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系統識別號 U0002-3107201214301700
中文論文名稱 二維光子晶體耦合共振光能量分配器之設計與分析
英文論文名稱 Design and Analysis of Coupled-Resonator Optical Power Divider in Two-Dimensional Photonic Crystal
校院名稱 淡江大學
系所名稱(中) 機械與機電工程學系碩士班
系所名稱(英) Department of Mechanical and Electro-Mechanical Engineering
學年度 100
學期 2
出版年 101
研究生中文姓名 孫振
研究生英文姓名 Chen Sun
學號 698370508
學位類別 碩士
語文別 中文
口試日期 2012-07-13
論文頁數 64頁
口試委員 指導教授-劉承揚
委員-張高德
委員-吳乾埼
中文關鍵字 光子晶體  耦合共振光能量分配器 
英文關鍵字 photonic crystals  coupled-resonator optical waveguide 
學科別分類 學科別應用科學機械工程
中文摘要 光子晶體結構是由週期性介電材料所組成,因為具有特殊的光子能帶,所以可以有效控制光波的傳播。本論文使用平面波展開法分析正方晶格的光子能隙,藉由時域耦合模態理論來設計光子晶體波導光能量分配器,並使用有限時域差分法模擬光波在分配器內的傳播情況,以探討分配器內波導的圓柱尺寸與傳遞係數的關係。此外,本論文亦對耦合共振光學波導的幾何結構進行建模與數值計算,由結果得知兩倍密四方晶格的排列方式在中心波長具有寬頻且高傳輸的特性。延伸此波導架構,本論文提出一個多模態的光子晶體光能量分光器,設計出同時兼具波導、分波與濾波能力的微米級光學元件,此研究成果應可用在日後的積體光子迴路設計中。
英文摘要 Photonic crystals are composed of periodic dielectric that has photonic band gap. It can effectively control the light of propagation. In this thesis, we analysis the band gaps of the square lattice photonic by plane wave expansion, and design of optical power divider by using time-domain coupled-mode theory. We simulated the light wave propagation in power divider by using finite-difference time-domain method. We also discussed the relationship of the cylindrical size and the transmission coefficient in the divider. Besides, We have simulated the structure of coupled-resonator optical waveguides. Simulation results show that the double dense cubic photonic crystals have wide high-transmission bandwidths near the center of wavelength. Further, we proposed the power splitter of multimode interference in photonic crystal waveguides. It is a nanometer scale of optical component and it has the ability to guide, split and filter. The results of this study should be applied for photonic integrated circuit in the future.
論文目次 目錄
中文摘要 Ⅰ
英文摘要 Ⅱ
目錄 III
圖目錄 V
表目錄 IX
第一章 前言 1
1.1 研究動機與目的 1
1.2 光學的歷史背景 2
1.3 光子晶體的研究與應用 3
1.4 論文架構 4
第二章 光子晶體的基本理論 6
2.1 晶格、倒晶格向量、週期函數與光子能隙 6
2.2 光子晶體波導 9
2.3 研究方法 10
第三章 數值模擬的計算方法 12
3.1 波動方程式 12
3.2 平面波展開法 15
3.3 有限時域差分法 17
第四章 光子晶體波導光能量分配器 19
4.1 設計架構 19
4.2 元件設計與分析 21
第五章 耦合共振光學波導之研究 29
5.1 單一區域的結構分析 29
5.1.1 改變CROW區域介電圓柱的數量 29
5.1.2 改變Taper區域介電圓柱的數量 31
5.2 單一區域不同圓柱數量的差異 32
5.2.1 改變CROW區域介電圓柱的數量 32
5.2.2 改變Taper區域介電圓柱的數量 32
5.3 改變共振腔間距的影響 33
5.4 耦合共振波導尺寸的改進 34
5.5 耦合共振波導與晶格排列方式之分析 35
第六章 多模態干涉結構 39
6.1 正方晶格多模態結構的最佳化 39
6.2 圓柱半徑與能量流的週期變化關係 48
6.3 兩倍密四方晶格耦合共振波導加多模態結構 50
6.4 分光比例的改變 54
第七章 結論及未來展望 57
參考文獻 59

圖目錄
圖1.1 空間中一維、二維、三維光子晶體示意圖 4
圖2.1 二維正方晶格之晶格向量與倒晶格向量示意圖 6
圖2.2 TE模態之光子能隙圖 7
圖2.3 TM模態之光子能隙圖 8
圖2.4 流程圖 11
圖3.1 二維光子晶體偏振方向示意圖 14
