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REVIEW 2 major objections 5 minor 60 references

Scattered-light noise in gravitational-wave detectors is governed by full optomechanical transfer factors, not static gains.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-01 12:49 UTC pith:3U7UAM4E

load-bearing objection The backscattering transfer factor is computed for the wrong source node, and the ET-LF enhancement claim is not supported; the diffraction part is a solid contribution worth keeping. the 2 major comments →

arxiv 2607.19299 v1 pith:3U7UAM4E submitted 2026-07-21 gr-qc astro-ph.IMphysics.ins-det

Optomechanical transfer factors for scattered light noise estimations in the beamtubes of ground-based gravitational wave detectors

M. Andr\'es-Carcasona This is my paper
classification gr-qc astro-ph.IMphysics.ins-det
keywords scattered light noisegravitational-wave detectorsoptomechanical transfer functionstwo-photon formalismradiation pressuresignal extraction cavitybackscatteringdiffraction noise
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tries to establish that scattered-light noise in ground-based gravitational-wave detectors cannot be captured by the static scalar couplings used in previous beamtube noise budgets. It derives frequency-dependent optomechanical transfer factors, in the two-photon quadrature formalism, that map field perturbations at the two arm-cavity nodes into the final strain readout, consistently including radiation-pressure back-action, signal-extraction dynamics, microscopic detunings, and the homodyne readout angle. Applied to representative current and next-generation interferometer parameters, the full factors agree with legacy estimates only in phase-dominated regimes and deviate substantially at low frequencies; for the low-frequency next-generation configuration studied, the revised backscattering noise is about an order of magnitude larger below a few hertz. The paper thereby provides a configuration-dependent framework for estimating scattered-light noise in present and future gravitational-wave detectors.

Core claim

The central claim is that the readout response to a scattered-light perturbation is a full quadrature transfer vector, not a scalar gain. A perturbation outgoing from the input test mass high-reflectivity side and one incoming to the end test mass high-reflectivity side each propagate through the coupled signal-extraction and arm cavities, including the nondiagonal reflection operator produced by radiation pressure on the test mass. The resulting transfer factors, given as Eqs. (13) and (14), show that an amplitude-quadrature perturbation can be converted into phase-readout noise through radiation pressure, with a characteristic low-frequency enhancement, and that a detuned signal-extraction

What carries the argument

The central object is the three-mirror coupled cavity formed by the signal-extraction mirror, input test mass, and end test mass, treated with the two-photon quadrature formalism. The load-bearing element inside it is the effective end-mirror reflectivity matrix, whose off-diagonal term encodes radiation-pressure coupling between the amplitude and phase quadratures. Two transfer-factor vectors are obtained by closing the arm and signal-extraction loops in the node-matrix formulation and projecting the outgoing field onto the readout quadrature selected by the homodyne angle.

Load-bearing premise

The load-bearing premise is that the differential-arm response of a dual-recycled Michelson interferometer is faithfully captured by the three-mirror coupled cavity of signal-extraction mirror, input test mass, and end test mass; if full power-recycling or recycled-Michelson dynamics, or higher-order spatial modes, contribute significantly at the scattered-light frequencies, the derived transfer factors and the low-frequency conclusions would change.

