Birefringence of AlGaAs/GaAs Coatings under Above-Band-Gap Illumination, GR Noise and Photo-Optic Transfer Function

Bin Wu; Satoshi Tanioka; Shreyan Goswami; Stefan Ballmer

REVIEW 4 major objections 5 minor 2 cited by

Birefringence of AlGaAs/GaAs Coatings under Above-Band-Gap Illumination, GR Noise and Photo-Optic Transfer Function

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read The illumination-to-birefringence coupling in AlGaAs/GaAs coatings is a single-pole low-pass filter whose pole frequency rises and DC gain falls with light intensity.

desk verdict Solid new measurement of the photo-induced birefringence transfer function in AlGaAs/GaAs coatings; the GR-noise scaling claims are conditional on an unverified generation-rate assumption and are oversold in the abstract. read the letter →

arxiv 2512.00594 v2 pith:G7IVXTV6 submitted 2025-11-29 physics.ins-det

Bin Wu , Shreyan Goswami , Satoshi Tanioka , Stefan Ballmer This is my paper · ORCID

classification physics.ins-det

keywords birefringenceAlGaAs/GaAscoatingscrystallinegravitational-wavedetectorsmasterequationgeneration-recombinationnoiseelectro-opticeffectlow-passtransferfunction

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper reports that the birefringence of AlGaAs/GaAs crystalline mirror coatings, candidates for gravitational-wave detector test masses, responds to above-band-gap illumination as a first-order low-pass filter: flat at low frequencies, rolling off above a pole frequency. The pole frequency increases and the DC gain decreases as the illumination or carrier intensity rises. The authors model this with a master equation for photo-excited charge carriers whose effective lifetime is shortened by higher light intensity, and the model reproduces both the frequency and intensity dependence. The same model predicts a generation-recombination noise in the coating birefringence that would be white below the pole frequency, scale with laser power like shot noise, and be independent of spot size for fixed power — a signature that could distinguish it from other noise sources. The paper cannot predict the magnitude of this GR noise, only its shape and scaling.

What carries the argument

The central object is the master equation for the number of photo-excited charge carriers N(t) trapped near the coating, whose area density σ = eN/A produces an internal electric field that changes the coating's birefringence through the electro-optic effect. Linearized about equilibrium, it gives a single-pole transfer function δN/δI = g_DC/(1 + iω/Γ) with decay rate Γ(I0, I1) and DC gain g_DC(I0, I1). The paper parametrizes these two functions with four parameters — a spontaneous decay rate Γ0 and two photo-induced recombination cross sections a0, a1 — and shows the resulting global fit reproduces the full dataset. The same linearized master equation, including shot noise in generation and

What would settle it

Measure the birefringence noise spectrum of a single AlGaAs/GaAs coating at fixed carrier power while changing the illumination spot size: if the noise changes with spot size, or is not white below the pole frequency, the GR-noise prediction fails. A second falsifier is a step-response measurement at carrier intensities below 2 MW/m²: if the pole frequency does not extrapolate linearly to the fitted rate, the four-parameter model is wrong.

Watch

Extended reading notes

Core claim

The central claim is that the coupling from above-band-gap illumination to birefringence in a high-reflectivity Al0.92Ga0.08As/GaAs coating is not a static coefficient but a dynamic, intensity-dependent transfer function. Measured with a 4-cm cavity whose output coupler is the coating, the transfer function is a single-pole low-pass: at DC it matches earlier static measurements, but above a pole frequency of a few hundred hertz it rolls off as 1/f. As the 700 nm LED illumination is raised from 0.6 to 5.1 W/m², the DC gain falls from about 2760 to 660 Hz/(W/m²) and the pole increases proportionally; raising the 1064 nm carrier intensity from 2.0 to 3.7 MW/m² shifts the curves the same way. Th

Load-bearing premise

The predicted GR-noise scaling rests on the assumption that the carrier generation rate is proportional to the total optical power on the coating (G = ΓN̄ + r ∝ P̄0 = AĪ0); if surface-trapping or diffusion-area effects break that proportionality, the noise scaling does not hold, and the fit also extrapolates a linear decay law to intensities roughly ten to fifty times beyond the measured range.

