  Some of the basic notions of nonlinear optics are summarized and then applied
to the case of the Dirac vacuum, as described by the Heisenberg-Euler effective
one-loop Lagrangian. The theoretical and experimental basis for the appearance
of nonlinear optical phenomena, such as the Kerr effect, Cotton-Mouton effect,
and four-wave mixing are discussed. Further effects due to more exotic
assumptions on the structure of spacetime, such as gravitational curvature and
the topology of the Casimir vacuum are also presented.
