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.

中文翻译：

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量化拓扑慢光的鲁棒性

反向散射平均自由程 $\xi$沿着波导的平均弹道传播长度，量化了慢速光对纳米结构的关键尺寸中的有害缺陷的抵抗力。该品质因数决定了当波导长度较长时，受最小散射损耗影响的可接受的慢光传输与强烈的后向散射引起的相消干涉之间的交叉$\mathrm{大号}$ 超过 $\xi$。在此，我们针对特定和确定的无序量，以及对于组索引的固定值，同样相关的拓扑光子波导，计算反向散射平均自由程${ñ}_G$这是相对于真空中光速的群速度的减慢因子。这两个优点，$\xi$ 和 ${ñ}_G$在量化纳米级拓扑和常规（非拓扑）慢光传输的鲁棒性时，应考虑。否则，没有任何理由主张拓扑导光灯比常规导光灯具有更好的性能。