當電子束通過週期性金屬結構時，會激發Smith-Purcell輻射(SPR)，而我們稱這些週期性金屬結構為光柵(Gratings)，輻射出去的角度會與光柵週期以及電子束速度有關，當然輻射的強度與角度還可以經由其他外在條件來改變，本論文針對光柵週期以及電子束速度來做討論。Smith-Purcell輻射與表面電漿不同之處在於表面電漿只能存在於金屬表面上，而Smith-Purcell卻可以在空間中傳播，因此我們可以將Smith-Purcell輻射應用在軍事用途、生物醫療等諸多領域上面，但目前Smith-Purcell輻射遇到最大的瓶頸在於輻射功率太小，所以我們需要找到能實際應用且提高功率的輻射機制。
本篇論文使用有限時域差分法(FDTD)的軟體:Lumerical來探討如何激發與調控Smith-Purcell輻射，由於使用的結構為中空圓柱結構內通以電子束，形成的IMI結構會產生對稱以及反對稱模態，本實驗會找出哪個模態的波長可以激發Smith-Purcell輻射。透過改變電子束的運動速度以及光柵週期可以調控Smith-Purcell輻射角度。最後再透過螺旋光柵來產生軌道角動量，並且測量輻射能量與電子束能量的比值，觀察其與軌道角動量之關係。

In this paper, an electron bunch was used to excite the surface plasmon(SP) inside the hollow metal cylinder, this structure can produce symmetry and antisymmetry modes. We are going to figure out which wavelength of surface plasmon resonation can be turn into Smith-Purcell radiation.We designed periodic gratings outside the hollow metal cylinder to convert surface plasmon into Smith-Purcell radiation.By changing the period of gratings and the speed of electron bunch so that we could control the angle of radiation.Then we used helical periodic gratings to replace the original periodic gratings. The helical periodic gratings could radiate the orbital angular momentum beam. Similar to the original periodic grating, we could also control the angle of radiation by changing the period of gratings and speed of electron bunch.

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