What would settle it

Compute the readout response of a full dual-recycled Michelson interferometer, including the power-recycling mirror and beam splitter, to a low-frequency amplitude-quadrature perturbation injected at the input test mass high-reflectivity node, and compare it with the transfer factors in Eqs. (13) and (14). If the full simulation differs by more than the mode-mixing bound derived in the paper, the three-mirror reduction is insufficient.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Legacy static-gain formulas remain valid only when the scattered perturbation is nearly purely phase-like and radiation pressure is negligible; otherwise the noise can be miscalculated by orders of magnitude at low frequencies.
  • In tuned detectors, the amplitude-quadrature part of diffraction noise couples to strain through radiation pressure with a roughly inverse-square frequency scaling, so a real component of the diffraction coupling can dominate at low frequency.
  • A detuned signal-extraction cavity, as in a low-frequency next-generation design, can make backscattering noise about an order of magnitude larger below the relevant optomechanical frequency.
  • Destructive interference between the direct phase coupling and the radiation-pressure-induced phase shift creates frequency-dependent blind spots where the full model predicts less noise than the legacy one.
  • For small-amplitude backscatterer motion, the cosine quadrature carries negligible AC content, so the constant radiation-pressure gain used in legacy models overestimates the noise; phase wrapping at larger amplitudes restores that gain.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same transfer-factor construction could be applied to scattered-light sources outside the arm cavities, such as input optics or the beam splitter, by recomputing the source nodes in the same loop-closing formalism.
  • Because the transfer factors depend on the operating point, scattered-light requirements for next-generation detectors should be evaluated jointly with the intended tuning state, not fixed to a single baseline configuration.
  • The paper's linearity criterion for diffraction could be used in practice to decide when nonlinear upconversion must be included in time-domain simulations for each baffle, potentially reducing computational cost.
  • The dependence on homodyne angle suggests an active mitigation strategy: choosing a readout quadrature that places a low-frequency scattered-light peak in a radiation-pressure blind spot, though practical optical design constraints may limit this freedom.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper derives frequency-dependent optomechanical transfer factors that map small scattered-light field perturbations at the HR surfaces of the ITM and ETM into the GW strain readout of a dual-recycled Fabry-Perot Michelson interferometer, modeled as a three-mirror coupled cavity. It presents full node-matrix results (Eqs. (13)-(14)), approximate closed-form expressions, and uses them to compute diffraction and backscattering strain noise PSDs. For representative LIGO, Cosmic Explorer, and ET-LF parameters, the full factors reproduce legacy static-gain estimates in phase-dominated regimes but deviate substantially at low frequencies and for detuned signal extraction; the headline result is that ET-LF backscattering noise is an order of magnitude larger below about 4 Hz than earlier estimates.

Significance. If the backscattering transfer factor is correct, this is a valuable contribution: it upgrades the legacy static-gain mapping used in SIS-based beamtube noise estimates to a first-principles, quadrature-resolved optomechanical response, and it identifies regimes where amplitude-quadrature content, cross terms, and signal-extraction dynamics matter. The derivation is explicit, the legacy limits are recovered analytically, and the diffraction linearization criterion in Appendix A is a practical addition. The results are directly usable with FFT propagation codes and measured vibration spectra. The main caveat is that the backscattering source-node convention needs justification; the diffraction results and the general formalism are largely unaffected by that issue.

major comments (2)
  1. [Sec. IV B, Eq. (13), Appendix B] The backscattering transfer factor is derived for a source injected at node a_iho (Appendix B, Eq. (B4)), and Eq. (13) is the response to that node. The physical process described in Sec. IV B, in which light scatters off a beamtube baffle and returns to the ITM, enters the ITM from the arm side as a perturbation of the backward-traveling field a_ihi, not of the forward field a_iho. Solving the same linear system with the source in the a_ihi equation gives T_i'^† = (t_s t_i)/sqrt(2) v† [I + r_s L_s R_a L_s]^{-1} L_s (I + r_i E_a)^{-1}, i.e., Eq. (13) with the trailing E_a removed. Since E_a = L_a R_e L_a is the arm round-trip operator carrying the radiation-pressure back-action, T_i and T_i' differ in quadrature mixing and in low-frequency magnitude. The sentence "recouples at the same mirror that has emitted the light" points to a_ihi, not a_iho. The paper must either justify the a_iho
  2. [Sec. II / Sec. V E] The three-mirror coupled-cavity equivalence used to model DARM dynamics is load-bearing for the transfer factors, but the paper does not quantify its validity for scattered-light paths that involve higher-order spatial modes or full power-recycling dynamics. The approximation is standard for the carrier response and is cited to Refs. [39,46], but the ET-LF noise-budget comparison in Sec. V E would be more convincing with a quantitative validation against a full dual-recycled Michelson simulation, or at least an explicit statement of the frequency range and parameter conditions under which the equivalence is expected to hold.
minor comments (5)
  1. [Appendix C vs Eq. (34)] There is a notational inconsistency in the inner product convention. Eq. (34) defines ⟨a,b⟩ = ∫_A a b* dA, but Eq. (C8) uses ∫ ψ* φ δψ⊥ dA. Using the stated convention, the expression would be ∫ ψ (φ δψ⊥)* dA. Please standardize the notation.
  2. [Eq. (53)] Typo: "Throne" should be "Thorne" in the reference to Thorne and Flanagan.
  3. [Table II and Sec. III] Table II lists T_e, L_e, T_i, L_i, etc., which appear to be power transmittances and losses, while the text uses amplitude reflectivities/transmissivities r_k, t_k. Please clarify the relationship (t_k = sqrt(T_k), r_k = sqrt(1 - T_k - L_k)) to avoid ambiguity.
  4. [Sec. V A] The statement that T_i and T_e are "qualitatively and quantitatively very similar" is used to justify dropping single-trip differences. Since T_i = T_e L_a (Eqs. (13)-(14)), the difference is not a simple scalar at all frequencies; please quantify the statement or rephrase in terms of the specific quadrature components shown in Fig. 2.
  5. [Sec. V E] The ET-LF comparison would be easier to reproduce if the exact baffle configuration and vibration spectra used from Ref. [26] were summarized or referenced by a table entry, rather than only by citation.