Editorial extensions

If this is right

The measured single-pole dynamics mean that at gravitational-wave detector carrier intensities (tens of kW/cm²) the pole frequency is pushed into the tens of kHz, above the detection band, so intensity-noise coupling from the coating is suppressed.
The GR-noise spectral shape — white below the pole, falling as 1/f above — is unique among known coating displacement noises in the GW band, so if present it would be identifiable.
GR noise scales with optical power as 1/P and is independent of spot size for fixed power, making it behave like laser shot noise; this sets a scaling constraint for future crystalline-coated interferometers.
The photo-optic transfer function from 1064 nm carrier light to birefringence has the same pole frequency as measured with 700 nm light, so a DC birefringence-vs-carrier-intensity measurement could fix the strength of this noise path.
The model implies that higher carrier intensity shortens the effective carrier lifetime, which is a design lever for suppressing intensity-to-phase coupling in crystalline coatings.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the master-equation form holds, the same intensity-dependent lifetime should appear in other observables that couple to carrier population, such as photoluminescence decay or photoconductivity; a time-resolved pump-probe measurement on the same coating could directly verify Γ(I) without relying on the transfer-function fit.
The predicted 1/P scaling of GR noise is testable with a dedicated noise measurement on a single coating by varying spot size at fixed total power; if the noise is independent of spot size, the carrier diffusion area must be smaller than the beam and the Debye-length assumption holds.
The negative fitted Γ0 suggests that at very low intensities the effective recombination rate could pass through zero, implying a regime where the linearized model breaks down; an experiment at lower carrier intensities could map where the pole frequency extrapolates to zero.
The model's symmetry in indices 0 and 1 means the 1064 nm intensity-to-phase coupling should exhibit the same pole as the 700 nm coupling; measuring the transfer function by modulating the 1064 nm power directly would test the master equation without relying on external illumination.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The part worth reading is the transfer-function measurement. They lock s- and p-polarized lasers to a short cavity with an AlGaAs/GaAs mirror, modulate a 700 nm LED, and see a clean single-pole low-pass response whose DC gain falls and pole frequency rises with illumination intensity. The global four-parameter master-equation fit reproduces dozens of curves across two 1064 nm intensities. That is new and looks credible. The low-frequency DC gains also match earlier JILA data, which is a good calibration check. The 430 nm data is muddier but they are honest about not using it in the global fit.

The weaknesses are mostly concentration in the noise section. The GR-noise scalings in the abstract — white below the pole, scaling like shot noise, spot-size independent — are not predictions from the data. They are derived after explicitly assuming the generation rate G is proportional to total power P0. That assumption is not measured and is actually suspect for the 1064 nm carrier: the paper itself notes that below-band-gap illumination can generate carriers via two-photon absorption. If G ∝ A I0² instead of A I0, the scalings flip: GR noise becomes power-independent and spot-size dependent. So the stress-test objection lands. Table III then extrapolates a fitted linear decay law to GW-detector intensities 10–50x beyond the measured range, despite their own caveat that this cannot be done with certainty. The negative Γ0 from the fit is unphysical but only affects the model outside the measured intensity range; still, it deserves a comment or constrained refit.

None of this touches the central measured result. The single-pole dynamics and intensity dependence are real and useful, and the master-equation framework is a reasonable way to parameterize them. The GR-noise part should be rewritten as a conditional projection, not a headline result, with the G∝P assumption clearly flagged and its failure modes discussed.

Bottom line: worth publishing after revision. Send it to referees, but ask them to focus on whether the GR-noise scaling is presented with the right epistemic weight. I would cite the transfer-function result even if the noise scalings get corrected.

