  Nonlinear optical signals in the condensed phase are often accompanied by
sequences of lower-order processes, known as cascades, which share the same
phase matching and power dependence on the incoming fields and are thus hard to
distinguish. The suppression of cascading in order to reveal the desired
nonlinear signal has been a major challenge in multidimensional Raman
spectroscopy, i.e., the $\chi^{(5)}$ signal being masked by cascading signals
given by a product of two $\chi^{(3)}$ processes. Since cascading originates
from the exchange of a virtual photon between molecules, it can be manipulated
by performing the experiment in an optical microcavity. Using a quantum
electrodynamical (QED) treatment we demonstrate that the $\chi^{(3)}$ cascading
contributions can be greatly suppressed. By optimizing the cavity size and the
incoming pulse directions, we show that up to $\sim$99.5\% suppression of the
cascading signal is possible.