Circularity Check

0 steps flagged

No circularity: transfer factors are derived from the standard two-photon node-matrix system; self-citations are only comparison baselines or simulation inputs.

full rationale

The derivation of the transfer factors, Eqs. (13)-(14) and Appendix B, is a direct solution of the node-matrix linear system using standard two-photon operators. No parameter is fitted to the quantities being predicted, and no output of the paper is used as an input to the derivation. The effective ETM reflectivity and the three-mirror coupled-cavity approximation are cited to external works, Refs. [39,46], not to the author's own prior results. The legacy formulas in Eqs. (50) and (67) enter only as comparison baselines, not as inputs to the derivation. The SIS simulation parameters reused from Ref. [26] are inputs to the numerical ET-LF example, not to the transfer-factor calculation; reusing them for a fair comparison is normal practice and does not make the result circular. The physical modeling choices that could be questioned, such as the three-mirror equivalence or the a_iho source node for backscattering, are validity/correctness assumptions rather than cases where a result is equivalent to its inputs by construction. Self-citations appear in the references and in the numerical comparison, but they are not load-bearing for the central claim that the transfer factors are frequency-dependent optomechanical responses.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 0 invented entities

The central derivation rests on the standard two-photon formalism and the three-mirror coupled-cavity approximation, both well documented in the cited literature. The main hand-chosen inputs are detector parameters from design references, with the ET-LF detuning values being the least well sourced. No new physical entities are introduced.

free parameters (3)
  • ET-LF signal-extraction detuning φ_s = π/2 + 0.6 rad
    Load-bearing for the claimed order-of-magnitude change in ET-LF noise. The value is presented as representative without a specific cited design specification, and the quantitative ET-LF result scales with it.
  • ET-LF homodyne angle ζ = π/2 + 0.6 rad
    Set equal to φ_s in the baseline; it determines which quadrature is read and therefore the transfer-factor magnitude. Same provenance issue as φ_s.
  • Backscatter vibration amplitude A in Fig. 4 = 10^{-13} to 10^{-8} m/Hz^{3/2}
    Illustrative A/f^2 motion spectra used for the ratio maps; not derived from measured data, but the qualitative conclusions do not depend on the exact value.
axioms (6)
  • standard math Two-photon quadrature formalism (Caves-Schumaker)
    Amplitude/phase quadratures and sideband conversion, Eq. (39), are accepted background used throughout the derivation.
  • domain assumption Three-mirror coupled cavity (SEM-ITM-ETM) describes DARM dynamics of a dual-recycled Michelson interferometer
    Sec. II, cited to Refs. [39,46]. If power-recycling dynamics or other degrees of freedom contribute to the scattered-light path, the transfer factors would change.
  • domain assumption ITM radiation pressure is accounted for by χ0 → 2χ0
    Footnote 1 in Sec. III: valid for equal ITM/ETM masses, differential arm mode, and no suspension asymmetry. ET-LF masses may not satisfy this exactly.
  • domain assumption Diffraction coupling is linear in baffle displacement
    Appendix A defines η_nl and argues it is small for the ET-LF baffles; the formalism itself assumes first-order expansion unless one adds the second-order term explicitly.
  • domain assumption Diffraction perturbation can be injected at the ETM incoming node
    Appendix C bounds the error via Eq. (C14) under the assumption of small surface roughness and small HOM power; this is a quantified but not experimentally verified assumption.
  • domain assumption The SIS simulation parameters and baffle configuration from Ref. [26] are valid for the ET-LF comparison
    Sec. V.E reuses the same SIS setup as Ref. [26] to isolate the transfer-factor effect; if those simulations are outdated, the revised ET-LF estimate changes.

