表面電漿子共振能在次波長尺度結構下產生很強且侷域性光學場，因此提供了廣泛的應用，包含了光電、材料以及生物醫學等等的領域，因此成為現今奈米科技當中最為重要的領域之一。在本篇論文中，我們利用有限差分時域法(FDTD)數值模擬的方式對於奈米銀球殼(Nano-shell)與半球殼(Hemispherical nano-shell)結構的單一結構與陣列結構之電場強度及電荷分佈進行模態上探討。在半球殼結構中，我們在頻譜上找到其對應的bonding與anti-bonding模態，並將其描繪出此結構之混成模型(Hybridization model)。第二個部份，我們討論二維正方形晶格(Square lattice)排列之奈米銀球殼與奈米銀半球殼在改變週期間距對於頻譜上的表現及相位共振所造成的Fano模態作分析。最後比較Fano模態與LSPR模態電荷分佈，發現了Fano共振的電荷分佈會與單一結構時LSPR模態電荷分佈作對應，並且Fano共振亦有將在單一結構不明顯之LSPR模態表現出來的效果。以上研究的分析在未來設計球殼的光學感測元件上提供重要的資訊。

Localized surface plasmon resonance (LSPR), observed in metal nanoparticle arrays interacting with an incident light field, is an emerging research area for surface-enhanced -Raman-scattering (SERS) biomedical sensing applications. The plasmonic properties of metal nanoparticles can be easily tuned by varying the shape, size and arrangement along with the dielectric environment. Particles with coreshell structure provide an extra degree of freedom to tune the LSPR wavelength. The array structure adds an extra tuning capability by setting the periodicity near the single particle LSPR wavelength to squeeze out a sharp Fano resonant peak. In nano fabrication, semi shell array has advantage over the spherical shell array by the top-down approach. Here, we investigate the LSPR cross section and mode distributions for nano-shell and semi-shell with core radius of 100 nm and shell thickness of 20nm for single and periodic structure using FDTD simulation. Higher order quadrapole modes with bonding and anti-bonding types were observed. Furthermore, we discussed Fano resonance effect on each LSPR modes by adjusting the interparticle spacing. The coupling between the dipole/quadrapole LSPR and the grating mode leads to different resonant properties. The charge distributions of dipole and quadrapole under the influence of Fano resonance are also discussed.

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