Gravitational wave search through electromagnetic telescopes

We study the graviton-photon conversion in the magnetic fields of the Earth, the Milky Way Galaxy, and intergalactic regions. Requiring that the photon flux converted from gravitons does not exceed the observed photon flux with telescopes, we derive upper limits on the stochastic gravitational waves in frequency ranges from $10^{7}$Hz to $10^{35}$Hz. Remarkably, the upper limits on $h^2 \Omega_{{\rm GW}}$ could be less than unity in the frequency range of $10^{18}$-$10^{23}$ Hz in a specific case. The detection of gravitational waves using telescopes would open up a new avenue for high frequency gravitational wave observations.