In this thesis, we develop a method to study of the localized surface plasmon (LSP) modes of nano particles (NP), having arbitrary shapes, by means of discrete dipole approximation (DDA), and implement a spherical harmonics transform (SHT) to analyze their spectral fingerprint. We developed an efficient solution within the DDA for the near and intermediate field terms of the interaction using the dyadic green function and determine the optical extinction efficiency with the far field term. By implementing this approach, one may combine the advantages of a spectral analysis along with a DDA flexibility to solve an arbitrary shaped model, and demonstrate the LSP dominant mode wavelength dependency. This method provides a metric to quantify the effects of minor changes in the model structure, or the external dielectric environment, in optical experiments. We further use the method to calculate the LSP on different NP of various shapes and materials as well as to study the effect a single BSA has on the LSP when attached to the surface of a gold nano shell. The theoretical basis provided in this work may be used not only to identify a single BSA conjugated nano particle, but also to determine the cavity content of the BSA by its refractive index properties, from optical measurements.

在此論文研究中，我們使用離散偶極近似法（discrete dipole approximation, 簡稱 DDA），發展出一種能研究任意形狀奈米粒子之局域表面電漿子(localized surface plasmon, 簡稱 LSP)模式的方法，此方法使用球諧變換（spherical harmonic transform, 簡稱 SHT）來分析奈米粒子的光譜特徵。在DDA近似法下使用二元格林函數，我們發展了一種處理近場及中間場交互作用的有效解決方案，並計算遠方場的光學衰减效率。人們可結合頻譜分析的優點與DDA的可用性來處理任意形狀的粒子，且可以用這個方法來研究LSP主導模式波長的依賴性。此方法提供一個標準量度法來量化光學實驗中模型結構或外部介質環境的微小變化。我們進一步使用這個方法來計算在各種不同形狀和材料奈米粒子上的LSP, 並研究金奈米球殼被單一蛋白質接觸時對LSP所產生的影響效果。這項研究所提供的理論依據不但可以用來識別單一蛋白質所結合的奈米粒子，也能使用它，藉由光學法測量折射率性質，來判定一個蛋白質的空腔內容。

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