Referee Report

4 major / 5 minor

Summary. The paper reports cavity beat-note measurements of illumination-induced birefringence in an Al0.92Ga0.08As/GaAs crystalline coating. Modulating 700 nm (and 430 nm) LED illumination on the coating and monitoring the 1064 nm carrier beat note between two polarizations, the authors find a single-pole low-pass transfer function whose DC gain decreases and whose pole frequency increases with illumination intensity, for both the external LED and the intracavity 1064 nm intensity. A four-parameter master-equation model with Γ = Γ0 + a0 I0 + a1 I1 and g_DC = K10/[Γ(I0,0)Γ(I0,I1)] reproduces the frequency and intensity dependence of the measured 700 nm transfer functions. The model is then used to predict a generation-recombination (GR) noise contribution to coating displacement noise that is white below the pole, scales with power like shot noise, and is independent of spot size at fixed power. The paper also extrapolates the fitted linear Γ(I0) law to gravitational-wave detector intensities in Table III.

Significance. If validated, the frequency-resolved measurement is a valuable new datum for AlGaAs/GaAs coatings: it is the first direct observation of the single-pole dynamics of the illumination-to-birefringence coupling, with DC values consistent with previous static measurements. The master-equation framework and the associated photo-optic and GR-noise expressions provide a useful organizing model. The paper's strengths include a clean transfer-function measurement with explicit calibration (Appendix C), a global four-parameter fit to many curves (Fig. 3 and Fig. 6), and an honest statement that the GR-noise magnitude is not predicted. The main risk is that the GR-noise scaling claims in the abstract and conclusions go beyond what the experiment and the model can establish without additional assumptions.

major comments (4)

[Appendix B, Eq. (48)] The headline GR-noise scalings — white below the pole, scaling like shot noise (1/P), and spot-size independence at fixed power — are not derived from measured quantities. They require the explicit assumption stated immediately before Eq. (48): that the generation rate G = ΓN̄ + r is proportional to the total power P̄0 = AĪ0. The experiment does not constrain G. For 1064 nm light, which is below the GaAs/AlGaAs bandgap, a natural alternative is two-photon generation, G ∝ A Ī0², which would replace Eq. (48) with a power-independent, spot-size-dependent scaling, opposite to the abstract. The authors should either provide a microscopic argument or a measurement selecting G ∝ P̄0, or explicitly delabel these scalings as conditional model predictions rather than established results.
[Table III] The pole frequencies quoted for aLIGO, A+, A#, and CE are obtained by extrapolating Γ ≈ a0Ī0 from the measured range 2.0–3.7 MW/m² (0.20–0.37 kW/cm²) to 3.3–17 kW/cm², i.e., a factor of 10–50 beyond the data. Section VI states that 'we cannot with certainty extrapolate the carrier intensity data much beyond our data range,' but Table III presents precise kHz values without a caveat. The table should be either removed, explicitly marked as a speculative extrapolation, or accompanied by a sensitivity statement showing the effect of plausible deviations from linear Γ(Ī0).
[Table II and Eq. (32)] The global fit returns Γ0 = −908 s⁻¹, labeled the 'spontaneous decay rate.' A negative spontaneous decay rate is unphysical as a literal rate, and this places the interpretation of Γ(Ii) as a physical recombination rate in question. The authors should explain whether Γ0 is merely an empirical offset that keeps Γ > 0 over the measured range, or whether a negative intercept implies a missing physical process. At a minimum, the paper should state that Γ0 is an effective parameter and discuss the implications for the model's predictive power beyond the fitted range.
[Section III D and Section VI] The 430 nm data, which also show the same low-pass trend, are not single-pole and are explicitly excluded from the global fit because they require a superposition of poles. The conclusion that the illumination-to-birefringence coupling is a single-pole process is therefore established only for 700 nm illumination. The abstract and Section VI should be scoped accordingly, or the 430 nm behavior should be discussed as a separate, unresolved feature rather than as consistent with the single-pole model.

