Parametric Type-II Dirac Photonic Lattices

Different from the Fermi surface of the type-I Dirac semimetal being a point, that of the type-II Dirac semimetal is a pair of crossing lines because the Dirac cone is tilted with open and hyperbolic isofrequency contours. As an optical analogy, type-II Dirac photonic lattices have been also designed. Here, type-II Dirac cones are reported in Lieb-like photonic lattices composed of identical waveguide channels, and the anisotropy of the band structure is due to neither the refractive index change nor the environment, but only the spatial symmetry of the lattice; therefore, the proposal is advantageous and benefits experimental observation. Conical diffractions and Klein tunneling in the parametric type-II photonic lattice are investigated in detail. The results provide a simple and experimentally feasible platform to study two-dimensional topological photonic and other nonrelativistic phenomena around type-II Dirac cones.