江衍偉臺灣大學：光電工程學研究所馬碩遠Ma, Shou-YuanShou-YuanMa2007-11-252018-07-052007-11-252018-07-052006http://ntur.lib.ntu.edu.tw//handle/246246/50655本論文中我們利用模擬退火法合成二維光子晶體以提高能隙之寬度並移動其中心頻率。模擬退火法為一處理最佳化問題之機率式迭代法則。在迭代的過程中，我們採用平面波展開法計算光子晶體之能帶，經多次迭代計算後即可合成最佳化之光子晶體。此外，我們亦利用類似方法合成具有低群速度的光子晶體結構，數值計算包括在不同極化與不同的波向量下降低群速度之探討。數值結果顯示模擬退火法確實可用來依不同需求合成光子晶體。The simulated annealing is used to synthesize two-dimensional photonic crystals so that the band gaps are enlarged and shifted. The simulated annealing is a probabilistic and iterative algorithm suitable for many optimization problems. Here the plane wave expansion method is adopted for calculating the band structure at each iteration. Then the photonic crystal can be optimized after iterations. Besides, we employ similar procedure to synthesize photonic crystals with low group velocity for both the TE and TM modes and at various wave vectors. The numerical results show that the simulated annealing can effectively be used to synthesize photonic crystals subject to different specifications.Chapter 1 Introduction...........................................................1 1.1 Photonic crystals……………...…………………………....1 1.2 Photonic band structure and photonic band gap (PBG)...2 1.3 Motivation of this work……………………………………3 1.4 Organization of the thesis………………………………….4 Chapter 2 Plane Wave Expansion Method………..6 2.1 Plane wave expansion method……………………...…….6 2.2 Fast plane wave expansion method for TE mode………..9 Chapter 3 Simulated Annealing………….....…………14 3.1 Simulated annealing…………...…………………………14 3.2 Synthesis of photonic crystals by using simulated annealing………...………………………………………..17 3.2.1 Enlarging the band gap and shifting the mid-gap frequency………………………………………...…18 3.2.2 Minimizing the group velocity…………………….20 Chapter 4 Numerical Results for Optimization of Photonic Band Gap……………………..26 4.1 Enlarging PBG and shifting mid-gap frequency…….....26 4.2 Enlarging PBG only……………………………………...30 4.3 Searching for large band gap from randomly generated structures………………………………………………....31 Chapter 5 Numerical Results for Minimization of Group Velocity……………….....................46 Chapter 6 Conclusions………………...................................74 References……………...................…………….............................763195781 bytesapplication/pdfen-US光子晶體模擬退火法平面波展開法光子晶體能隙photonic crystalssimulated annealingplane wave expansion methodphotonic band gapthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/50655/1/ntu-95-R93941051-1.pdf