pith-pipeline@v1.3.0-alltime-deepseek · 23283 in / 18811 out tokens · 188929 ms · 2026-08-01T12:49:48.114754+00:00 · methodology

0 comments
read the original abstract

Scattered light is a relevant noise source in current ground-based gravitational-wave detectors and a critical design concern for next-generation observatories. Beamtube scattered light estimates usually combine optical propagation simulations with analytical couplings that do not fully propagate the frequency-dependent optomechanical response of the interferometer to the strain readout. In this work, we use improved analytical transfer factors to convert scattered-light field perturbations in the Fabry--P\'erot arm cavities into equivalent strain noise, consistently including radiation-pressure coupling, signal-extraction dynamics, microscopic detunings, and the homodyne readout angle. The formalism keeps the full amplitude and phase quadrature content of the scattered field, including the cross terms that arise in both diffraction and backscattering noise. For diffraction, we also identify the regime in which the linearized coupling to baffle motion is valid, avoiding unnecessary phase wrapping. Using representative LIGO, Cosmic Explorer (CE), and Einstein Telescope - Low Frequency (ET-LF) configurations, we show that legacy estimates are recovered in phase dominated regimes, but can differ when radiation-pressure coupling, quadrature correlations, or detuned signal extraction become important. In particular, the revised ET-LF estimate changes substantially with respect to previous beamtube noise budgets due to the detuned signal extraction cavity. These results provide a more complete framework for scattered light noise estimations for present and future gravitational-wave detectors.

Figures

Figures reproduced from arXiv: 2607.19299 by M. Andr\'es-Carcasona.

Figure 1
Figure 1. Figure 1: FIG. 1. Simplified signal-flow diagram of the three-mirror coupled cavity used in this work, formed by the SEM, ITM, and [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Amplitude and phase of the baseline transfer factors [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Contour plot of the quotient of the model derived in this work and the previous literature one, [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Contour plot of the quotient of the model derived in this work and the previous literature one, [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Magnitude of the transfer factor [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Relative non-linear contribution as defined in [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. ( [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗

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Reference graph

Works this paper leans on

60 extracted references · 33 linked inside Pith

  1. [1]

    Acerneseet al.(VIRGO), Advanced Virgo: a second- generation interferometric gravitational wave detector, Class

    F. Acerneseet al.(VIRGO), Advanced Virgo: a second- generation interferometric gravitational wave detector, Class. Quant. Grav.32, 024001 (2015), arXiv:1408.3978 [gr-qc]

    Pith/arXiv arXiv 2015

  2. [2]

    Aasiet al.(LIGO Scientific), Advanced LIGO, Class

    J. Aasiet al.(LIGO Scientific), Advanced LIGO, Class. Quant. Grav.32, 074001 (2015), arXiv:1411.4547 [gr-qc]

    Pith/arXiv arXiv 2015

  3. [3]

    Capoteet al., Advanced LIGO detector performance in the fourth observing run, Phys

    E. Capoteet al., Advanced LIGO detector performance in the fourth observing run, Phys. Rev. D111, 062002 (2025), arXiv:2411.14607 [gr-qc]

    Pith/arXiv arXiv 2025

  4. [4]

    Y. Aso, Y. Michimura, K. Somiya, M. Ando, O. Miyakawa, T. Sekiguchi, D. Tatsumi, and H. Ya- mamoto (KAGRA), Interferometer design of the KA- GRA gravitational wave detector, Phys. Rev. D88, 043007 (2013), arXiv:1306.6747 [gr-qc]

    Pith/arXiv arXiv 2013

  5. [5]

    B. P. Abbottet al.(LIGO Scientific, Virgo), GWTC- 1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs, Phys. Rev. X9, 031040 (2019), arXiv:1811.12907 [astro-ph.HE]

    Pith/arXiv arXiv 2019

  6. [6]

