  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.
