  There exist corresponding metric perturbations of the relic gravitational
waves (GWs) in the region of approximately h~10^(-30)-10^(-32)in the GHz band.
A detector for these GWs is described in which we measure the perturbative
photon flux (PPF) or signal generated by such high-frequency relic GWs (HFRGWs)
via a coupling system of fractal membranes and a Gaussian beam (GB) passing
through a static magnetic field. It is found that under the synchro-resonance
condition in which the frequency of the GB is set equal to the frequency of the
expected HFRGWs (h~2.00*10^(-31), v_g=10^10Hz in the quintessential
inflationary models (QIM) and h~6.32*10^(-31), v_g=10^10Hz in the pre-big bang
scenario (PBBS) may produce the PPFs of ~4.04*10^2/s and ~1.27*10^3/s in a
surface of 100cm^2 area at the waist of the GB, respectively. The relatively
weak first-order PPF, directed at right angles to the expected HFRGWs, is
reflected by fractal membrane and the resulting reflected PPF (signal) exhibits
a very small decay in transit to the detector (tunable microwave receiver)
compared with the much stronger background photon flux, which allows for
detection of the reflected PPF with signal to background noise ratios greater
than one at the distance of the detector. We also discuss the selection
capability of system and directional sensitivity for the resonance components
from the stochastic relic GW background. The resolution of tiny difference
between the PPFs generated by the relic GWs in the QIM and in the PBBS may be
established and will be of cosmological significance. PACS numbers: 04.30.Nk,
04.30.Db, and 98.80.Cq.