    Abbottet al.(LIGO Scientific, Virgo), GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run, Phys

    R. Abbottet al.(LIGO Scientific, Virgo), GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run, Phys. Rev. X11, 021053 (2021), arXiv:2010.14527 [gr- qc]

    Pith/arXiv arXiv 2021

  7. [7]

    R. Abbottet al.(LIGO Scientific, VIRGO), GWTC-2.1: Deep extended catalog of compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run, Phys. Rev. D109, 022001 (2024), arXiv:2108.01045 [gr-qc]

    Pith/arXiv arXiv 2024

  8. [8]

    Abbottet al.(KAGRA, VIRGO, LIGO Scien- tific), GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the 15 Third Observing Run, Phys

    R. Abbottet al.(KAGRA, VIRGO, LIGO Scien- tific), GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the 15 Third Observing Run, Phys. Rev. X13, 041039 (2023), arXiv:2111.03606 [gr-qc]

    Pith/arXiv arXiv 2023

  9. [9]

    A. G. Abacet al.(LIGO Scientific, VIRGO, KAGRA), GWTC-4.0: Updating the Gravitational-Wave Transient Catalog with Observations from the First Part of the Fourth LIGO-Virgo-KAGRA Observing Run, (2025), arXiv:2508.18082 [gr-qc]

    Pith/arXiv arXiv 2025

  10. [10]

    A. G. Abacet al.(LIGO Scientific, VIRGO, KAGRA), GWTC-5.0: Observations from the Second Part of the Fourth LIGO-Virgo-KAGRA Observing Run and Updates to the Gravitational-Wave Transient Catalog, (2026), arXiv:2605.27225 [gr-qc]

    Pith/arXiv arXiv 2026

  11. [11]

    Accadiaet al., Noise from scattered light in Virgo’s second science run data, Class

    T. Accadiaet al., Noise from scattered light in Virgo’s second science run data, Class. Quant. Grav.27, 194011 (2010)

    2010

  12. [12]

    Fioriet al., The Hunt for Environmental Noise in Virgo during the Third Observing Run, Galaxies8, 82 (2020)

    I. Fioriet al., The Hunt for Environmental Noise in Virgo during the Third Observing Run, Galaxies8, 82 (2020)

    2020

  13. [13]

    M. Was, R. Gouaty, and R. Bonnand, End benches scat- tered light modelling and subtraction in advanced Virgo, Class. Quant. Grav.38, 075020 (2021), arXiv:2011.03539 [astro-ph.IM]

    Pith/arXiv arXiv 2021

  14. [14]

    Soniet al.(LIGO), Reducing scattered light in LIGO’s third observing run, Class

    S. Soniet al.(LIGO), Reducing scattered light in LIGO’s third observing run, Class. Quant. Grav.38, 025016 (2020), arXiv:2007.14876 [astro-ph.IM]

    Pith/arXiv arXiv 2020

  15. [15]

    Longo, S

    A. Longo, S. Bianchi, W. Plastino, N. Arnaud, A. Chi- ummo, I. Fiori, B. Swinkels, and M. Was, Scattered light noise characterisation at the Virgo interferometer with tvf-EMD adaptive algorithm, Class. Quant. Grav.37, 145011 (2020), arXiv:2002.10529 [astro-ph.IM]

    Pith/arXiv arXiv 2020

  16. [16]

    Longo, S

    A. Longo, S. Bianchi, G. Valdes, N. Arnaud, and W. Plas- tino, Daily monitoring of scattered light noise due to mi- croseismic variability at the Virgo interferometer, Class. Quant. Grav.39, 035001 (2022), arXiv:2112.06046 [astro- ph.IM]

    Pith/arXiv arXiv 2022

  17. [17]

    Longo, S

    A. Longo, S. Bianchi, G. Valdes, N. Arnaud, and W. Plas- tino, Scattered light monitoring system at the Virgo in- terferometer: performance improvement and automation based on O3 data, Class. Quant. Grav.41, 015004 (2024)

    2024

  18. [18]

    Bianchi, A

    S. Bianchi, A. Longo, G. Valdes, G. Gonz´ alez, and W. Plastino, An automated pipeline for scattered light noise characterization, Class. Quant. Grav.39, 195005 (2022), arXiv:2107.07565 [astro-ph.IM]

