Signatures of high-frequency gravitational waves in electromagnetic cavities

Similar to axions, gravitational waves (GWs) can induce oscillating electromagnetic fields inside electromagnetic cavities. We explore their experimental sensitivity to monochromatic and non-monochromatic GW signals, using the total deposited energy as a primary measure. Focusing on cylindrical and spherical cavities, we present the coupling coefficients of GWs to the dominant electromagnetic resonances in transverse-traceless gauge, which is most appropriate in this regime. By considering the superposition of degenerate modes, we further examine their angular sensitivity. In addition, we calculate the response of a spherical cavity to non-monochromatic GWs emitted by primordial black hole mergers. We find that, for transient signals, a high quality factor with Q ≳ 10$^5$ does not necessarily enhance experimental sensitivity. In fact, even in the most optimistic scenario, only mergers within the solar system yield an observable energy deposit in the cavity.