I carried my research on both the two computation methods and fruitful results were obtained . for the fdtd method , i solved the instability problem of the method in the non - orthogonal coordinate system . for the pwe method , i introduce the linear transform in to calculate analytically the fourier coefficients of complicated photonic crystals 对于有限时域差分方法,我解决了一个影响这种方法在斜坐标使用的稳定性问题,得到了传统的yee型差分在斜坐标里的扩充;对于平面波展开方法,我引入了线性变化求富里叶展开的系数,这种方法的好处可以很方便快捷的获得复杂光子晶体的富里叶系数。