Linear spectroscopy is used to learn about transitions from the ground states of systems. Nonlinear spectroscopies, such as transient absorption (TA) spectroscopy, first excite the system and then probe after some time delay, giving dynamical information about excited states and spectral information about their excitations. If the pump pulses are strong enough, then some molecules are excited multiple times, and the signal has contributions from singly excited molecules mixed with those from multiply excited molecules. Such mixed signals are hard to interpret, so TA spectra are often acquired with a sufficiently weak pump pulse that the higher-order contributions can be neglected. But the signal-to-noise ratio becomes worse when the pump is weak.
I will describe a general method to systematically separate spectroscopic orders of response by acquiring spectra with multiple pump-pulse energies, with applications in many forms of spectroscopy. This method allows acquisitions with increased pump intensities that improve signal-to-noise while systematically removing contaminations from higher-order processes. High-order responses have not previously been separable, and I will give examples of the spectral and dynamical information that they can contain, from exciton-exciton-annihilation kinetics to revealing masked signals in congested spectra. I will show experimental demonstrations from TA and two-dimensional electronic spectroscopy. I will show how to choose the pulse intensities to give the best extractions of response orders, given the noise present.