Nonlinearities in Long-Range Compact Michelson Interferometers

TL;DR

This paper investigates the nonlinearities in a compact Michelson interferometer used for displacement sensing, identifying key sources of nonlinearity, verifying models experimentally, and assessing their impact on gravitational-wave detector readouts.

Contribution

It provides a detailed analysis of the main nonlinearities in a deep frequency modulation Michelson interferometer and evaluates their effects in gravitational-wave detection contexts.

Findings

Identified three primary sources of nonlinearity in the sensor.

Experimentally verified theoretical models of nonlinearity.

Simulated nonlinear effects show they are not dominant below 10 Hz.

Abstract

Compact Michelson interferometers are well positioned to replace existing displacement sensors in the readout of seismometers and suspension systems, such as those used in contemporary gravitational-wave detectors. Here, we continue our previous investigation of a customised compact displacement sensor built by SmarAct, which operated on the principle of deep frequency modulation. The focus of this paper is on the linearity of this device. We show the three primary sources of nonlinearity that arise in the sensor -- residual ellipticity, intrinsic distortion of the Lissajous figure, and distortion caused by exceeding the velocity limit imposed by the demodulation algorithm. We verify the theoretical models through an experimental demonstration designed to maximise the nonlinear noise to dominate regions of the readout's power spectrum. We finally simulate the effect that these nonlinearities are likely to have if implemented in the readout of the Advanced LIGO suspensions and show that the noise nonlinearities should not dominate across the key sub-\SI{10}{\Hz} frequency band.