摘 要
表面等離子體的發(fā)現(xiàn)及應(yīng)用，為實(shí)現(xiàn)納米尺度的光學(xué)控制提供了有力的工具。金屬納米粒子對表面等離子體的研究至關(guān)重要，選擇合適形狀、尺寸以及排列結(jié)構(gòu)的納米粒子結(jié)構(gòu)，可以提高表面等離子體的光場強(qiáng)度，更好地實(shí)現(xiàn)基于納米粒子陣列的表面等離子體的聚焦和導(dǎo)波。
本文主要研究了金膜上納米粒子拋物鏈在外電場激勵下的表面等離子體的聚焦和導(dǎo)波：
（1）針對格林函數(shù)分量計算中涉及到的Sommerfeld積分，研究了快速算法實(shí)現(xiàn)高效的積分運(yùn)算，給出了沿最陡下降路徑積分的計算實(shí)例，并與國外的結(jié)果進(jìn)行分析對比，證明了運(yùn)用的計算方法結(jié)果正確，算法快?；赟ommerfeld積分的快速算法，分析和計算了半空間中任意方向的電偶極子的輻射和散射。
（2）從電磁基本理論出發(fā)，深入研究了金膜上基于納米粒子拋物鏈的表面等離子體的相互作用，由并矢格林函數(shù)求解波動方程，建立分層參考系統(tǒng)的電磁場模型。將納米粒子拋物鏈劃分為一系列立方單元，并利用耦合偶極子法將該積分方程轉(zhuǎn)化為矩陣方程，從而計算出空間任意點(diǎn)的電場。
（3）應(yīng)用格林函數(shù)體積積分法，研究了金膜上球形納米粒子鏈在高斯光束照射下的SPPs激發(fā)、聚焦和導(dǎo)波。研究了入射光斑大小、入射光沿鏈的位置、粒子間距和粒子鏈的曲率半徑對SPPs激發(fā)、聚焦和導(dǎo)波影響。結(jié)果表明，粒子間距、入射光斑大小對SPPs聚焦及其分布有很大影響。入射光斑尺寸減小，激發(fā)的SPPs光束的衍射發(fā)散的增加，SPPs聚焦效果減弱。SPPs場在很大程度上也取決于粒子間距，在粒子間距小于SPPs波長時，可以實(shí)現(xiàn)較好的SPPs聚焦和導(dǎo)波效果。

關(guān)鍵詞　表面等離子體；納米粒子；格林函數(shù)法；耦合偶極子法；數(shù)值模擬





































Abstract
Surface plasmon polaritons (SPPs) have been proved to better powerful tool for the optical manipulation on nanoscale. The nanoparticle on the metal thin film plays an important role of surface plasmon polaritons. If the metallic nanoparticles are designed with suitable shape, size and arrangement, electric field magnitude can be highly improved. Further, excitation, focusing and directing of surface plasmon polaritons with nanoparticles located on a finite metal layer could be accomplished theoretically.
No matter which method is used for the calculation of scattered fields, there will be a common difficulty: the eva luation of Sommerfeld integrals, which is extremely time consuming. The integration along steepest descent paths is introduced to eva luate these Sommerfeld integrals. Numerical results show that the fast method can greatly accelerate the computation for scattering problems. Based on the fast eva luation of Sommerfeld integrals, the radiation of an arbitrarily oriented electric dipole in a half space is first analyzed and computed.
Excitation, focusing and directing of surface plasmon polaritons with curved chains of nanoparticles located on a finite gold layer are investigated theoretically. The theory of Green’s dyadic functions on a layered reference system is outlined and electromagnetic properties of surface plasmons are discussed. A curved chain of nanoparticles in upper half-space is divided into a number of cubic cells and the integral equation is reduced to a matrix equation using coupled dipole formalism. Then we calculate the electric fields at any point on gold surface.
Numerical simulations of the configuration investigated experimentally are carried out based on the Green’s tensor formalism and dipole approximation. We demonstrate that, by using a relatively narrow Gaussian beam (at normal incidence) interacting only with a portion of a curved chain of nanoparticles, one can excite an SPP beam whose divergence and propagation direction are dictated by the incident light spot size and its position along the chain. It is also found that the SPPs focusing regime is strongly influenced by the chain inter-particle distance. Comparison of numerical results with experimental data shows good agreement with respect to the observed features in SPPs focusing and directing, providing the guidelines for a proper choice of the system parameters.

Keywords　surface plasmon polaritons (SPPs); nanoparticles; Green’s dyadic function; coupled dipole formalism; numerical modeling

目 錄
摘要 I
Abstract III
第1章 緒論 1
1.1表面等離子體的研究背景 1
1.2表面等離子體的研究現(xiàn)狀和應(yīng)用 1
1.3表面等離子體的研究目的與意義 5
1.4本文研究的內(nèi)容 6
第2章 金屬結(jié)構(gòu)的表面等離子體 8
2.1表面等離子體與金屬納米材料 8
2.2金屬塊狀材料的光學(xué)性質(zhì) 8
2.3 表面等離子體的基本原理 11
2.3.1 SPPs色散關(guān)系 11
2.3.2 SPPs特征長度 14
2.3.3 SPPs的激發(fā)方式 17
2.4 金屬納米粒子的局域化表面等離激元 19
2.5 本章小結(jié) 21
第3章 數(shù)值方法 22
3.1 數(shù)值方法的概述 22
3.1.1矩量法 22
3.1.2有限元法 23
3.1.3 時域有限差分法 23
3.1.4 格林函數(shù)法 24
3.2并矢格林函數(shù) 24
3.2.1 并矢的定義 25
3.2.2 并矢格林函數(shù)的空間表示 26
3.2.3 并矢格林函數(shù)奇異性的處理 29
3.3格林函數(shù)分量計算 31
3.3.1任意方向偶極子的電場計算 31
3.3.2 Sommerfeld積分的快速計算 34
3.3.3輻射和散射數(shù)值結(jié)果 37
3.4本章小結(jié) 39
第4章 基于納米粒子鏈的表面等離子體的研究 40
4.1基于納米粒子鏈的SPP..