用折射率阶梯增加的二维正方晶格光子晶体获得宽带隙

Obtaining Wide Band Gap by Using a Two-Dimensional Quadrangular Photonic Crystal with Refractive Index Step Increase

摘要: 为了在二维光子晶体材料中获得宽的带隙，并能够按照要求进行带隙位置和宽度调控，文章提出了一种新的二维光子晶体结构：均匀介质圆柱排列成正方形结构，圆柱介质折射率在空间上阶梯性增加。构造二维圆柱介质的正方形光子晶体为：每两层的圆柱介质折射率相同，在y方向折射率阶梯增加。用有限时域差分(FDTD)方法，计算平面光波通过该二维光子晶体后的透射率，得到光子晶体的带隙。发现折射率阶梯增加的紧密型圆柱介质正方形光子晶体，完全带隙不存在，说明当圆形介质柱相切时，不能获得完全带隙；填充率在0.1962~0.3488之间，随着晶格常数增加，带隙的中心波长向长波长方向移动；在相同的填充率下，折射率阶梯增加，并呈周期性变化时，带隙位置没有变，但是带隙宽度变小。

Abstract: In order to obtain wide band gap in two-dimensional photonic crystal materials and adjust the band gap position and width according to the requirements, a new two-dimensional photonic crystal structure is proposed in this paper: the uniform dielectric cylinder is arranged into a square structure, and the refractive index of the cylinder increases in space by steps. The square photonic crystal of two-dimensional cylindrical medium is constructed as follows: the refractive index of cylindrical medium in each two layers was the same, and the refractive index stepsise increased in the y direction. By using the finite time domain difference (FDTD) method, the transmittance of planar light wave through the two-dimensional photonic crystal is calculated, and the band gap of the photonic crystal is obtained. It is found that the compact cylindrical dielectric square photonic crystal with increasing refractive index stepsise does not have a complete band gap, indicating that when the circular medium column is tangent, the complete band gap cannot be obtained. The filling rate is between 0.1962 and 0.3488. As the lattice constant increases, the central wavelength of the bandgap moves to the longer wavelength. At the same filling rate, when the refractive index stepwise increases and shows a periodic change, the bandgap position does not change, but the bandgap width decreases.