Search for gravitational waves through the electromagnetic Faraday rotation

A method is given which renders indirect detection of strong gravitational waves possible. This is based on the reflection (collision) of a linearly polarized electromagnetic shock wave from (with) a cross polarized impulsive and shock gravitational waves in accordance with the general theory of relativity. This highly nonlinear process induces a detectable Faraday rotation in the polarization vector of the electromagnetic field.

Figure 1

The spacetime diagram describes the collision of a plane em wave propagating in one of the incoming regions and a plane GW propagating in the other incoming region. The singular hypersurface occurs when $f+g=0$ in the interaction region.

Figure 2

The $\tan \theta$ plot when the electromagnetic shock wave encounters a gravitational plane impulsive wave with the ($\times$) polarization angle for $\alpha =45°$, for frequencies (a) $b=0.1$, (b) $b=1$, and (c) $b=100$.

Figure 3

The $\tan \theta$ plot when the electromagnetic shock wave encounters a gravitational shock wave with the ($\times$) polarization angle for $\alpha =45°$, for frequencies (a) $b=0.1$, (b) $b=1$, and (c) $b=10$.