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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。
Two-dimensional photonic crystals have only pseudo-band gaps, so it is of interest and practical significance to use two-dimensional photonic crystals to effectively control spontaneous emission of atoms. One of the most important factors is the nature of state density and local density of states. The density of states and the density of local states of two-dimensional square lattice photonic crystals are calculated by the combination of plane wave expansion and crystal group theory. The scatterer is an air cylinder placed on a uniform dielectric background. The results show two characteristics: first, the total density of states and the density of local states are not zero at the original two-dimensional photonic crystal pseudogap; however, the values are obviously lower than those outside the pseudo- A quasi photonic bandgap. Second, the local density of states changes abruptly at the air-scattering interface and the local density of states in the air-scattering sub-area is relatively large, which can be understood by the continuity of the electric displacement vector. Since these two features are also found in other two-dimensional photonic crystals, they may be ubiquitous.