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We show the presence of Floquet-Weyl and Floquet-topological-insulator phasesin a stacked two-dimensional ring-network lattice. The Weyl points in thethree-dimensional Brillouin zone and Fermi-arc surface states are clearlydemonstrated in the quasienergy spectrum of the system in the Weyl phase. Inaddition, chiral surface states coexist in this phase. TheFloquet-topological-insulator phase is characterized by the winding number oftwo in the reflection matrices of the semi-infinite system and resulting twogapless surface states in the quasienergy g ap of the bulk. The phase diagramof the system is derived in the two-parameter space of hopping S-matrices amongthe rings. We also discuss a possible optical realization of the systemtogether with the introduction of synthetic gauge fields.

Floquet-Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice