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系統識別號 U0026-0812200915284128
論文名稱(中文) 第三類近軸波動方程本徵模: Ince-Gaussian Modes於光鉗應用之探討
論文名稱(英文) The 3rd Eigen Modes of PWE: Study for the Ince-Gaussian Modes in Optical Trapping and its Application
校院名稱 成功大學
系所名稱(中) 物理學系碩博士班
系所名稱(英) Department of Physics
學年度 97
學期 2
出版年 98
研究生(中文) 楊朝舜
研究生(英文) Chao-Shun Yang
電子信箱 lovingkist0618@gmail.com
學號 l2696113
學位類別 碩士
語文別 中文
論文頁數 78頁
口試委員 指導教授-朱淑君
口試委員-蔡錦俊
口試委員-柯景元
中文關鍵字 近軸波動方程本徵模  光鉗 
英文關鍵字 Ince polynomial  IGMs 
學科別分類
中文摘要 摘要

Ince- Gaussian modes(IGMs)為在實驗中可見的一種嶄新型態的光學模態,對於我們在應用和設計上的實現,擁有許多潛力;然而,由於IGMs是在橢圓圓柱座標系下的數學來表示,造成了我們無法直覺的去了解,也成了我們在使用上的一大考驗; IGMs的不易親近,也讓我們無從進一步去了解其物理特性,若純粹以數學出發,又包含了龐大的運算,無法達到普遍的運用,是故我希望能在這篇論文使用簡單的數學描述來達成對IGMs較平易近人的理解。

週期性位能井的構成,一直是一個受到重視的議題,多點侷限也被廣泛的運用在許多的領域,然而,在實際運用的過程,我們對這樣光學工具,有更多的期待,深入研究也發現許多值得克服的問題,科學家亦投入其中發表了許多傑出的工作。本篇論文經由對IGMs的解析,得以利用簡單的數學描述方法提出IGMs的特點,我也試圖將其特點運用在週期位能的實踐上,透過可實踐的設計,我得以在本篇論文中提出IGMs所建構週期性位能井的優勢。

最後,我也將引進統計理論,試圖更完整的將已有的物理方法或概念與所建立的光學機制作結合,透過物理的法則,我得以從理論推測可能引發的結果,也從另外一個角度提出,對於IGMs建構出的光學工具的評估,我得以描述這樣工具的穩定性(藉著侷限物的逃脫機率),也提供了此類光場在光鉗應用上的一個參考的理論機制。
英文摘要 Abstract

IGMs are a kind of experimentally new-identified optical mode, standing with apparent potential in design and application. However, the mathematical expression of IGMs under Elliptic Cylindrical coordinates, preventing us from understanding IGMs instinctively, stands a formidable challenge in application. The pure mathematical expressions of IGMs are composed by a great deal of calculation, which also bids us no help in common use. I am, therefore, prompted to build an easier mathematical approach in this study.


While the composition periodic potential well has been being a focused issue, and the multi-point trap has been applied wildly in many fields, such optical tool has been expected more in application and many issue has also been identified for potential further research, which indeed many outstanding work had been done so far by the scientists.Here, with the analytical form of IGMs, a simplified mathematical expression of IGMs feathers can be achieved. This was also introduced on periodic potential well issues and, via a practicable design, the advantage of periodic potential well model with IGMs was presented.

Finally, statistical theory was also introduced in order to combine the available physical concepts and methods with the optical model built in this research, enabling the prediction of possible results through these physical laws. The stability of this optical tool has also been discussed by the possibility of the escaping trap, which also provides a theoretical reference for further application of optical trap.
論文目次 目錄

摘要 I
Abstract III
致謝 IV
目錄. V
圖目錄. VII


Ch1 簡介(introduction) 1

Ch2 Theorem 4
2-1 IGMs的相關討論 4
2-1-1 從MAXWELL’s方程出發 4
2-1-2 Ince-Gaussian modes 7
2-1-3 Ince polynomial的函數特性及補充 11
2-1-4 IGMs與LGMs的投射關係 14
2-2 光鉗 18
2-2-1 光鉗歷史回顧 18
2-2-2 A Tweezer model: Eletrical Magnetic Approximation 21
2-2-3 EM Approximation的特別例子Rayleigh 24
2-2-4 A Tweezer model:Ray optics approximation 26
Ch3 IGMS的暗紋解析及應用 29
3-1解析的找出IGMS上場強為零之處 29
3-2 vortex lattice 34
3-2-1 動機 34
3-2-2 分析 36
Ch4 IGMs運用在Optical trapping 41
4-1 Introduction 41
4-2動機 43
4-3 Ince Gaussian Modes(IGMS)對於侷限所展現的特性 46
4-4引入統計的概念分析 55
4-4-1 統計的理論推導 55
4-4-2模擬結果分析 65
Ch5 結論與未來展望 74
5-1結論 74
5-2 未來展望 77
參考文獻 78
參考文獻 參考文獻
[ 1 ]M. W. Beijersbergen , “Astigmatic laser mode converters and transfer of orbital angular momentum”,Opt. Commun. 96, 123-132(1993)
[ 2 ]M. A. Bandres and J. C. Gutie’rrez-Vega , “Ince–Gaussian modes of the paraxial wave equation and stable resonators”,J. Opt. Soc. Am. A 21, 873-880 (2004)
[ 3 ]A. Ashkin and J. M. Dziedzic , “Observation of a single-beam gradient force optical trap for dielectric particles”,Opt. Lett. 11, 288- (1986)
[ 4 ]Y. R. Chang , L. Hsu , and S. Chi , “Optical trapping of a spherically symmetric sphere in the ray-optics regime: a model for optical tweezers upon cells”,Appl. Opt. 45, 3885-3892 (2006)
[ 5 ]S. C. Chu , C. S. Yang , and K. Otsuka ,” Vortex array laser beam generation from a Dove prism-embedded unbalanced Mach-Zehnder
interferometer”, Opt. Express 16, 19934-19949 (2008)
[ 6 ]T. Tlusty, A. Meller, and R. Bar-Ziv ,” Optical Gradient Forces of Strongly Localized Fields”,Phys. Rev. Lett. 81, 1738(1998)
[ 7 ]A. R. Sidorov ,Y. Zhang ,A. N. Grigorenko ,M. R. Dickinson,” Nanometric laser trapping of microbubbles based on nanostructured substrates”,Opt. Commun. 278,439–444(2007)
[ 8 ] R. K. Pathria,Statistical Mechanics,2nd edition,Chap. 14.
[ 9 ] H. A. Kramers ,” BROWNIAN MOTION IN A FIELD OF FORCE
AND THE DIFFUSION MODEL OF CHEMICAL REACTIONS”,Physica VII .4,284-304(1940)
[10] Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of Nonconservative Optical Forces on the Dynamics of Optically Trapped Colloidal Spheres: The Fountain of Probability”,Phys. Rev. Lett. 101, 128301 (2008)
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