Exact solution to the homogeneous Maxwell equations in the field of a gravitational wave in linearized theory

We present the exact solution to the linearized Maxwell equations in spacet ime slightly curved by a gravitational wave. We show that in general, even dealing with a first-order theory in the strength of the gravitational fiel d, the solution cannot be written as the sum of the fiat spacetime one and a weak perturbation due to the external field. Such an impossibility arises when either the frequency of the gravitational wave is too low or too high with respect to that of the electromagnetic field. We also provide an appl ication of the solution to the case of an electromagnetic held bounced betw een two parallel conducting planes.