圖3.2 正方晶格之單位晶胞結構示意圖 15
圖3.3 FDTD電場與磁場以交叉位置所組成的晶格點 18
圖4.1 分配器的架構圖 19
圖4.2 分光器之細部結構 22
圖4.3 當d = 3a、ri = 0, 0.07a, 0.09a、rw = 0、rc = 0.2a時的傳輸頻譜 22
圖4.4 入射波長1550 nm、d = 3a、ri = 0.09a、rw = 0、rc = 0.2a時的電場分佈圖 23
圖4.5 當d = 3a、ri = 0.07a、rw = 0, 0.07a, 0.09a、rc = 0.2a時的傳輸頻譜 24
圖4.6 入射波長1550 nm、d = 3a、ri = 0.07a、rw = 0.07a、rc = 0.2a時的電場分佈圖 24
圖4.7 當d = 3a、ri = 0.07a、rw = 0、rc = 0, 0.2a, 0.235a時的傳輸頻譜 25
圖4.8 入射波長1550 nm、當d = 3a、ri = 0.07a、rw = 0、rc = 0時的電場分佈圖 25
圖4.9 上下方輸出波導中圓柱不對稱時的傳輸頻譜 26
圖4.10 入射波長1550 nm上下方輸出波導中圓柱不對稱時的電場分佈圖 27
圖4.11 當d = 4a、ri = 0.08a、rw = 0、rc = 0.23a時的傳輸頻譜 27
圖5.1 耦合共振光學波導 29
圖5.2 在CROW區域改變介電圓柱的數量 30
圖5.3 (a)當C分別為2和4的傳輸頻譜 (b)當C分別為6和8的傳輸頻譜 30
圖5.4 在錐形區域改變介電圓柱的數量 31
圖5.5 當C固定為2,L分別為3和9時的傳輸頻譜 31
圖5.6 當L固定為9,C分別為5和9時的傳輸頻譜 32
圖5.7 當C固定為7,L分別為0、3、9時的傳輸頻譜 33
圖5.8 改變共振腔間距 34
圖5.9 相鄰的介電圓柱彼此圓心的距離為2a、2.5a、3a時的傳輸頻譜 34
圖5.10 晶格常數a分別為558nm和600nm的傳輸頻譜 35
圖5.11 平移耦合共振波導朝向線缺陷波導方向 35
圖5.12 比較平移0.5a前後差異的傳輸頻譜 36
圖5.13 耦合共振波導平移0.5a後之結構 36
圖5.14 兩倍密四方晶格排列 36
圖5.15 進行傳輸頻譜的比較 37
圖5.16 改變縱軸晶格的長度圖 37
圖5.17 (a)縱軸長度分別為√3 a、1.8a、1.9a的傳輸頻譜 (b)縱軸長度分別為2a、2.1a、2.2a的傳輸頻譜 38
圖6.1 縱向長度為4a的多模態結構 39
圖6.2 縱向長度4a,入射波長1550nm時的能量流 39
圖6.3 縱向長度為4a、橫向長度為5.5a之電場分佈圖 40
圖6.4 縱向長度為4a,改變橫軸長度的傳輸頻譜 41
圖6.5 橫軸長度分別為5.5a、5.6a及5.7a的傳輸頻譜 41
圖6.6 縱向長度6a,入射波長1550nm時的能量流 42
圖6.7 縱向長度為6a,改變橫軸長度的傳輸頻譜 43
圖6.8 橫軸長度為11.3a與11.4a的傳輸頻譜 43
圖6.9 縱向長度8a,入射波長1550nm時的能量流 44
圖6.10 縱向長度為8a,改變橫軸長度的傳輸頻譜 45
圖6.11 橫軸長度為6.3a與6.4a的傳輸頻譜 45
圖6.12 橫軸長度為7.6a與7.7a的傳輸頻譜 46
圖6.13 縱向長度4a、6a及8a最佳結構的傳輸頻譜 46
圖6.14 縱向長度為4a、橫向長度為5.5a多模態結構與d = 3a、ri = 0.07a、rw = 0、rc = 0.235a單一模態複合共振腔結構的傳輸頻譜 47
圖6.15 導入圓柱半徑為0.08a的結構 48
圖6.16 圓柱半徑為0.08a時的電場分佈圖 49
圖6.17 圓柱半徑為0.08a時的能量流 49
圖6.18 圓柱半徑為0.09a時的電場分佈圖 49
圖6.19 圓柱半徑為0.09a時的能量流 49
圖6.20 圓柱半徑與能量流的週期變化關係 50
圖6.21 正方排列的耦合共振波導加多模態結構 50
圖6.22 (a)正方晶格排列的能量流 (b)兩倍密四方晶格排列的能量流 51
圖6.23 耦合共振波導加多模態結構 (a)正方晶格 (b)兩倍密四方晶格 52
圖6.24 兩倍密四方晶格排列下 (a)橫軸長度為5a的傳輸頻譜 (b)橫軸長度為5.5a的傳輸頻譜 (c)橫軸長度為6a的傳輸頻譜 53
圖6.25 (a)多模態結構前無耦合共振波導的傳輸頻譜 (b)多模態結構前有耦合共振波導的傳輸頻譜 53
圖6.26 左邊輸出波導加入圓柱半徑0.07a示意圖 54
圖6.27 (a)輸出波導端加入圓柱半徑為0.06a的傳輸頻譜圖 (b)輸出波導無圓柱半徑的傳輸頻譜圖 55
圖6.28 (a)輸出波導端加入圓柱半徑為0.07a的傳輸頻譜圖 (b)輸出波導無圓柱半徑的傳輸頻譜圖 55
圖6.29 (a)輸出波導端加入圓柱半徑為0.08a的傳輸頻譜圖 (b)輸出波導無圓柱半徑的傳輸頻譜圖 56
圖6.30 (a)輸出波導端加入圓柱半徑為0.09a的傳輸頻譜圖 (b)輸出波導無圓柱半徑的傳輸頻譜圖 56

表目錄
表4.1 當d = 3a、ri = 0, 0.07a, 0.09a、rw = 0、rc = 0.2a時的傳輸頻譜比較表 23
表4.2當d = 3a、ri = 0.07a、rw = 0、rc = 0, 0.2a, 0.235a時的傳輸頻譜比較表 26
表4.3當d = 4a、ri = 0.08a、rw = 0、rc = 0.23a時的傳輸頻譜比較表 28
表6.1 縱向長度為4a,各個橫軸長度的傳輸頻譜比較表 40
表6.2 縱向長度為6a,各個橫軸長度的傳輸頻譜比較表 42
表6.3 縱向長度為8a,各個橫軸長度的傳輸頻譜比較表 44
表6.4 縱向長度4a、6a及8a最佳結構的傳輸頻譜比較表 47
表6.5 縱向長度為4a、橫向長度為5.5a多模態結構與d = 3a、ri = 0.07a、rw = 0、rc = 0.235a單一模態複合共振腔結構的傳輸頻譜比較表 48
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