2维复式正方晶格结构的完全带隙研究

为了获得较大的完全带隙,采用平面波展开法对2维光子晶体的带隙结构进行计算,通过栅格结构连接方形硅介质柱对正方晶格的带隙结构进行优化。在适当调整介质柱宽度和栅格宽度后,所构成的复式结构获得了较大的完全带隙。结果表明,在正方晶格结构的情况下,只有方形硅介质柱且其宽度为0.5a(a为晶格常数)时,仅存在TE模的带隙;只有同周期硅介质栅格结构且栅格宽度为0.22a时,仅存在TM模的带隙;复式结构的情况下,适当调整介质柱宽度w和栅格宽度d,在w=0.5a和d=0.05a时,可以获得较大的完全带隙,其宽度为0.0417ωe(ωe为中心频率);在w不变时,随着d的变化,在0.04a～0.11a出现完全带隙;在d不变时,随着w的变化,在0.42a～0.76a出现完全带隙;在4～36的范围内调整介电常数,在8.41～36之间能够出现不同宽度的完全带隙。这些结果对2维光子晶体的制作和应用是很有帮助的。

Research of complete band gap of 2-D compound square lattice structure

Wiih the method of plane wave expansion, the band gap structures of 2-D photonic crystal were calculated.Connecting square dielectric cylinder of silicon with the grid structure,the band gap structure of square lattice was optimized to gain bigger full band gap. After adjusting the media at the appropriate width of dielectric cylinder of silicon and the width of grid, a larger complete band gap was obtained in the compound structure of square lattice. The results show that in case of square lattice structure, only the TE mode band gap is found in the square dielectric cylinder in 0.5a width(a is the lattice constant), only the band gap of TM mode is formed in the structure of the same periodic grid in 0.22a width. In the case of compound structure,adjusting the width of w and d appropriately, when media column width is 0.5a and the grid width is 0.05a,a larger complete band gap in 0.0417ωe could be obtained(ωe is center frequency).In the case of w constant, full band gap can be formed with the grid width of 0.04a-0.11a;in the case of the grid width d unchanged, full band gap can be found with the dielectric pillar width of 0.42a-0.76a; adjusting the dielectric constant within 4-36,it can find different full band gaps are found with the dielectric constant of 8.41-36. The results are very useful to the production and application of two-dimension photonic crystal.