    Pith/arXiv arXiv 2022

  19. [19]

    ET science team,Einstein gravitational wave telescope conceptual design study, Tech. Rep. ET-0106C-10 (ET, 2011)

    2011

  20. [20]

    ET steering committee,ET design report update 2020, Tech. Rep. ET-0007B-20 (ET, 2020)

    2020

  21. [21]

    B. P. Abbottet al.(LIGO Scientific Collaboration), Ex- ploring the sensitivity of next generation gravitational wave detectors, Class. Quant. Grav.34, 044001 (2017), arXiv:1607.08697 [astro-ph.IM]

    Pith/arXiv arXiv 2017

  22. [22]

    Reitzeet al., The US Program in Ground-Based Grav- itational Wave Science: Contribution from the LIGO Laboratory, Bull

    D. Reitzeet al., The US Program in Ground-Based Grav- itational Wave Science: Contribution from the LIGO Laboratory, Bull. Am. Astron. Soc.51, 141 (2019), arXiv:1903.04615 [astro-ph.IM]

    Pith/arXiv arXiv 2019

  23. [23]

    Reitzeet al., Cosmic Explorer: The U.S

    D. Reitzeet al., Cosmic Explorer: The U.S. Contribu- tion to Gravitational-Wave Astronomy beyond LIGO, Bull. Am. Astron. Soc.51, 035 (2019), arXiv:1907.04833 [astro-ph.IM]

    Pith/arXiv arXiv 2019

  24. [24]

    Romero and H

    A. Romero and H. Yamamoto,SIS20 documents, Tech. Rep. LIGO-T2000311-v7 (LIGO, 2024)

    2024

  25. [25]

    Andr´ es-Carcasona, A

    M. Andr´ es-Carcasona, A. Macquet, M. Mart ´ ınez, L. M. Mir, and H. Yamamoto, Study of scattered light in the main arms of the Einstein Telescope gravitational wave detector, Phys. Rev. D108, 102001 (2023), arXiv:2307.14104 [gr-qc]

    Pith/arXiv arXiv 2023

  26. [26]

    Andr´ es-Carcasona, J

    M. Andr´ es-Carcasona, J. G. Umbert, D. Gonz´ alez- Lociga, M. Mart ´ ınez, L. M. Mir, and H. Yamamoto, New modeling of the stray light noise in the main arms of the Einstein Telescope, Class. Quant. Grav.42, 215021 (2025), arXiv:2506.18083 [physics.ins-det]

    Pith/arXiv arXiv 2025

  27. [27]

    Thorne,Light Scattering and Proposed Baffle Con- figuration for the LIGO, Tech

    K. Thorne,Light Scattering and Proposed Baffle Con- figuration for the LIGO, Tech. Rep. LIGO-T890017-00 (LIGO, 1989)

    1989

  28. [28]

    Flanagan and K

    E. Flanagan and K. Thorne,Light Scattering and Baffle Configuration for LIGO, Tech. Rep. LIGO-T950101-00 (LIGO, 1995)

    1995

  29. [29]

    Flanagan and K

    E. Flanagan and K. Thorne,Noise Due to Backscatter Off Baffles, the Nearby Wall, and Objects at the Fare End of the Beam Tube; and Recommended Actions, Tech. Rep. LIGO-T940063-00-R (LIGO, 1994)

    1994

  30. [30]

    Flanagan and K

    E. Flanagan and K. Thorne,Scattered-Light Noise for LIGO, Tech. Rep. LIGO-T950033-00 (LIGO, 1995)

    1995

  31. [31]

    Vinet, V

    J.-Y. Vinet, V. Brisson, and S. Braccini, Scattered light noise in gravitational wave interferometric detectors: Co- herent effects, Phys. Rev. D54, 1276 (1996)

    1996

  32. [32]

    Vinet, V

    J. Vinet, V. Brisson, S. Braccini, I. Ferrante, L. Pinard, F. Bondu, and E. Tourni´ e, Scattered light noise in gravi- tational wave interferometric detectors: A statistical ap- proach, Phys. Rev. D56, 6085 (1997)

    1997

  33. [33]

    Brisson and J

    V. Brisson and J. Vinet,Summary of scattered light noise calculations and baffle design in the long cavities, Tech. Rep. VIR-NOT-LAL-1390-123 (VIRGO, 1998)

