Eigenmode symmetry assignment of triangular-lattice photonic crystal slabs and their Dirac cones materialized by effective degeneracy in the mid-infrared region

We measured angle-resolved reflection spectra of triangular-lattice photonic crystal slabs fabricated in a silicon-on-insulator wafer in the mid-infrared region. We achieved a high angle-resolution measurement by means of our homemade optical setup integrated in the sample chamber of an FT-IR spectrometer. By examining the reflection peak frequency as a function of the lateral component of the wave vector of the incident light and applying the selection rules expected from the spatial symmetry of electromagnetic eigenmodes in C6v-symmetric structures, we successfully obtained the dispersion relation and the mode symmetry of the photonic crystal slabs, which agreed well with numerical calculations by the finite element method. We also found the redistribution of diffraction loss between A1- and E1-symmetric modes, which was caused by the Dirac-cone formation due to their effective degeneracy.