Abstract
This thesis is mainly concerned to how non-parabolic effect impacts on the donor level of the photonic crystal cavity. According to the equation of envelope function in the periodic dielectric structure --- Wannier-like equation, we can solve the impurity level in analogy. We can estimate the non-parabolic effect by photonic band structure and the range of the wave function. Then we calculated the non-parabolic effect to the impurity level in real case of photonic crystal cavity and show the difference from the parabolic approximation. We can use the filling fraction of the lattice to approximate some kinds of photonic crystal cavity, including the single missing hole defect and the donor-type cavity in a graded lattice of air holes. The model we calculated is the photonic crystal cavity which published by O. Painter in 2003[1]，and the effective refraction of the dielectric is 2.65. The result of the calculation shows that the non-parabolic effect is more obvious in smaller defect. And in the same deep of the defect, the non-parabolic effect is more obvious when we use the photonic crystal with larger air hole.