Time-resolved terahertz time-domain spectroscopy (THz-TDS) is an ideal tool for probing photoinduced nonequilibrium metallic and superconducting states. Here, we focus on the interpretation of the two-dimensional response function $Sigma(omega;t)$ that it measures, examining whether it provides an accurate snapshot of the instantaneous optical conductivity, $sigma(omega;t)$. For the Drude model with a time-dependent carrier density, we show that $Sigma(omega;t)$ is not simply related to $sigma(omega;t)$. The difference in the two response functions is most pronounced when the momentum relaxation rate of photocarriers is long, as would be the case in a system that becomes superconducting following pulsed photoexcitation. From the analysis of our model, we identify signatures of photoinduced superconductivity that could be seen by time-resolved THz-TDS.
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