根據本論文中的研究結果中，在週期型排列結構下，正方形寬度為0.442a、波長為0.794a時有最佳能量傳遞效率，將其換算成美國海軍研究實驗室的Scope-M 計畫中所使用的頻率9.7 GHz，得到a為3.895公分。本論文之結構為一個15a x 20a的環形中空方柱波導結構，其體積直徑為113 cm，體積高度為77.9 cm，比美國海軍研究實驗室所使用的直徑為5.4 m的圓盤發射器來的小非常多。;Based on the previous research by Dr. Ya-Lun Tsai, the circular cross-section of the torus hollow waveguide structure was modified to be square. The periodical squares are arranged in a square lattice to facilitate the fabrication process. The refractive index of the tori was 3.3. We use the Cylindrical Coordinates Finite-Difference Time-Domain method to analyze the light propagation passing through the torus waveguide. By scanning the width of the square and the wavelength of the input light, we aimed to obtain the structure parameters of the torus waveguide to minimize the divergence angle of the output light and to obtain a higher energy transmission efficiency of the light. We also modified the arrangement of the position of the squares according to the minima of the Bessel function. The divergence angle of the output light and the energy transmission efficiency of the light were analyzed.
The simulation results show that for the periodic arrangement, the best energy transmission efficiency reached 27.33%, and the smallest divergence angle was 1.38°. In contrast, the Bessel-type arrangement performed worse than the periodic one in both energy transmission efficiency and divergence angle. Additionally, compared with the hexagonal lattice waveguide structure studied by I-Chen Ou of our lab, the structure in square lattice performed better in both energy transmission efficiency and divergence angle in the periodic arrangement. In the Bessel-type arrangement, the square lattice structure also exhibited slightly better performance than the hexagonal lattice in terms of both energy transmission efficiency and divergence angle. Overall, in both square and hexagonal lattice structures, the periodic arrangement exhibited better performance in energy transmission efficiency and divergence angle compared to the Bessel-type arrangement.
According to the optimal research results presented in our research, the best energy transmission efficiency was achieved when the square width was 0.442a and the wavelength was 0.794a. Converting this to the frequency of 9.7 GHz used in the U.S. Naval Research Laboratory′s Scope-M program, we obtain a=3.895 cm. The structure proposed in our research was a torus hollow waveguide structure with dimensions of 15a × 20a with diameter of 113 cm and height of 77.9 cm, which is significantly smaller than the transmitter used by the U.S. Naval Research Laboratory, which has a diameter of 5.4 m.
