由於奈米金粒子可以利用Au–S 鍵結與光熱療法中的目標癌細胞組織表面產生作用附著於其上，故奈米金粒子成為光熱療法中熱門的研究對象，在所有的金奈米粒子結構中又以奈米雙層柱狀殼核結構對於生物窗口波段上的吸收效率最高並且具有最好的光學調控性，在本篇論文中使用Compact FDTD演算法來深入了解金奈米雙層柱狀殼核結構的色散關係與表面電漿響應模態，在分析目標結構前我們先分析奈米金孔洞、奈米金柱於金孔洞之中與奈米金球殼結構以對各種奈米柱狀波導結構有初步的了解，在熟悉各圓柱結構波導的色散特性後我們繪製在light cone內外的電場分布以及電荷分佈來對各結構下的模態特性有進一步的了解，在大尺度之下我們利用角動量分裂的概念來分析表面電漿模態以及圓柱波導模態，也使用了混成模型來分析光學特性以及解釋表面電漿模態的相互耦合作用並探討表面電漿共振如何造成了色散曲線的分裂，在論文的最後我們試著將金奈米雙層柱狀殼核結構縮小至生物醫學領域上所適用的尺度並透過改變其內層空氣層厚度與外層金球殼厚度來調控此結構下的色散曲線。

The gold nanoparticles are promising candidates for the application of Photothermal therapy because their surface is easier to functionalize with the ligands targeted to the tumor cells using the Au–S bond. Among all the structures gold nano rod-in-shell structures has more absorption efficiency in therapeutic window and more optical tunability. In this thesis, we use compact FDTD algorithm to solve waveguide dispersion relation of a core-shell nano-cylindrical structures for in-depth investigation of the dispersion relation and plasmonic resonance mode. Before analyzing core-shell nano-cylindrical structures we fist analyze the hollow cylindrical structure, core in cylindrical hole and shell cylindrical structure to have rudimentary grasp of nano-cylindrical structures. After knowing the dispersion relation of each structure we comparing the mode characteristics within and outside the light cone by plotting the mode pattern and charge distribution to have further grasp of each structure. We use angular mode to analyze the higher order SPP waveguide mode for cylindrical waveguide with larger diameters. We also use the Hybridization Model to analyze the optical property and mode interaction of the plasmonic resonance mode and discuss how the surface plasmon polarization leads to the splitting of dispersion curve. In the end of the thesis, we try to minimize the scale of core-shell nano-cylindrical structures and by changing its gap size and shell size to tune the dispersion of nano-cylindrical structures.

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