Edge states and edge solitons in counter-rotating trimer helical waveguide arrays

The trimer lattice is an extended Su-Schrieffer-Heeger (SSH) lattice that supports richer topological states than the conventional SSH lattice. Yet, the influence of the Floquet mechanism on these topological states remains largely unexplored. Here, we investigate trimer helical waveguide arrays featuring counter-directional rotations, analyzing both equal and unequal intra-cell coupling regimes. Our findings demonstrate that the effective Floquet mechanism-driven by the helical modulation of waveguide arrays-lifts the parametric Dirac points and opens topological band gaps that host robust pairs of boundary states. This elaborated Floquet scheme significantly expands the existence domains of edge states, as compared to those in straight waveguide arrays. Furthermore, incorporating optical nonlinearity into the model enables these topological states to form stable topological solitons whose propagation constants are continuously tuned by the beam power, while maintaining periodic dynamical stability throughout propagation. Our results establish a versatile photonic platform for robust beam localization and topological control of the nonlinear Floquet edge states.