  The semi-classical theory of radiation-matter coupling misses local-field
effects that may alter the pulse time-ordering and cascading that leads to the
generation of new signals. These are then introduced macroscopically by solving
Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We
show that both effects emerge naturally by including coupling to quantum modes
of the radiation field in the vacuum state to second order. This approach is
systematic and suggests a more general class of corrections that only arise in
a QED framework. In the semi-classical theory, which only includes classical
field modes, the susceptibility of a collection of $N$ non-interacting
molecules is additive and scales as $N$. Second-order coupling to a vacuum mode
generates an effective retarded interaction that leads to cascading and local
field effects both of which scale as $N^2$.
