  The studies of topological phases of matter have been extended from condensed
matter physics to photonic systems, resulting in fascinating designs of robust
photonic devices. Recently, higher-order topological insulators (HOTIs) have
been investigated as a novel topological phase of matter beyond the
conventional bulk-boundary correspondence. Previous studies of HOTIs have been
mainly focused on the topological multipole systems with negative coupling
between lattice sites. Here we experimentally demonstrate that second-order
topological insulating phases without negative coupling can be realized in
two-dimensional dielectric photonic crystals (PCs). We visualize both
one-dimensional topological edge states and zero-dimensional topological corner
states by using near-field scanning technique. To characterize the topological
properties of PCs, we define a novel topological invariant based on the bulk
polarizations. Our findings open new research frontiers for searching HOTIs in
dielectric PCs and provide a new mechanism for light-manipulating in a
hierarchical way.
