  We treat a model based upon nonlinear optics for the semiclassical
gravitational effects of quantum fields upon light propagation. Our model uses
a nonlinear material with a nonzero third order polarizability. Here a probe
light pulse satisfies a wave equation containing the expectation value of the
squared electric field. This expectation value depends upon the presence of
lower frequency quanta, the background field, and modifies the effective index
of refraction, and hence the speed of the probe pulse. If the mean squared
electric field is positive, then the pulse is slowed, which is analogous to the
gravitational effects of ordinary matter. Such matter satisfies the null energy
condition and produce gravitational lensing and time delay. If the mean squared
field is negative, then the pulse has a higher speed than in the absence of the
background field. This is analogous to the gravitational effects of exotic
matter, such as stress tensor expectation values with locally negative energy
densities, which lead to repulsive gravitational effects, such as defocussing
and time advance. We give some estimates of the magnitude of the effects in our
model, and find that they may be large enough to be observable. We also briefly
discuss the possibility that the mean squared electric field could be produced
by the Casimir vacuum near a reflecting boundary.
