在此篇論文中，涵蓋了三個主題。第一是研究缺陷模態垂直入射到對稱和反對稱多層窄頻濾波器的簡單例子。藉由轉換矩陣的方式來計算出波長和透射率關係圖。在反對稱濾波器，只有一個缺陷模態存在光子能隙中缺陷模態的位置隨著設計波長而改變。在對稱結構的濾波器，發現到會有兩個缺陷模態。使用Bloch waveapproximation 方法，這兩個缺陷模態分別是缺陷層在對稱和反對稱結構中場的解答。第二主題是延伸第一主題的相同結構但改變入射傾斜角。藉由對TE 和TM 波計算波長和透射率關係做缺陷模態的研究。缺陷模態和入射角的關係也被圖解之。此外,也觀察到缺陷層的厚度也會影響缺陷模態的數目。第三部份是研究在一維超導光子晶體中角度,厚度和光子能帶結構的關係。這是研究permittivity 為0 超導材料的臨界頻率。能帶結構可視為由兩個超導和介電材料所組成的厚度解析方程。在角度和能帶關係中，在TM 偏振，會存在一個強大局部疊置能帶近似於臨界頻率。當角度增加所顯示出的能帶也會增強。

In this thesis, we have three topics. The first one is to study the defect modes in the asymmetric and symmetric multilayer narrowband transmission filters in the simple case of normal incidence. It is based on the wavelength-dependent transmittance calculated by making use of the transfer matrix method. In an asymmetric filter, there exists only one defect mode within the photonic band gap and its position can be changed when the design wavelength is varied. In a symmetric filter, it is found that there are two defect modes. Using Bloch wave approximation, these two defect modes respectively correspond to the symmetric and the asymmetric field solutions in the defect layer.
　　The second part is to extend the first part to the oblique incidence for the same structures. The defect modes are investigated by the calculated wavelength-dependent transmittance for both TE and TM waves. The dependences of defect modes on the angle of incidence are illustrated. Additionally, the effect of defect thickness on the number of defect modes is also examined.
　　The third part is to study the angle- and thickness-dependent photonic band structures in a one-dimensional superconducting photonic crystal. It is studied near and below the threshold frequency at which the superconducting material has a zero permittivity. The gap structure is analyzed as a function of the thicknesses of the two constituent superconducting and dielectric materials. In the angular dependence of the band structure, in TM-polarization, there exists a strongly localized superpolariton gap approximately the threshold frequency. This gap is shown to be enhanced as the angle increases.

1. E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10, 283-295 (1993).
2. J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton University Press, Princeton, 1995).
3. C. M. Soukoulis, Photonic Band Gap Materials (Kluwer Academic, Dordrecht, 1996).
4. P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, New York, 1998).
5. S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers University, 2008), ww.ece.rutgers.edu/~orfanidi/ewa.
6. D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, and P. M. Platzman, “Photonic band structure and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314-321 (1993).
7. Orfanidis, S. J., Electromagnetic Waves and Antennas, Chapter 7, Rutger University, 2008, www.ece.rutgers.edu/~orfanidi/ewa.
8. Yeh, P., Optical Waves in Layered Media, John Wiley & Sons, Singapore, 1991.
9. Born, M., E. Wolf, Principles of Optics, Cambridge, London, 1999.
10. Hecht, E., Optics, Addison Wesley, New York, 2002, Ch. 9.
11. Yablonovitch, E., “Inhibited spontaneous emission in solid state physics and electronics,” Phys. Rev. Lett., Vol. 58, 2059-2062, 1987.
12. John, S., “Strong localization of photons in certain disordered lattices,” Phys. Rev. Lett., Vol. 58, 2486-2489, 1987.
13. Joannopoulos, J. D., R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton University Press, Princeton, NJ, 1995.
14. Yariv, A., and P. Yeh, Photonics, Oxford University Press, New York, 2007.
15. Veselago, V. G., “The electrodynamics of substances with simultaneously negative values of permittivity and permeability”, Sov. Phys. Usp., Vol. 10, 509-514, 1968.
