博碩士論文 106226003 詳細資訊




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姓名 周宏宇(Hong-Yu Zhou)  查詢紙本館藏   畢業系所 光電科學與工程學系
論文名稱 以時域有限差分法研究色散介質及其光傳播行為
(Research on Dispersive Media and its Light Propagation Behavior Based on Finite Difference Time Domain Method)
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摘要(中) 本篇論文採用時域有限差分法(Finite Difference Time Domain,FDTD)探討非色散光子晶體與色散光子晶體的能帶結構及其光傳播行為。在FDTD運算過程中,我們使用Z轉換方法處理金屬、磁化電漿等色散介質的本構關係。並且介紹如何以FDTD計算能帶結構。本篇研究主要討論二維情況,探討不同填充率、不同偏振態下的非色散光子晶體能帶結構變化,以及色散光子晶體在不同電漿頻率、不同外加磁場的狀況下對於能帶結構的影響,並且應用計算出的能帶結構結果,觀察特定頻率的電磁波在光子晶體中的傳播行為。最後,利用光子晶體平板的光學特性產生次波長成像現象,並探討在不同外加磁場下,磁場對於金屬光子晶體平板的次波長成像影響。
摘要(英) In this thesis, we use Finite Difference Time Domain (FDTD) method to calculate the band structure and light propagation behavior in non-dispersive photonic crystals and dispersive photonic crystals. In the FDTD calculation process, we apply the Z-transform method to deal with the constitutive relations of dispersive media such as metal and magnetized plasma. We also introduce how to calculate the band structure with FDTD. This research mainly discusses the two-dimensional situations. For the non-dispersive photonic crystals, we discuss the change in band structure with different filling factors and different polarization states. For the dispersive photonic crystals, we study the influences on the band structure under different plasma frequencies and different external magnetic fields, and apply the calculated band structure results to predict the propagation behavior of electromagnetic waves of a specific frequency in the photonic crystals structure. Finally, we use the optical characteristics of the photonic crystal slab to generate the subwavelength imaging phenomena and discuss the effects of different external magnetic fields on the subwavelength imaging of the metallic photonic crystal slab.
關鍵字(中) ★ 時域有限差分法
★ 色散介質
★ 光子晶體
★ 磁化電漿
★ Z轉換
★ 次波長成像
關鍵字(英) ★ Finite Difference Time Domain
★ Dispersive Media
★ Photonic Crystal
★ Magnetized Plasma
★ Z Transform
★ Subwavelength Imaging
論文目次 摘要 (I)
Abstract (II)
誌謝 (III)
目錄 (IV)
圖目錄 (VII)
表目錄 (X)
一、緒論 (1)
1.1 光子晶體發展背景 (1)
1.2 光子晶體特性 (1)
1.3 研究方向 (5)
二、時域有限差分法(Finite Difference Time Domain, FDTD) (6)
2.1 FDTD的發展 (6)
2.2 馬克斯威爾方程式及其改寫形式 (7)
2.3 Yee晶格與電磁場遞迴關係 (9)
2.3.1 一維情況 (10)
2.3.2 二維情況 (13)
2.3.3 三維情況 (18)
2.4 邊界條件 (20)
2.4.1 完美導體邊界 (20)
2.4.2 週期邊界 (21)
2.4.3 完美匹配邊界 (22)
2.5 穩定性條件 (32)
2.5.1 時間離散間隔的穩定性要求 (32)
2.5.2 Courant – Friedrichs – Lewy Condition (33)
2.5.3 數值色散對於空間離散間隔的要求 (35)
三、色散介質的FDTD (38)
3.1 色散介質 (38)
3.2 Z轉換(Z-Transform)方法 (38)
3.2.1 Z轉換的基本定義 (38)
3.2.2 Z轉換的捲積定理 (39)
3.2.3 Z轉換的移位定理 (41)
3.3 杜德模型(Drude Model) (42)
3.3.1 頻域模型 (42)
3.3.2 杜德模型的Z-FDTD (43)
3.4 磁化電漿(Magnetized Plasma) (44)
3.4.1 頻域模型 (44)
3.4.2 磁化電漿的Z-FDTD (45)
四、以FDTD計算能帶結構 (52)
4.1 計算區域 (52)
4.2 週期邊界條件 (53)
4.3 初始條件 (54)
4.4 材料響應分析 (54)
五、光子晶體特性模擬 (57)
5.1 非色散光子晶體特性模擬 (57)
5.1.1 正方晶格光子晶體特性 (57)
5.1.2 填充率不同的影響 (60)
5.2 色散光子晶體特性模擬 (62)
5.2.1 金屬圓柱光子晶體特性 (62)
5.2.2 填充率不同的影響 (63)
5.2.3 電漿頻率不同的影響 (65)
5.2.3 外加磁場的影響 (66)
5.3 次波長成像 (68)
5.3.1 非色散光子晶體平板成像 (68)
5.3.2 色散光子晶體平板成像 (71)
六、結論與未來展望 (78)
6.1 結論 (78)
6.2 未來展望 (79)
參考文獻 (80)
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指導教授 欒丕綱(Pi-Gang Luan) 審核日期 2020-1-14
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