In order to study the properties of the complete bandgap of 2-D columnar photonic crystal in square lattice, two types of 2-D photonic crystals were studied based on the plane wave expansion method. The dependence of the complete bandgap on the variation of column radius and the refractive index was studied for a fixed lattice constant. Results show that when the radius of dielectric rods increases, the width of the complete photonic bandgap of photonic crystal composed of Ge cylinders in air background firstly increased, then declined and disappeared at last. When the filling fraction was 38. 3% , as the dielectricrnconstant of dielectric rods increased, the obtained maximum complete photonic band gap was 0.02754(ωa/2πc) when the refractivernindex was 4. 2. It was also found that the bandgap frequency increased when the radius of air rods in Ge background increased. When the filling fraction was 48.3% , as the dielectric constant increased in the background, three complete bandgaps could bernfound, and the width of the largest complete bandgap was 0.02922(ωa/2πc)when the background index was 6.2. The photonicrnband structure was also shown by the frequency analysis of TE/TM. These results provide theoretical instructions for 2-D square photonic crystals with big photonic bandgap.%为了研究2维正方晶格光子晶体的完全带隙特性,采用平面波展开方法模拟了两种结构2维光子晶体,在固定光子晶体周期常数α的前提下,研究了2维正方晶格光子晶体的完全禁带随柱半径和折射率的变化规律.结果表明,以空气为背景的锗介质柱组成的光子晶体,随着半径的增大,完全带隙宽度先增大后减小最后消失,填充比为38.3％时,同时增大介质柱的介电常数,在介质柱折射率为4.2处,完全带隙最大,带宽是0.02754((ωa)/(2πc));以锗为背景的空气柱组成的光子晶体,光子禁带对应的无量纲频率随半径的增大而增大,填充比为48.3％时,同时增大背景介质的介电常数,出现多个完全带隙,在背景折射率为6.2处,完全禁带最大,带宽为0.02922((ωa)/(2πc)).光子晶体带隙的频谱响应也表明了完全带隙的范围.这为大带隙2维正方晶格光子晶体的设计和制备提供了依据.
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