  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,
we report type-II Dirac cones 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 advantage and
benefits experimental observation. Conical diffractions and Klein tunneling in
the parametric type-II photonic lattice are investigated in detail. Our results
provide a simple and experimental feasible platform to study two-dimensional
topological photonic and other nonrelativistic phenomena around type-II Dirac
cones.
