Sub/Super-luminal space-time slab: Fundamental scattering symmetries

Space-time (ST) media are regaining interest due to their capability to modify the ST spectra (k-ω) and amplitudes of waves, and their subsequent multiple potential applications. Many fundamental related problems have not been resolved yet, including the scattering of an oblique wave on a superluminal ST slab. Here, we address this problem for the first time and highlight fundamental symmetries in the deflection angles of sub- and super-luminal slabs. An insightful diagrammatic approach, conveying the symmetry information at a glance, is proposed.