Space group theory and Fourier space analysis of two-dimensional photonic crystal waveguides

The symmetry, Fourier space and space group properties of two-dimensional photonic crystal waveguides are discussed. The modes of the standard single missing line defect waveguide can be classified as even or odd along the transverse direction. This is contrasted with the modes of line defect waveguides with a glide plane along the propagation direction. In this case the spatial Fourier series components of a single mode alternate between even and odd. The theory of symmorphic and nonsymmorphic space groups is used to classify the modes of these two waveguides, and the pairwise degeneracy at the Brillouin zone boundary is predicted for the waveguide with a glide-plane. Three-dimensional finite-difference time-domain numerical calculations are used to illustrate the investigated symmetry properties.