  I find nearly plane-wave solutions for the Gauss-Ampere law for the 4-vector
potential, subject to the Lorenz gauge condition, in the spacetime of a plane
gravitational plane wave. I assume that the gravitational wave is weak, in the
sense that the dimensionless strain amplitude h is much less than 1. I find a
solution for the homogeneous scalar wave equation in this spacetime, and then
find a 4-vector potential that solves the Gauss-Ampere law and Lorenz gauge
condition in the absence of sources. The solutions are plane waves in Minkowski
spacetime, plus additional scattered waves of order h. The problem is analogous
to diffraction from a transmission grating, or Brillouin scattering from sound
waves in matter. The corrections solve the inhomogeneous wave equation in
Minkowski spacetime, with a "distributed source" of order h comprised of terms
arising from the non-Minkowski metric and the zero-order solution. The scalar
wave solution requires two scattered waves, which can be combined to form a
phase correction h phi that varies at the gravitational-wave frequency. This
phase correction yields the same time delay and deflection at the observer as
for propagation along null geodesics, in the ray approximation. The
electromagnetic-wave solution requires four scattered waves. Two correspond to
the phase correction h phi found for the scalar field. The other two scattered
waves introduce amplitude and polarization changes of order h to the
electromagnetic wave. The time delay and deflection match those for the scalar
waves. The solution predicts variations of the intensity of the electromagnetic
wave of first order in h, at the wavenumber of the gravitational wave. These
arise from interference of the first-order scattered waves and the zero-order
solution. I briefly discuss possible observations of this effect.
