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中文摘要：
为了研究二维光子晶体完全带隙的规律，采用平面波展开法模拟了4种结构二维光子晶体，在固定光子晶体周期常数a的情况下，研究完全带隙随柱半径r的变化规律。研究发现，六角晶格空气孔型光子晶体的完全带隙出现在r=0．42～0．50μm的范围，最大带隙宽度△ω1=0．08（ωa／2πc）；方形晶格空气柱型光子晶体在r=0．47～0．50μm范围内存在完全带隙，带隙宽度△ω2=0．02（ωa／2πc）。完全带隙中心频率随r的增加而增加。六角周期和方形周期的GaAs介质柱型光子晶体不存在完全带隙。
英文摘要：
Photonics crystal （PhC）is the material in which the refractive index changes periodically and the PhC has a band structure and location mode, this structure can control light. In order to study two-dimensional PhC complete band gap,in this paper, plane wave expansion method was employed to simulate four types of two-dimensional PhC. We study the relationship between the complete bandgap and the variation of column radius r with a fixed lattice constant. We found that hexagonal lattice PhC air holes complete band gap appears in the r = 0.42 - 0.50μm range, complete band gap width does not increase with the air column radiu r, but there is a maximum width. The maximum band gap width is Δω1 = 0.08 （ωa/2πc）. When air column radiu r =0.47 -0.50 μm,square lattice PhC exists complete bandgap, the band gap width Δω2=0.02（ωa/2πc）, And complete band gap center frequency increases with r. Results indicate that for hexagonal and aquare GaAs columnar PhC there is no complete band gap.
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