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研究生:張鐵明
研究生(外文):Tieh-Ming Chang
論文名稱:利用時域有限差分法對奈米銀柱結構的奈米成像性質之研究
論文名稱(外文):FDTD simulation of nano imaging with silver nano rod structure
指導教授:蔡定平
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:中文
論文頁數:59
中文關鍵詞:時域有限差分法奈米銀柱
外文關鍵詞:FDTDsilver nano rod
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  • 被引用被引用:1
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在傳統光學微影技術(optical lithography)中,若欲縮小圖形(pattern)線寬時必須利用較短的光源波長,但伴隨而來的卻是成本的增加及製程技術上的困難。在現有光微影技術下,藉由奈米銀柱的結構對於光場的良好侷域性,使得利用可見光波段的光源在近場範圍中產生次波長線寬之圖形成為可能。本文採用三維時域有限差分法(3D-FDTD)的方法,應用至近場光學的領域,有系統的探討奈米銀柱陣列在各種不同參數之下,其對於奈米尺度大小之光源的光場傳輸現象,以及經過此奈米銀柱陣列之後光強(intensity)在近場範圍的分佈特性與光場強的增益作用。並研究表面電漿的局域性與近場光強增強效果之關連性。本文在內容上分為以下四個主題:
一、 建立一套求解電磁散射問題的數學模式,並從數值方法特性的分析,建構出最佳之格式與程式設計之技巧。
二、 研究單一柱狀結構之近場光強分佈,模擬結果顯示:在沿著電場偏振方向上的奈米銀柱截面寬度變化對光場分佈有較顯著的影響。
三、 比較奈米平行銀柱陣列各項參數對近場光強分佈之影響。
四、 研究奈米平行銀柱陣列在不同孔洞大小及孔洞間距下對解析度的影響。
Silver nanorods have an excellent localization of the transmitted wave; especially the localized spot has a space below the bottom of the nanorods. In this dissertation, the near field distribution of silver nanorods is investigated. The numerical method knows as finite difference time domain (FDTD) is introduced into near field optics. The effects of various radius, lengths, gaps and separations of silver nanorod array are investigated. Results of the calculation provide a direct theoretical basis for the relation between the localization of surface Plasmon and the enhance of near field.
The near field distribution of nano hexagonal rod, and the parallel nanorod array are studies systematically using our FDTD method. It is found that the image is highly dependent on the spacing and radius of nanorods. Results of single nanorod show similar near field distribution to an electrical dipole. Due to the boundary condition at the interface, the polarized incident wave enhance the field at boundary of the nanorod. The influence of nanorods on contrast is studied with FDTD method as well.
Silver nanorods have an excellent effect on localizing the transmitted wave, especially, the enhancements below the bottom of the nanorods. In this dissertation, a systematic apparoach to studying the near-field distributions, from a single nanorod to an array of nanorods, is carried out. The three-dimensional finite difference time domain (3D FDTD) which is a well known and powerful numerical method is used to simulate the interactions of the optical waves with the silver nanorods.
The near-field distribution of a single nanorod is similar to an electrical dipole. The effects of radius variation, lengths of nanorods, gaps and spacings in the silver nanorod array are investigated. It is found that the image formed from the transmitted wave is highly dependent on the spacing and radius of nanorods. According to the relation between the localization of surface plasmon and the enhancement of near field, the optimal criteria can be obtained in constructing optical nanolithographic sturcutures.
中文摘要 II
英文摘要 III
目錄 V
圖目錄 VII
1 第一章、前言 1
參考文獻 2
2 第二章、光與物質交互作用之基礎理論 3
2. 1 光在光學介質中的傳遞 3
(a) 原子振盪子(atomic oscillators) 5
(b) 振動振盪子(vibrational oscillators) 8
(c) 自由電子振盪子(free electron oscillators) 8
2. 2 電漿子共振(plasmon resonance) 9
(a) 表面電漿子(surface plasmon) 10
(b) 顆粒電漿子(particle plasmon) 11
參考文獻 15
3 第三章、時域有限差分法之數學模式 16
3. 1 理論背景與數學公式的推導 17
3. 2 FDTD之數學模式 20
3.2.1 一維FDTD 20
3.2.2 單胞大小的選取及數值分析之穩定準則 22
3.2.3 激發源的處理 23
3.2.4在耗損(lossy)介質中的傳遞 24
3.2.5在色散(dispersion)介質中的傳播 25
3.2.6吸收邊界條件(absorbing boundary condition, ABC) 28
3.2.7 APML的基本原理 29
3.2.8全場/散射場模型的建立 34
3. 3 三維FDTD 36
參考文獻 37
4 第四章、奈米銀柱對近場成像之研究 38
4. 1 單一六角柱狀結構之近場光強分佈 40
4. 2 平行銀柱陣列之近場光強分佈 43
4.2.1改變圓柱半徑的近場分佈 44
4.2.2改變圓柱中心點之間間距的近場分佈 47
4.2.3改變光罩和圓柱之間距離的近場分佈 49
4.2.4改變圓柱高度的近場分佈 51
4.2.5奈米銀柱層對近場強度分佈的影響 53
4. 3 銀柱陣列對解析度的影響 54
5 第五章、結論與展望 58
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