本論文選擇折射率為3.3的Teflon做為製作波導的材料，我們使用2.5維的圓柱座標有限時域差分法(Finite-Difference-Time-Domain in cylindrical coordinates, CC-FDTD)來加速模擬3維空間中六角晶格排列環狀波導架構中的光場傳播，並探討如何獲得適當參數，使環狀波導產生低發散出射光，最後比較六角晶格排列環狀波導之週期型和Bessel型架構，得到週期型排列有最小的擴散半角1.91°，Bessel型排列有最好的能量傳輸效率6.29%的結果。而在本實驗室的林冠毅同學負責的四方晶格排列環狀波導架構下，週期型架構表現最佳，同時擁有全架構中最小的擴散半角1.38°以及最好的能量傳輸效率27.33%。最後將我們的數據和美國海軍研究實驗室和日本京都大學METLAB的實驗結果比較，得到在未來我們需要將擴散半角縮小至0.06°以下，使其能夠實際應用在MPT(Microwave Power Transmission)技術中的結論。;We have developed a waveguide system consisting of a square-cross-section tori with a hexagonal lattice arrangement in Teflon with a refractive index of 3.3. Using the two-dimensional Finite-Difference Time-Domain (FDTD) method in cylindrical coordinates, we simulate light propagation within this three-dimensional toroidal waveguide structure. In this configuration, the two-dimensional method fully replaces the three-dimensional approach, significantly reducing computational time. This study also illustrates how to obtain and optimize the parameters necessary for achieving low-divergence output beams from the toroidal waveguide. In comparing the simulation results of the periodic and Bessel-type configurations of the hexagonal lattice-arranged toroidal waveguide, we find that the periodic configuration achieves the smallest divergence half-angle of 1.91°, while the Bessel-type configuration exhibits the higher energy transmission efficiency of 6.29%. By contrast, in the square lattice-arranged toroidal waveguide structure handled by Lin Guan Yi from our laboratory, the periodic configuration of the square lattice outperforms all other configurations, achieving both the smallest divergence half-angle of 1.38° and the highest energy transmission efficiency of 27.33%, showing a better performance among the hexagonal and square lattice configurations. Finally, we compare our data with experimental results from the U.S. Naval Research Laboratory and METLAB at Kyoto University, Japan, concluding that for future applications in Microwave Power Transmission (MPT) technology, the divergence half-angle must be reduced to below 0.06°.
