利用平面波展开法, 发现双原子正方晶格光子晶体中ΓM方向边界面存在着快慢两类边界模式, 并且通过计算色散关系和电场分布研究了边界参量对这两类边界模式传输特性的影响.依据两种模式的色散关系, 计算了群指数和群速度色散参量, 结果表明边界参量的变化对第一类边界模式传输特性的影响较小, 该模式的平均群指数始终维持在5.0左右; 第二类边界模式与第一类模式明显不同, 边界参量的变化能够有效地影响到这种模式的传输特性, 该模式的最大平均群指数可达178左右.利用时域有限差分法记录了不同时刻电场强度在边界附近的分布及监测点处的电场幅度变化情况, 结果表明, 两类模式都能够被限制在边界附近并向前传播, 时域有限差分法得到的群速度与平面波展开法的结果完全吻合.

Utilizing the plane wave expansion method, it is found that there are two types of edge states existing on the surface termination along the ΓM direction of a diatomic photonic crystal. Through analying the surface mode band structure and the field distribution, the effect of the edge parameter on the waveguiding properties of these edge states were investigated. The group index and group velocity dispersion parameter were calculated according to the dispersion curves. The results demonstrate that the variation of the edge parameter has a very slight effect on the light propagation properties of first type of edge state. Its average group index is always around 5.0. The second edge state is obviously different with the first state and the variation of edge parameters can control the propagation performance of this mode efficiently. The maximal average group index of this edge state can achieve 178. The finite difference time domain methods was used to record the electric field distributions and amplitudes near the surface at different times. From the obtained results, it is found that these edge states can be confined in the area near the surface termination and propagate forward. The group velocity extracted from the finite difference time domain method is consistent with the result from the plane wave expansion method.