Topological photonics in open systems

Topological order has raised great research interests in optical systems over the past years, while most of the efforts have been focused on closed and lossless (Hermitian) systems. Here, I will present some of the recent progresses in studying topological states in optical systems with open boundary conditions. On the one hand, radiation losses in these non-Hermitian systems give rise to new topological states that are not possible in Hermitian ones. On the other hand, the concept of topological invariants gives us new means to control the radiation fields, both in their amplitudes and polarization states.