Edge modes in strongly nonlinear saturable SSH photonic lattices: Tracing a bulk-edge correspondence through instabilities and bifurcations

Photonic lattices with a saturable nonlinear response generally exhibit a second linear regime at high light intensities. Here, we perform a detailed numerical analysis of nonlinear continuations of the topological edge mode of a Su–Schrieffer–Heeger (SSH) chain, following the family of exact nonlinear stationary solutions through instabilities and bifurcations from the low-intensity to the high-intensity linear limit. The properties of the nonlinear edge modes define several regimes corresponding to qualitatively different dynamics for edge excitations. For each of these nonlinear regimes we numerically calculate the evolution of two commonly used indicators of nontrivial bulk topology: the mean field displacement and the Zak phase obtained from projector matrices. Thus, we determine the extent to which one may establish an approximate bulk-edge correspondence, characterized by dynamically stable nonlinear edge modes and well defined approximate Zak phases, in the full nonlinear regime of the saturable lattice.