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.

J. Chem. Phys.

Schins, J. M., Hendry, E., Bonn, M., & Muller, H. G. (2007). Retrieving the susceptibility from time-resolved terahertz experiments. J. Chem. Phys., 127(Article number: 94308), 1–10. doi:10.1063/1.2761915