  Measuring an electric field waveform beyond radio frequencies is often
accomplished via a second-order nonlinear interaction with a laser pulse
shorter than half of the field's oscillation period. However, synthesizing such
a gate pulse is extremely challenging when sampling mid- (MIR) and near- (NIR)
infrared transients. Here, we demonstrate an alternative approach: a
third-order nonlinear interaction with a relatively long multi-cycle pulse
directly retrieves an electric-field transient whose central frequency is 156
THz. A theoretical model, exploring the different nonlinear frequency mixing
processes, accurately reproduces our results. Furthermore, we demonstrate a
measurement of the real part of a sample's dielectric function, information
that is challenging to retrieve in time-resolved spectroscopy and is therefore
often overlooked. The new method paves the way towards experimentally simple
MIR-to-NIR time-resolved spectroscopy that simultaneously extracts the spectral
amplitude and phase information, an important extension of optical pump-probe
spectroscopy of, e.g., molecular vibrations and fundamental excitations in
condensed-matter physics.
