二维光子晶体的负折射现象

Negative refractive behaviors of two-dimensional photonic crystals

研究了由多层周期圆柱阵构成的二维光子晶体对电磁波的散射,并通过算例从数值上证实了负折射现象的存在。采用的是有效而精确的T-矩阵方法。首先利用单个圆柱的T-矩阵和体现层阵列周期性的栅和得到每一层周期阵的空间谐波散射与透射矩阵,再将每一层的散射与透射矩阵级联起来而得到多层周期圆柱阵的广义散射与透射矩阵。给出了具体的算例,画出了该光子晶体上部空间和下部空间的场的幅值分布,还给出了晶体内部和外部坡印亭矢量的分布图。这些图清楚地显示了负折射现象的存在。

The scattering of two-dimensional photonic crystals composed of multilayered periodic arrays of circular cylinders are studied. Negative refraction behavior is numerically verified. A very efficient and accurate T--matrix method is applied for analysis. Firstly, the reflection and transmission matrices of space harmonics for one layer periodic array of circular cylinders are expressed using the T-- matrix of single cylinder and the lattice sums characterizing the periodic arrangement of circular cylinders. Then the generalized reflection and transmission matrices are obtained by concatenating those of each single layer. The field distribution is illustrated both above and below an example photonic crystal. And the map of Poyrlting vector is given also for the same photonic crystal. All of the figures show the negative refraction clearly.