The relationship between the filling factor and the circumcircle radius of the regular polygon scatter is deduced in a two-dimensional triangular lattice photonic crystal. The photonic band gaps ( PBGs) are calculated with the plane wave expansion method in Ge-based two-dimensional triangular lattice photonic crystals. When Ge cylinder is placed in air background , the TM band gaps and TE band gaps appear with the TM band gaps dominating. As Ge filling factor increases, the width of the photonic band gaps increase initially but then decrease and the center frequency decrease. The width of the first band gap of the TM band gaps reaches the maximum at the radius of 0. 14a. On the contrary, when air cylinder is placed in Ge background, the TM band gaps and TE band gaps as well as the complete band gaps appear with the TE band gaps dominating. With the air filling factor increasing, the width of the photonic band gaps also increase initially then decrease, whereas the center frequency increase. The width of the first band gap of TE band gaps and the largest complete band gap reaches the maximum at the radius of 0.46a and 0.49a, respectively.%导出了二维三角晶格光子晶体的填充系数与正多边形散射子外接圆半径的普适关系,并利用平面波展开法计算了Ge基二维三角晶格光子晶体的光子带隙.计算表明:Ge圆柱置于空气背景中时,可产生TM、TE带隙,TM带隙占优势；随着Ge填充系数的增大,光子带隙的宽度先增大后减小,其中心频率由高频向低频移动；TM模第一带隙宽度在半径为0.14a处达峰值.空气圆柱置于Ge背景中时,可产生TM、TE及完全带隙,TE带隙占优势；随着空气填充系数的增大,光子带隙的宽度先增大后减小,其中心频率由低频向高频移动；TE模第一带隙宽度和最大完全带隙宽度分别在半径为0.46a和0.49a处达峰值.
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