系統識別號 U0026-2708201921033400
論文名稱(中文) 有限差分時域法下二維週期奈米結構之連續頻譜內的束縛態分析與運用帕德近似法計算高品質因子
論文名稱(英文) Bound States in the Continuum for 2D Periodic nanostructures analyzed by Finite-difference Time-Domain method with Pade Approximation for high Q factor
校院名稱 成功大學
系所名稱(中) 光電科學與工程學系
系所名稱(英) Department of Photonics
學年度 107
學期 2
出版年 108
研究生(中文) 黃漢廷
研究生(英文) Han-Ting Huang
學號 L76051223
學位類別 碩士
語文別 中文
論文頁數 118頁
口試委員 指導教授-張世慧
中文關鍵字 連續頻譜內的束縛態  帕得近似法  斜向入射  週期排列結構  表面電漿  快速傅立葉轉換 
英文關鍵字 BIC  Padé approximant  Oblique incident  Periodic structure  Surface plasmons  Fast Fourier Transform 
中文摘要 從許多近期的文獻中發現,可藉由共振模態之間互相耦合的方式得到連續頻譜內束縛態(Bound states in the continuum,BIC)的特性,其擁有著無窮的生命週期以及無窮大的品質因子,可應用在雷射、感測、濾波等方面。
本篇論文內,我們使用有限時域差分法(Finite-difference time-domain,FDTD)數值模擬的方式探討BIC的概念與特性。首先,由單層週期排列介電質結構的穿透頻譜分析出發,說明了波導共振模態之定義與其激發條件的不同,並接著從雙層錯位週期排列的結構進一步討論模態耦合所造成的暗波導共振模態(Dark guided resonances mode)。之後運用斜向入射的平面波取代結構錯位的方式,透過觀察能帶結構(Band structure)以討論產生BIC的可能性與呈現的模態,再以快速傅立葉轉換(Fast Fourier Transform, FFT)配合帕得近似法(Padé approximant)達到減少模擬時間與計算品質因子之功效,藉此找出發生BIC的條件。最後推廣至單層排列的金屬結構並討論其表面電漿效應,且與週期性介電質結構的特性比對,是否有同樣能產生BIC的機會。
英文摘要 Photonic bound states in the continuum (BIC) are found in photonic crystal structures with infinite lifetime or infinite cavity quality factor. This peculiar property is due to the coupling of certain guided resonant modes that leads the cancellation of radiation channels. BIC has great potential in the applications of lasers, sensors, and filters.
The purpose of this study is to investigate and characteristics BIC in Plasmonic and dielectric structures by the Finite-difference time-domain (FDTD) method. First, single layered dielectric periodic structure is analyzed through the transmission spectrum to find the guided resonant mode. By shifting double layer dielectric periodic structure, a dark guided resonances mode which can be identified as BIC appears. Without shifting the double layered structure, an oblique angle incident excitation could also observe such BIC states. The Photonic Band structure is calculated to further analyze the appearance of the BIC states. Due to the infinite life time of BIC, it is difficult to analyze the quality factor of BIC. A combination of Padé approximant and Fast Fourier Transform (FFT) is developed to shorten the simulated time and obtain the correct cavity quality factors to help identifying BIC in FDTD calculation. Finally, a single layered metallic periodic structure is found to exhibit a quasi BIC state with propagating surface plasmon polaritons.
論文目次 口試委員審定書 I
中文摘要 II
Abstract III
誌謝 XII
圖目錄 XV
表目錄 XX
第一章 序論 1
1.1 前言 1
1.2 研究動機 2
1.3 本文內容 2
第二章 相關研究理論簡介 3
2.1 連續頻譜內束縛態的簡介(Bound States in the Continuum) 3
2.2 布洛赫定理(Bloch’s Theorem) 4
2.3 能帶結構(Band Structure)以及倒易晶格向量(Reciprocal Lattice Vectors) 5
2.4 表面電漿簡介(Surface Plasmon,SP) 7
2.5 表面電漿共振(Surface Plasmon Resonance,SPR) 8
2.6 金屬色散關係式 11
2.7 帕德近似法(Padé approximant) 14
第三章 數值模擬方法 15
3.1 有限時域差分法(Finite-difference time-domain, FDTD)和Yee式演算法簡介 15
3.2 馬克士威方程式與FDTD數值計算 17
3.2.1有限差分法(Finite difference method) 17
3.2.2 馬克士威方程組(Maxwell’s equation) 17
3.2.3 有限時域差分法(FDTD)推導 19
3.3 完美匹配層(Perfectly matched layer, PML) 23
3.4德魯德模型(Drude model) 30
3.5 週期邊界條件(Periodic boundary condition,PBC)和常數波向量(Constant K) 33
3.6 Order N 34
3.7 模擬結構設置 36
第四章 模擬結果與分析 37
4.1 錯位型週期性排列介電質結構 38
4.1.1 正向入射下的單層週期性排列介電質方塊 38
4.1.2 正向入射下的雙層週期性排列介電質方塊 45
4.1.3 斜向入射下的雙層週期性排列介電質方塊 55
4.2 斜向入射下週期性排列介電質結構 68
4.2.1 斜向入射下的週期性排列介電質長條 69
4.2.2 長條形介電質的能帶結構 74
4.2.3 快速傅立葉轉換與帕德近似法對品質因子計算 83
4.3 斜向入射下週期性排列金屬結構 95
第五章 結論與未來展望 114
5.1 結論 114
5.2 未來展望 115
參考文獻 116
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