圆柱形散射子二维光子晶体的态密度与局域态密度

二维光子晶体只有赝带隙,因此能否利用二维光子晶体有效控制原子自发辐射是令人感兴趣也是有实际意义的问题。其中最重要的因素是态密度和局域态密度的性质。采用平面波展开结合晶体群论的方法计算了二维正方格子光子晶体的态密度和局域态密度。其中散射子为空气圆柱,放置在均匀的电介质背景上。结果显示两个特点:第一,总态密度和局域态密度在原来二维光子晶体赝带隙处虽然已经不为零,但是取值明显低于赝带隙范围之外的值,即存在一个准光子带隙。第二,局域态密度在空气散射子界面处发生突变,空气散射子区域的局域态密度相对较大,这可由电位移矢量的连续性来理解。由于这两个特点在其他二维光子晶体中也被发现过,它们可能是普遍存在的。

Density of Sates and Local Density of States of Two-Dimensional Photonic Crystals with Cylinder Scatter in Square Lattice

Two-dimensional photonic crystal possess only pseudo photonic band gaps,so it is interesting and meaningful that whether the spontaneous emission of the atoms in two-dimensional photonic crystals can be controlled effectively.The density of photonic states and local density of photonic states are most important to determine the properties of atomic spontaneous emission.the density of states and local density of states of the two-dimensional photonic crystal composed of air cylinders on square lattice are investigated by plane wave expansion method and group theory.The air cylinder as scatter is positioned on uniform dielectric background,the calculated results show that the density of states and local density of states exhibit nonzero values but evidently lower than those outside the peseudo-gap range in the frequency range of pseudo-gap,and it may be regarded as a quasi-photonic band gap.The local density of states takes much larger values in the air cylinders areas and drops down at the boundary between the air cylinders and dielectric medium background,and this phenomenon is due to the continuity of electric displacement vector.Considering that the above two characteristics are also found in other two-dimensional photonic crystal sample,it is believed they are universal in two-dimensional photonic crystal.