Asynchronous Topological Phase Transition in Trimer Lattices

We propose a model of a non-reciprocal double-layer trimer photonic lattice. In this model, two types of topological phases are presented. By adjusting the imaginary coupling coefficients and intra-cell coupling coefficients in this model, two topological phases appear in different coefficient ranges. They exhibit asynchronous topological phase transitions as the coupling coefficients change. We discover that these asynchronous topological phase transitions can impact the light transmission properties of the system. When the coupling coefficients are adjusted to put the system in a topologically non-trivial state, the injected light beam tends to localize at the edge. Moreover, before and after the phase transition, the lowest energy band exhibits oscillatory and non-oscillatory behavior in the evolution of the light beam at the boundary. Asynchronous topological phase transitions can be utilized to manipulate the light transmission properties of the system, offering potential applications in optical communication and the development of photonic integrated circuits.