Effect of point defect geometry on localized defect modes in two-dimensional photonic crystals

A numerical study of point defect modes in two-dimensional square array of dielectric cylinders in air is presented. Three kinds of defect are considered, namely, circular, square and rectangular, respectively. The results show that for square defects, the defect modes are only dependent of the defect filling fraction Fd, regardless of the defect orientations. Further evidence shows that the defect modes for square defects have almost the same features as those of the circular defects having the same defect filling fraction, exhibiting the independence of these two geometries. However, for the rectangular defects, the defect modes show a dependence on their geometry. When the aspect ratio of the rectangle defect is big enough, the defect modes exhibit the splitting feature. This provides a way to split the degenerate defect modes.