Motion of photons in a gravitational wave background**Supported by National Natural Science Foundation of China (11275207, 11375203, 11690022, 11675182) and Strategic Priority Research Program of the Chinese Academy of Sciences “Multi-waveband Gravitational Wave Universe” (XDB23040000)

Abstract

Photon motion in a Michelson interferometer is re-analyzed in terms of both geometrical optics and wave optics. The classical paths of the photons in the background of a gravitational wave are derived from the Fermat principle, which is the same as the null geodesics in general relativity. The deformed Maxwell equations and the wave equations of electric fields in the background of a gravitational wave are presented in a flat-space approximation. Both methods show that even the envelope of the response of an interferometer depends on the frequency of a gravitational wave, but it is almost independent of the frequency of the mirror’s vibrations.