Synthetic topological insulator with periodically modulated effective gauge fields.

We study both theoretically and numerically the topological edge states in synthetic photonic lattice with finitely periodic gauge potentials. The effective gauge fields are implemented by tailoring the phase alternatively and periodically, which finally results in symmetric total reflection at two boundaries of the one-dimensional synthetic lattice. Further tuning the nearest-neighbor coupling anisotropically, topological edge states occur at the two boundaries. Our work provides a new way to study the topological physics of one-dimensional coupled waveguide arrays with synthetic photonic lattice.