Electromagnetic response of a Gaussian beam to high-frequency relic gravitational waves in quintessential inflationary models

Maximal signal and peak of high-frequency relic gravitational waves (GW's), recently expected by quintessential inflationary models, may be firmly localized in the GHz region, the energy density of the relic gravitons in critical units (i.e., $ h_0^2 \Omega_{GW}$) is of the order $10^{-6}$, roughly eight orders of magnitude larger than in ordinary inflationary models. This is just right best frequency band of the electromagnetic (EM) response to the high-frequency GW's in smaller EM detecting systems. We consider the EM response of a Gaussian beam passing through a static magnetic field to a high-frequency relic GW. It is found that under the synchroresonance condition, the first-order perturbative EM power fluxes will contain "left circular wave" and "right circular wave" around the symmetrical axis of the Gaussian beam, but the perturbative effects produced by the states of + polarization and $\times$ polarization of the relic GW have different properties, and the perturbations on behavior are obviously different from that of the background EM fields in the local regions. For the high-frequency relic GW with the typical parameters $ \nu_g = 10^{10}Hz$, $ h = 10^{- 30} $ in the quintessential inflationary models, the corresponding perturbative photon flux passing through the region $ 10^{- 2} m^{2} $ would be expected to be $ 10^{3}s^{-1} $. This is largest perturbative photon flux we recently analyzed and estimated using the typical laboratory parameters. In addition, we also discuss geometrical phase shift generated by the high-frequency relic GW in the Gaussian beam and estimate possible physical effects.