本篇論文是利用平面波展開法、多重散射法以及耦合模態理論，研究由缺陷 態所組成的濾波器結構，目標是能對窄頻的波段做濾波。我們根據耦合模態理論 (coupled-mode theory)分析此元件的特性，發現實際模擬結果與理論的配合不是 很理想，但是理論對穿透率的預測整體趨勢與模擬結果相符。雖然理論預測與實 際模擬的結果有出入，但理論提供了設計時所必須考慮的因素，在定性上仍有價 值。實際可行的結構可根據模擬結果做多次的調整而得到。由於是使用光子晶體 為基本結構設計而成，因此原則上可以積體化。相信以後在積體光學方面會有相 當大的發揮空間。 In this thesis we present a general theoretical analysis of channel drop filter structures composed of two photonic crystal waveguides and a resonator system. The device is designed to be a narrow band pass filter. Plane wave expansion method is used for calculating the band gap of the photonic crystal, whereas the multiple scattering method is employed to obtain the specific field pattern and the eigenfrequencies of the defect modes for the resonator system. On the other hand, coupled-mode theory is applied to analyze qualitatively the transmission characteristics of the filter. Although the agreement between the numerical results obtained directly from multiple scattering method and the ideal results from coupled-mode theory are not good enough, the coupled-mode theory still provides the key factors that must be considered in a practical design. The practical filter device can be constructed according to the optimal design. Since the filter is based on photonic crystals, thus it can be integrated with other components. We do believe the filter will play a role in the future in the integrated optics.
