利用不同波源入射金屬結構時，會激發產生不同的表面電漿特性，而當電子束通過金屬週期性光柵上方時，不僅會激發出表面電漿，表面電漿還會透過光柵耦合的方式將能量輻射出去形成Smith-Purcell輻射。依據Smith-Purcell輻射公式，Smith-Purcell輻射可以經由光柵週期以及電子束速度等等來做調控，本論文將針對此二者進行探討。Smith-Purcell輻射與表面電漿最大的不同在於表面電漿僅能存在於金屬表面附近，而Smith-Purcell輻射則可以在空間中傳播，這個特色也使其可以應用在一些生活中的領域上如生物醫療、感測器、軍事用途等等，但礙於Smith-Purcell輻射功率非常低，若要有更多的應用，需要針對功率太小的問題做改善。
本論文使用Meep模擬軟體來做研究，透過有限時域差分法(FDTD)來對空間中的電磁場做運算及模擬，探討表面電漿的激發以及Smith-Purcell輻射的調控，使用的結構則是等半徑金螺旋光柵以及下寬上窄金螺旋光柵，並以電子束和其他波源入射。本研究會透過傅立葉轉換的方式找出輻射出去的表面電漿共振頻率，接著透過改變光柵週期以及電子束速度來觀察Smith-Purcell輻射圖的變化以及表面電漿在等半徑金螺旋光柵結構附近的輻射情況，最後使用不同波源打入下寬上窄金螺旋光柵，觀察不同波源對光柵結構的表面電漿激發情形，以及找到激發出的表面電漿共振頻率。

This thesis discusses the excitation of surface plasmons and the manipulation of Smith-Purcell radiation. When the electron bunch passes through periodic gratings on a metal surface, not only surface plasmons are excited but the energy also couples with the gratings to generate Smith-Purcell radiation and propagate outward. According to the formula, Smith-Purcell radiation can be controlled by varying the grating period and the velocity of the electron bunch. The major difference between Smith-Purcell radiation and surface plasmons lies in the fact that surface plasmons can only exist near the metal surface, while Smith-Purcell radiation can propagate in space. This property gives rise to various applications such as biomedical, sensing, and military applications.
This thesis utilizes the Finite-Difference Time-Domain (FDTD) method in the Meep simulation software to compute and simulate the electromagnetic field in space. We employ the electron bunch and other wave sources to illuminate semi-circular spiral gratings with equal radii and tapered spiral gratings with a narrower upper section. Through Fourier transformation, we identify the resonant frequencies of the radiated surface plasmons and observe the variations in the Smith-Purcell radiation diagram by altering the grating period and electron beam velocity. Additionally, we investigate the radiation characteristics of surface plasmons near the structure of the semi-circular spiral gratings. Lastly, we examine the excitation of surface plasmons near the structure of the tapered spiral gratings under different wave sources, and identify the resonant frequencies of the excited surface plasmons.

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