光子晶體(PCs)是具有空間週期性特性的光學介質，它的基本特徵是存在一些光子能隙(PBGs)，頻率介於其中的電磁波無法在光子晶體結構中傳播。本論文目的是在設計含有單負材料(SNG)俱缺陷之光子晶體濾波器並研究其特性。在此篇論文中，共研究了兩個主題。藉由轉移矩陣法（TMM）計算透射率對頻率的關係圖。
第一個主題是研究單負材料的缺陷模態於一維光子晶體中的影響。考慮分別含有負介電常數材料(ENG)以及負導磁常數材料(MNG)的光子晶體異質結構。我們探討缺陷厚度以及其介電常數和導磁常數的變化會如何影響濾波特性。我們也研究濾波器在TE和TM不同模態下改變入射角度的特性。
第二個主題是延伸第一主題，使用單負材料為缺陷的雙通道可調變濾波器的設計和分析。我們發現可藉由改變缺陷厚度及其介電常數、導磁常數和電漿頻率來調變濾波的特性。不同的入射角度在TE和TM模態下也可做為一個濾波器調變因子。

In this thesis, the filtering properties in one-dimensional photonic crystals (1D PCs) containing SNG materials are investigated. We consider two filtering structures of (1/2)nA(2/1)n and (1/2)nB(2/1)n, in which both layers 1 and 2 are dielectrics, n is the stack number, and the defect layers A and B are taken to be ENG and MNG materials, respectively. Two main topics are involved.
The first part is to investigate the effect of SNG material on the defect mode in a 1D defective PC. It is found that the channel frequency can be tuned by the variation of permittivity, permeability and thickness of the defect layer. We also investigate the influence of incident angle for both transverse electric (TE) wave and transverse magnetic (TM) wave.
The second part is to design and analysis of tunable double-channel filter based on the use of an SNG defect. The embedded SNG material plays a role of tuning factor for the double-channel filter. The tunable characteristics are studied by changing the static positive parameter, plasma frequency, angle of incidence and the thickness of the defect layer. The proposed filter could be of technical use in signal processing and communication applications.

Chapter 1
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[34]Y. H. Chen, J. W. Dong, and H. Z. Wang, “Twin defect modes in one-dimensional pho-tonic crystals with a single-negative material defect,” Appl. Phys. Lett., Vol. 89, 141101, 2006.

