光子晶體最重要的特性就是它具有光子能隙，可以用來阻擋某頻率的光波通過該晶體，形成光子絕緣體，然而目前二維光子晶體的應用最為廣泛，因此計算二維光子能隙是重點所在，若能將這二維的計算簡化至一維的計算，則可以節省許多時間與精力。
由於先前已做過一維等效模型(一種平均場理論)的研究，但該一維等效模型在TE mode (H-polarization)情形下，結果不盡理想，因此，本篇論文的研究目的在於改善先前的一維等效模型，期望能用此模型迅速且有效率地求得二維光子晶體低能帶能隙。

Photonic band gap is the most important characteristic of photonic crystals. It is used to confine of EM waves within the crystal, so that photonic crystals perform like photonic insulators. At present, 2D photonic crystals are popularly applied. The focus is to calculate the photonic band gap. And if we can reduce the calculation of 2D to 1D, it will save us a lot of time and troubles.
We had investigated a 1D effective model (a mean field theory) before, but the result of this kind of model for TE mode was not good enough. The purpose of this thesis is to improve the previous model and calculate the low-lying bands of photonic crystal simply and efficiently in a systematic way.

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