a, Fit of a Lorentzian oscillator to the 1,139 cm−1 absorption of (low-concentration) DMSO 2 . Black line, intensity transmission through pure, molecular DMSO 2 , determined by referencing the transmission spectrum of a 1 mg ml−1 solution to that of water, measured via FTIR, and normalizing to a 1-µm path. Green line, least-squares fit (1,080–1,190 cm−1) of a Lorentzian oscillator to the 1,139 cm−1 absorption, yielding a full width at half depth of 13.47 cm−1 and an absorption coefficient α = 11.96 cm−1. The numerical example shows the instantaneous and resonant parts of the electric field as described by equations (1) to (4) in Supplementary Information section II. The initial pulse is a Gaussian pulse with an intensity envelope (full width at half maximum) of 190 fs. The Lorentzian absorption band has a peak of α 2 z with α 2 = 0.0024 cm−1, corresponding to a 200 ng ml−1 solution of DMSO 2 in water, and a width δυ = 13.47 cm−1. These values were obtained from fitting a Lorentzian absorber to the 1,139 cm−1 band of the transmission spectrum of a 1 mg ml−1 solution obtained with FTIR and linear extrapolation to a concentration 5,000 times lower. b, Time-domain representation of the normalized envelope functions of the electric fields described (see key). A value of t B = 1.5 ps is chosen. The green vertical bars indicate the boundaries of the band-pass-filtered resonant response shown in green: 1.5 ps and 4 ps. c, Magnitudes of the Fourier transforms of the envelopes shown in a, normalized to C. At the absorption maximum, the discrepancy between the resonant response as in Supplementary Information section 2 and its approximation as in Supplementary Information section 3 is 1%, justifying this convenient approximation. The error introduced by band-pass filtering the resonant response between 1.5 ps and 4 ps compared to the high-pass time-filtered signal is 4%. Source Data