Scattering similarities and differences in space and time discontinuous media

Wave propagation in sub-cycle switched media is explored in connection with causality. The fast switching is modeled by abrupt change in the medium refractive index. The analysis reveals similarities and differences in wave behavior at spatial and temporal discontinuities. In both cases, a frequency shift (spatial and angular, respectively) takes place, while in a medium with temporal discontinuities multiple reflections do not occur due to causality.