  Gravitational waves from astrophysical sources can interact with background
electromagnetic fields, giving rise to distinctive and potentially detectable
electromagnetic signatures. In this paper, we study such interactions for
far-field gravitational radiation using the 1+3 approach to relativity.
Linearised equations for the electromagnetic field on perturbed Minkowski space
are derived and solved analytically. The inverse Gertsenshtein conversion of
gravitational waves in a static electromagnetic field is rederived, and the
resultant electromagnetic radiation is shown to be significant for highly
magnetised pulsars in compact binary systems. We also obtain a variety of
nonlinear interference effects for interacting gravitational and
electromagnetic waves, although wave-wave resonances previously described in
the literature are absent when the electric-magnetic self-interaction is taken
into account. The fluctuation and amplification of electromagnetic energy flux
as the gravitational wave strength increases towards the
gravitational-electromagnetic frequency ratio is a possible signature of
gravitational radiation from extended astrophysical sources.
