  Ultra-fast and multi-dimensional spectroscopy gives a powerful looking glass
into the dynamics of molecular systems. In particular two-dimensional
electronic spectroscopy (2DES) provides a probe of coherence and the flow of
energy within quantum systems which is not possible with more conventional
techniques. While heterodyne-detected (HD) 2DES is increasingly common, more
recently fluorescence-detected (FD) 2DES offers new opportunities, including
single-molecule experiments. However in both techniques it can be difficult to
unambiguously identify the pathways which dominate the signal. Therefore the
use of numerically modelling of 2DES is vitally important, which in turn
requires approximating the pulsing scheme to some degree. Here we employ
non-pertubative time evolution to investigate the effects of finite pulse width
and amplitude on 2DES signals. In doing so we identify key differences in the
response of HD and FD detection schemes, as well as the regions of parameter
space where the signal is obscured by unwanted artefacts in either technique.
Mapping out parameter space in this way provides a guide to choosing
experimental conditions and also shows in which limits the usual theoretical
approximations work well and which limits more sophisticated approaches are
required.
