拉蓋爾-高斯光束因獨有的相位特性和角動量屬性，利用光場來調控電子運動提供了一種新的可能。拉蓋爾-高斯光束的特殊相位和螺旋狀電場分佈可以精確地控制電子的運動，從而實現更高效和更精確的電子束調節。拉蓋爾-高斯光束具有自旋角動量和軌道角動量兩種形式的角動量。當拉蓋爾-高斯光束作用於電子時，光束的角動量可以轉移給電子，從而改變電子的運動狀態，形成所謂的渦旋電子束。
本研究使用模擬軟體Vsim進行模擬，藉由有限時域差分法與粒子網格法，在離散化的時空中進行電磁場模擬計算，再利用Matlab軟體進行數據整理計算與繪圖，對電場強度分佈圖、電子束分佈圖、粒子軌跡圖進行分析。
本研究首先對Vsim進行了拉蓋爾-高斯光束模擬的理論驗證，進行電場強度分佈的理論計算，確定使用Vsim研究模擬的可行性。接著針對不同自旋角動量與軌道角動量的拉蓋爾-高斯光束，分析其的傳播方向電場強度分佈、橫向電場強度分佈、橫向總電場向量分佈以及電子束分佈，接著討論了在相同自旋角動量與軌道角動量的拉蓋爾-高斯光束中，改變電場頻率與電場強度對電子迴旋運動的影響。最後，比較電子在拉蓋爾-高斯光束中進行迴旋運動以及電子在外加磁場中進行迴旋共振的差別。

The Laguerre-Gaussian beam, with its unique phase characteristics and angular momentum properties, offers a novel approach to manipulating electron motion using optical fields. The distinctive phase and helical electric field distribution of the Laguerre-Gaussian beam can precisely control electron motion, thereby achieving more efficient and accurate electron beam modulation. The Laguerre-Gaussian beam possesses two forms of angular momentum: spin angular momentum and orbital angular momentum. When the Laguerre-Gaussian beam interacts with electrons, the beam's angular momentum can be transferred to the electrons, altering their motion and forming what is known as an electron vortex beam.

This study first conducted a theoretical validation of the Laguerre-Gaussian beam simulation using Vsim, performing theoretical calculations of the electric field intensity distribution to confirm the feasibility of using Vsim for this research. Subsequently, the study analyzed the propagation direction electric field intensity distribution, transverse electric field intensity distribution, transverse total electric field vector distribution, and electron beam distribution for Laguerre-Gaussian beams with different spin angular momentum and orbital angular momentum. It then explored the effects of changing the electric field frequency and electric field intensity on electron cyclotron motion in Laguerre-Gaussian beams with the same spin angular momentum and orbital angular momentum. Finally, it compared the differences between electron cyclotron motion in Laguerre-Gaussian beams and electron cyclotron resonance in an applied magnetic field.

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