光子晶體是一種由兩種不同折率介質交互排列所形成的週期性結構人工介質，而光子晶體最主要的特徵是電磁波在某些頻段範圍不能被傳播出去，而這段範圍稱做光子帶隙(簡稱PBG)。
在本篇論文我們首先研究三元金屬介電質光子晶體的全方向性光子帶隙，我們發現光子帶隙會被明顯的增大當我們把金屬層夾在兩個介電質層之間當作一個單一周期的三元光子晶體，而我們是根據轉移矩陣法和Drude模型來計算分析我們的理論結果。
接下來我們研究三元金屬介電質光子晶體的有效電漿頻率，我們發現他的有效電漿頻率會隨著金屬層厚度的改變而有明顯的變動，當金屬層厚度增加，有效電漿頻率會往較短波長的方向移動，而我們的分析是經由Bloch定理而得來的。

Photonic crystal (PC) is an artificial medium with a periodic structure stacked by alternating two different materials with distinct refractive indices. The main feature of PC is that the electromagnetic waves are prohibited to propagate within a certain frequency range called photonic band gap (PBG).

In this thesis, we first study the omnidirectional PBG in a ternary metal-dielectric photonic crystal (MDPC). We show that PBG can be significantly enhanced by using metal layer sandwiched by two dielectric layers as a unit period in such a ternary PC. The analysis is made based on the transfer matrix method and the Drude model for the metal.

Next, we investigate the effective plasma frequency for the ternary MDPC. It is found that effective plasma frequency is strongly dependent on the thickness of the metal layer. That is, it will be moved to the shorter wavelength as the metal thickness increases. In this analysis, the band diagram is also given based on the Bloch theorem.

