  We compute the graviton induced corrections to Maxwell's equations in the
one-loop and weak field approximations. The corrected equations are analogous
to the classical equations in anisotropic and inhomogeneous media. We analyze
in particular the corrections to the dispersion relations. When the wavelength
of the electromagnetic field is much smaller than a typical length scale of the
graviton two-point function, the speed of light depends on the direction of
propagation and on the polarisation of the radiation. In the opposite case, the
speed of light may also depend on the energy of the electromagnetic radiation.
We study in detail wave propagation in two special backgrounds, flat
Robertson-Walker and static, spherically symmetric spacetimes. In the case of a
flat Robertson-Walker gravitational background we find that the corrected
electromagnetic field equations correspond to an isotropic medium with a
time-dependent effective refractive index. For a static, spherically symmetric
background the graviton fluctuations induce a vacuum structure which causes
birefringence in the propagation of light.
