手徵超材料之研究

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姓名

王耀霆(Yao-ting Wang) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

手徵超材料之研究
(Research of chiral metamaterials)

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摘要(中)

近年來，超材料的研究日新月異，各式各樣的研究主題如完美成像、光儲存器、幻象光學與人造黑洞等，無不引起了極大的注目和響應。本論文所探討的手徵超材料是一種特殊設計的人工結構。於 2004 年 John B. Pendry 提出後，相關的文章數量迅速累積。至今儼然已成為超材料領域一個獨立的分支。
本論文探討的內容有：(1) 利用等效電路法計算手徵超材料的本構關係；(2) 利用電動力學法計算手徵材料中的能量密度形式，並和 SRR-Wires 超材料結構中的能量密度做比較；(3) 手徵材料的 Casirmir 效應的研究。
尋找排斥性的 Casimir 力是現今的熱門的研究主題。去年起，Soukoulis 教授團隊發現，若適當選擇結構與材料參數，兩塊手徵超材料之間的 Casimir 力有可能成為排斥性的。此篇論文利用 Lifshitz 理論推導手徵超材料中 Casimir 能量與 Casimir 力，並與 Soukoulis 教授團隊的結果進行比較。根據我們的研究結果，我們認為手徵超材料並不能產生排斥性的 Casimir 力。
期望本文的研究結果能對手徵材料研究做出一些貢獻。

摘要(英)

In these years, the researches related to metamaterials are revolutionary. Diversified topics, such as perfect imaging, light storage, illusion optics, and artificial black hole, cause great responses and attention. This thesis discusses that chiral metamaterials is an artificial structure which is designed specifically. Concerning papers grow speedily after Prof. John. B. Pendry mentioned in 2004. Nowadays, it’s an independent branch in the field of metamaterials.
Content in this paper: (1) Calculate the constitutive relations of chiral metamaterials via equivalent circuit method; (2) Calculate the energy density of chiral metamaterials via electrodynamics method, and compare with energy density of SRR-Wires structure; (3) Do a research of Casimir effect in chiral media.
Searching for repulsive Casimir force is a popular research topic. Last year Prof. Soukoulis discovered that if choosing structure and parameters of media properly, Casimir force between two chiral materials is possible to be repulsive. This thesis utilizes Lifshitz’s theory so as to derive Casimir force and energy in chiral material, and compares with result of Prof. Soukoulis’s group. However, we consider that chiral material is impossible to generate repulsive Casimir force from our research result.
May this essay have significant contribution to works of chiral metamaterials.

關鍵字(中)

★ 超材料
★ 能量密度
★ 手徵超材料
★ 卡西米爾效應

關鍵字(英)

★ metamaterials
★ Casimir effect
★ energy density
★ chiral metamaterials

論文目次

摘要 i
Abstract ii
誌謝 iii
圖目錄 iv
Chapter 1：論文簡介 1
Chapter 2：超材料研究回顧 4
2-1 雙負介質與隱形斗篷 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2-2 光儲存器與人造黑洞. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2-3 第二章結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Chapter 3：本構關係 8
3-1 超材料的本構關係推導. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3-2 手徵材料本構關係推導 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3-3 第三章結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Chapter 4：手徵材料的能量密度，群速度與相速度 15
4-1 超材料中的電磁能量密度. . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4-2 手徵超材料中的電磁能量密度. . . . . . . . . . . . . . . . . . . . . . . . 17
4-3 第四章結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Chapter 5：手徵材料之Casimir效應 25
5-1 Casimir效應與真空電磁漲落. . . . . . . . . . . . . . . . . . . . . . . . . 25
5-2 Casimir-Lifshitz 能量公式. . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5-3 手徵超材料之Casimir效應. . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5-4 手徵Casimir效應的數值積分結果. . . . . . . . . . . . . . . . . . . . . 34
5-5 第五章結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Chapter 6：總結與未來展望 38
6-1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
6-2 未來展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Reference 40
附錄 I：手徵Casimir效應的方程式推導 45
附錄 II：手徵Casimir效應的解的詳細計算 49
附錄 III： Z轉換與手徵有限時域差分法 51

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指導教授

欒丕綱(Pi-gang Luan)

審核日期

2010-7-23

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