Degeneracy Analysis Based on the Symmetry Relations of Two-Dimensional Photonic Crystal Resonant Modes
由光子晶体局域模对称关系分析其简并性

Various resonant modes of single-point defects two-dimensional square dielectric photonic crystals cavity are calculated by using the plane-waves expansion method. The degeneracy of resonant modes is investigated based on the symmetry relation of the cavity modes. The C4v symmetry photonic crystal cavity tends to have either a pair of doubly degenerate modes or non-degenerate modes. Dipoles and hexapoles are doubly degenerate modes, a quadrupole and a monopole are non-degenerate modes, and the 90°rotated state is its orthogonal state for doubly degenerate modes. Thus, we can determine the degeneracy of modes by simply inspecting mode symmetries.