二维三角格子光子晶体的带隙结构

Band Gap Structures of 2D Triangular Lattice Photonic Crystals

用平面波展开法对二维光子晶体的电磁波理论及周期排列的电介质中电磁波的B loch波解进行了详细的推导,计算出以G aA s为背景的空气柱构成的二维三角格子光子晶体的能带结构,研究了H偏振和E偏振带隙宽度随填充比f的变化。计算结果表明,当f=0.8时,H偏振和E偏振出现重叠的最大绝对光子带隙,带隙位于0.458—0.529ωe(ωe=2πc/a,a为晶格常数,c为光速),带隙宽度为0.071ωe,相应的带隙波长范围为472.6—545.9nm,处于可见光波段。

The Bloch wave solution in periodic dielectric was deduced in detail according to the electromagnetic wave theory of 2D photonic crystals,and the band gap structures of two-dimensional （2D） triangular lattice photonic crystals constructed from air rods in GaAs dielectric matrix was calculated by using plan wave expansion method. The dependences of filling factor f in the photonic crystals were studied in both H polarization and E polarization. It was found that the crystal constructed from air rods in GaAs dielectric matrix can generate an maximum absolute photonic band gap with width 0. 071 in the low frequency range of 0. 458-0. 529ωc（ωc=2πc/α）,corresponding to the wavelength range of 472. 6-545.9nm,which belongs to visible light range.