Interface states and optical coupling functionalities in the super-SSH lattices.

We theoretically address the coupling between trimer lattices and reveal the existence of stable multiple edge and interface states. It is shown the superlattice can provides a tunable number of topologically protected edge and interface states depending on the coupling strength and topological phase of the connecting lattices. Dynamics and transport properties of interface states are also investigated, Due to the interference of linear modes with different propagation constants, stable oscillations resulted from the coupling of interface states in finite trimerized waveguide arrays are observed and can give rise to optical coupling functionalities, including directional coupling, beam splitting and beam oscillator.