以光子晶體能帶為基礎的多層膜等效晶體理論

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姓名	盧士盟(Shih-Meng Lu) 查詢紙本館藏	畢業系所	光電科學與工程學系
論文名稱	以光子晶體能帶為基礎的多層膜等效晶體理論 (Effective Crystal Theory of Multilayer Thin Films Based on Photonic Crystal Band Structure)
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摘要(中)	本論文探討光波在多層膜中的各向異性 (anisotropic) 傳播特性。我們以晶體光學與光子晶體理論模擬多層介質膜的等效光學參數，並闡釋其物理意義。本論文嘗試結合幾項現有等效理論的優點，分析並比較各等效理論的應用與侷限，並從模擬結果中總結出本論文等效理論的「適用條件」：即單一週期光學厚度，不得超過0.4個入射波長(Nd<0.4λ)，並發現在該條件之下，等效晶體理論具有不錯的預測性。文中引入傳統EMA (effective medium approximation) 作為對照，與本文引入等頻率曲線 (iso-frequency curve) 的等效晶體理論相比較。兩者最大的差異，在於等效介電常數的計算方式。我們從模擬數據中分析造成結果差異的物理成因，同時臚列兩者的優劣之處。文內前三章，主要介紹現有理論與相關細節的推導，以便在後面章節使用。第四章則為本文等效介質理論的理論構擬，後面章節接續分析結果數據。文章的最後，總結全文，再試著提出未來工作及可能應用。
摘要(英)	In this thesis we discuss the anisotropic propagation properties of light waves in multilayer films. The effective optical parameters of the multilayer dielectric films are obtained by using crystal optics and photonic crystal theories, and their physical meanings are explained. We analyze and compare the applicability and limitation of each effective medium theory in the literature, and try to combine their advantages in our newly developed theory. Based on a lot number of numerical simulations, we propose the "applicability condition" of our effective crystal theory as: the optical thickness of a single period must not exceed 0.4 wavelength of the incident light (Nd<0.4λ). Under this condition, our effective crystal theory has good predictability. In this thesis, the traditional EMA (effective medium approximation) is used as the reference, and compared in the simulations with our effective crystal theory based on the iso-frequency curve. The essential difference between these two kinds of theory is the calculation method of the effective dielectric constants. We analyze the physical causes for the difference in the simulation results, and list the advantages and disadvantages of both. The first three chapters focus on the introduction of existing theories and the related derivation details which will be used later. In the fourth chapter we construct the effective crystal theory in detail, and analyze the simulation results according to this theory. In the last chapter we propose some future works and possible applications.
關鍵字(中)	★ 等效晶體理論 ★ 多層膜 ★ 等頻率曲線	關鍵字(英)	★ EMA ★ iso-frequency curve ★ effective crystal theory
論文目次	摘要 I Abstract IV 致謝 IIV 目錄 IVV 圖目錄 VI 一、緒論 1 1-1 綜觀多層膜等效理論發展 1 1-2介質等效理論的實際應用 4 二、介質中傳遞的電磁波 6 2-1 在各向同性(Isotropic)介質中傳遞的電磁波 7 2-2 在各向異性(Anisotropic)介質中傳遞的電磁波 7 2-2-1 Normal Surface (K-Surface) 9 2-2-2色散關係(Dispertion Relation) 142 2-2-3單軸晶體 (uniaxial Crystal) 14 三、穿透率及反射率 16 3-1多層各向同性(Isotropic)介質的穿透率及反射率 16 3-1-1膜矩陣 16 3-2 各向異性(Anisotropic)介質的穿透率及反射率 19 3-2-1平面電磁波在單軸異向性介質內的傳播 19 3-2-2平面電磁波向單軸異向性介質的反射與透射 20 3-3多層膜結構的各向異性特性 23 3-3-1 串並聯近似(Series and Parallel Mixing Rules)的等效介電常數 23 3-3-2等頻率曲線(Iso-frequency Curve) 23 3-4等效晶體理論 27 3-4-1傳統EMA(Effective Medium Approximation)的等效介質理論 27 3-4-2引入等頻率曲線(Iso-Frequency Curve)的等效晶體理論 28 四、模擬數據與分析 31 4-1傳統EMA的等效介質理論 31 4-1-1改變單一週期厚度(純介電質結構) 31 4-1-2改變入射角度(純介電質結構) 34 4-1-3改變單一週期厚度(介電質-金屬結構) 35 4-1-4改變入射角度(介電質-金屬結構) 37 4-2引入等頻率曲線的等效晶體理論 38 4-2-1改變單一週期厚度(純介電質結構) 38 4-2-2改變入射角度(純介電質結構) 41 4-2-3改變單一週期厚度(介電質-金屬結構) 43 4-2-4改變入射角度(介電質-金屬結構) 44 4-3數據分析和比較 46 4-3-1改變單一週期厚度(純介電質結構) 數據分析 46 4-3-2改變入射角度(純介電質結構) 數據分析 49 4-3-3改變單一週期厚度(介電質-金屬結構) 數據分析 50 4-3-4改變入射角度(介電質-金屬結構) 數據分析 51 4-3-5等效參數的優化 52 4-4表面阻抗對穿透、反射率光譜的影響 56 4-4-1反射率零點與表面阻抗(Surface Impedance)的關係 57 五、結論與未來展望 59 5-1 結論 59 5-2 未來展望 59 參考文獻 61
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指導教授	李正中欒丕綱	審核日期	2020-8-20
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