Edge states supported by different boundaries of two helical lattices with opposite helicity

Abstract

We discuss linear and nonlinear topological edge states on the bearded-bearded edge (BBE) and armchair-armchair edge (AAE) of two helical waveguide arrays with opposite helicity. The robustness of the linear topological edge state can be controlled by the helix radius, the angle of the incidence, and the amplitude of lattice potentials. In the nonlinear regime, multipole-like lattice quasisolitons may be found with a certain saturable nonlinear factor for AAE. The long-distance propagation dynamics of such quasisolitons are numerically studied from the evolution of their intensity patterns and the “center of mass”. On the contrary, no quasisoltion exists for BBE under the same conditions.