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 of a weak gravitational wave with a microwave beam in a coupling electromagnetic system, which consists of a Gaussian beam with double polarized transverse electric modes, a static magnetic field and fractal membranes. We find that under the synchroresonance condition, a high-frequency gravitational wave in amplitude 10^-30 and frequency 3 GHz may produce the perturbative photon flux of 2.15 × 10s^-1 in a surface of 10^-2 m². The perturbative photon flux can be pumped out from the background photon fluxes and one may obtain the amplified signal photon flux of 2.15 × 10⁴ s^-1 by cascade fractal membranes. It is worth studying this effect for the detection of high-frequency relic gravitational waves in quintessential inflationary models and the high-frequency gravitational waves expected by possible laboratory schemes.