中文摘要：

利用Order-N算法及超晶格技术讨论了位置无序及尺寸无序对石墨点阵柱状光子晶体光子带隙的影响．计算结果表明，对于电场偏振模，光子带隙对尺寸无序更加敏感．在此基础上，利用三维时域有限差分方法进一步讨论了无序光子晶体对石墨点阵柱状中心柱光子晶体GaN发光二极管模型光输出效率的影响．计算结果表明，无序对这种光子晶体发光二极管模型光输出效率的影响较小，且这种影响也是随机的.

英文摘要：

The effects of cylinder site displacements （site randomness） and cylinder radius variations （size randomness） on photonic band gaps of the photonic crystals, which consist of a graphite lattice of dielectric cylinders, have been discussed by the Order-N method with a supercell technique. The numerical result shows that the variation of the photonic band gaps for the E polarization mode is far more sensitive to disorders with a size randomness than with a site randomness. Furthermore, the influence of the disorder on light extraction of a GaN light- emitting diodes model, which has a disordered photonic crystal slab, has been investigated by three-dimensional finite-difference time-domain method. The numerical result shows that the influence of the disorder is small on light extraction of this light-emitting diodes model, and the influence is random.