minor comments (5)

[Abstract] Typo: 'theoretical mode' should be 'theoretical model'.
[Fig. 4] The y-axis label 'Induced birefringence [Hz/(W/m²)]' is dimensionally a coupling coefficient, not a birefringence. Please clarify the label to avoid confusion with the frequency splitting itself.
[Appendix C, LED calibration] The paper reports illumination intensities without correcting for the 45° incidence angle or coating reflectivity. This affects the absolute values of a1 and the reported gain, though not the frequency dependence. A sentence quantifying the expected correction would be useful.
[Appendix A, Eq. (35)] The logarithm in the integrated expression uses Γ/Γ1, which is dimensionless; please make this explicit so the reader does not worry about units.
[Reference [20]] Reference [20] is a web resource (Ioffe database). Please provide a stable citation or access date.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the transfer-function measurement and global fit are self-contained, and the GR-noise scaling is a transparently labeled conditional assumption rather than an input disguised as a prediction.

full rationale

The central experimental result is an independently measured transfer function: the beat-note frequency shift is converted to birefringence through eq. 2, and the full calibration chain (LED drive to intensity to phase) is detailed in Appendix C. The four-parameter global fit (eqs. 32–33) reproduces the measured DC gains and pole frequencies across a family of illumination intensities, and the low-frequency DC values are compared with external JILA results rather than being assumed. The master-equation model is a framework used to interpret the data, not a result whose conclusion is fed back into the fit. The photo-optic 1064 nm transfer function shares the measured pole frequency by model symmetry, and the paper explicitly does not claim to have measured its magnitude. The GR-noise spectral shape and scaling are derived in Appendix B from the master equation, but the authors clearly identify the unmeasured integration constant N̄ and remainder r, and they state the required power-scaling hypothesis verbatim: 'To nevertheless predict a power scaling, we have to assume that the generation rate G = Γ N̄ + r is proportional to the total power P̄0 = A Ī0 on the optic.' This is a conditional, falsifiable extrapolation, not a fitted parameter renamed as a prediction. The use of C_ext_EO from prior work [14] is a laboratory calibration constant, and the paper explicitly reports only the product ηK10, so no load-bearing argument reduces to an unverified self-citation. No uniqueness theorem, hidden ansatz, or renaming of a known result is employed. The paper's own limitations—inability to predict GR-noise magnitude and caution about extrapolating beyond 2.0–3.7 MW/m²—are stated rather than concealed. Accordingly, no circular step meets the evidentiary bar required by the review rules.

Assumptions & free parameters 7 free parameters · 7 assumptions · 1 invented entities

The measured TF data support the single-pole structure and the intensity dependence of pole and DC gain. However, the model's predictive content beyond the data is carried by four fitted parameters (one unphysical), two undetermined constants (N̄₀, r), one borrowed external coefficient (C^ext_EO), and the explicit G ∝ P assumption that anchors the GR-noise scaling. The qualitative physics (trapped carriers, electro-optic effect) is standard; the quantitative predictions are not closed without the missing measurements the paper itself names.

free parameters (7)

