The finite mass beamsplitter in high power interferometers

TL;DR

This paper analyzes the effects of radiation-pressure fluctuations on the beam splitter in high-power interferometers, revealing how input-output relations are affected and how this impacts noise and sensitivity in gravitational-wave detectors.

Contribution

It provides a comprehensive transfer function for the beam splitter including radiation-pressure effects and applies it to realistic interferometer configurations.

Findings

Bright-port dark-port coupling affects noise contributions.

Technical laser noise impacts low-frequency sensitivity without arm cavities.

The influence of radiation-pressure fluctuations is quantitatively characterized.

Abstract

The beamplitter in high-power interferometers is subject to significant radiation-pressure fluctuations. As a consequence, the phase relations which appear in the beamsplitter coupling equations oscillate and phase modulation fields are generated which add to the reflected fields. In this paper, the transfer function of the various input fields impinging on the beamsplitter from all four ports onto the output field is presented including radiation-pressure effects. We apply the general solution of the coupling equations to evaluate the input-output relations of the dual-recycled laser-interferometer topology of the gravitational-wave detector GEO600 and the power-recycling, signal-extraction topology of advanced LIGO. We show that the input-output relation exhibits a bright-port dark-port coupling. This mechanism is responsible for bright-port contributions to the noise density of the output field and technical laser noise is expected to decrease the interferometer's sensitivity at low frequencies. It is shown quantitatively that the issue of technical laser noise is unimportant in this context if the interferometer contains arm cavities.