Polarization Properties of the Electromagnetic Response to High-frequency Gravitational Wave

Electromagnetic waves (EMWs) can be generated by gravitational waves (GWs) within a magnetic field via the Gertsenshtein effect. The conversion probability between GWs and EMWs can be enhanced by inhomogeneities in the electron density and magnetic field within the magnetized plasma of both the Milky Way (MW) and the intergalactic medium in the expanding Universe. Polarized GWs can induce polarized EMWs, and the polarization properties of these EMWs can be altered by Faraday rotation as they propagate through magnetized plasma. Additionally, the polarization intensity of the EMWs may be weakened due to depolarization effects. In this study, we calculate the enhanced GW-EMW conversion in inhomogeneous magnetized plasma during the propagation of GWs through the Universe and our galaxy. We analyze the polarization states of the EMWs generated by polarized GWs and discuss the depolarization effects induced by the medium's irregularities, as well as the differential Faraday rotation occurring in multilayer polarized radiation. Our work provides alternative methods for detecting GWs and exploring their polarization states, and potentially constraining the parameters of the possible GW sources, especially the primordial black hole, contributing to the advancement of very-high-frequency GW detection and research.