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We investigate the resonant interaction to the weak gravitational waves in acoupling electromagnetic system, which consists of a Gaussian beam with thedouble polarized transverse electric modes, a static magnetic field and thefractal membranes. We find that under the syncroresonance condition ahigh-frequency GW (HFGW) of h=10^-30,v_g=3GHz may produce the perturbativephoton flux (PPF) of 2.15*10/s in a surface of 0.01m^2. The PPF can be pumpedout from the background photon fluxes and one might obtain the amplified signalphoton flux of 2.15*10^4s^-1 by cascade fractal membranes. It appears to beworthwhile to study this effect for the detection of the high-frequency relicGWs in quintessential inflationary models and the HFGWs expected by possiblelaboratory schemes.Comment: 10page

Resonant Interaction Between a Weak Gravitational Wave and a Microwave Beam in the Double Polarized States Through a Static Magnetic Field