Transmission Properties Research In 2D Photonic Crystals

People has expected to control the propagation of light freely as they do in controling current flowing in the wire. This idea has becoming reality with the emergence of photonic crystal(PhC)——a new material. In the late 80s of last century, Eli Yablonovitch and Sajeev John first brought up the concept of photonic crystal. From then on, a new era of light propagation controling began.Photonic crystal is a periodic arrangement of media with differing dielectric constants. There may be gaps in the energy band structure of the semiconductor crystal, meaning that electrons are forbidden to propagate with certain energies in certain directions. Similarly, photonic crystal influence the light propagation in its internal by periodic varying index. In particular, we can design and construct photonic crystals with photonic band gaps, preventing light from propagation in certain directions with specified frequencies. With the special transmission characteristic of PhCs, people fabricate PhC fiber, PhC waveguide, PhC laser, micro resonator, and etc. PhC can also be metamaterial to produce electromagnetic wave negative phenomenon, and that brings up superlens and perfect lens. Recently, PhCs have been applied to compose light-emitting diodes(LEDs) to improve the light extraction efficiency. We will discuss the application and the transmission characteristic of PhCs in this thesis.THE MAIN CONTENTS:1. Using Maxwell equations to produce electromagnetic field expressions which consistence with the characteristic of PhCs and the calculation method of getting photonic band gaps. Making a brief introduction of Finite-Difference Time-Domain(FDTD) method. Discussing the numeric stability and boundary condition of FDTD method.2. Analyzing the trasmission characteristic of two-dimension(2D) holographical PhCs. Discussing how parameters, filling ratio of PhCs, lattice constant, cell shape, lattice and etc., influence the photonic band gap and transmission characteristic.3. Analyzing the negative refraction characteristic of the holographical PhCs.4. Research how to improve LED light extraction efficiency by using 2D PhCs. THE INNOVATIONS:1. Theoretically research the band gap and transmission characteristic of holographical PhCs, simulating by using FDTD method. Get large amount of data by scanning the parameters of PhC (lattice constant, filling ratio, dielectric constant, and etc.). And achieve a new way to design and optimize PhC waveguide.2. Finding the condition and frequency range in which negarive refraction phenomenons occur by analyzing the EFS plots of holographical PhCs from lots of parameters. Simulating by using FDTD method, observed a clear negative refraction phenomenon.3. Proposing a LED model with PhCs to improve the light extraction efficiency, Veryfing the result by numerical simulation.In summary, this thesis analyzes the parameters that influence the transmission characteristic of PhCs, and then proposes a new way to design and optimize the PhC waveguide. The band structure and equi-frequency contours for the holographical photonic crystals (PhCs) are calculated by using plane wave extension method, and the conditions for negative refraction in PhCs are analyzed as well as the frequency band. The finite-difference time-domain method is used to verify the conclusion, and it is shown that negative refraction can be clearly observed in the holographical PhCs within a wide frequency band and a large incident angle scope. The research on the negative refraction in holographical PhCs will provide a new idea for the design and fabrication of the left-handed negative-index materials. At the same time, the thesis makes a great deal of study in improve the LED light extraction efficiency and the result can be a reference for designing and fabricating high energy efficiency LED.