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.