  Higher-order topological insulators (HOTIs) which go beyond the description
of conventional bulk-boundary correspondence, broaden the understanding of
topological insulating phases. Being mainly focused on electronic materials,
HOTIs have not been found in photonic systems yet. In this article, we propose
a type of two-dimensional second-order photonic crystals with zero-dimensional
corner states and one-dimensional boundary states for optical frequencies. All
of these states are topologically non-trivial and can be understood based on
the theory of topological polarization. Moreover, by tuning the
easily-fabricated structure of the photonic crystals, we can realize different
topological phases with unique topological boundary states straightforwardly.
Our result can be generalized to higher dimensions and provides unprecedented
venues for higher-order photonic topological insulators and semimetals.