1. Joannopoulos, J. D., R. D. Meade, and J. N. Winn, PhotonicCrystals: Molding the Flow of Light, Princeton University Press,Princeton, NJ, 1995.
2. Sakoda, K., Optical Properties of Photonic Crystals, Springer-Verlag, Berlin, 2001.
3. Orfanidis, S. J., Electromagnetic Waves and Antennas, Rutger University, 2008, www.ece.rutgers.edu/ orfanidi/ewa.
4. Hsu, H.-T. and C.-J. Wu, “Design rules for a Fabry-Perot narrowband transmission filter containing a metamaterial negative-index defect,” Progress In Electromagnetics Research Letters, Vol. 9,101-107, 2009.
5. Srivastava, R., K. B. Thapa, S. Pati, and S. P. Ojha, “Omni-direction refection in one dimensional photonic crystal,” Progress In Electromagnetics Research B, Vol. 7, 133-143, 2008.
6. Banerjee, A., “Binary number sequence multilayer structure based on refractometric optical sensing element,” Journal of Electromagnetic Waves and Applications, Vol. 22, No. 17-18, 2439-2449, 2008.
7. Wang, X., X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett., Vol. 80, 4291-4293, 2002.
8. Fink, Y., J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopou-los, and L. E. Thomas, “A dielectric omnidirectional reflector,” Science, Vol. 282, 1679-1682, 1998.
9. Yablonovitch, E., “Inhibited spontaneous emission in solid state physics and electronics,” Phys. Rev. Lett., Vol. 58, 2059-2062,1987.
10. John, S., “Strong localization of photons in certain disordered lattices,” Phys. Rev. Lett., Vol. 58, 2486-2489, 1987.
11. Yeh, P., Optical Waves in Layered Media, John Wiley & Sons, Singapore, 1991.
12. Wu, C.-J., B.-H. Chu, M.-T. Weng, and H.-L. Lee, “Enhancement of bandwidth in a chirped quarter-wave dielectric mirror,” Journal of Electromagnetic Waves and Applications, Vol. 23, No. 4, 437-447, 2009.
13. Wu, C.-J., B.-H. Chu, and M.-T. Weng, “Analysis of optical reflection in a chirped distributed Bragg reflector,” Journal of Electromagnetic Waves and Applications, Vol. 23, No. 1, 129-138, 2009.
14. Wu, C.-J., Y.-N. Rao, and W.-H. Han, “Enhancement of photonic band gap in a disordered quarter-wave dielectric photonic crystal,” Progress In Electromagnetics Research, PIER 100, 27-36, 2010.
15. Li, H., H. Chen, and X. Qiu, “Bandgap extension of disordered 1D binary photonic crystals,” Physica B, Vol. 279, 164-167, 2000.
16. Tolmachev, V. A., T. S. Perova, J. A. Pilyugina, and R. A. Moore, “Experimental evidence of photonic band gap extension for disordered 1D photonic crystals based on Si,” Optics Comm.,Vol. 259, 104-106, 2006.
17. Qi, L., Z. Yang, X. Gao, F. Lan, Z. Shi, and Z. Liang, “Bandgap extension of disordered one-dimensional metallic-dielectric photonic crystals,” IEEE International Vacuum Electronics Conference, IVEC, 158-159, 2008.
18. Wang, X., X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, ”Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett., Vol. 80, No. 23, 4291-4293, 2002.
19. Zi, J., J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett., Vol. 73, No. 15, 2084-2086, 1998.
20. Srivastava, R., S. Pati, and S. P. Ojha, “Enhancement of omnidirectional reflection in photonic crystal heterostructures,” Progress In Electromagnetics Research B, Vol. 1, 197-208, 2008.
21. Awasthi, S. K., U. Malaviya, and S. P. Ojha, “Enhancement of omnidirectional total-reflection wavelength range by using one-dimensional ternary photonic bandgap material,” J. Opt. Soc. Am. B: Optical Physics, Vol. 23, 2566-2571, 2006.
22. Awasthi, S. K. and S. P. Ojha, “Design of a tunable optical filter by using a one-dimensional ternary photonic ban gap material,” Progress In Electromagnetics Research M, Vol. 4, 117-132, 2008.
23. Banerjee, A., “Enhanced temperature sensing by using one-dimensional ternary photonic band gap structures,” Progress In Electromagnetics Research Letters, Vol. 11, 129-137, 2009.
24. Banerjee, A., “Enhanced refractometric optical sensing by using one-dimensional ternary photonic crystals,” Progress In Electromagnetics Research, PIER 89, 11-22, 2009.
25. Prasad, S., V. Singh, and A. K. Singh, “Modal propagation characteristics of EM waves in ternary one-dimensional photonic crystals,” Optik, 2009.
26. Contopanagos, H., E. Yablonovitch, and N. G. Alexopoulous, “Electromagnetic properties of periodic multilayers of ultrathin metallic films from dc to ultraviolet frequencies,” J. Opt. Soc. Am. A, Vol. 16, 2294-2306, 1999.
27. Contopanagos, H., N. G. Alexopoulous, and E. Yablonovitch, “High-Q radio-frequency structures using one-dimensionally periodic metallic films,” IEEE Trans. Microwave Theory Technol., Vol. 46, 1310-1312, 1998.
28. Keskinen, M. J., P. Loschialpo, D. Forester, and J. Schelleng, “Photonic band structure and transmissivity of frequency-dependent metallic-dielectric systems,” J. Appl. Phys., Vol. 88, 5785-5790, 2000.
29. Xu, X., Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett., Vol. 86, 091112, 2005.
30. Born, M. and E. Wolf, Principles of Optics, Cambridge, London, 1999.
31. Marquez-Islas, R., B. Flores-Desirena, and F. P’erez-Rodr’iguez, “Exciton polaritons in one-dimensional metal-semiconductor photonic crystal,” J. Nanosci. Nanotechnol., Vol. 8, 6584-6588, 2008.
32. Markos, P. and C. M. Soukoulis, Wave Propagation: From Electrons to Photonic Crystals and Left-handed Materials, Princeton University Press, New Jersey, 2008.