Weakly gravitating isotropic waveguides

Abstract

We analyse the effect of post-Newtonian gravitational fields on propagation of light in a cylindrical waveguide in both a straight configuration and a spool configuration. We derive an equation for the dependence of the wave vector upon the vertical location of the waveguide. It is shown that the gravitational field produces a small shift in the wave vector, which we determine, while the spooling creates additional modes which could perhaps be measurable in future accurate experiments.

The Electromagnetic Field in Gravitational Wave Interferometers

“…and inserting the explicit form of a from (E.7), one arrives at where j denotes the j-imaginary part. Summarizing, given a polarization vector of the form 2) , (E. 23) the vector obtained by applying the reflection operator (E.4) is…”

The Response of Optical Fibres to Gravitational Waves

“…In this section, we write the Einstein-Maxwell equations in a 3+1 form, following Ref. [18] with c = 1. To this end, set…”

“…, the space-time split of the Faraday two-form F and the displacement bivector F given in Ref. [18] yields…”

“…The first parameter set is the same as in Refs. [18] and [19], where the influence of Earth's gravitational field and its rotation on waveguides was analysed. We have implemented our calculations in Wolfram Mathematica and computed the quantities c 1 , c 2 and β which arise in (5.110) and (5.128).…”

“…Further motivation for such investigations is provided by recent analyses of the perturbation of fibre-modes by Earth's gravitational field [18] and by Earth's rotation [19].…”