Figure 2: Network model description of the topological structure and its topological transition.

(a) Schematic of a unit cell in a two-dimensional lattice of coupled ring waveguides. (b) The equivalent periodic network. Within the unit cell, we define a surface (red rectangle) which is penetrated by input amplitudes |a〉 and output amplitudes |b〉, related by |b〉=e^−iφ|a〉. These amplitudes also scatter with those of neighbouring cells, with coupling matrices S_x and S_y. (c) Topological transition as the inter-ring coupling strength θ is tuned from weak to strong. Before and after the transition, all bands have zero Chern number C=0. Red and blue lines denote edge states confined to the upper and lower edges of the strip, respectively.