在光子晶體迴路中，波導與濾波元件為整個迴路最主要的基本元件。傳統上，由於波導與濾波元件的設計概念是各別獨立的，因此對應的元件大小與空間上的放置也是各自獨立，而使得整個迴路的體積也相對較大。在本論文中，我們探討如何將波導與共振腔結合在一起，以設計出一種具有濾波功能的光子晶體波導。根據耦合理論，特定的共振腔幾何架構設計可以篩選出特定的頻率。由於共振腔可結合在光子晶體波導之中，因此可大大地降低整個迴路的體積。本論文中所採用的數值模擬方法為平面展開法與多重散射法，藉由上述的方法，我們可以快速地得到光子晶體共振腔的特徵頻率，以及光子晶體波導的穿透率。為了達到高效率的濾波效果，我們對光子晶體共振腔與波導結構之間的連接結構作最佳化的分析。從模擬的結果顯示，在共振腔週圍的結構作微調可以有效地提昇濾波效果，而在多個共振腔組合的結構下，可將濾波後的頻譜平坦化。 Waveguides and filters are the essential building blocks in constructing photonic crystal circuits. Traditionally, the designing rules and hence the arrangement of these two kinds of devices in the photonic circuit are unrelated, therefore, the feature size of the whole circuit structure cannot be reduced much. In this thesis, based on the coupling effect between waveguide modes and cavity modes, we design the waveguide-filter structures that consist of several waveguides and cavities embedded in the two-dimensional photonic-crystal background. According to the coupled-mode theory, waveguide-filter structures can be designed to filter waves of specific frequencies by appropriately choosing the parameters such as the locations and sizes of the cavities and their distances to the waveguides. Since the cavities are embedded in the photonic crystal background, the feature size of the whole photonic circuitry can be reduced dramatically. The numerical simulation methods we used in this thesis are the plane wave expansion method and multiple scattering method. Utilizing these two methods, the eigen-frequencies of the cavities can be determined and the transmissions of the waveguides can be obtained. In order to achieve the highest filter efficiency, we optimize the structure by appropriately tuning the parameters of the cavities and waveguides. The results reveal that tuning the surrounding structures of the cavities can improve much of the efficiency of the filter. Besides, the throughput spectrum can be made smoother by using the multi-cavity structure.
