用路徑積分方法解二維色散金屬光子晶體

Abstract

本篇論文主要研究使用路徑積分的方法去求解勞倫茲(Lorentz)色散介質模型。我們使用Yee網格離散化模型方程式並且把原問題透過路徑積分投影在想要的特徵空間。然而，路徑積分演算法的效率以及精確度取決於某些參數。因此，我們藉著許多數值實驗去確認如何把這些參數取的理想。並且，我們也成功的計算出群聚區中相當多的特徵值。計算如此多的特徵值並精確確認其數量未來可以用於計算狀態密度，其在物理與工程都有廣泛的應用。透過這樣的特徵分析，我們也可以更有效率的繪製能帶結構圖。

In this thesis,we study how to use Contour Integral Method to solve Lorentz model.We discretize the model equation using Yee's grid and project the research question to desired eigenspace.However,the efficiency and accuracy depend on some parameters of this algorithm.By doing numerical experiments,we reveal how to adopt good parameters and solve many more eigenvalues when clustering happens.The results can be applied to count the density of states and is useful for engineering.Based on the easy parallel algorithm and this eigenvalue analysis,we can also show the band structure more efficiently..