In the case of an optical probe, this interaction is formally a non-linear optical
process that is third-order in
polarization. The excitation intensity to create
the
excited state constitutes a two-field interaction and the determination of
the change in the time-dependent optical properties involves a third field
monitoring
the induced time-dependent changes in the '
linear susceptibility'.
Diffractive probes (e.g., electrons and X-rays) can also be used, in which case one
measures a
diffraction pattern as a function of time.