渦旋光束相較於一般的光束不同之處在於，一般光束只具有線性動量，但渦旋光束由於其特殊的相位結構，使得它還具有角動量。這種光學角動量可以轉移到物質上，從而對物質產生旋轉的力矩。由於具有特殊的旋轉力矩特性，使它在微細通訊編碼、光通信、量子通訊等領域有重要的應用。
本研究首先在模擬空間中LG光束光源，根據縱向切面之振幅理論值，研究模擬的可行性。接著針對不同的腰寬和拓樸電荷數的LG光束，分析所產生之波源的相位結構、強度分佈、電場向量分佈，接著將相同的波源靠近並部分疊加，觀察波源在三維空間下產生的相位分佈和電場強度變化，最後，本研究將展示m=1之LG光束與銀金屬球產生的散射波圖形，探討銀金屬球大小與銀金屬球在模擬空間中擺放位置對於產生之散射波源之影響。
本研究使用了Meep模擬軟體進行研究，藉由有限時域差分法，將離散化之時域與空間分割成網格進行電磁模擬計算，最後將dft.H5檔輸出至Matlab軟體進行繪圖，分別產生動畫圖、二維電場分佈圖、電場向量分佈圖、相位結構圖，進行分析。
關鍵字: 拉蓋爾高斯光束、光學模擬、有限時域差分

The difference between a vortex beam and a general beam is that a regular beam only has linear momentum, but a vortex beam, due to its special phase structure, also possesses angular momentum which can be transferred to matter. Vortex beam generate a rotational torque on the material because of unique rotational torque characteristic. It has many applications in areas such as fine communication encoding, optical communication, and quantum communication.
This research first generates a Laguerre-Gaussian (LG) light source in the simulation space, and based on the theoretical amplitude values of the longitudinal cross-section, studies the feasibility of the simulation. Following that, for the LG beams with different waist widths and topological charge numbers, the phase structure, intensity distribution, and electric field vector distribution of the generated wave source are analyzed. Then, the two LG sources are brought close together and partially superimposed to observe the phase structure and changes in electric field strength produced by the wave source in three-dimensional space. Finally, this research will showcase the scattering wave pattern generated by the LG beam with m=1 and a silver metal sphere, and explore the correlation between the size and position of the silver metal sphere in the simulation space and the scattering wave source generated. Key words: Laguerre-Gaussian Beams, Meep simulation, FDTD

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