  We predict that the effective nonlinear optical susceptibility can be
tailored using the Purcell effect. While this is a general physical principle
that applies to a wide variety of nonlinearities, we specifically investigate
the Kerr nonlinearity. We show theoretically that using the Purcell effect for
frequencies close to an atomic resonance can substantially influence the
resultant Kerr nonlinearity for light of all (even highly detuned) frequencies.
For example, in realistic physical systems, enhancement of the Kerr coefficient
by one to two orders of magnitude could be achieved.
