  We propose a generic scattering matrix model implementable in photonics to
engineer a new Floquet metallic phase that combines two distinct topological
properties: the winding of the bulk bands and the existence of robust chiral
edge states. The winding of the bulk bands gives rise to a wavepacket
oscillations in real space while conserving its initial momentum. Our findings
open the way to the study of a new class of winding Floquet systems.
