電磁晶體是一種利用介電常數週期性變化來造成電磁能隙的物質，頻率落在能隙中的電磁波將無法穿越此晶體。本文主要是研究以有限元素法（Finite Element Method）求解正方晶格及三角晶格的電磁能帶結構，並瞭解其能隙特性。另外也分析有限高度的電磁晶體薄板系統（Electromagnetic Crystal Slabs）的能帶結構，因為這種平面式的週期性結構除了易與其它的微波元件整合於同一基板上，製作上也比較容易。本研究採用商用電磁模擬軟體－高頻模擬器（High Frequency Structure Simulator，HFSS）做為分析電磁晶體能隙的工具，並且建構相對應的透射模型求其散射參數的頻率響應，並將兩者所得的能隙範圍做一交叉驗證。
在實驗上，我們設計一在Γ→X方向上，TM-like mode能隙位置在35.6－37.5 GHz之間的正方晶格電磁晶體薄板系統。透過完成一正方晶格電磁晶體薄板系統，並測量其散射參數的頻率響應，藉此驗證模擬計算的準確性，而模擬計算出的能隙位置與實際量測的結果36－38 GHz，兩者相當接近。同時也測量不同排數，4、8、11排的週期性空氣孔洞的散射參數，藉此觀察能隙的生成情形。
此外，我們也探討當空氣孔洞排數一定的情況下，改變孔洞直徑，透過散射參數的頻率響應，觀察能隙的變化情形。結果我們發現，當孔洞直徑從原來的0.6 mm，縮小到0.5 mm時，能隙位置則由原來的36－38 GHz，移動到頻率較低的34－35.5 GHz；至於孔洞直徑縮小到0.4 mm後，觀察其散射參數的頻率響應，能隙已經變得不明顯。

When electromagnetic waves penetrate a system that is composed of periodically modulated dielectric material in space, it behaves like electrons in a crystal. Such systems are called Electromagnetic Crystals when they are used for microwave regime. Contrast to electrons in a crystal, in electromagnetic crystals we can fabricate an electromagnetic bandgap in which no propagating modes will exist.
The goal of this study is to solve band structures of square and triangular lattice by Finite Element Method（FEM）. Another structure, electromagnetic crystal slabs, are also considered due to its easy fabrication and integration with other planar microwave passive devices on a substrate. Here we adopt commercial EM simulation software－High Frequency Structure Simulator（HFSS）as our tools. After solving band structure, we construct a driven model to calculate S parameter of finite periods and compare with each other.
In experiment, we fabricate Electromagnetism Crystal Slabs with a square arranged air holes of different rows in Γ→X direction. By measuring S parameter using HP 8510C, we can see the formation of TM-like mode bandgap which occurs in 36－38 GHz. Comparison of the bandgap position between the measurement data, 36－38 GHz, and the simulation results, 35.6－37.5 GHz, shows that they agree with each other.
Besides, another structure is also obtained by changing the diameter of the air holes. We can find that when the diameter of air holes decreases from 0.6 mm to 0.5 mm, the bandgap center frequency of TM-like mode will shift from 37 GHz to 34.5 GHz. When the diameter of air holes decreases below 0.4 mm, the TM-like mode bandgap becomes unobvious.

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