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We study the effects of a synthetic gauge field and pseudospin-orbitinteraction in a stacked two-dimensional ring-network model. The model wasintroduced to simulate light propagation in the corresponding ring-resonatorlattice, and is thus completely bosonic. Without these two items, the modelexhibits Floquet-Weyl and Floquet-topological-insulator phases withtopologically gapless and gapped band structures, respectively. The syntheticmagnetic field implemented in the model results in a three-dimensionalHofstadter-butterfly-type spectrum in a photonic platform. The resulting gapsare characterization by the winding number of relevant S-matrices together withthe Chern number of the bulk bands. The pseudospin-orbit interaction is definedas the mixing term between two pseudospin degrees of freedom in the rings,namely, the clockwise and counter-clockwise modes. It destroys theFloquet-topological-insulator phases, while the Floquet-Weyl phase withmultiple Weyl points can be preserved by breaking the space-inversion symmetry.Implementing both the synthetic gauge field and pseudospin-orbit interactionrequires a certain nonreciprocity.

Synthetic gauge field and pseudospin-orbit interaction in a stacked two-dimensional ring-network lattice