Abstract
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.
The main feature of PCs is that they can prohibit the propagation of electromagnetic waves within a certain frequency range called photonic band gap (PBG). The 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, we study the electromagnetic and optical properties of PCs by using the transfer matrix method (TMM).The thesis consists of six chapters. The first chapter is to give a brief review of PCs. The second describes the theoretical background that will be used in our calculation. Some topics under study are given in chapter 3, 4, 5. The conclusion is summarized in chapter 6.
In our considered topics, we first give a theoretical analysis of optical reflection for a dielectric chirped distributed Bragg reflector (DBR). The chirped DBR is modeled by several sub-DBRs stacked successively with different values in the thickness ratio. We demonstrate how a chirped structure can affect the photonic bandgaps (PBGs). In the second one, we shall design a multilayer Fabry-Perot resonator (FPR) which is formed by taking the left-handed material (LHM) as the structure defect in a one-dimensional PC. We find some useful design rules for a FPR made by the quarter-wave stacks. In the third topic, we theoretically studied the omnidirectional total reflection frequency range of a multilayered dielectric heterostructures.

Abstract
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.
The main feature of PCs is that they can prohibit the propagation of electromagnetic waves within a certain frequency range called photonic band gap (PBG). The 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, we study the electromagnetic and optical properties of PCs by using the transfer matrix method (TMM).The thesis consists of six chapters. The first chapter is to give a brief review of PCs. The second describes the theoretical background that will be used in our calculation. Some topics under study are given in chapter 3, 4, 5. The conclusion is summarized in chapter 6.
In our considered topics, we first give a theoretical analysis of optical reflection for a dielectric chirped distributed Bragg reflector (DBR). The chirped DBR is modeled by several sub-DBRs stacked successively with different values in the thickness ratio. We demonstrate how a chirped structure can affect the photonic bandgaps (PBGs). In the second one, we shall design a multilayer Fabry-Perot resonator (FPR) which is formed by taking the left-handed material (LHM) as the structure defect in a one-dimensional PC. We find some useful design rules for a FPR made by the quarter-wave stacks. In the third topic, we theoretically studied the omnidirectional total reflection frequency range of a multilayered dielectric heterostructures.

References
[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, no. 147, pp. 145-159, 1887.
[2] E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. Vol. 58, pp. 2059-2062, 1987.
[3] S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. Vol. 58, pp. 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] V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Soviet Phys. Uspekhi, Vol. 10, No. 4, pp. 509–514, Jan. 1968.
[8] J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett., Vol. 76, No. 25, pp. 4773–4795, 1996.
[9] J. B. Pendry, A. J. Holden, and D. J. Robbins, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory and Tech., Vol. 47, No. 11, pp. 2075–2096, 1999.
[10] D. R. Smith, W. J. Padilla, and D. C. Vier, “A composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett., Vol. 84, No. 18, pp. 4184–4187, 2000.
[11] C. Caloz, T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications, Hoboken, N.J.: John Wiley & Sons, 2006.
[12] Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and L. E. Thomas, “A dielectric omnidirectional reflector,” Science, Vol. 282, pp. 1679-1682, 1998.
[13] J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett., Vol. 23, pp. 1573-1575, 1998.
[14] S. K. Srivastava, and S. P. Ojha, “Enhancement of omnidirectional reflection bands in one-dimensional photonic crystal structures with left-handed materials,” Progress In Electromagnetics Research, PIER 68, pp. 91–111, 2007.
[15] S. K. Singh, J. P. Pandey, K. B. Thapa, and S. P. Ojha, “Structural parameters in the formation of omnidirectional high reflectors,” Progress In Electromagnetics Research, PIER 70, pp. 53-78, 2007.35, 2008.
[16] R. Srivastava, K. B. Thapa, S. Pati, and S. P. Ojha, “Omnidirection reflection in one dimensional photonic crystal,” Progress In Electromagnetics Research B, Vol. 7, pp. 133-143, 2008.
[17] S. J. Orfanidis, Electromagnetic Waves and Antennas, Rutger University, 2008, www.ece.rutgers.edu/~orfanidi/ewa
[18] R. Srivastava, S. Pati, and S. P. Ojha, “Enhancement of omnidirectional reflection in photonic crystal heterostructures,” Progress In Electromagnetic Research B, Vol. 1, pp. 197-208, 2008.