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Ultrafast optical excitations trigger in materials a range of dynamics. Aninteresting range of dynamics is the ones that unfold within the picosecondtimescale, corresponding to the THz frequency range. Within this shorttimescale, the material's properties, and therefore its response toelectromagnetic fields, dynamically change. For this reason, any THz radiationused to probe the material will interact with the multilayer undergoingtime-dependent modifications of the dielectric responses within a singleoptical cycle (a very similar situation arises for THz radiation produced inspintronics THz emitters). Such interaction goes beyond typical quasistaticapproaches. It is, therefore paramount to be able to describe accurately allthe interaction of THz radiation with out-of-equilibrium multilayers. Wedevelop here a theoretical framework called PTMM (Perturbative Transfer MatrixMethod) to model the production of THz accurately and its interaction withmultilayers undergoing ultrafast changes in their dielectric properties.  That analysis allows us to propose two novel ways to utilize Terahertztime-domain spectroscopy. We will first show that a simple analysis of the timeresolved Optical-Pump-Terahertz-Probe spectra can provide not only the timescale of processes that are slower than the THz pulse time-width, but it canaccurately measure the timescale of sub-picosecond and faster processes aswell. Further, we will apply our method to THz probed spintronics THz emitters,and compute the interference between the produced THz and the THz probe. Wewill show that an analysis of the delay-resolved transmission spectra allowsfor a direct measurement of the time distance between the laser excitation andthe peak of the spin current, allowing an unprecedented insight into theultrafast spin-to-charge conversion mechanism.

Perturbative Transfer Matrix Method for optical-pump-THz-probe of ultrafast dynamics