The Research On Band Structure And Waveguide Characteristics Of Two Dimensional Photonic Crystals

In 1987, a remarkble step was made by Yablonovitch and John, who pointed out the possibility of the realization of photonic band gaps, localized defect modes, and their applications to various optoelectronic devices, and by John who discussed the strong localization of electromagnetic waves in disordered photonic crystals and also predicted many interesting quantum optical phenomena that can be realized in photonic crystals such as the bound state of photons and non-exponential decay of spontaneous emission. Since 1987, many researchers have been engaged in the realization of photonic band gaps, localized defect modes, and other optical properties peculiar to the photonic crystals. Because photonic crystals are artificial crystals, it is our studying issue to design and fabricate the photonic crystals. Many accurate numerical calculations could be performed thanks to the development of computing facilities. These calculations were really useful for the design of the photonic crystal structures. As for the experiment studies, many researchers in various fields have been collaborating to make new photonic crystals and measure their properties.Two-dimensional photonic crystals have been studied, since they are easier to fabricate and may be employed in waveguide configurations. First, we give a complete deduction for the electromagnetic wave theory of photonic crystal of two dimensions and Bloch wave solution in stratified periodic dielectric, offer the academic foundation of the existence of band gap. Second, we demonstrate that dielectric pods in air background can generate a common band gap, which is called absolute photonic band gap, for both orthogonal TE and TM mode. At last, we design a U-waveguide, and give the energy distribution of the TM mode.Designing a two-dimensional photonic crystal of square lattice with rotating square cylinders, which the structural symmetry is reduced, we have found a larger absolute band gap in the low and high frequency. By using the plane wave expansion and finite-different time-domain (FDTD) methods, we can find a larger absolute band gap in the low and high frequency. When/is about 0.5, we get the photonic band structure of a two-dimensional photonic crystals of square lattice with rotating square cylinders. There is a band gap when f=0.5. A maximum absolute PBG exists while θ = 45° and the absolute PBG lies in the high frequency range for θ = 0°. Furthermore, the FDTD method is applied for examining and analyzing the waveguide characteristics and theelectric field distribution of TE mode of 2-D photonic crystals created by a square lattice with square cylinders while θ = 45°.The characteristics (dispersion relation and photonic density of states) of thewaveguide modes of photonic crystal are investigated using plane-wave method. We obtain the dispersion relation and photonic density of states for the waveguide modes created in a two dimension photonic crystals. Because of the periodic nature of the waveguide boundary, photonic crystal waveguide exhibits the behavior similar to fiber Bragg gratings, in that the particular wavelengths can be strongly reflected from the waveguide. They have been termed "mini-stop bands". Thus by correct engineering of the periodicity of the side walls and the waveguide width, both waveguiding and filtering action can be achieved.