Time-varying media, dispersion, and the principle of causality Invited

The article reviews general properties of time-varying dispersive materials. We first briefly discuss different dispersion models that have been proposed in the literature, the role of the causality principle, and the generalization of the Kramers-Kronig relations for the susceptibility of linear time-dependent media. Furthermore, we discuss the Kramers-Kronig-like relations for nonlinear optical processes, with a focus on those processes that may be used to realize strong and fast temporal modulations at optical frequencies to enable, for instance, photonic time-crystal phenomena.