The response of optical fibres to gravitational waves

Abstract

The response of optical fibre modes to plane gravitational waves (GW’s) of low frequency is computed. By solving perturbatively the Maxwell equations for step-index optical fibres in a GW background and implementing appropriate boundary conditions to describe single-mode fibres, explicit formulae for the perturbations of the phase and the polarisation of the fibre modes are obtained.

The Electromagnetic Field in Gravitational Wave Interferometers

“…Moreover, by including a dielectric refractive index, we were able to generalise our previous result [21] (which relied on the geometric optics approximation), and compare with analogous calculations for fibre optic [20]. In both cases, we find agreement of the essential results.…”

“…Hence, we find good agreement of the phase perturbations acquired by plane waves in infinitely extended dielectrics and Bessel modes (of azimuthal mode index m = 1) in step-index optical fibres. Concerning perturbations of the amplitude and polarisation, we note that such effects arise in the current setup only at next-to-leading order in the ratio ω g /ω, which was neglected in [20]. Nonetheless, perturbations of this kind were obtained for optical fibres [20,Sect.…”

“…Concerning perturbations of the amplitude and polarisation, we note that such effects arise in the current setup only at next-to-leading order in the ratio ω g /ω, which was neglected in [20]. Nonetheless, perturbations of this kind were obtained for optical fibres [20,Sect. 7], but they were found to be suppressed relatively to the phase perturbation by a factor (1 − n 2 /n 1 ) 2 which vanishes in the case considered here.…”

“…(with the phase offset χ added as needed), where we have adapted the overall sign of the phase for consistency with the sign convention used here. The multiplicative coefficient c 1 in (8.6.3) had to be determined numerically as a function of the core and cladding refractive indices n 1 , n 2 , and also of the core radius ρ, but was generally found to be close to the effective refractive index c 1 ≈ n ≈ n 1 [20,Sect. 8].…”

The electromagnetic field in gravitational wave interferometers *

“…Our analysis applies not only to vacuum but also to linear dielectrics with refractive index n 1, so that the results can be compared with those obtained for optical fibres [20], see section 8.6. Another motivation for this is to investigate whether new phenomena arise from different propagation speeds of the gravitational and electromagnetic waves.…”