Quantifying the Robustness of Topological Slow Light

Low-dimensional nanostructured materials can guide light propagating with very low group velocity vg. However, this slow light is significantly sensitive to unwanted imperfections in the critical dimensions of the nanostructure. The backscattering mean free path, xi, the average ballistic propagation length along the waveguide, quantifies the robustness of slow light against this type of structural disorder. This figure of merit determines the crossover between acceptable slow-light transmission affected by minimal scattering losses and a strong backscattering-induced destructive interference when xi exceeds the waveguide length L. Here, we calculate the backscattering mean free path for a topological photonic waveguide for a specific and determined amount of disorder and, equally relevant, for a fixed value of the group index ng which is the slowdown factor of the group velocity with respect to the speed of light in vacuum. These two figures of merit, xi and ng, should be taken into account when quantifying the robustness of topological and conventional (non-topological) slow-light transport at the nanoscale. Otherwise, any claim on a better performance of topological guided light over conventional one is not justified.