CC BY 4.0 UnportedFranca, SelmaHassler, FabianFulga, Ion Cosma2021-11-242021-11-242021https://oa.tib.eu/renate/handle/123456789/7427https://doi.org/10.34657/6474We show that scattering from the boundary of static, higher-order topological insulators (HOTIs) can be used to simulate the behavior of (time-periodic) Floquet topological insulators. We consider D-dimensional HOTIs with gapless corner states which are weakly probed by external waves in a scattering setup. We find that the unitary reflection matrix describing back-scattering from the boundary of the HOTI is topologically equivalent to a (D-1)-dimensional nontrivial Floquet operator. To characterize the topology of the reflection matrix, we introduce the concept of `nested' scattering matrices. Our results provide a route to engineer topological Floquet systems in the lab without the need for external driving. As benefit, the topological system does not to suffer from decoherence and heating.enghttps://creativecommons.org/licenses/by/4.0/530Floquet statesTopological phasesTopological systemArticle