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

Synthetic topological insulator with periodically modulated effective gauge fields