光子晶體最初是在1987年被Yablonovitch and John 兩人所分別提出。在近二十年內光子晶體在光電科技上具有重大地位。光子晶體是由不同的折射率層周期排列而成，此種排列方式使光子晶體具有與固態晶體相同的能帶結構，當其週期與所處理光波長相當時，所造成的強散射效應，便形成光子能隙。光子晶體有許多方面的應用，在一維上即為薄膜，可讓需要的波段反射，二維的可做為波導。
在此論文中，我們使光子晶體中的各層厚度皆些微不同，即無秩序(Disorder)來觀察不同的光子能隙頻譜增寬效應。首先，我們使用Drude model 理論來討論在不同的頻率下，金屬的損耗項的變化。在金屬-介電質光子晶體(MDPC)與介電質-介電質光子晶體(DDPC)中，我們除了改變厚度Disorder的程度。第二部分。還改變不同的結構周期。

Photonic crystals (PCs) introduced by Yablonovitch and John in 1987 are the periodical structure. Over the past two decades, researches in PCs have become an important role in modern optical and photonic science and technology. PCs have an important feature, i.e., the existence of the photonic band gaps (PBGs) in certain frequencies, which are produced due to the Bragg reflections in the periodic interfaces. The applications of PCs include, for examples, the optical reflector in one-dimensional PC and optical waveguide in two-dimensional PCs, and so on.
In this thesis, in the first part, we use the Drude model to discuss the loss issue of metal at different frequencies. In the second part, we study the band gap enhancement in the disordered PCs. We shall consider the metal-dielectric and dielectric-dielectric PCs. By designing the disordered thicknesses in PCs, the enhancement in PBGs will be shown.

[1] E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. Vol. 58, pp. 2059-2062, 1987.
[2] S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. Vol. 58, pp. 2486-2488, 1987.
[3] J. W. S. Rayleigh, "On the remarkable phenomenon of crystalline reflexion described by Prof. Stokes." Phil. Mag. 26, 256-265. (1888)
[4] Drude, Paul (1900). "Zur Elektronentheorie der metalle". Annalen der Physik 306 (3): 566.
[5] Drude, Paul (1900). "Zur Elektronentheorie der Metalle; II. Teil. Galvanomagnetische und thermomagnetische Effecte". Annalen der Physik 308 (11): 369.
[6] A. J. Ward, J. B. Pendry, and W. J. Stewart, J. Phys.: Condens. Matter 7,2217 s1995d.
[7] J. Yu, Y. Shen, X. Liu, R. Fu, J. Zi, and Z. Zhu, J. Phys.: Condens. Matter16, L51 s2004d.
[8] X. Xu, Y. Xi, D. Han, X. Lin, and J. Zi, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” App. Phys. Lett. 86, 091112. (2005)
[9] Daozhong Zhang, Zhaolin Li, Wei Hu, and Bingying Cheng, “Broadband optical reflector—an application of light localization in one dimension,” Appl. Phys.Lett.,vol. 67, no. 17, pp.2431-2432, 1995.
[10] Srivastava, R., K. B. Thapa, S. Pati, and S. P. Ojha, “Omni-direction reflection in one dimensional photonic crystal," Progress In Electromagnetics Research B, Vol. 7, 133{143, 2008.
[11] Steinberg, A. M. and R. Y. Chiao, “Subfemtosecond determina-tion of transmission delay times for a dielectric mirror (photonic band gap) as a function of the angle of incidence," Phys. Rev. A,Vol. 51, No. 5, 3525-3528, 1995.
[12] Hattori, T., N. Tsurumachi, and H. Nakatsuka, “Analysis of optical nonlinearity by defect states in one-dimensional photonic crystals," J. Opt. Soc. Am. B, Vol. 14, No. 2, 348-355, 1997.
[13] 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.
[14] Tocci, M. D., M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode," Appl. Phys. Lett., Vol. 66, No. 18, 2324-2326, 1995.
[15] Banerjee, A., “Enhanced temperature sensing by using one-dimensional ternary photonic band gap structures," Progress In Electromagnetics Research Letters, Vol. 11, 129-137, 2009.
[16] Banerjee, A., “Binary number sequence multilayer structure based refractometric optical sensing element," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 17-18, 2439-2449, 2008.
[17] Li, H., H. Chen, and X. Qiu, “Bandgap extension of disordered 1D binary photonic crystals," Physica B, Vol. 279, No. 1-3, 164-167, 2000.
[18] Yeh, P., Optical Waves in Layered Media, John Wiley & Sons, Singapore, 1991.
[19] Orfanidis, S. J., Electromagnetic Waves and Antennas (Rutgers University, 2008), ww.ece.rutgers.edu/ ~orfanidi/ewa.
[20] Zhang, D., Z. Li, W. Hu, and B. Cheng, “Broadband optical reflector-an application of light localization in one dimension,"Appl. Phys. Lett., Vol. 67, No. 17, 2431-2432, 1995.