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Maximal signal and peak of high-frequency relic gravitational waves (GW's),recently expected by quintessential inflationary models, may be firmlylocalized in the GHz region, the energy density of the relic gravitons incritical units (i.e., $ h_0^2 \Omega_{GW}$) is of the order $10^{-6}$, roughlyeight orders of magnitude larger than in ordinary inflationary models. This isjust right best frequency band of the electromagnetic (EM) response to thehigh-frequency GW's in smaller EM detecting systems. We consider the EMresponse of a Gaussian beam passing through a static magnetic field to ahigh-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, butthe perturbative effects produced by the states of + polarization and $\times$polarization of the relic GW have different properties, and the perturbationson behavior are obviously different from that of the background EM fields inthe local regions. For the high-frequency relic GW with the typical parameters$ \nu_g = 10^{10}Hz$, $ h = 10^{- 30} $ in the quintessential inflationarymodels, the corresponding perturbative photon flux passing through the region $10^{- 2} m^{2} $ would be expected to be $ 10^{3}s^{-1} $. This is largestperturbative photon flux we recently analyzed and estimated using the typicallaboratory parameters. In addition, we also discuss geometrical phase shiftgenerated by the high-frequency relic GW in the Gaussian beam and estimatepossible physical effects.Comment: 36 pages, 5 figure

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