Quantifying the Robustness of Topological Slow Light

The backscattering mean free path xi, the average ballistic propagation length along a waveguide, quantifies the resistance of slow light against unwanted imperfections in the critical dimensions of the nanostructure. 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 the waveguide length L exceeds xi. 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 n(g) 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 n(g), should be taken into account when quantifying the robustness of topological and conventional (nontopological) slow-light transport at the nanoscale. Otherwise, any claim on a better performance of topological guided light over a conventional one is not justified.