  In the presence of crystalline symmetries, second-order topological
insulators can be featured by the polarization which is believed identical to
the Wannier center. In this Letter, we show that second-order topological
insulators are present in the full process of topological phase transition
between a pair of degenerate photonic bands resulting from the non-symmorphic
glide symmetry in all-dielectric photonic crystals. Due to the coupling
(hybridization) of the Wannier functions, the center of the maximally localized
Wannier function always locates at the origin, not equal to the addition of
constituent polarization. In this case, the corner states are ascribed to the
hybridized Wannier functions obstructed by the boundary. In combination with
the local density of states, the second-order topology is clearly confirmed and
characterized. That ensures corner states which are fundamentally different to
either the type-I corner state localized in particular sublattice, or the
type-II corner state originated from interacting topological edge states. This
type of corner states is regarded as type-III here and provides an alternative
method to explore higher-order topological physics, which may lead to
interesting applications in integrated and quantum photonics.

Optics