Thermal noise of beam splitters in laser gravitational wave detectors

TL;DR

This paper calculates the thermal noise contribution of beam splitters in gravitational wave detectors using a first-principles method, showing significant impact on GEO600 and minor effect on aLIGO's sensitivity.

Contribution

It introduces a first-principles method to evaluate beam splitter thermal noise, including substrate and coating effects, for the first time in gravitational wave detectors.

Findings

Beam splitter thermal noise significantly affects GEO600 sensitivity.

The contribution of beam splitters to aLIGO noise is negligible (~0.3%).

Beam splitter noise limits GEO-HF design sensitivity by about 50%.

Abstract

We present the calculation of thermal noise in interferometric gravitational-wave detectors due to the thermal fluctuations of the beam splitter (BS). This work makes use of a recently developed method of the analysis of thermal noise in mirrors from first principles, based on the fluctuation dissipation theorem. The evaluation of BS thermal noise is carried out for the two different grav- itational wave observatories, GEO600 and the Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO). The analysis evaluates thermal noise from both the substrate and the optical reflective and antireflective stacks located on the BS surface. We demonstrate that the fluctuations of both reflecting and anti-reflecting surfaces significantly contribute to the total thermal noise of the BS. The oscillating intensity pattern couples small-scale distortions of the surface to the overall phase readout, and therefore increases the overall thermal noise. In the case of aLIGO, the BS contribution is with $0.3\%$ negligibly small. At a frequency of 500Hz, the BS causes about $10\%$ of GEO600's sensitivity limit. BS noise impairs the feasible sensitivity of the GEO-HF design proposal by about $50\%$.