TY - JOUR

T1 - Non-geometric tilt-to-length coupling in precision interferometry: mechanisms and analytical descriptions

AU - Hartig, Marie Sophie

AU - Schuster, Sönke

AU - Heinzel, Gerhard

AU - Wanner, Gudrun

N1 - Funding Information: This work was made possible by funds of both the Deutsche Forschungsgemeinschaft (DFG) and the German Space Agency, DLR. We gratefully acknowledge the Deutsche Forschungsgemeinschaft (DFG) for funding the Sonderforschungsbereich (SFB 1128: geo-Q) ‘Relativistic Geodesy and Gravimetry with Quantum Sensors’, Project A05 and all work contributions to this paper made by Sönke Schuster. Furthermore, we acknowledge DFG for funding the Clusters of Excellence PhoenixD (EXC 2122, Project ID 390833453) and QuantumFrontiers (EXC 2123, Project ID 390837967). Likewise, we gratefully acknowledge the German Space Agency, DLR and support by the Federal Ministry for Economic Affairs and Energy based on a resolution of the German Bundestag (FKZ 50OQ1801). Finally, we would like to acknowledge the Max Planck Society (MPG) for supporting the framework LEGACY on low-frequency gravitational wave astronomy, a cooperation between the Chinese Academy of Sciences (CAS) and the MPG (M.IF.A.QOP18098).

PY - 2023/5

Y1 - 2023/5

N2 - This paper is the second in a set of two investigating tilt-to-length (TTL) coupling. TTL describes the cross-coupling of angular or translational jitter into an interferometric phase signal and is an important noise source in precision interferometers, including space gravitational wave detectors like LISA. We discussed in Hartig et al (2022 J. Opt. 24 065601) the TTL coupling effects originating from optical path length changes, i.e. geometric TTL coupling. Within this work, we focus on the wavefront and detector geometry dependent TTL coupling, called non-geometric TTL coupling, in the case of two interfering fundamental Gaussian beams. We characterise the coupling originating from the properties of the interfering beams, i.e. their absolute and relative angle at the detector, their relative offset and the individual beam parameters. Furthermore, we discuss the dependency of the TTL coupling on the geometry of the detecting photodiode. Wherever possible, we provide analytical expressions for the expected TTL coupling effects. We investigate the non-geometric coupling effects originating from beam walk due to the angular or translational jitter of a mirror or a receiving system. These effects are directly compared with the corresponding detected optical path length changes in Hartig et al (2022 J. Opt. 24 065601). Both together provide the total interferometric readout. We discuss in which cases the geometric and non-geometric TTL effects cancel one-another. Additionally, we list linear TTL contributions that can be used to counteract other TTL effects. Altogether, our results provide key knowledge to minimise the total TTL coupling noise in experiments by design or realignment.

AB - This paper is the second in a set of two investigating tilt-to-length (TTL) coupling. TTL describes the cross-coupling of angular or translational jitter into an interferometric phase signal and is an important noise source in precision interferometers, including space gravitational wave detectors like LISA. We discussed in Hartig et al (2022 J. Opt. 24 065601) the TTL coupling effects originating from optical path length changes, i.e. geometric TTL coupling. Within this work, we focus on the wavefront and detector geometry dependent TTL coupling, called non-geometric TTL coupling, in the case of two interfering fundamental Gaussian beams. We characterise the coupling originating from the properties of the interfering beams, i.e. their absolute and relative angle at the detector, their relative offset and the individual beam parameters. Furthermore, we discuss the dependency of the TTL coupling on the geometry of the detecting photodiode. Wherever possible, we provide analytical expressions for the expected TTL coupling effects. We investigate the non-geometric coupling effects originating from beam walk due to the angular or translational jitter of a mirror or a receiving system. These effects are directly compared with the corresponding detected optical path length changes in Hartig et al (2022 J. Opt. 24 065601). Both together provide the total interferometric readout. We discuss in which cases the geometric and non-geometric TTL effects cancel one-another. Additionally, we list linear TTL contributions that can be used to counteract other TTL effects. Altogether, our results provide key knowledge to minimise the total TTL coupling noise in experiments by design or realignment.

KW - interferometric noise sources

KW - laser interferometry

KW - LISA

KW - optical cross-talk

KW - space interferometry

KW - tilt-to-length coupling

KW - wavefront properties

UR - http://www.scopus.com/inward/record.url?scp=85152484381&partnerID=8YFLogxK

U2 - 10.1088/2040-8986/acc3ac

DO - 10.1088/2040-8986/acc3ac

M3 - Article

AN - SCOPUS:85152484381

VL - 25

JO - Journal of Optics (United Kingdom)

JF - Journal of Optics (United Kingdom)

SN - 2040-8978

IS - 5

M1 - 055601

ER -