2维各向异性正方介质柱的带隙研究

The research of band gap of 2-D anisotropic dielectric cylinders

因各向同性介质组成的正方晶格方形介质柱不能产生绝对带隙,而三角晶格正方介质柱可以产生很小的带隙,为了得到更大带隙,引入各向异性介质来代替各向同性介质,由于各向异性介质在不同方向上的介电常数不同,可以产生较大的绝对带隙,利用平面波展开法分别计算了正方晶格各向异性介质柱产生的绝对带隙宽度为0.03095ω_e(ω_e为中心频率),三角晶格各向异性正方介质柱产生的完全禁带宽度为0.03831ω_e,是各向同性介质所产生带宽的3.6倍。这一结果对光子晶体带隙的研究是很有帮助的。

The square lattice of isotropic dielectric cylinders in air can not bring about the absolute band gap and the triangular lattice of dielectric cylinders can produce small absolute band gap. In order to get the bigger band gap, the anisotropic material is used instead of the isotropic material, for it can bring about big absolute band gap because of the dielectric constants of the anisotropic material are different in some directions. Based on plane wave method, calculation results show that the width of the absolute band gap for the square lattice is 0. 03095（oe. For the triangular lattice the width is 0. 03831too, which is 3.6 times wider than the absolute band gap produced by the isotropic dielectric cylinders. It is very useful for research of the band gap of photonic crystal.