Detecting Very-High-Frequency Relic Gravitational Waves by a Waveguide

The polarization vector (PV) of an electromagnetic wave (EW) will experience a rotation in a region of spacetime perturbed by gravitational waves (GWs). Based on this consideration, Cruise's group has built an annular waveguide to detect GWs. We give detailed calculations of the rotations of polarization vector of an EW caused by incident GWs from various directions and in various polarization states, and then analyze the accumulative effects on the polarization vector when the EW passes n cycles along the annular waveguide. We reexamine the feasibility and limitation of this method to detect GWs of high frequency around 100 MHz, in particular the relic gravitational waves (RGWs). By comparing the spectrum of RGWs in the accelerating universe with the detector sensitivity of the current waveguide, it is found that the amplitude of the RGWs is too low to be detected by the waveguide detectors currently operating. Possible ways of improvements on detection are suggested.