Photonic crystals (PCs) are periodic structures made of materials with different refractive indices. 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. For instance, a dielectric layered structure can be used to design as a Fabry-Perot interferometer, dielectric reflectors, and antireflection coating.
In this thesis, using lithium niobate (LiNbO3) as an electro-optical defect layer in a quarter-wave photonic crystal, a theoretical analysis of the tunable resonance in a multilayer Fabry-Perot resonator (FPR) is given. With the fact that the refractive index of LiNbO3 is voltage-dependent, in the first part, we have investigated the tunable filtering properties in the visible and near infrared regions as a function of the applied voltage and of the angle of incidence for both TE and TM waves.
In the second part, by varying the thickness of the defect layer, we found that a multichannel filter can be achieved. This multichannel resonant peaks in the transmittance appears to be the common feature for the defective PC filter containing the nonlinear defect like the LiNbO3 or the ferroelectric or even the metamaterial.
The theoretical analysis in this thesis is based on the transfer matrix method. The format of thesis is as follows: The Chapter 1 is to give a brief review of PCs. The Chapter 2 describes the theoretical method used in our calculation. Some topics under study are arranged in Chapters 3 and 4, respectively. The conclusion is summarized in Chapter 5.

[1] J. W. Strutt, Lord Rayleigh, “On the maintenance of vibrations by forces of double frequency, and on the propagation of waves through a medium endowed with a periodic structure,” Phil. Mag., S.5, Vol. 24, 145-159, 1887.
[2] E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. Vol. 58, 2059-2062, 1987.
[3] S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. Vol. 58, 2486-2488, 1987.
[4] J. D. Jounnaopoulos, R.D. Meade and J. N. Winn, Photonic Crystals-Molding the Flow of Light, 1995, http://ab-initio.mit.edu/book/.
[5] Pochi Yeh, Optical Waves in Layered Media, John Wiley & Sons, Singapore, 1991.
[6] M. Born and E. Wolf, Principle of Optics, Cambridge, London, 1999.
[7] W. H. Zachariasen, Skr. Norske Vid-Ada, Oslo, Mat. Naturv. No.4, 1928.
[8] A. A. Ballman, J. American Ceram.Soc.48, 112, 1965.
[9] R. Srivastava, 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.
[10] R. Srivastava, S. Pati, and S. P. Ojha, “Enhancement of omnidirectional reflection in photonic crystal heterostructures,” Progress In Electromagnetics Research B, Vol. 1, 197-208, 2008.
[11] S. K. Awasthi, U. Malaviya, S. P. Ojha, N. K. Mishra, and B. Singh, "Design of a tunable polarizer using a one–dimensional nano sized photonic bandgap structure," Progress In Electromagnetics Research B, Vol. 5, 133-152, 2008.
[12] S. Golmohammadi, Y. Rouhani, K. Abbasian, and A. Rostami, “Photonic bandgaps in quasiperiodic multilayer using Fourier transform of the refractive index profile,” Progress In Electromagnetics Research B, Vol. 18, 311-325, 2009.
[13] R. Srivastava, K. B. Thapa, S. Pati, and S. P. Ojha, “Design of photonic band gap filter," Progress In Electromagnetic Research, PIER 81, 225-235, 2008.
[14] N. Kumar, and S. P. Ojha, "Photonic crystals as infrared broadband reflectors with different angles of incidence: a comparative study," Progress In Electromagnetics Research, PIER 80, 431-445, 2008.
[15] S. J. Orfanidis, Electromagnetic Waves and Antennas, Chapter 7, Rutger University, 2008, www.ece.rutgers.edu/~orfanidi/ewa
[16] 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.
[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, PIER 80, 421-430, 2008.
[18] G. Boedecker, and C. Henkle, “All-frequency effective medium theory of a photonic crystal,” Optics Express, Vol. 13, 1590-1595, 2003.
[19] J. A. Monsoriu, C. J. Zapata-Rodriguez, and E. Silvestre, “Cantor-like fractal photonic crystal waveguides,” Optics Communications, Vol. 252, 46-51, 2005.
[20] H. Inouye, M. Arkawa, J. Y. Ye, T. Hattori, H. Nakatsuka, and K. Hirao, “Optical properties of a total-reflection-type one-dimensional photonic crystal,” IEEE J. Quantum Electronics, Vol. 38, 867-871, 2002.
[21] G. J. Schneider, and G. H. Watson, “Nonlinear optical spectroscopy in one-dimensional photonic crystals,” Appl. Phys. Lett., Vol. 83, 5350-5352, 2003.
[22] B. Shi, Z. M. Jiang, and X. Wang, “Defective photonic crystals with greatly enhanced second-harmonic generation,” Optics Letters, Vol. 26, 1194-1196, 2001.
[23] D. R. Smith, 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.
[24] 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 Communications, Vol. 282, 242-246, 2009.
[25] Y.-H. Chang, C.-C. Liu, T.-J. Yang, and C.-J. Wu, “Angular dependent of a narrow band reflection-and-transmission filter containing an ultra thin metallic film,” J. Opt. Soc. Am. B: Optical Physics, Vol. 26, 1141-1145, 2009.
[26] C. C. Liu, Y.-H. Chang, T.-J. Yang, and C.-J. Wu, “Narrowband filter in a heterostructured multilayer containing ultrathin metallic films,” Progress In Electromagnetics Research, PIER. 96, 329-349, 2009.
[27] Y. K. Ha, 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.
[28] Y. Q. Lu, 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.
[29] Q. Zhu, and Y. Zhang, “Defect modes and wavelength tuning of one-dimensional photonic crystal with lithium niobate,” Optik, Vol. 120, 195-198, 2009.
[30] P. Yeh, Optical Waves in Layered Media, John Wiley & Sons, Singapore, 1991.
[31] See Chapter 8, Ref.[9].
[32] A. Banerjee, “Enhancement refractometric optical sensing by using one-dimensional ternary photonic crystals,” Progress In Electromagnetics Research, Vol. 89, 11-22, 2009.
[33] Xiaoyong Hu, Qihuang Gong, Shuai Feng, Bingying Cheng, Daozhong Zhang, Optics Communications 253, 138–144, 2005.
[34] Jing Liu, JunqiangSun, ChongqingHuang, WenjingHu, DexiuHuang, Optik
120, 35–39, 2009.