光子晶體的各種應用之多不計其數，其最大的關鍵就在於光子晶體具有的光子能隙，能夠令特定頻率範圍的電磁波無法在其中傳播。為了尋找具有較大頻寬能隙的光子晶體，我們需要檢視光子晶體的能帶結構。因此快速計算光子晶體的能帶結構，便成為相當重要的課題。
我們研究室由平均場理論建立了一個一維等效模型，來計算二維光子晶體的能帶結構。加上簡併微擾理論的修正後，可以準確估計二維光子晶體沿著任意方向的低階能帶結構。我們將這個理論推廣到三維光子晶體，並且加以修正，以達到可以計算完整的能帶結構為目標，並比較誤差跟計算時間，以求迅速且準確的計算出能帶結構。

Applications of photonic crystal are numerous. The key point to the application of photonic crystals is the photonic band gap, a range of forbidden frequencies for electro-magnetic waves which propagate in the crystal. In order to find photonic crystals with large photonic band gap, we need to calculate band structures of photonic crystals. For this reason, calculation of band structure with high efficiency is an important topic.
Our lab has constructed an 1D effective model to calculate the band structure of 2D photonic crystals. With the inclusion of degenerate perturbation, the approximation of the effective model works well in the case of 2D photonic crystal band structure calculated along any direction. We extend this method to 3D photonic crystal calculation with modification specifically made to take into account the 3D nature of the crystal. We make error/accuracy analysis of different approximations, to achieve a solution with high efficiency.

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