  Photonic Floquet lattices provide an excellent platform for manipulating
different topologically protect-ed edge states. However, anti-chiral edge
states have not been discussed much in Floquet lattices. Here, we propose a
waveguide structure by combining two honeycomb Floquet photonic lattices with
oppo-site rotation directions. In this structure, we find that the anti-chiral
edge states have the same trans-mission direction on two parallel body edges.
With an increasing modulation phase difference between the two sublattices in
one direction, the width of the band gap becomes smaller and the robustness of
the edge states becomes weaker. Interestingly, the transmission speed is also
controlled by the phase difference. In addition to their relevance for the
topological properties of the Floquet lattice system, these results may be
applied to multi-channel optical switches, optical functional devices, and in
other fields.
