Motion of photons in a background of gravitational wave

TL;DR

This paper re-analyzes photon motion in a gravitational wave background using geometrical and wave optics, showing the interferometer's response depends on gravitational wave frequency but not significantly on mirror vibrations.

Contribution

It derives photon paths from Fermat's principle and presents wave equations in a gravitational wave background, highlighting differences from mirror vibrations.

Findings

Interferometer response depends on gravitational wave frequency.

Photon paths follow null geodesics in general relativity.

Mirror vibrations do not mimic gravitational waves effectively.

Abstract

The photon motion in a Michelson interferometer is re-analyzed in both geometrical optics and wave optics. The classical paths of the photons in the background of gravitational wave are derived from 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 gravitational wave are presented in flat-space approximation. Both methods show that the response of an interferometer depends on the frequency of a gravitational wave, however it is almost independent of the frequency of the mirror's vibrations. It implies that the vibrating mirror cannot mimic a gravitational wave very well.