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We have recently derived a manifestly covariant evolution law, under thegeometrical optics approximation of the vacuum Maxwell's equations, for theelectric field along null geodesics in a general spacetime, relative to anarbitrary set of instantaneous observers [arXiv:2004.03496]. As one of itsapplications, we derive here the final detected intensity signal arising from aprototypical laser interferometric gravitational wave (GW) Michelson-Morleydetector, comoving with transverse traceless (TT) observers, valid for bothlong and short GW wavelengths. One of our main results is the presentation ofthe integrated null geodesic parametric equations exchanged between two TTobservers in terms of explicitly observable quantities and the profile of theplane GW packet. This allows us to revisit the derivation of the consequentialradar distance and Doppler shift, taking the opportunity to discuss somerelated subtle conceptual issues and how they might affect the interferometricprocess. Another achievement is the calculation of the electric field in eacharm up to the detection event, for any relative orientations of the arms andthe GW direction. The main quantitative result is the new expression for thefinal interference pattern, for normal GW incidence, which turns out to havethree contributions: (i) the well-known traditional one due to the differencein optical paths, and two new ones due to (ii) the Doppler effect, and (iii)the divergence of the laser beams. The quantitative relevance of the last twocontributions is compared to the traditional one and shown to be negligiblewithin the geometrical optics regime of light. Although in general furthercontributions from the non-parallel transport of the polarization vector areexpected, again in the case of GW normal incidence, such a vector is indeedparallel transported, and those contributions are absent.

Influence of gravitational waves upon light in the Minkowski background: from null geodesics to interferometry