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 yet been found in photonic crystals. Here, 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 nontrivial and can be understood based on the theory of topological polarization. Moreover, by tuning the easily fabricated structure of the photonic crystals, different topological phases can be realized straightforwardly. Our study can be generalized to higher dimensions and provides a platform for higher-order photonic topological insulators and semimetals.

We demonstrate experimentally that a photonic crystal made of ${\mathrm{Al}}_2{\mathrm{O}}_3$ cylinders exhibits topological time-reversal symmetric electromagnetic propagation, similar to the quantum spin Hall effect in electronic systems. A pseudospin degree of freedom in the electromagnetic system representing different states of orbital angular momentum arises due to a deformation of the photonic crystal from the ideal honeycomb lattice. It serves as the photonic analogue to the electronic Kramers pair. We visualized qualitatively and measured quantitatively that microwaves of a specific pseudospin propagate only in one direction along the interface between a topological photonic crystal and a trivial one. As only a conventional dielectric material is used and only local real-space manipulations are required, our scheme can be extended to visible light to inspire many future applications in the field of photonics and beyond.

Beyond the scope of Hermitian physics, non-Hermiticity fundamentally changes the topological band theory, leading to interesting phenomena, e.g., non-Hermitian skin effect, as confirmed in one-dimensional systems. However, in higher dimensions, these effects remain elusive. Here, we demonstrate the spin-polarized, higher-order non-Hermitian skin effect in two-dimensional acoustic higher-order topological insulators. We find that non-Hermiticity drives wave localizations toward opposite edges upon different spin polarizations. More interestingly, for finite systems with both edges and corners, the higher-order non-Hermitian skin effect leads to wave localizations toward two opposite corners for all the bulk, edge and corner states in a spin-dependent manner. We further show that such a skin effect enables rich wave manipulation by configuring the non-Hermiticity. Our study reveals the intriguing interplay between higher-order topology and non-Hermiticity, which is further enriched by the pseudospin degree of freedom, unveiling a horizon in the study of non-Hermitian physics.