Topological bound modes in optical waveguide arrays with alternating positive and negative couplings

We investigate the topological bound modes in a binary waveguide array with alternating positive and negative couplings. The negative coupling is realized by incorporating additional waveguides into the bare array and suitably tuning the refractive index. We show the band structures close and Dirac point emerges at the Brillouin zone center when the absolute values of real and negative couplings are equal, indicating topological phase transition. The topological bound modes emerge at the edge of topological non-trivial arrays or at the interface of two arrays with different topologies. Moreover, we show the topological bound mode can be isolated from the trivial defect mode by tuning the coupling strength, which is reflected from wave propagation. The study provides a promising approach to realizing robust light transport.