Coupling Light Waves to Gravitational Waves

We demonstrate analytically that gravitational waves, upon interacting with co-propagating electromagnetic radiation in a plasma, induce distinctive sidebands on the modulated light, thereby providing a detectable signature of their presence. Employing a fully covariant coupled-wave framework, we envision gravitational waves as phase-insensitive ``luminal moving gratings'' and derive explicit phase-matching conditions that articulate such an interaction whilst conserving both energy and momentum. Beyond preserving the directional signature of gravitational waves, the coupling mechanism imposes no coherence requirements on the photon-by-graviton scattering, hence enabling possibilities for exploiting cosmic microwave background radiation. Although detection at low frequencies is constrained by the requirement of long interaction lengths, advances in laser technology are poised to enable high-frequency gravitational wave detection, potentially unveiling insights into the primordial spacetime ripples that have been traversing the cosmos since the inflationary epoch.