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

We investigate the resonant interaction to the weak gravitational waves in a coupling electromagnetic system, which consists of a Gaussian beam with the double polarized transverse electric modes, a static magnetic field and the fractal membranes. We find that under the syncroresonance condition a high-frequency GW (HFGW) of h=10^-30,v_g=3GHz may produce the perturbative photon flux (PPF) of 2.15*10/s in a surface of 0.01m^2. The PPF can be pumped out from the background photon fluxes and one might obtain the amplified signal photon flux of 2.15*10^4s^-1 by cascade fractal membranes. It appears to be worthwhile to study this effect for the detection of the high-frequency relic GWs in quintessential inflationary models and the HFGWs expected by possible laboratory schemes.