正方形具有缺陷结构二维光子晶体结构参数对本征模的影响

The influences of the structure parameters of a square lattice photonic crystal with a defect in it on its defect mode

由于正方形二维光子晶体具有光子禁带,所以在光子晶体缺陷处可形成对光子束缚的缺陷本征模。本征模的频率应在光子禁带频率范围内,而光子禁带频率又取决于光子晶体的结构参数。通过有限元法数值计算得到并图示了正方形具有缺陷结构二维光子晶体本征频率和介质柱半径、晶格常数以及介质柱介电常数之间的关系。利用这些关系当增大介质柱半径而相应减小介质柱介电常数时,本征频率将会保持不变。此外由于光子晶体结构参数的不同,本征模对应的电磁场在晶体中的分布也不同。

The localized eigen mode frequencies of a square lattice photonic crystal with a defect in it are calculated numerically with the finite element method. The defect mode eigenfrequency dependence of its structure parameters is obtained. The distributions of the magnitude of the electric field in some of these photonic crystal structures are also presented. From these relations between eigenfrequencies and structure parameters, if one or more dielectric cylinders are replaced with others with different radius and a corresponding dielectric constant, the eigenfrequency will keep unchanged.