本論文主要在研究二維光子晶體共振腔對量子點雷射的特性。光子晶體共振腔因為本身有高品質因子和低模態體積的特性，使得光在腔體內具有很強量子增益機制及高Purcell效應，有助於改善雷射的特性，例如低臨界功率、高自發性輻射耦合係數和高微分量子效益。
在本研究中，為了模擬光子晶體共振腔內載子和光子的交互作用，我們從雷射速率方程式推導，並引用雷射量子臨界功率的定義和計算共振腔體的基本物理參數，建立一個二維量子點光子晶體雷射的分析模組。我們利用此模組分別模擬品質因子、模態體積和Purcell效應對雷射特性的影響。最後我們利用雷射動態方程式，估計 quasi-L2共振腔雷射的小訊號調變速率可達到約400 GHz，並進一步找出影響調變速率的參數，使光子晶體雷射調變速度提升至THz的等級。

This thesis describes the characteristics of two dimensional photonic crystal cavity lasers. Photonic crystal cavities provide high quality factor (Q) and low mode volume (), which lead to enhanced light emission rate through Purcell effect. They can be used for improving the performance of lasers; for instance, lowering the threshold, increasing the spontaneous emission coupling efficiency and differential quantum efficiency.
In this work, we construct an analytic model for two dimensional quantum dot photonic crystal laser to simulate the interplay of carriers and photons in photonic crystal cavity based on rate equations. Then, we use the model to predict the spontaneous emission coupling efficiency as well as the effects of quality factor, mode volume and Purcell effect on the characteristics of photonic crystal cavity lasers. Small signal modulation speed as high as 400 GHz is predicted for a quasi-L2 cavity laser. Photon crystal cavity parameters for achieving modulation speeds up to the order of THz are also proposed and discussed.

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