Mid-IR Dirac-cone dispersion relation materialized in SOI photonic crystal slabs.

We materialized the isotropic Dirac-cone dispersion relation in the mid-infrared range by fabricating photonic crystal slabs of the C4v symmetry in SOI (silicon-on-insulator) wafers by electron beam lithography. The dispersion relation was examined by the angle-resolved reflection spectra with our home-made high-resolution apparatus, which showed a good agreement with the dispersion relation and the reflection spectra calculated by the finite element method. The reflection spectra also agreed with the selection rules derived from the spatial symmetry of the Dirac-cone modes, which proved to be a powerful tool for the mode assignment.