Approximations used in the analysis of signals in pump-probe spectroscopy

In pump-probe spectroscopy, one often needs to analyse the transmission or reflection of electromagnetic waves through optically pumped media. Here, it is common practice to approximate the analysis in order to extract non-equilibrium values for the optical constants of the media. Concentrating on optical pump-THz probe spectroscopy, and using the transfer matrix approach, we present a general method for evaluating the applicability of the most common approximations. Somewhat surprisingly, we find that these approximations are truly valid only in extreme cases where the optical thickness of the sample is several orders of magnitude smaller or larger than the probe wavelength.