Retrieving the susceptibility from time-resolved terahertz experiments

We present an analytical expression for the observed signal in time- and phase-resolved pump-probe studies, with particular emphasis on terahertz time-domain spectroscopy. Maxwell's equations are solved for the response of damped, harmonic oscillators to a driving probe field in the perturbative regime. Our analytical expressions agree with the one previously reported in the literature [Nemec et al., J. Chem. Phys. 122, 104503 (2005)] in the Drude limit; however, they differ in the case of a vibrational resonance.