渦漩光束具有特殊的螺旋相位結構，使其可以攜帶軌道角動量，而拉蓋爾高斯光束就是一種可以攜帶軌道角動量的渦漩光束。這種光束與物質相互作用時，其光學角動量可以傳遞到物質上，導致物質的旋轉或其他動態行為。在現今，光學渦漩已廣泛應用於許多領域。例如，在生物物理領域中，渦漩光束可以施加扭矩，使粒子在光場中旋轉，從而捕獲和控制微小粒子。此外，渦漩光束的螺旋相位結構能提高光學成像的分辨率和對比度，有助於超分辨顯微成像技術的發展。由於渦漩光束能攜帶較高的軌道角動量，它成為多維度量子信息編碼和通信的理想選擇。
本研究使用COMSOL軟體進行模擬一拉蓋爾高斯光束，並且在其中心打入一束電子束，研究在不同條件下的拉蓋爾高斯光束對電子造成的影響。
本研究所改變的條件有在通過改變不同m值下改變電場強度、電子初始動能、改變電子入射孔徑大小以及改變光束之光腰大小等條件下，研究電子在光束中的運動軌跡，並進行分析與討論。

Vortex beams possess a unique helical phase structure, enabling them to carry orbital angular momentum. A Laguerre-Gaussian beam is a type of vortex beam that can carry orbital angular momentum. When such beams interact with matter, their optical angular momentum can be transferred to the matter, causing rotational or other dynamic behaviors. This characteristic makes vortex beams applicable in areas such as microparticle manipulation, optical communication, and astronomy.
In this study, COMSOL software was used to simulate a Laguerre-Gaussian beam. An electron beam was introduced at the center of this beam to investigate the effects of the Laguerre-Gaussian beam on the electrons under different conditions. The conditions varied in this study include changing the electric field intensity for different m-values, the initial kinetic energy of the electrons for different m-values, the size of the electron injection aperture, and the beam waist size. The trajectories of electrons in the beam were studied and analyzed under these varying conditions.

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