Topological Edge States and Solitons on a Dynamically Tunable Domain Wall of Two Opposing Helical Waveguide Arrays

We study linear and nonlinear topological edge states on the domain wall (DW) of two helical waveguide arrays with opposite helicities. This composite helical structure is constructed by using the multibeam interference (MBI) method, in which the helix pitch and helicity is readily modulated by varying the topological charge of an interfering vortex beam. The topological edge states are characterized by the gap Chern number, and their propagation dynamics are controlled by the tunable lattice DW structure. In the linear region, we find the edge states exist only within a threshold value of the helical radius and for a certain disorder of the helix pitch. In the nonlinear region, surprisingly, we find that it is possible to form quasi-solitons along the DW, including multipole-like edge solitons whose different poles on either side of the DW exhibit opposite helicities. The long-distance propagation dynamics of such DW solitons are numerically studied from the evolution of their intensity patterns and the "center of mass".