| dc.description.abstract | 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. | en_US |