The Response of Laser Interferometric Gravitational Wave Detectors Beyond the Eikonal Equation

TL;DR

This paper calculates the response of laser interferometric gravitational wave detectors with higher accuracy than the eikonal approximation, including amplitude and polarisation effects, providing explicit formulas for different readout schemes.

Contribution

It introduces a method to compute interferometer responses beyond the eikonal approximation, accounting for amplitude and polarisation modulations with explicit formulas.

Findings

Derived explicit formulas for interferometer signals including amplitude and polarisation effects.

Showed that the signals are insensitive to polarisation perturbations.

Extended the theoretical understanding of detector responses beyond the eikonal approximation.

Abstract

The response of Michelson interferometers to weak plane gravitational waves is computed at one order of accuracy beyond the eikonal equation. The modulation of the electromagnetic field amplitude and polarisation are taken into account by solving the transport equations of geometrical optics with boundary conditions adapted to laser interferometry. Considering both DC and balanced homodyne readout schemes, explicit formulae for the interferometer output signals are derived. These signals comprise perturbations of the optical path length, frequency and amplitude, and are shown to be insensitive to polarisation perturbations.