Su-Schrieffer-Heeger-type Floquet network

A network model that can describe light propagation in one-dimensional ring-resonator arrays with a dimer structure is studied as a Su-Schrieffer-Heeger-type Floquet network. The model can be regarded as a Floquet system without periodic driving and exhibits quasienergy band structures of the ring propagation phase. Resulting band gaps support deterministic edge states depending on hopping S-matrices between adjacent rings. The number of edge states is one if the Zak phase is $\pi$. If the Zak phase is 0, the number is either zero or two. The criterion of the latter number is given analytically in terms of the reflection matrix of the semi-infinite system. These properties are directly verified by changing S-matrix parameters and boundary condition continuously.