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In this second article of the series, we apply our recently derived equationfor the electric field propagation along light rays [arXiv:2004.03496], validon the electromagnetic geometrical optics limit, to the special case of a toyinterferometer used to detect gravitational waves in a flat background. Such anequation shows that, assuming the detector is in the transverse-tracelessframe, which has a local shearing relative motion due to the gravitational waveperturbations, the electric field does not propagate as in an inertialreference frame in Minkowski spacetime. We present the electric field at theend of the interferometric process, for arbitrary arm configurations withrespect to the plane gravitational wave packet propagation direction. Then, fornormal incidence, we compute the interference pattern and, in addition to theusual term associated with the difference in path traveled by light in thearms, we deduce two new contributions to the final intensity, arising from: (i)the round-trip electromagnetic frequency shift and (ii) the divergence of thelight beam. Their quantitative relevance is compared to the traditionalcontribution and shown to be typically negligible due to the geometrical opticsregime of light. Moreover, a non-parallel transport of the polarization vectortakes place, in general, because of the gravitational wave, a feature whichcould generate further contributions. However, we conclude that for the normalincidence case such vector is parallel transported, preventing this kind ofcorrection.

Influence of gravitational waves upon light. Part II. Electric field propagation and interference pattern in a gravitational wave detector