二維與三維光子晶體特性研究與應用

Abstract

本文總共分為六章。第一章包括光子晶體的簡介、文獻的回顧；第二章介紹在本文中所用的數值方法，將平面波展開法分為1、2、3維倒出理論公式。平面波展開法是一種非常直接且方便計算光子晶體能帶的數值方法；我們可以利用求解其特徵率，而得到光子能帶結構。第三章我們首先分析光子晶體在二維三角排列與蜂窩排列能帶圖，並採用一般色散關係來畫無周期性介質，與論文做比對，以驗證我們計算的正確性。然後我們改變結構的參數，以探討光子晶體的特性。接著再將其延伸至表面模態與平面波的收斂關係，最後再討論三維中fcc與diamond晶格的能帶關係；第四章則介紹缺陷的理論基礎，並且找出三角晶格與蜂窩狀晶格的模態，與應用於光子晶體在光通訊元件。最後利用光子晶體缺陷具有共振腔的特性，在光子晶體中製造兩條缺陷，利用基本耦合的效應，我們可以得到一方向耦合器(directional couplers)。並且利用defect mode 與波導管mode去得到我們想要波前進的方向,最後再利用FDTD方法去討論三維波導管(waveguide)的能量損失性；本模擬都與論文與期刊中的數據做比較，幾乎可以得到正確的結果，用來驗證本論文程式的正確性。

The thesis has divided into six chapters .the first includes the introduction of photonic crystal and reviewer. Second we investigate the frequency domain method and the 1D、2D、3D formulas. The plane wave method is very convenient and directly numerical method。The Maxwell equations are represented eigenvalue-eigenfunction form and the bands caused by different periodic lattice arrangement are calculated。 The third chapter we analyze the band gap in honeycomb and triangular structure to compare the structure uniform。Then we change the index and discuss the properties of photonic crystal. The influence on the accuracy due to different grid number in reciprocal lattice space is also examined. We analyze optical cavity and directional coupled to find the properties of mode and control the direction of wave propagation by matching up defect mode and waveguide mode。 Finally we use FDTD numerical method to analyze 3D waveguide propagation and discuss it `s lose . Comparing the simulation result with those available in journals or experiments we almost get correct results with them and excellent agreement has been obtain in all case we can prove the accuracy of program codes within the thesis