Chapter 3
[1]S. John, “Strong localization of photons in certain disordered lattices,” Phys. Rev. Lett., Vol. 58, 2486-2489, 1987.
[2]E. Yablonovitch, “Inhibited spontaneous emission in solid state physics and electronics,” Phys. Rev. Lett., Vol. 58, 2059-2062, 1987.
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[5]Y. Zhang and B. Y. Gu, “Aperiodic photonic quantum-well structures for multiplechanneled filtering at arbitrary preassigned frequencies,” Opt. Express, Vol. 2, 5910–5915, 2004.
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[8]W.-H. Lin, C.-J. Wu, T.-J. Yang, and S.-J. Chang, “Terahertz multichanneled filter in a superconducting photonic crystal,” Optics Express, Vol. 18, 27155-27166, 2010.
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[17]C.-J. Wu, M.-H. Lee, and J.-Z. Jian, “Design and analysis of multichannel transmission filter based on the single-negative photonic crystal,” Progress In Electromagnetics Research Letters, Vol. 136, 561-578, 2013.
[18]D.-W. Yeh, and C.-J. Wu, “Analysis of photonic band structure in a one-dimensional photonic crystal containing single-negative material,” Optics Express, Vol. 17, 16666-16680, 2009.
[19]W.-H. Lin, C.-J. Wu, and S.-J. Chang, “Analysis of angle-dependent unusual transmission in lossy single-negative (SNG) materials,” Solid State Communications, Vol. 150, 1729-1732, 2010.
[20]D.-W. Yeh, and C.-J. Wu, “Thickness-dependent photonic bandgap in a one-dimensional single-negative photonic crystal,” Journal of Optical Society of America B, Vol. 26, 1506-1510, 2009.
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[24]Y. H. Chen, J. W. Dong, and H. Z. Wang, “Twin defect modes in one-dimensional photonic crystals with a single-negative material defect,” Appl. Phys. Lett., Vol. 89, 141101, 2006.
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Chapter 4
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[2]R. L. Nelson, and J. W. Haus, “One-dimensional photonic crystalsin reflection geometry for optical applications,” Appl. Phys. Lett., Vol. 83, 1089-1091, 2003.
[3]Y., J. Fink, N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and L. E. Thomas, “A dielectric omnidirectional reflector,” Science, Vol. 282, 1679-1682, 1998.
[4]X. Z. Sun, , P. F. Gu, W. D. Shen, X. Liu, Y. Wang, and Y. G. Zhang, “Design and fabrication of a novel reflection filter,” Applied Optics, Vol. 46, 2899-2902, 2007.
[5]Y.-H. Ye, J. Ding, D.-Y. Jeong, I. C. Khoo, and Q. M. Zhang, “Finite-size effect on one-dimensional coupled-resonator optical waveguides,” Phys. Rev. E, Vol. 69, 056604, 2004.
[6]D. Chen, M.-L. Vincent Tse, and H.-Y. Tam, “Optical properties of photonic crystal fibers with a fiber core of arrays of subwavelength circular air holes: Birefringence and dispersion,” Progress In Electromagnetics Research, Vol. 105, 193-212, 2010.
[7]H. Li, and X. Yang, “Larger absolute band gaps in two-dimensional photonic crystals fabricated by a three-order-effect method,” Progress In Electromagnetics Research, Vol. 108, 385-400, 2010.
[8]C.-J. Wu, J.-J. Liao, and T. W. Chang, “Tunable multilayer Fabry-Perot resonator using electro-optical defect layer,” Journal of Electromagnetic Waves and Applications, Vol. 24, No. 4, 531-542, 2010.
[9]Y. Shi, “A compact polarization beam splitter based on a multimode photonic crystal waveguide with an internal photonic crystal section,” Progress In Electromagnetics Research, Vol. 103,393-401, 2010.
[10]L.-M. Qi, and Z. Yang, “Modified plane wave method analysis of dielectric plasma photonic crystal,” Progress In Electromagnetics Research, Vol. 91, 319-332, 2009.
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[14]W. Shen, , X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, ”Narrow band filter in both transmission and reflection with metal/dielectric thin films," Optics Communication, Vol. 282, 242-246, 2009.
[15]H.-T. Hsu, and C.-J. Wu, “Design rules for a Fabry-Perot narrow band transmission filter containing a metamaterial negative-index defect,” Progress In Electromagnetics Research Letters, Vol. 9, 101-107, 2009.
[16]C.-J. Wu, M.-H. Lee, and J.-Z. Jian, “Design and analysis of multichannel transmission filter based on the single-negative photonic crystal,” Progress In Electromagnetics Research Letters, Vol. 136, 561-578, 2013.
[17]Z. Y. Wang, X. M. Cheng, X. Q. He, S. L. Fan, and W. Z. Yan, “Photonic crystal narrow filters with negative refractive index structural defects,” Progress In Electromagnetics Research, Vol. 80, 421-430, 2008.
[18]P. Yeh, Optical Waves in Layered Media, John Wiley & Sons, Singapore, 1991.
[19]M. Born and E. Wolf, Principles of Optics, Cambridge, London, 1999.
[20]L. G. Wang, H. Chen, and S. Y. Zhou, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single negative materials,” Physical Review B, Vol. 70, 245102, 2004.
[21]D.-W. Yeh, and C.-J. Wu, “Analysis of photonic band structure in a one-dimensional photonic crystal containing single-negative material,” Optics Express, Vol. 17, 16666-16680, 2009.
[22]W.-H. Lin, C.-J. Wu, and S.-J. Chang, “Analysis of angle-dependent unusual transmission in lossy single-negative (SNG) materials,” Solid State Communications, Vol. 150, 1729-1732, 2010.
[23]D.-W. Yeh, and C.-J. Wu, “Thickness-dependent photonic bandgap in a one-dimensional single-negative photonic crystal,” Journal of Optical Society of America B, Vol. 26, 1506-1510, 2009.
[24]Y. Chen, X. Wang, Z. Yong, Y. Zhang, Z. Chen, L. He, P. F. Lee, H. L. W. Chan, C. W. Leung, and Y. Wang, “Experimental investigation of photonic band gap in one-dimensional photonic crystals with metamaterials,” Physics Letters A, Vol. 376, 1396-1400, 2012.
[25]V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp., Vol. 10, 509–514, 1968.
[26]D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneous negative permeability and permittivity,” Phys. Rev. Lett., Vol. 84, 4184-4187, 2000.
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[28]G. S. Guan, H. T. Jiang, H. Q. Li, Y. W. Zhang, H. Chen, and S. Y. Zhu, “Tunneling modes of photonic heterostructures consisting of single-negative materials,” Appl. Phys. Lett., Vol. 88, 211112, 2006.
[29]Y. H. Chen, J. W. Dong, and H. Z. Wang, “Twin defect modes in one-dimensional photonic crystals with a single-negative material defect,” Appl. Phys. Lett., Vol. 89, 141101, 2006.