本篇論文採用時域有限差分法(Finite Difference Time Domain,FDTD)探討非色散光子晶體與色散光子晶體的能帶結構及其光傳播行為。在FDTD運算過程中，我們使用Z轉換方法處理金屬、磁化電漿等色散介質的本構關係。並且介紹如何以FDTD計算能帶結構。本篇研究主要討論二維情況，探討不同填充率、不同偏振態下的非色散光子晶體能帶結構變化，以及色散光子晶體在不同電漿頻率、不同外加磁場的狀況下對於能帶結構的影響，並且應用計算出的能帶結構結果，觀察特定頻率的電磁波在光子晶體中的傳播行為。最後，利用光子晶體平板的光學特性產生次波長成像現象，並探討在不同外加磁場下，磁場對於金屬光子晶體平板的次波長成像影響。

In this thesis, we use Finite Difference Time Domain (FDTD) method to calculate the band structure and light propagation behavior in non-dispersive photonic crystals and dispersive photonic crystals. In the FDTD calculation process, we apply the Z-transform method to deal with the constitutive relations of dispersive media such as metal and magnetized plasma. We also introduce how to calculate the band structure with FDTD. This research mainly discusses the two-dimensional situations. For the non-dispersive photonic crystals, we discuss the change in band structure with different filling factors and different polarization states. For the dispersive photonic crystals, we study the influences on the band structure under different plasma frequencies and different external magnetic fields, and apply the calculated band structure results to predict the propagation behavior of electromagnetic waves of a specific frequency in the photonic crystals structure. Finally, we use the optical characteristics of the photonic crystal slab to generate the subwavelength imaging phenomena and discuss the effects of different external magnetic fields on the subwavelength imaging of the metallic photonic crystal slab.

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