  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.
