各種納米結構的光學反應，已成為一被相當關注的課題，在物理理論和應用技術的層面上被廣泛研究。在本文中，我們利用格林函數方法(GFF)，研究了新月形圓柱体和兩接近中的圓柱体的靜電共振。格林函數方法裏涉及一表面積分方程式，我們求該方程的解便可以得出各不同形狀的納米結構的電勢。格林函數方法是一容易使用、高效率的方法，並且在研究納米結構的光學行為的問題上得出準確結果。 / 在論文的第一部分，我們計算了新月形圓柱体和兩接近中的圓柱体的杆光譜，從而研究該兩個結構的靜電共振。然而，當這兩個結構中有接觸點時，系統中便有一奇點，因此我們不能直接使用格林函數方法研究這情況。為了解決這問題，我們首先使用了變換光學的方法，求得該結構的雙極因子，再從中得到其有效介電常數的譜密度。為了比較非接觸情況中離散的杆光譜和接觸情況中的連續杆光譜，我們進一步定義了一累積分佈函數，它是其譜密度的累積分佈函數。我們從而發現當系統由非接觸的情況漸近接觸時，其離散的杆光譜便趨向其相應的連續杆光譜。 / 在論文的第二部分，我們直接研究了新月形圓柱体和兩接近中的圓柱体的勢分佈和電埸分佈。我們發現在新月形圓柱体和兩接近中的圓柱体的系統中，能量會分別將集中於其金屬間隔和空氣間隔附近的區域。當我們適當地選擇系統的參數時，其共振及能量更能進一步增強。我們亦確認了使用格林函數方法和使用保角變換方法兩者得出的結果的是吻合的。我們的研究結果可以幫助設計電漿子捕光裝置。 / The optical responses of various nanostructures have attracted a considerable attention and they have been extensively studied from the theoretical and technological points of view. In this thesis, we have studied the electrostatic resonance of crescent-shaped cylinder and two approaching cylinders by the Green function formalism (GFF). In the GFF, a surface integral equation is formulated for the scalar potential for an arbitrary number of nanostructures of various shapes. GFF is easy to apply and gives accurate results for the optical behaviors of these nanostructures. / In the first part of the thesis, we have studied the electrostatic resonance of crescent-shaped cylinder and two approaching cylinders by calculating the pole spectrum. However, in the touching case, there is a singular point and thus the GFF cannot be applied directly. To circumvent this problem, the spectral density is found from the polarizability of the nanostructure, which can be obtained analytically by the transformation optics approach. To compare the discrete pole spectrum of the non-touching cases with the continuous spectrum of the touching case, we have used the cumulative distribution function of the spectral density. We are then able to show that the discrete pole spectrum approaches to the continuous pole spectrum as the system approaches from non-touching cases to the touching case. / In the second part of the thesis, the electrostatic resonance is investigated by directly finding the local field distributions of crescent and two approaching cylinders under a uniform applied electric field. It is shown that there is an energy concentration within the metal narrow gap and the air narrow gap in the cases of crescent and two approaching cylinders respectively. It is also found that when parameters are carefully chosen, the nanoconcentration of energy will be greatly enhanced. The numerical GFF results are confirmed with the analytic results by conformal transformation. The results are useful in designing plasmonic light-harvesting devices. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Yung, Sai Kit = 電漿子納米結構中的能量集中 : 格林函數方法 / 翁世杰. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 71-74). / Abstracts also in Chinese. / Yung, Sai Kit = Dian jiang zi na mi jie gou zhong de neng liang ji zhong : Gelin han shu fang fa / Weng Shijie. / Abstract --- p.i / 摘要 --- p.iii / Acknowledgements --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Optical responses in plasmonic systems --- p.1 / Chapter 1.2 --- Objective of the thesis --- p.5 / Chapter 2 --- Review on Green function formalism --- p.7 / Chapter 2.1 --- Integral equation formalism --- p.7 / Chapter 2.2 --- Periodic corrugated interfaces --- p.11 / Chapter 2.3 --- Solution by mode expansion --- p.16 / Chapter 2.4 --- Numerical solution --- p.18 / Chapter 3 --- Pole spectrums of crescent-shaped cylinder and approaching cylinders --- p.21 / Chapter 3.1 --- Review of Green function formalism on the spectral representation of the effective dielectric constant --- p.22 / Chapter 3.2 --- Numerical results --- p.29 / Chapter 3.2.1 --- Spectral representation of the effective dielectric constant of crescent-shaped cylinders --- p.29 / Chapter 3.2.2 --- Spectral representation of the effective dielectric constant of approaching cylinders --- p.37 / Chapter 4 --- Energy concentration of crescent and approaching cylinders --- p.44 / Chapter 4.1 --- Energy concentration of crescent-shaped cylinder --- p.45 / Chapter 4.2 --- Energy concentration of approaching cylinders --- p.53 / Chapter 5 --- Conclusion --- p.58 / Chapter 5.1 --- Suggestion of future works --- p.60 / Chapter A --- Conformal transformation --- p.61 / Chapter A.1 --- Conformal transformation on crescent-shaped cylinder: nontouching case --- p.61 / Chapter A.2 --- Conformal transformation on approaching crescent-shaped cylinders --- p.66 / Bibliography --- p.71
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328595 |
| Date | January 2012 |
| Contributors | Yung, Sai Kit., Chinese University of Hong Kong Graduate School. Division of Physics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (xiii, 74 leaves) : ill. (some col.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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