Interference of Electromagnetic waves in the background of the gravitational waves

Based on the relationship between proper distance and coordinate distance, the geometrical phenomenon caused by the passing gravitational waves can not be observed locally. The electromagnetic wave equations in the background gravitational waves are studied. We find that the expansion and contraction of wave lengths are always synchronous with the objects it measures. The background of the gravitational waves leads to dissipation and dispersion in the propagation of electromagnetic wave. The phase of the gravitational waves control the dissipation term and dispersion term in the telegrapher's equation. The linearly polarized laser beam propagating in the direction of the incoming gravitational waves can give a possible measurement on the local metric. In case of the pulsed beats passing by, the relaxation time is greater than the period of the gravitational waves, thus the detector may only show a signal of the modulation of the beats. Finally we proposed a non-local interference experiment to detect the high-frequency gravitational waves. It is similar to the measurement of redshift caused by gravitation. Together with the ordinary detector, it will give us further and mutually measurements of the gravitational waves.