Topological and Geometrical Effects in the Bulk Hall Response of Driven-Dissipative Photonic Lattices

Although originally found and explored in solid-state electron systems, topological phases of matter have been found to play important roles in various other systems of waves in periodic media. In particular, engineering photonic lattices with non-trivial topological properties is the rapidly growing area of research in photonics [1]. Topological phases of photons and electrons have similarities and also differences. One major difference is that photons are bosons and they are often dissipative. Many of the phenomena known in topological phases of electron systems assume that, quite naturally, electrons are fermions and they are not lost from the system. It is thus an important question to ask how such phenomena known in fermionic non-dissipative systems can appear in bosonic dissipative setup of photonics. One of such phenomena that I will analyze in this talk is the quantum Hall effect, an effect which states that the Hall current is proportional to the topological Chern number of occupied energy bands.