低频和高频区域内大禁带的二维各向异性光子晶体

Large complete band gap at low and high frequencies in a two-dimensional anisotropic photonic crystal

采用一种改进的平面波展开法 ,运用一种有效的设计二维各向异性光子晶体的方法 ,在低频和高频区域内获得了具有较大禁带的两种二维光子晶体 .低频区域内 ,找到具有最大禁带宽度的光子晶体的禁带宽度为Δω =0 0 76 (2πc a) ,中心频率为 0 76 9(2πc a) (这里的a为晶格常量 ) .高频区域内 ,找到的光子晶体的最大禁带宽度为Δω =0 1(2πc α) ,中心频率为 1 6 5 3(2πc a) .同时在低频区域内 ,发现一种很简单的正方网格结构 ,它的禁带宽度为Δω =0 0 5 74 (2πc a) ,禁带宽度与禁带的中心频率之比为Δω ωc =11 782 % .

A revised plane-wave expansion method for calculating the band structure of photonic crystals is presented. Using an effective method for designing two-dimensional anisotropic photonic crystals of square lattice, we have found two structures which have a large absolute band gap in the low and high frequencies. The sizes of the absolute bandgap are Deltaomega = 0.076(2pic/a) with a midgap frequency of 0.769(2pic/a)) and Deltaomega = 0.1(2pic/a) with a midgap frequency of 1.653(2pic/a) in the low and high frequencies respectively, where a is the lattice constant. Morever, we have found a simple photonic crystal consisting of dielectric veins in air in the low frequency. The size of the absolute bandgap is Deltaomega = 0.0574(2pic/a) and the ratio of the bandgap width to the centre frequency of the bandgap is Deltaomega/omega(c) = 11.782%.