本論文針對鐵電材料鉭酸鋰、氧化鋅鋁與氧化鋅所組成的半導體超穎材料及介電材料與單負材料界面間之負折射作理論性的研究。
首先，我們探討鐵電材料鉭酸鋰之遠紅外光波特性，針對三種模型結構作表面阻抗計算分析，第一種模型結構為半無窮塊材，第二種模型結構為板材，第二種模型結構則為於介電機板上沉積薄膜之層狀結構。
此外，我們也針對在負折射率區域含有鉭酸鋰之電磁偏極化光子晶體作光子能隙結構之理論性討論，此區域包含一窄頻之不規則散射，及一寬頻之規則散射，結果顯示此電磁偏極化光子晶體含有多樣性之光子能隙結構，即一位於不規則散射區域之能階及其他位於規則散射區域之能階
接著，我們探討一維半導體超穎材料光子晶體之近紅外光光子能帶，探討的光子結構為(AB)N，N為堆疊的數目，A為一介電質，而B為一氧化鋅鋁與氧化鋅所組成之半導體超穎材料，在橫向磁波斜向入射的條件下，由於半導體超穎材料的非等向性介電常數，存在著多個縱向電漿子-電磁偏極子能隙，此種能隙歸因於光子與超穎材料塊材電漿子之間的耦合效應。
我們也針對一含有半導體超穎材料缺陷的缺陷光子晶體作缺陷模態特性的分析，分析的結構為(LH)N/DP/(LH)N，N和P分別為堆疊的數目，L為二氧化矽，H為磷化銦，而缺陷層D為一氧化鋅鋁與氧化鋅所組成之半導體超穎材料。
最後，我們針對介電材料與單負材料界面間之負折射特性作理論性的探討，探討的單負材料的種類分別為負介電常數材料及負導磁係數材料，負折射現象可以藉由運用異質波理論計算負折射角度而得知。

This dissertation is theoretically devoted to the studies of photonic properties in the ferroelectric material, Lithium Tantalate (LiTaO3), semiconductor metamaterial composed of Al-doped ZnO (AZO) and ZnO , and negative refraction in an interface between a dielectric and a single-negative (SNG) material.
First, we investigate the far-infrared (FIR) wave properties for a ferroelectric material, Lithium Tantalate (LiTaO3). The analysis has been done based on the calculated surface impedances for three model structures, i.e., material occupying semi-infinite space (structure I), material of a slab immersed in free space (structure II), and a layered structure made of film on a dielectric substrate (structure III).
Besides, photonic band gap (PBG) structure for a polaritonic photonic crystal (PPC) containing Lithium Tantalate (LiTaO3) in negative refractive index (NRI) region has also been theoretically investigated. This region consists of a narrow frequency range of anomalous dispersion and a wide range of normal dispersion. The result shows that such PPC has a multiple-PBG structure with one gap locating in the anomalous dispersion region and others in the normal dispersion region.
Next, we theoretically investigate the near-infrared (NIR) photonic band structure (PBS) in a one-dimensional semiconductor metamaterial (MM) photonic crystal (PC). The considered PC is (AB)N, where N is the stack number, A is a dielectric, and B is a semiconductor MM composed of Al-doped ZnO (AZO) and ZnO. For oblique incidence under transverse magnetic mode, it is found that, due to the anisotropic permittivity of semiconductor metamaterial, there exist multiple longitudinal plasmon polariton gaps which are ascribed to the coupling between photon mode and metamaterial bulk electric plasmon.
The properties of defect modes in a defective photonic crystal containing a semiconductor metamaterial defect are also elucidated. We consider the structure, (LH)N/DP/(LH)N, where N and P are respectively the stack numbers, L is SiO2, H is InP, and defect layer D is a semiconductor metamaterial composed of Al-doped ZnO (AZO) and ZnO.
Finally, we theoretically investigate the properties of negative refraction in an interface between a dielectric and a single-negative (SNG) material. The kinds of SNG materials, epsilon-negative (ENG) and mu-negative (MNG), will be considered, respectively. The phenomenon of negative refraction (NR) can be seen due to the presence of negative refractive angle calculated by making use of the inhomogeneous wave theory.

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References in chapter 3
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References in chapter 4
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References in chapter 5
[1]T. Tang, “Photonic band gap in a one-dimensional periodic structure with semiconductor metamaterial in the near infrared”, Optik, vol. 124, pp. 6657-6660, 2013.
[2]P. Yeh, Optical Waves in Layered Media (Singapore, Wiley, 1991).
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References in chapter 6
[1]T. Tang, “Photonic band gap in a one-dimensional periodic structure with semiconductor metamaterial in the near infrared”, Optik, vol. 124, pp. 6657-6660, 2013.
[2]P. Yeh, Optical Waves in Layered Media, Singapore, Wiley, 1991.
[3]E. Reyes-Gómez, S. B. Cavalcanti, C. A. A. de Carvalho, and L. E. Oliveira, “Bulk-plasmon polaritons in metamaterial-metamaterial one-dimensional photonic superlattices,” Superlatt. Microstruc., vol. 54, pp. 96-106, 2013.
[4]R. A. Depine, M. L. Martínez-Ricci, J. A. Monsoriu, E. Silvestre c, P. Andrés, “Zero permeability and zero permittivity band gaps in 1D metamaterial photonic crystals,” Phys. Lett. A, vol. 364, pp. 352-355, 2007.
[5]M.-S. Chen, C.-J. Wu, T.-J. Yang, A. Y.-G. Fuh, “Wave properties of Fibonacci-sequence photonic crystals containing single-negative materials” Solid State Comm., vol. 168, pp. 42-51, 2013.

References in chapter 7
[1]T. Tang, “Photonic band gap in a one-dimensional periodic structure with semiconductor metamaterial in the near infrared,” Optik, vol. 124, pp. 6657-6660, 2013.
[2]S. J. Orfanidis, Electromagnetic Waves and Antennas, Rutger University, 2008, www.ece.rutgers.edu/∼orfanidi/ewa.
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[4]C.-C. Liu, C.-J. Wu, “Near infrared filtering properties in photonic crystal containing extrinsic and dispersive semiconductor defect,” Prog. Electromagn. Res., vol . 137, pp. 359-370, 2013.

References in chapter 8
[1]V. Yu. Fedorov and T. Nakajima, “Negative refraction of inhomogeneous waves in lossy isotropic matamaterials,” arXiv: 1305.6393v3, pp. 1–17, 2013.
[2]F. Zhang, S. M. Feng, and Y. H. Shan, “Research of negative refraction direction on P-light in metal,” Optik, vol. 125, pp. 338–340, 2014.
[3]L. Dong, G. Du, H. Jiang, H. Chen, and Y. Shi, “Transmission properties of lossy single-negative materials,” J. Opt. Soc. Amer. B, vol. 26, pp. 1091–1096, 2009.