Isotropic Double Dirac Cones in the Electromagnetic Dispersion Relation Detected by High-Resolution Angle-Resolved Reflection Spectroscopy

We previously reported that various types of Dirac cones, that is, isotropic linear dispersion relations, can be materialized in the zone center (F $\Gamma$ point) of photonic crystals (PhCs) by accidental degeneracy of eigenmodes with particular combinations of their spatial symmetries (See Ref. [1] and references therein). Those Dirac cones are characterized by a vanishing effective refractive index, so they can materialize cloaking and scatter-free wave guides. Recently another application to single-mode surface-emitting lasers was proposed [2]. Some of the Dirac cones were confirmed by experimental studies on two-dimensional PhCs (See Ref. [3], for example). However, the double Dirac cones were difficult to detect because of the dense distribution of eigenmodes in the vicinity of the Dirac point frequency although they have a unique character of the absence of flat bands, which is advantageous for their applications.