Topological gap solitons in equidistant lithium niobate waveguide arrays

Abstract: Equidistant 1D arrays of thin film lithium niobate waveguides can exhibit non-trivial topology due to a specific interplay between inter- and intra-modal couplings of two families of guided modes. In this work we analyze two-colour spatial solitons, emerging due to $\chi_2$ nonlinear interactions between the modes of non-trivial topology in the fundamental harmonic field, and modes of trivial topology in the second harmonic field. We discuss solitons localized in the bulk of the array (bulk solitons), and at an edge of a finite-size array (edge solitons). The latter emerge due to the nonlinear interactions between a topological edge mode in the fundamental harmonic and bulk modes in the second harmonic. We reveal that for each type of soliton, bulk or edge, there generally exist two families of solutions with different internal structures and ranges of propagation constants. All bulk solitons can only be excited above a certain power threshold dictated by the coupling strength in the second harmonic field and the phase matching between the fundamental and second harmonics. The power threshold for edge solitons generally appears to be much lower, and, by tuning the phase matching, it can be reduced to zero.