光子晶體是由不同折射率材料所構成的週期性結構. 隨著它們那令人感興趣及驚奇的電磁學性質, 光子晶體的研究在最近幾年一直是光子學熱門的項目. 在本篇論文中, 我們的研究題目是集中在於討論厚度非次序排列的光子晶體, 包括金屬-介電質光子晶體以及帶有缺陷部分的光子晶體.
而光子晶體最主要的特徵就是電磁波在其中行進需有一個頻率範圍, 稱為光子能隙(PBG). 而擁有光子能隙(PBG)的材料在光電子學以及光學通訊方面有很多有潛力的應用. 我們可以發現當厚度非次序排列應用在一維MDPC,DDPC時, 可以產生更寬的光子能隙(PBG). 而此光子晶體的厚度非次序排列可以藉由使用介質層厚度的數學分布來設計. 此外, 隨著厚度非次序分布程度以及週期數的改變, 更多的光學性質會被發現. 並且也可發現對於帶有缺陷部分的光子晶體而言, 藉由光子晶體的厚度非次序分布, 一些有關透射波峰的光學性質是可調的.

Photonic crystals (PCs) are periodic structures made of materials with different refractive indices. With their interesting and amazing electromagnetic properties, research on PCs continues to be a hot issue in photonics in recent years. In this thesis, our research topic has focused on the disordered PCs, including the metallic-dielectric PC (MDPC) and PCs with defect slabs.
The main feature of PCs is that electromagnetic waves are prohibited to propagate within a certain frequency range called photonic band gap (PBG). Materials containing PBG have many potential applications in optoelectronics and optical communication. We found that the wider PBG can be obtained when the disorder is introduced in the one-dimensional (1D) MDPC, and dielectric-dielectric PC (DDPC). The disorder in a PC can be introduced and designed by making use of a certain statistical distribution of layer thicknesses, namely by adjusting the degree of disorder and number of periods. Other PBG properties of disordered PCs are found. For a PC with some defect slabs, the filtering properties and the number of transmission peaks can be tuned by introducing the disorder.

[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] 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)
[5] 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.
[6] 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.
[7] 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.
[8] 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.
[9] 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.
[10] Banerjee, A., “Enhanced temperature sensing by using one-dimensional ternary photonic band gap structures," Progress In Electromagnetics Research Letters, Vol. 11, 129-137, 2009.
[11] 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.
[12] 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.
[13] Yeh, P., Optical Waves in Layered Media, John Wiley & Sons, Singapore, 1991.
[14] Orfanidis, S. J., Electromagnetic Waves and Antennas (Rutgers University, 2008), ww.ece.rutgers.edu/ ~orfanidi/ewa.
[15] 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.
[16] Yablonovitch E, Gmitter T J, Meade R D, Rappe A M, Brommer K D and Joannopoulous J D , 1990, Phys. Rev. Lett. 67, 3380
[17] D.R. Solli, C.F. McCormick, R.Y. Chiao, J.M. Hickmann, J. Appl. Phys. 93 (2003) 9429.
[18] M. Okano, S. Kako, S. Noda, Phys. Rev. B 68 (2003)235110.
[19] D.M. Pustai, A. Sharkawy, S. Shi, D.W. Prather, Appl. Opt. 41 (2002) 5574.
[20] W. Suh, S.H. Fan, Opt. Lett. 28 (2003) 1763.
[21] Y.H. Li, H.T. Jiang, L. He, H.Q. Li, Y.W. Zhang, H. Chena, Multichanneled filter based on branchy defect in microstrip photonic crystal, Appl. Phys. Lett. 88 (2006) 081106.
[22] E.V. Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, et al., Compact wavelength monitor- ing by lateral outcoupling in wedged photonic crystal multimode waveguides, Appl. Phys. Lett. 87 (2005) 101107.
[23] A. Taflove, Computational Electrodynamics: The Finite- Difference Time-Domain Method, Artech House, Boston, 1995.
[24] S. Blair, J. Goeckeritz, Effect of vertical mode matching on defect resonances in one-dimensional photonic crystal slabs, J. Lightwave Technol. 24 (3) (2006) 1456–1461.