    1998

  34. [34]

    D. J. Ottaway, P. Fritschel, and S. J. Waldman, Impact of upconverted scattered light on advanced interferomet- ric gravitational wave detectors, Opt. Express20, 8329 (2012)

    2012

  35. [35]

    Fritschel and H

    P. Fritschel and H. Yamamoto,Scattered light noise due to the ETM coating ripple, Tech. Rep. LIGO-T1300354 (LIGO, 2013)

    2013

  36. [36]

    Bai,Cosmic Explorer: Back-scattering Noise and Design Recommendations, Tech

    Y. Bai,Cosmic Explorer: Back-scattering Noise and Design Recommendations, Tech. Rep. LIGO-T1900854 (LIGO, 2020)

    2020

  37. [37]

    E. D. Hallet al., Gravitational-wave physics with Cosmic Explorer: Limits to low-frequency sensitivity, Phys. Rev. D103, 122004 (2021), arXiv:2012.03608 [gr-qc]

    Pith/arXiv arXiv 2021

  38. [38]

    McCulleret al., LIGO’s quantum response to squeezed states, Phys

    L. McCulleret al., LIGO’s quantum response to squeezed states, Phys. Rev. D104, 062006 (2021), arXiv:2105.12052 [physics.ins-det]

    arXiv 2021

  39. [39]

    E. D. Hall and K. Kuns, True and apparent motion of optomechanical resonators, with applications to feed- back cooling of gravitational wave detector test masses, (2024), arXiv:2408.14341 [quant-ph]

    Pith/arXiv arXiv 2024

  40. [40]

    H. Miao, N. D. Smith, and M. Evans, Quantum limit for laser interferometric gravitational wave detectors from optical dissipation, Phys. Rev. X9, 011053 (2019), arXiv:1807.11734 [quant-ph]

    Pith/arXiv arXiv 2019

  41. [41]

    Buonanno and Y.-b

    A. Buonanno and Y.-b. Chen, Quantum noise in second generation, signal recycled laser interferometric gravita- tional wave detectors, Phys. Rev. D64, 042006 (2001), arXiv:gr-qc/0102012

    Pith/arXiv arXiv 2001

  42. [42]

    S. L. Danilishin and F. Y. Khalili, Quantum Measure- ment Theory in Gravitational-Wave Detectors, Living Rev. Rel.15, 5 (2012), arXiv:1203.1706 [quant-ph]

    Pith/arXiv arXiv 2012

  43. [43]

    Harms, Y.-b

    J. Harms, Y.-b. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, and R. Schnabel, Squeezed input, optical spring, signal recycled gravitational wave detectors, Phys. Rev. D68, 042001 (2003), arXiv:gr- 16 qc/0303066

    arXiv 2003

  44. [44]

    H. J. Kimble, Y. Levin, A. B. Matsko, K. S. Thorne, and S. P. Vyatchanin, Conversion of conventional grav- itational wave interferometers into QND interferometers by modifying their input and / or output optics, Phys. Rev. D65, 022002 (2002), arXiv:gr-qc/0008026

    Pith/arXiv arXiv 2002

  45. [45]

    Polini and A

    E. Polini and A. Chiummo, Stray Light Analysis and Mit- igation Perspectives for Next Generation Gravitational- Wave Detectors, Galaxies14, 5 (2026)

    2026

  46. [46]

    Kuns and D

    K. Kuns and D. Brown, Squeezed state degradations due to mode mismatch and thermal aberrations in gravitational wave detectors, (2026), arXiv:2604.23835 [physics.ins-det]

    Pith/arXiv arXiv 2026

  47. [47]

    C. M. Caves and B. L. Schumaker, New formalism for two-photon quantum optics. 1. Quadrature phases and squeezed states, Phys. Rev. A31, 3068 (1985)

    1985

  48. [48]

    B. L. Schumaker and C. M. Caves, New formalism for two-photon quantum optics. 2. Mathematical foundation and compact notation, Phys. Rev. A31, 3093 (1985)

    1985

  49. [49]

    Vajente, Analytical expressions for the clipping of laguerre– and hermite–gauss modes by circular apertures, J

