  Given the recent direct measurement of gravitational waves (GWs) by the
LIGO-VIRGO collab- oration, the coupling between electromagnetic fields and
gravity have a special relevance since it opens new perspectives for future GW
detectors and also potentially provides information on the physics of highly
energetic GW sources. We explore such couplings using the field equations of
electrodynamics on (pseudo) Riemann manifolds and apply it to the background of
a GW, seen as a linear perturbation of Minkowski geometry. Electric and
magnetic oscillations are induced that propagate as electromagnetic waves and
contain information about the GW which generates them. The most relevant
results are the presence of longitudinal modes and dynamical polarization
patterns of electromagnetic radiation induced by GWs. These effects might be
amplified using appropriate resonators, effectively improving the signal to
noise ratio around a specific frequency. We also briefly address the generation
of charge density fluctuations induced by GWs and the implications for
astrophysics.