16. Hsu, H.-T., 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.
17. Wang, Z.-Y., 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, PIER 80, 421-430, 2008.
18. Boedecker, G., and C. Henkle, “All-frequency effective medium theory of a photonic crystal,” Optics Express, Vol. 13, 1590-1595, 2003.
19. Ha, Y. K., Y. C. Yang, J. E. Kim, and H. Y. Park, “Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band gap structure with liquid crystals, ” Appl. Phys. Lett., Vol. 79, 15-17, 2001.
20. Lu, Y. Q., and J. J. Zheng, “Frequency tuning of optical parametric generator in Periodically poled optical superlattice LiNbO3 by electro-optic effect,” Appl. Phys. Lett., Vol. 74, 123-125, 1999.
21. Zhu, Q., and Y. Zhang, “Defect modes and wavelength tuning of one-dimensional photonic crystal with lithium niobate,” Optik, Vol. 120, 195-198, 2009.
22. Wu, C.-J., J.-J. Liao, and T. W. Chang, “Tunable multilayer Fabry-Perot resonator using electro-optical defect layer,” J. Electromagn. Waves and Appl., Vol. 24, 531-542, 2010.
23. Hu, X., Q. Gong, S. Feng, B. Cheng, and D. Zhang, “Tunable multichannel
24. filter in nonlinear ferroelectric photonic crystal,” Optics Communication, Vol. 253, 138-144, 2005.
25. Liu, J., J. Sun, C. Huang, W. Hu, and D. Huang, “Optimizing the spectral efficiency of photonic quantum well structures”, Optik, Vol. 120, 35-39, 2009.
26. Smith, D. R., R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, and P. M. Platzman, “Photonic band structure without and with defect in one-dimensional photonic crystal,” J. Opt. Soc. Am. B: Optical Physics, Vol. 10, 314-321, 1993.
27. Qiao, F., C. Zhang, and J. Wan, “Photonic quantum-well structure: Multiple channeled filtering phenomena,” Appl. Phys. Lett. Vol. 77, 3698-3700, 2000.
28. Liu, J., J. Sun, C. Huang, W. Hu, and D. Huang, “Optimizing the spectral efficiency of photonic quantum well structures,” Optik, Vol. 120, 35-39, 2009.
29. E. Yablonovitch, E.: Phys. Rev. Lett. 58, 2059 (1987).
30. John, S.: Phys. Rev. Lett. 58, 2486 (1987).
31. J. D. Joannopoulos, J. D., Meade, R. D., Winn, J. N.:Photonic Crystals, Princeton University Press, New Jersey, P.41 (1995).
32. Soukoulis, C. M.:Photonic Band Gap Materials, Kluwer Academic, Dordrecht, (1996).
33. Raymond Ooi, C. H., Au Yeung, T. C., Kam, C. H., Lim, T. K.: Phys. Rev. B 61, 5920 (2000).
34. Wu, C.-J., Chen, M.-S., Yang, T.-J.: Physica C 432, 133 (2005).
35. Berman, O. L., Lozovik, Y. E., Eiderman, S. L., Coalson, R. D.: Phys. Rev. B 74, 092505 (2006).
36. Wu, C.-J., Yang, T.-J.: PIERS Online 4, 801 (2008).
37. Aly, A. H., Hsu, H.-T., Yang, T.-J., Wu, C.-J., Hwangbo, C. K: J. Appl. Phys. 105, 083917 (2009).
38. Born, M., Wolf, E: Principles of Optics, Cambridge, London (1999).
39. Duzer, T. V., Turner, C. W.: Principles of Superductive Devices and Circuits, Edward Arnold, London (1981).
40. Wu, C.-J., Liu, C.-L. Yang, T.-J.: J. Opt. Soc. Am. B: Optical Physics 26, 2089 (2009).