建立於本實驗曾經對於一維光子晶體[1] [2] [3][4]研究的基礎再加上近幾年來光子晶體理論的快速發展。所以實驗室開始著手於光子晶體的研究。
而本論文的目的將是介紹電磁波在二維的光子晶體中傳遞現象。首先，我將從平面波展開法出發，藉由平面波的展開來瞭解在不同週期性結構的光子晶體，其可允許的傳送頻段與不被允許傳送的頻段的分佈，使我們之後在波源的選擇上有所依據。在數種電磁波解析的方法中，有限差分時域法[7]（Finite Difference Time Domain）是分析空間中電場跟磁場在各方向分量有效的方法。所以我們另外再以FDTD法來模擬電磁波在光子晶體中傳遞的過程。
而本論文共分六章，第一章是主要簡單的介紹完光子晶體，從第二章開始我們將從光子晶體的理論出發。在第二章裡，我們會著重於平面波展開法（Plane Wave Expansion）[5] [6]，藉由平面波展開的方式，讓我們可以更容易瞭解晶體結構與電磁波傳導模態之間的關係。為了瞭解電磁波如何在光子晶體中傳輸！我們在第三章裡將介紹K.S.Yee在1966年提出的有限差分時域法(Finite Difference Time Domain)來分析呈現電磁波在光子晶體中的傳輸。因為要避免電腦模擬計算時，會耗費太多的時間及記憶體空間，我們將引進在第四章裡所介紹的完美耦合的吸收介質層[8] [9] [10]（ Perfectly Matched Layers _ Absorbing Boundary Condition ），來增進電腦模擬時的效率。之後，第五章裡，我們會以(1)平面波展開法、(2)有限差分時域法之完美耦合的吸收介質層 兩種模擬計算的方法，交互分析並討論電磁波在不同光子晶體中的傳輸行為。最後在第六章中，則是簡單地把本論文作一個總結。

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