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研究生:張乃文
研究生(外文):Nai-wen Zhang
論文名稱:含液晶可調式橢圓柱光子晶體負折射分析
論文名稱(外文):Negative refraction of tunable elliptical-rod photonic crystals achieved by liquid crystals
指導教授:陳聯文
指導教授(外文):Lien-wen Chen
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:99
中文關鍵詞:負折射光子晶體橢圓柱
外文關鍵詞:Photonic crystalselliptical-rodnegative refraction
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光子晶體是由週期性結構所組成的結構,假若經由適度的設計則具備改變光波傳遞的效果。而近幾年發現在其傳導區擁有獨特的色散性質,尤其是負折射的特性,使得該方面的研究成為最近學術界極度熱門的話題。
本文以平面波展開法求得二維光子晶體等頻圖,利用等頻圖來預測負折射角度,再使用時域有限插分法和有限元素法模擬光子晶體的異常折射現象。
為了調變改變光波傳遞的方向,將光子晶體的圓柱以橢圓柱取代,因為橢圓柱的幾何非等向性,使得等頻圖明顯產生變化,讓垂直入射的光波可以發生折射,分析觀察橢圓柱不同的旋轉角,來獲得不同的折射角度,將不同方向的晶格排列進而控制光波傳遞的方向,可以利用橢圓柱光子晶體的概念設計出光開關、可調式分光器。
我們選用液晶材料當可調變的材料,利用其液晶材料的非等向性和藉由電場控制液晶導軸角度的特性,將液晶材料加入光子晶體橢圓柱中,來觀察與分析不同液晶導軸角度和橢圓柱之幾何非等向性的關係,對折射角度的影響。發現負折射角度有較大的範圍,適合作為可調折射角之光學元件。最後,對於調至臨界角度之後的全反射,則提出可做為光開關之用途。還有改善其邊界條件,讓光開關的效果更好。
Photonic crystals (PhCs) are synthetic periodic structures that,when suitably designed, have the ability to change the propagation of light. Recently, it was proved that the diffraction effects of PhCs can produce the effective negative refraction or the negative index. Hence, the studying of PhCs is not limited in the band gap region. The anomalous refractive properties (especially negative refraction) of PhCs have become hot topics of scientific research over the past few years.
In this thesis, the plane wave expansion method is used to get the equifrequency surface. The anomalous refractive properties of photonic crystal are analyzed by using the equifrequency surface. Then we use the finite difference time domain method and the finite element method to simulate the light propagation in PhCs and compare the refractive angle with that predicted by the equifrequency surface.
In order to change the direction of the light propagation, the two-dimension columns within photonic crystals are replaced by elliptic rod. Due to the geometric anisotropy of elliptic rods, we can rotate the elliptic rods to obtain different structure factors. The anisotropic property can then be used to tune the refraction direction. The results can be applied to develop various photonic crystal devices, such as optical switches and tunable optical splitters.
The material properties of liquid crystals (LCs) can be altered easily by applying an external electric field. The LCs are infiltrated into the photonic crystal of elliptic rods and the relationship between the refractive angle and the angle of the director is studied. Owing to the large anisotropy consisting of elliptic rods, the range of negative refraction angle is superior to column. The direction of the negative refraction is controlled by changing the direction of the LCs director. The tunability was analysed at the specified frequency and a large tunable range of the negative refraction is achieved. The refraction of a tunable PhCs with nematic liquid crystals can be used to design an optical switch. Besides, the transmission of the optical switch can be improved by properly adjusting the boundary conditions.
目 錄
摘要 I
Abstract II
誌謝 III
目錄 Ⅴ
圖目錄 Ⅶ
符號 Ⅹ
第一章 緒論 1
1-1前言 1
1-2 光子晶體負折射現象介紹 1
1-3 文獻回顧 3
1-4 本文架構 4
第二章 數值方法 9
2-1 前言 9
2-2 平面波展開法 9
2-2-1 倒晶格(Reciprocal lattice) 9
2-2-2 布拉克理論(Bloch Theorem) 10
2-2-3 平面波展開法 10
2-2-4 介電常數密度 14
2-2-5 正方晶格(square lattice) 15
2-2-6 三角晶格(Triangular lattice) 16
2-3時域有限差分法 17
2-3-1 時域有限差分法推導 17
2-3-2 完美匹配吸收層 20
2-4有限元素法 23
2-4-1 有限元素推導 23
2-4-2 邊界條件 25
2-4-2-1兩介質之連續條件 25
2-4-2-2散射邊界條件 26
第三章 圓柱光子晶體的負折射現象 34
3-1 前言 34
3-2 等頻圖分析與光子晶體負折射 34
3-3 光子晶體折射光種類 37
3-4 等頻圖預測與時域有限差分法模擬之折射角誤差 38
3-5圓柱光子晶體負折射現象之分析與模擬 38
3-5-1 正方晶格負折射現象 39
3-5-2 正方晶格成像系統 39
3-5-3 三角晶格負折射現象 41
3-5-4 三角晶格成像系統 42
第四章 橢圓柱光子晶體的折射現象之調變 56
4-1前言 56
4-2橢圓柱光子晶體 56
4-2-1 正方晶格橢圓柱光子晶體 57
4-2-2 三角晶格橢圓柱光子晶體 59
4-3光子晶體橢圓柱之應用 61
4-3-1分波器 61
第五章 添加液晶之橢圓柱光子晶體 73
5-1 前言 73
5-2 液晶特性 73
5-3 向列型液晶(5CB)的特性 74
5-4 添加液晶光子晶體之平面波展開計算 74
5-5 液晶背景之正方晶格橢圓柱光子晶體 75
5-6 三角晶格橢圓液晶柱光子晶體 76
5-6-1改變邊界條件 79
第六章 結論與未來展望 94
6-1 結論 94
6-2 未來展望 94
參考文獻 96
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