Generalized plasma waves in layered systems: general properties and relevance for THz spectroscopy

In a layered and strongly anisotropic system the hybrid modes provided by the propagation of electromagnetic waves in the matter identify two well separate energy scales connected to the large in-plane plasma frequency and to the soft out-of-plane Josephson plasmon. Due to such a large spectrum of excitations, there is a wide interest in the detection and manipulation of plasmons, by means of different experimental protocols, in layered systems. Indeed, the anisotropy of the superfluid response leads to two intertwined hybrid light-matter modes with mixed longitudinal and transverse character, also known as generalized plasmons. In this talk, I will discuss the relevance of such modes for ultrafast phenomena, such as pump-probe oscillations and third-harmonic generation, which have been recently observed in layered cuprates by means of non-linear terahertz spectroscopy. I will first illustrate the case of in-plane and out-of plane light polarization, for which our predictions for plasma waves are in excellent agreement with the experiments. Lastly, I will discuss the case of arbitrary light polarization, for which the inclusion of longitudinal-transverse mixing effects is crucial.