacturing parameter, N.A. is the numerical aperture, ? is the light wavelength). Because of the limitation of diffraction limit, it is necessary to continuously reduce the wavelength of light to improve the resolution of optical lithography technology. If the effect of breaking the diffraction limit in the visible light band can be achieved, the cost of expensive light sources can be greatly reduced.
    We use the Hyperbolic Metamaterials as a negative refractive index material. The perfect lens formed by Hyperbolic Metamaterials can achieve a focusing effect that breaks the limit of diffraction. Then, by analyzing the dispersion relation of light in the three-layer, five-layer, and infinite-layer perfect lens. We can find the wavelength that matches the negative refractive index in the dispersion relation. After we pick out the wavelength of light that conforms to the phenomenon of negative refractive index. Furthermore, the Finite Difference Time Domain numerical simulation method is used to simulate the result of focusing images, and we can discuss the feasibility of this technology.

    摘要 I Abstract II 誌謝 XII 目錄 XIII 圖目錄XVI 第一章 緒論 1 1-1 研究背景 1 1-2 研究動機 1 1-3 論文架構 2 第二章 光學微影及負折射率材料 3 2-1 文獻回顧及探討 3 2-2 光學微影技術的繞射極限 4 2-3 負折射介質原理介紹 6 2-4 Hyperbolic Metamaterials介紹 10 2-5 Hyperbolic Metamaterials傳遞光線的物理機制 12 第三章 數值方法 14 3-1 差分法(Finite Difference method) 14 3-2 馬克斯威爾方程組(Maxwell’s equation) 14 3-3 Finite Difference Time Domain (FDTD) 15 3-4 Compact FDTD演算法 18 3-5 Total Field Scatter Field (TFSF) 23 3-6 Transfer matrix method 26 3-7 Drude model 32 3-8 Convolutional Perfect Match Layer(CPML) 33 第四章 結論與分析 40 4-1 SPPs在metal/dielectric單層介面的色散關係 40 4-2 SPPs在MDM和DMD三層波導結構的色散關係 42 4-3 SPPs在MDMDM五層波導結構的色散關係 46 4-4利用Transfer Matrix Method求在MDMDM中SPPs的isofrequency contour關係 48 4-5 SPPs在MDMDM中的2D-FDTD電磁模擬結果 53 4-6 利用Transfer Matrix Method求在HMMs中 SPPs的isofrequency contour 56 4-7 SPPs在HMMs中的2D-FDTD電磁模擬結果 59 第五章 結論與討論 62 第六章 未來展望 64 6-1 HMMs光學微影技術三維FDTD的電磁模擬及成像分析 64 參考文獻 66

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