中文摘要：

利用频域有限差分方法分析了两种二维磁性光子晶体结构（方形和圆形空气孔结构）的模场分布和有效折射率．结果表明：在该种结构的材料中，原本简并的基模被分为两个不简并的偏振模——左旋模和右旋模，且两种模式的有效折射率不同；其次，该种结构材料的法拉第旋转角较连续分布的磁光介质有显著增加．通过选择适当的空气孔参数，方孔结构材料的法拉第旋转角可增大约一个数量级，而圆孔结构可增加4倍左右．同时发现，当光通过这类材料后偏振态发生了变化，随着法拉第旋转角的增加出射光的椭圆率也在增加．最后分析了产生这一现象的原因并提出了解决偏振态变化这一问题的方法，即在材料中心处引入缺陷．

英文摘要：

The mode field and effective index of two structures （square air core and circular air core） of two-dimensional magnetophotonic crystals is analyzed using finite-difference frequency-domain （FDFD） method. According to the result of numerical analysis, the two degenerate fundamental modes become non-degenerate （L-mode and R-mode） in the structures, and the two corresponding effective indices are different. The Faraday rotation of these two structures is enhanced compared with that of the continuous magneto-optical materials. By choosing proper parameters of the air core, the Faraday rotation can be increased by one order for the square air core structure and 4 times for the circular core structure. The polarization state of optical waves is changed after passing through the structure. With the increasing of Faraday rotation, the ellipticity of outgoing optical waves is increased. Finally, we discuss the cause of the phenomena and present a method to resolve the problem of variation of ellipticity by introducing defect in the structure.