具有介质柱缺陷的二维正方晶格光子晶体的带隙

The Band Gaps of Two-Dimensional Tetragonal Lattice Photonic Crystals with Dielectric Column Defects

摘要: 为了在二维光子晶体中对带隙位置和宽度进行调控，观察介质柱缺陷对光子晶体带隙的影响，文章研究了这样的二维光子晶体结构：介质圆柱排列成正方形结构，圆柱介质折射率沿半径阶梯性增加，在该种光子晶体中设置介质柱缺陷。文章对比研究了下列几种结构：1) 半径r = 0.6 μm，晶格常数a = 1.8 μm，折射率沿半径分3层增加幅度不同，在晶体中预设1~3个空气柱缺陷；2) 半径r = 0.8 μm，晶格常数a = 2.4 μm，折射率沿半径分4层增加幅度不同，在晶体中预设1~2个空气柱缺陷；3) 半径r = 0.8 μm，晶格常数a = 2.4 μm，折射率沿半径分4层增加幅度不同，在晶体中预设1~2个介质柱缺陷；4) 半径r = 0.8 μm，晶格常数a = 2.4 μm，折射率沿半径分4层增加幅度不同，在晶体中分别预设5个空气柱缺陷和介质柱缺陷。用有限时域差分(FDTD)方法，计算平面光波通过上述几种二维光子晶体后的透射率，得到光子晶体的带隙。发现在相同结构下，光子晶体的带隙主要由填充率和结构决定，设置的空气柱缺陷和介质柱缺陷对光子晶体的带隙影响很小。

Abstract: In order to control band gap width and position in two-dimensional photonic crystal, to observe the influence of medium column defect with photonic crystal band gap, this article studied two-dimensional photonic crystal structure: dielectric cylinder arranged in a square construction, cylindrical dielectric refractive index stepwise increase along the radius, setting medium columns in this kind of photonic crystal as defect. The following structures are compared and studied: 1) The radius r = 0.6 μm, the lattice constant a = 1.8 μm, the refractive index increases by three layers along the radius, and 1~3 air column defects are preset in the crystal; 2) The radius r = 0.8 μm, the lattice constant a = 2.4 μm, the refractive index increases by four layers along the radius, and 1~2 air column defects are preset in the crystal; 3) The radius r = 0.8 μm, the lattice constant a = 2.4 μm, the refractive index increases by four layers along the radius, and 1~2 dielectric column defects are preset in the crystal; 4) The radius r = 0.8 μm, the lattice constant a = 2.4 μm, the refractive index increases by four layers along the radius, 5 air column defects and medium column defects are preset in the crystal, respectively. The band gaps of photonic crystals are obtained by using the finite difference time domain (FDTD) method to calculate the transmittance of plane light waves passing through the above two dimensional photonic crystals. It is found that for the same structure, the band gap of photonic crystals is mainly determined by the filling rate and structure, and the defects of air column and medium column have little effect on the band gap of photonic crystals.