π-mode solitons in photonic Floquet lattices

We report on the existence and stability of π-mode solitons in both one-dimensional (1D) and two-dimensional (2D) nonlinear Su-Schrieffer-Heeger (SSH) arrays with periodic longitudinal modulation that mimics temporal periodic driving in Floquet systems. The SSH array is a paradigmatic example of the topological insulator, where edge states appear for the proper ratio of the intra- and intercell couplings. When the SSH array is additionally periodically driven due to longitudinal oscillations of waveguide centers, so that for half of the driving cycle it is in trivial phase, while on other half it is in topological phase, a new type of anomalous topological π-mode emerges at the edges of the driven lattice. We consider π-mode solitons with propagation constants in the gap of this equivalent Floquet system bifurcating under the action of nonlinearity from anomalous linear π-mode states. In the 1D case such periodically oscillating solitons become more robust with an increase of the amplitude of oscillations of waveguide positions and survive over hundreds of longitudinal lattice periods. We also found that they can be very robust in the 2D equivalent Floquet SSH arrays. Furthermore, we show that π-mode solitons can be directly excited by Gaussian beams launched into the array at the proper distance. Our results suggest a framework for experimental observation of the π-mode solitons, including in higher-order topological Floquet systems.