Photonic Crystals With Low Dispersion Of The Waveguide

Photonic Crystal, an artificial micro-structure with dielectric constant periodic arranged, can effectively control the light propagation for its unique band structure. Slow light is a powerful proof that its ability to control the light propagation. Being strongly modulated by scattering cell arranged periodic, the optical signal achieves slow light propagation, meanwhile it also induces severe group velocity dispersion that will result waveform distortion and time-width broadening. The information can not be downloaded correctly from the distorted signal. In the summary, compress the group velocity dispersion and even eliminate it in slow light transmission is a vital step for photonic crystal used in all-optical network in the future. Focus on the dispersion problem, our work and research result are arranged as follows:1. Before the waveguide designing, two core algorithms have been detailed explained, they are Plane Wave Expansion method and Finite-Difference Time-Domain method. Based on the explanation of these two algorithms, three important parameters, equivalent index, radius of circular air-holes and their positions, are being analyzed in this part. The influence of band structure and band shape induced by the adjustment of those three parameters are carefully investigated, such as increasing the equivalent index, adjusting the radius of air holes in the first two rows and also perpendicularly changing their positions.2. The concept of Hetero type photonic crystal low dispersion waveguide and its principle of dispersion modification are explained firstly. The dispersion property of P type element waveguide and N type element waveguide are analyzed by Plane Wave Expansion method. As the radius of air-holes in the second row changing, not only the shape of dispersion curve changes, but also the cut-off frequency. Through the dispersion anaylsis, the range of dispersion compensation is determined, from1547.6nm to1552.5nm, and the value of equivalent group index is25. The simulation result in the time domain proves the low dispersion property of hetero type photonic crystal waveguide. The broadening of time-width is only5.3%and the theory value of group index agrees with simulation result. Because of low transmission in hetero type photonic crystal waveguide, a new photonic crystal waveguide, named PLN is designed. A linear part is added to relief the mismatch of group index and improves the transmission efficiency remarkably. The transmission coefficient is improved about63.2%.3. Methods, proposed in the current literature and papers, which introduce linear part into band structure are summarized at first. Those methods are adjusting the radius of scattering cell, changing the shape of scattering cell, optimizing the position of scattering cell and controlling the width of waveguide. The new method is proposed after contrast the methods that summarized in the former part. The linear band is introduced into band structure by adjusting the position of air-holes and enlarging their radius. Using Plane Wave Expansion method, influence of air-hole displacement and adjustment of their radius are detailed analyzed. We find that the linear part is induced by moving air-hole and the radius of air-hole controls the value of group velocity and the bandwidth of low dispersion. We choose a photonic crystal waveguide with6nm low dispersion bandwidth as a sample to execute simulation. The simulation result in time domain proves the low dispersion property of new photonic crystal waveguide, the broadening of time-width is only3.9%and the theory value of group index agrees with simulation result.