利用模擬退火法與等效折射率法合成光子晶體平板線型波導

Abstract

本論文中，我們結合模擬退火法與等效折射率法來合成光子晶體平板線型波導，使其缺陷模態具有最低或固定群速度。模擬退火法是處理非線性最佳化問題之機率迭代法。迭代過程中，我們以傳統平面波展開法計算二維光子晶體之能帶。等效折射率法乃利用二維計算來作等效近似，以處理三維平板波導問題。使用等效折射率法時，我們結合傳統及修訂的平面波展開法來得出最終之色散關係圖。數值結果顯示模擬退火法與等效折射率法的結合，確實可以合成ㄧ具有最低或固定群速度之光子晶體平板線型波導。

The simulated annealing and effective index methods are used to synthesize a photonic crystal slab line-defect waveguide with its line-defect mode at a minimal group velocity or a fixed group velocity. The simulated annealing is a probabilistic iterative algorithm for finding a global extremum in a nonlinear optimization problem. In this thesis, the conventional plane wave expansion method is used to calculate the band diagram at each step of the simulated annealing process. The effective index method is an approximation algorithm for reducing the three-dimensional slab waveguide problem to an approximate two-dimensional one. The conventional and revised plane wave expansion methods are used together with the effective index method to calculate the final band diagram. The numerical results show that the simulated annealing and effective index methods can effectively be used to synthesize a photonic crystal slab line-defect waveguide with its line-defect mode at a minimal group velocity or a fixed group velocity.