Research On Dynamic Control Of Light Pulse And Dispersion Relationship In Photonic Crystal

Devices based on photonic crystal follows photonic band gap guiding mechanisms. They are ideal choices for future integrated optical circuit components, with many advantages which traditional devices don't have, and also very small sizes. Therefore, they have attracted a lot of attention of researchers and have been studied intensively and extensively during the past decade. This thesis studied some key technologies of the device of dynamic control of Q factor and slow light waveguide based on photonic crystal. The whole paper is mainly divided into two parts. First,we design and analyze the cavity based on photonic crystal, which can enlarge the range of dynamic control the Q factor compared to the traditional devices in literatures. Second, we study the dispersion relationship on several structure based on photonic crystals, especially including the single-side-wall waveguide used for slow light transmission, which is characterized by both low group velocity and reduced dispersion.This dissertation is organized as follows:In the chapter of introduction, the main theoretic foundations and research background of this thesis are reviewed. First the basic concepts of photonic crystal are introduced. Then the theoretic foundations and the mathematic models for carrying out research and calculation of photonic crystal, including PWE and FDTD method, are introduced. Based on these, the coupling features of photonic crystal waveguides are studied, which are the theoretic bases for the designs structures of dynamic control of Q factor later on. Last, the concept of slow light is introduced, and research updates are presented.In Chapter 2, we propose a novel device of dynamic control of the Q factor of cavity which is based on nanocavity and line defect waveguide in the photonic crystal with a perfect mirror. By changing the refractive of the waveguide due to Kerr effect, the lifetime of the photons in the cavity can be controlled dynamically. At last, the pulse can be dynamic controlled in the nanocavity of photonic crystal. There is a bigger range of dynamic control in the structure than that which is proposed before. The simulation with plan wave expansion and finite-difference time-domain demonstrates the time of dynamic control is congruent with the theoretic analysis.In Chapter 3, a single-side-grating (one dimension photonic crystal) waveguide (SSWG) is proposed for slow light transmission. In order to obtain high delay bandwidth product (DBP), low dispersion and slow group velocity, some parameters of this SSWG are optimized. Three structural parameters are carefully adjusted: the width of grating, and the length of the grating, and the width of the waveguide. In the asymmetric waveguide, it is possible to obtain flat band modes with low group velocity 0.023c and zero dispersion. The simulation with finite-difference time domain demonstrates the transmitting and field distribution of slow light in the SSWG. At last, the mathematical model is deduced and the delay-bandwidth product (DBP) of the proposed slow-light device is analyzed.In Chapter 4, based on the SSWG, we study the nonlinear effect, including third-harmonic generation and parametric amplification. At first, the third harmonic generation (THG) formula in periodic structures and parametric amplification formula are derived. The formula demonstrates that the third harmonic generation can be enhanced by the slow light. At last, we use the FDTD method to simulate the effect of THG and parametric amplification which can validate our theoretic analysis.In Chapter 5, we study the self-collimation in two-dimension photonic crystal with triangle lattice. It is a potential matter for the integrated on-chip since the light can transmit in the normal photonic crystal by self-collimation. Based on the triangle photonic crystal, we analyze the dispersion curve and the constant frequency curve of the structure. We find that there is a self-collimation phenomenon on the first band. We utilize the finite difference time-domain method (FDTD) to verify the self-collimation phenomenon in the triangle photonic crystal. Based on the above structure, we design a bend device with self-collimation. The result of simulation demonstrates that the bend device can change the route of light in the triangle photonic crystal.In Chapter 6, we design and analyze the dispersion compensation based on cascaded two photonic crystals. First, we design a waveguide with cascaded two photonic crystal waveguides by introducing the theory in dispersion fiber into the photonic crystals. The matched dispersion curve, which one of waveguide has positive dispersion and the other has negative dispersion, is designed for the device and we choose the frequency on slow light regime. Also, the FDTD simulation demonstrates the slow light with zero dispersion by dispersion compensation in the cascaded two photonic crystals.