利用緊束縛理論(tight binding theory)推導直線缺陷型光子晶體中缺陷模的色散關係方程式。得到色散關係方程式後‚可以進一步計算群速度與色散係數。掌握缺陷模的特徵則脈衝在光子晶體內的傳播可以加以設計並分析。所以我們可以簡單的設計分析光子晶體波導。這篇論文中討論線型缺陷與耦合共振腔兩種實例。分別計算群速度與色散係數並與相關論文的數值及有限時域差分法模擬結果做比較，結果相當吻合。最後並模擬脈衝於光子晶體中的傳播並觀察其衰減趨勢。

We have used tight-binding theory to derive an analytic expression describing the dispersion relation of defect mode in a line defect photonic crystal waveguide (PCW). With this expression, group velocity and dispersion coefficient can be directly obtained and pulse propagation in the PCW can be easily characterized. We discuss both line defect and coupled cavity PCWs in this paper. Group velocity, dispersion coefficient and pulse propagation in both PCWs are calculated and compared with the previous reports and the FDTD simulation. The results show reasonable good agreement with the previous reports and our FDTD simulation.

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