Liu Jianjun, Fan Zhigang, Xiao Haosu, Zhang Wang, Guan Chunying, Yuan Libo
School of Astronautics, Harbin Institute of Technology, 92, West Dazhi Street, Harbin 150001, China.
Appl Opt. 2011 Aug 20;50(24):4868-72. doi: 10.1364/AO.50.004868.
Based on the infrared optical material germanium, in the basic structural unit of a two-dimensional decagonal photonic quasi-crystal, photonic bandgaps of four square unit cells with a scattering radius in the range of [0,0.3a] have been calculated within two cases of construction (i.e., air cylinders arranged in germanium and germanium cylinders arranged in air) by using the plane wave expansion method. In considering the Bragg-like scattering effect in two-dimensional photonic quasi-crystals as the elastic collision in physics, we put forward the photonic bandgap impact function F=q(1)q(2)q(3)επr(2) for the first time, to the best of our knowledge. A certain unit cell structure shares some similar photonic bandgap properties with a periodic structure. For a certain structure of the unit cell, the center frequency change trends of the photonic bandgap and the type of photonic bandgap generated are not related with the period of the photonic crystal, but with the relative dielectric constant and the construction, respectively. Different unit cell structures own different photonic bandgap structures. This occurs because the high degree of rotational symmetry of the quasi-periodic structure and weak long-range order of the basic structural unit lead to different Bragg-like scattering effects within the unit cell structures.
基于红外光学材料锗，在二维十边形光子准晶体的基本结构单元中，通过平面波展开法，在两种结构情形（即锗中排列空气圆柱和空气中排列锗圆柱）下，计算了散射半径在[0,0.3a]范围内的四个正方形晶胞的光子带隙。据我们所知，在将二维光子准晶体中的类布拉格散射效应视为物理学中的弹性碰撞时，我们首次提出了光子带隙影响函数F = q(1)q(2)q(3)επr(2)。某一晶胞结构与周期性结构具有一些相似的光子带隙特性。对于某一结构的晶胞，光子带隙的中心频率变化趋势和所产生的光子带隙类型分别与光子晶体的周期无关，而是与相对介电常数和结构有关。不同的晶胞结构具有不同的光子带隙结构。这是因为准周期结构的高度旋转对称性和基本结构单元的弱长程有序导致了晶胞结构内不同的类布拉格散射效应。
