光波在一维光子晶体中传播行为的数值研究

由Kronig-Penney模型导出了光波在一雏光子晶体中传播的群速度的解析表达式，利用传输矩阵法对一维光子晶体的色散关系和群速度分布特征进行了数值研究．结果表明，光波在光子晶体中传播的群速度与光子带隙结构及色散特性有着密切的联系，光子导带内的群速度为有限值，在光子禁带的边缘，群速度迅速减小而趋于0，光的传播具有显著的带边延迟效应．同时，在反常色散区，群速度为负值，光的传播表现出明显的超光速现象．光子晶体的结构参数直接影响光波在光子晶体中的群速度．

Numerical Simulation to Propagation of Optical Waves Through One-Dimensional Photonic Crystals

The group velocity of optical waves through one-dimensional photonic crystals is investigated based on Kronig-Penney model, whose exact analytic expression is derived via the transfer matrix method. The dispersion relation and the characteristics of group velocity distribution are discussed. The simulated result indicates that the group velocity within the allowed bands is finite real number, but near the bandgap edge the group velocity reduces rapidly and approaches zero to demonstrate an exceedingly long optical length and much delay time in the photonic crystal. Especially, within the anomalous dispersion regions, the superluminal propagation at a negative group velocity arises obviously, and the group velocity is affected by the dielectric layer thickness ratio and refraction index contrast remarkably.