Topological Properties of Photonic Bands with Synthetic Momentum (2111.02843v4)

Abstract: We investigate topological aspects of photonic crystal bands in a hybrid momentum space consisting of a genuine momentum and a synthetic one. The system is realised by a one-dimensional system of bilayer photonic grating, with the translational displacement between the two layers naturally taking the role of the synthetic momentum. Remarkably, the unconventional behaviour of the synthetic momentum allows for the existence of non-trivial topological phases of the system associated with a non-zero total Berry flux without breaking the time-reversal symmetry. Moreover, the resulting band structure in the hybrid momentum space realises the interesting dynamics of merging and splitting of twin Dirac points, as well as gap opening as the system parameters vary. Introducing a simple topological argument, we explain all the changes of the total Berry flux associated with the topological phase transitions. As a signature of different topological phases, edge states at their interface are calculated and analysed in detail. The optomechanical nature of the system also allows for the investigation of the adiabatic evolution of the edge states. Our results pave the way to the paradigm of rich topological phenomena of photonic systems with hybrid momentum space.