Manipulating winding numbers and multiple topological bound states via long-range coupling in chiral photonic lattices

The topological bound states are limited to one pair in traditional one-dimensional (1D) topological chiral models as the winding number can only take the value of 0 or 1. It was increased to 2 or 3 via long-range couplings (LRCs) that were restricted to second- or third-order in recent experimental or theoretical researches. How to generate larger winding number to manipulate more topological bound states remains a challenge. Here, we propose an effective method by introducing arbitrary Nth order LRC stronger than the sum of other order couplings. The resulting winding number has been computed by getting the winding loop's envelope in parameter space. The coupling-inverted 1D photonic topological insulators supporting up to three pairs of highly localized multiple topological bound states are realized by fabricating photonic lattices with multi-layer waveguide arrays. Furthermore, these topological bound states are closely spaced, offering a promising implementation approach of multimode topological lasers in gain media. Our work highlights the advantages of LRCs in manipulating the topological phases of matter. Published by the American Physical Society 2024