    G. Vajente, Analytical expressions for the clipping of laguerre– and hermite–gauss modes by circular apertures, J. Opt. Soc. Am. A39, 352 (2022)

    2022

  50. [50]

    Vajente,Noise from clipping on Cosmic Explorer beam tube baffles, Tech

    G. Vajente,Noise from clipping on Cosmic Explorer beam tube baffles, Tech. Rep. CE-T2100011-v2 (CE, 2021)

    2021

  51. [51]

    Andr´ es-Carcasona and M

    M. Andr´ es-Carcasona and M. Evans, Beam tube bound- ary effects in stray light modeling of long Fabry- P´ erot arm cavities for third-generation gravitational- wave detectors, Phys. Rev. D113, 102003 (2026), arXiv:2602.21303 [gr-qc]

    arXiv 2026

  52. [52]

    Rakhmanov, J

    M. Rakhmanov, J. D. Romano, and J. T. Whelan, High- frequency corrections to the detector response and their effect on searches for gravitational waves, Class. Quant. Grav.25, 184017 (2008), arXiv:0808.3805 [gr-qc]

    Pith/arXiv arXiv 2008

  53. [53]

    Essick, S

    R. Essick, S. Vitale, and M. Evans, Frequency-dependent responses in third generation gravitational-wave detec- tors, Phys. Rev. D96, 084004 (2017), arXiv:1708.06843 [gr-qc]

    Pith/arXiv arXiv 2017

  54. [54]

    Andr´ es-Carcasona, M

    M. Andr´ es-Carcasona, M. Mart ´ ınez, L. M. Mir, J. Mundet, and H. Yamamoto, Performance of an instru- mented baffle placed at the entrance of Virgo’s end mir- ror vacuum tower during O5, Phys. Rev. D111, 042001 (2025), arXiv:2412.11592 [physics.ins-det]

    Pith/arXiv arXiv 2025

  55. [55]

    Romero-Rodr ´ ıguez, A

    A. Romero-Rodr ´ ıguez, A. Allocca, A. Chiummo, M. Mart ´ ınez, L. M. Mir, and H. Yamamoto, Determi- nation of the light exposure on the photodiodes of a new instrumented baffle for the Virgo input mode cleaner end-mirror, Class. Quant. Grav.38, 045002 (2021), arXiv:2008.13740 [physics.ins-det]

    Pith/arXiv arXiv 2021

  56. [56]

    Romero-Rodr ´ ıguez, M

    A. Romero-Rodr ´ ıguez, M. Mart ´ ınez, L. M. Mir, and H. Yamamoto, Determination of the Stray Light-Induced Noise from the Baffle in the Cryogenic Trapping Area of Advanced Virgo in O5, Galaxies10, 86 (2022)

    2022

  57. [57]

    Macquet, M

    A. Macquet, M. Andr´ es-Carcasona, M. Martinez, L.-M. Mir, A. Romero-Rodriguez, and H. Yamamoto, Simula- tions of light distribution on new instrumented baffles surrounding Virgo end mirrors, Class. Quant. Grav.40, 077001 (2023), arXiv:2210.16308 [physics.ins-det]

    Pith/arXiv arXiv 2023

  58. [58]

    Evanset al., A Horizon Study for Cosmic Ex- plorer: Science, Observatories, and Community, (2021), arXiv:2109.09882 [astro-ph.IM]

    M. Evanset al., A Horizon Study for Cosmic Ex- plorer: Science, Observatories, and Community, (2021), arXiv:2109.09882 [astro-ph.IM]

    Pith/arXiv arXiv 2021

  59. [59]

    Hildet al., Sensitivity studies for third-generation gravitational wave observatories, Classical and Quantum Gravity28, 094013 (2011)

    S. Hildet al., Sensitivity studies for third-generation gravitational wave observatories, Classical and Quantum Gravity28, 094013 (2011)

    2011

  60. [60]

    J. G. Rollins, E. Hall, C. Wipf, and L. McCuller, pygwinc: Gravitational Wave Interferometer Noise Calculator, As- trophysics Source Code Library, record ascl:2007.020 (2020), ascl:2007.020. Appendix A: Phase-wrapping for diffraction Let’s consider that the exact coupling of the field with the resonating TEM 00 mode is a non-linear function of the baffle ...

    2007