廣義非均向性介質的光傳播研究

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陳鴻介(Hung-Chieh Chen) 查詢紙本館藏

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光電科學研究所碩士在職專班

論文名稱

廣義非均向性介質的光傳播研究
(EM-wave propagation properties of indefinite media)

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摘要(中)

在晶體光學所探討的介質中，各個介電常數都是正的，而且導磁率都設為1，符合大部份的自然晶體。本世紀初，科學家們實現了左手介質，並探討它們的負折射特性與非均向性，大幅地擴展了介質參數的範圍。
因應這方面的發展趨勢，本論文承襲著適用於右手介質的電磁理論，重新由馬克斯威爾方程組開始，解析出適用於廣義非均向性介質(indefinite medium)的方程式與應用規則。該介質的可對角化介電與導磁張量中，總共有6個主軸元素，分別可以是正的或是負的常數，範圍包括並超越了右手與左手介質。我們也把得到的結果用色散曲線與傳播向量圖來表示，目視化的表達方便於初期作特性上的判別與選擇。
以數值模擬高斯光束的傳播情形，可以檢驗解析的正確性，並分別呈現了電場振幅與能流密度的空間分佈。更進一步，探討介質主軸與空間座標系分離的情況，使適用的範圍再擴大。最後，應用研究的成果，找到了可以激發表面波的條件與介質的參數組合。相信本篇論文與相關的數值程式可以做為後續廣義介質光學研究的基礎與工具。

摘要(英)

In conventional crystal optics, the permittivity of an optical medium is assumed to be positive and the relative permeability is always set as 1, in accord with the situations encountered for natural crystals. Around the beginning of this century, scientists had successfully realized the first prototype of left-handed metamaterial by constructing artificial structures consisting of periodic arrays of metallic wires and split rings. The negative-refraction behavior and anisotropic properties for electromagnetic waves propagating in these media have widened the available range of parameters in optics.
Responding to this developing trend, we study in this thesis according to Maxwell’’s equations the propagation behaviors of electromagnetic waves in indefinite media. In these media, each of the principal elements of the permittivity and permeability tensors can be any positive or negative real number. The analytic results are expressed by vectorial diagrams with dispersion curves, which help us to choose the appropriate characteristics of the media in the beginning.
Propagation of Gaussian beams incident onto various kinds of indefinite media with arbitrary signs of permittivity and permeability tensors are then studied numerically using k-spectrum method (“summing over plane waves” method). The simulation results confirm the predictions made from analytical method on the transmission and reflection directions of the beams. We have also considered the situations that the principal and spatial coordinates are not parallel to each other.
By appropriately combining the medium parameters, we further discuss and illustrate four application examples, which include the omnidirectional polarizer, 2-in-1 polarizer, full transmittance collimator, and the excitation of surface waves. The analytical and simulation results and numerical tools provided here might be valuable for future researches on related topics.

關鍵字(中)

★ 表面波
★ 偏振版
★ 非均向性
★ 高斯光束
★ 光傳播

關鍵字(英)

★ Polarizer
★ anisotropic
★ EM-wave propagation
★ Gaussian Beam
★ Surface wave

論文目次

摘要 ......................................................... Ⅰ
英文摘要 ..................................................... Ⅱ
致謝 ......................................................... Ⅲ
目錄 ......................................................... Ⅳ
圖索引 ....................................................... VI
表索引 ........................................................ VII
第一章序論 ................................................... 1
1.1 傳統非均向性介質 .................................................................................... 1
1.2 負折射與左手介質 .................................................................................... 2
1.3 廣義非均向性介質 .................................................................................... 3
1.4 研究的動機與架構 .................................................................................... 4
第二章光與波的傳播理論 ....................................... 6
2.1 系統的規劃 ................................................................................................ 6
2.2 E-偏振波的傳播理論
2.2.1 波動方程式 ......................................................................................... 7
2.2.2 色散關係與分類 ................................................................................. 8
2.2.3 光與波的傳播特性 ......................................................................... 11
2.3 光與波的傳播特性圖
2.3.1 傳播角與入射角的關係圖 .............................................................. 14
2.3.2 傳播特性的類型 .............................................................................. 17
2.3.3 傳播向量圖 ................................................................................................... 18
2.4 反射與透射係數
2.4.1 單介面的規劃 ............................................................................................ 20
2.4.2 双介面的規劃 ............................................................................................ 21
V
2.4.3 原點不在介面上的規劃 .................................................................. 24
2.5 H–偏振波的傳播公式 ............................................................................. 25
第三章高斯光束的傳播 ........................................ 27
3.1 高斯光束的解析
3.1.1 重疊原理 ........................................................................................... 27
3.1.2 高斯頻譜 .................................................................................................... 28
3.1.3 高斯光束 .................................................................................................... 29
3.1.4 各區場量的計算 ....................................................................................... 30
3.2 E-偏振波的模擬 ................................................................................................. 31
第四章任意角度的主軸 ........................................ 37
4.1 H-偏振波的傳播理論
4.1.1 相似變換 .......................................................................................... 37
4.1.2 各傳播向量 ...................................................................................... 39
4.2 高斯光束的解析解
4.2.1 單介面的規劃 .................................................................................. 42
4.2.2 双介面的規劃 .................................................................................. 44
4.3 數值模擬 ................................................................................................... 45
第五章應用例 ................................................ 49
5.1 全方位的線偏振板
5.1.1 介質參數的組合條件 ............................................................................... 49
5.1.2 數值模擬 .................................................................................................... 51
5.1.3 2 合1 偏振板 ............................................................................................. 54
5.1.4 全方位全透射集光板 ............................................................................... 55
5.2 表面波的激發
5.2.1 形成的條件 ...................................................................................... 56
5.2.2 數值模擬 .......................................................................................... 57
第六章結論 ................................................... 61
參考資料 ....................................................... 62

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指導教授

欒丕綱(Pi-Gang Luan)

審核日期

2007-7-5

推文