Effects of gravitational waves on electromagnetic fields

We study the interaction between a plane gravitational wave and electromagnetic fields, analyzing this interaction in the proper detector frame. The gravitational field is treated as an effective electromagnetic medium, and within this framework, we demonstrate that the coupling between pre-existing electromagnetic fields and the gravitational wave generates new effective currents. This approach, an alternative to previously explored methods, has the advantage of employing Fermi coordinates, which enable direct reference to measurable quantities. To assess the impact of the effect of gravitational waves, we solve Maxwell’s equations for some standard configurations of the electric and magnetic fields.