Γ₀ (spontaneous decay rate) = −908 s⁻¹
Fitted in the global four-parameter model (Table II). Returns an unphysical negative value; the paper notes this but uses the model anyway.
a₀ (1064 nm recombination cross section) = 1.96×10⁻²² m²
Fitted parameter in Γ = Γ₀ + a₀Ī₀ + a₁Ī₁ (Table II); controls the carrier-intensity dependence of pole and gain.
a₁ (700 nm recombination cross section) = 4.79×10⁻¹⁶ m²
Fitted parameter (Table II); controls the 700 nm LED-intensity dependence.
ηK₁₀/A (gain) = 0.80 s⁻¹
Fitted overall gain (Table II); only the product ηK₁₀ is measurable in this experiment, with η the unknown coupling efficiency of internal vs. external fields.
C^ext_EO (electro-optic coupling) = 1.3×10⁻¹⁰ rad/(V/m)
Borrowed from the authors' prior measurement [14]; converts fitted gain to capture probability and enters the GR-noise magnitude. Not fitted here, but the GR-noise predictions depend on it.
N̄₀(I₀) (integration constant of the master equation) = undetermined
Explicitly admitted unknown (App. A eq. 35); enters the GR-noise magnitude directly and cannot be fixed by the transfer-function data.
r(N̄) (remainder term in recombination rate) = undetermined
Explicitly admitted unknown (App. A eqs. 30–31; App. B eq. 38); enters the GR-noise magnitude and the G ∝ P assumption.

assumptions (7)

domain assumption Birefringence change is linear in the electric field from trapped charge carriers: Δφ_biref = 2 C_EO Δσ / ε₀ (eq. 13).
Assumes electro-optic dominance and linearity; the internal-field geometry is admitted unknown via η < 1 (eq. 34), so the absolute scale is not fixed.
standard math Carrier dynamics follow a single-species birth-death master equation Ṅ = G(N,I) − R(N,I) with shot-noise sources √(2G), √(2R) (eqs. 15, 38).
Standard kinetic and GR-noise framework from [21]; the 430 nm data (superposition of poles) indicate the single-species picture is an approximation.
domain assumption Linearization is valid: |δN| ≪ N̄ (eq. 18).
Required for the single-pole transfer function. The Fig. 2 modulation index m = 0.67 is not small; the authors assert the coupling values are unchanged, but no linearity scan is shown.
ad hoc to paper Specific phenomenological forms: Γ = Γ₀ + a₀Ī₀ + a₁Ī₁ and g_DC = K₁₀/[Γ(Ī₀,0)Γ(Īᵢ)] (eqs. 32–33).
Four-parameter forms chosen to fit the data; the unphysical negative Γ₀ indicates the form is unlikely to be the true physics at low intensity.
ad hoc to paper Generation rate G = ΓN̄ + r is proportional to total power P̄₀ = AĪ₀ (App. B, before eq. 48).
Explicitly stated as an assumption ('we have to assume'); it is the load-bearing premise for the GR-noise 1/P scaling and spot-size independence.
domain assumption At GW-detector intensities Γ ≈ a₀Ī₀ dominates (App. B).
Extrapolates the fitted linear Γ law to 33–170 MW/m², 10–50× beyond the measured 2.0–3.7 MW/m² range, feeding Table III's pole frequencies.
domain assumption Debye-length diffusion picture: for w ≫ λ_D, A is the readout spot area; GR noise is uncorrelated beyond λ_D (App. A and B).
Underpins the spot-size independence claim; λ_D is never measured and the diffusion area could replace the beam area in the noise formulas.

invented entities (1)

Trapped near-interface carrier population (GaAs band-bending well plus DX-center metastable traps)
purpose: Explains the measured few-hundred-microsecond carrier lifetime (pole ≈ 300 Hz) and the persistent-photoconductivity mechanism invoked in Section V.
Band bending [15] and DX centers [22,23] are known semiconductor phenomena, but their presence, density, and role in this specific coating are not directly measured here; the long lifetime 'is longer than what could be expected from the natural decay of a semiconductor.'

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Cite this review

Pith. "Pith review of Birefringence of AlGaAs/GaAs Coatings under Above-Band-Gap Illumination, GR Noise and Photo-Optic Transfer Function." pith.science (2026). https://pith.science/paper/G7IVXTV6

@misc{pith2026251200594,
  author       = {Pith},
  title        = {Pith review of: Birefringence of AlGaAs/GaAs Coatings under Above-Band-Gap Illumination, GR Noise and Photo-Optic Transfer Function},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/G7IVXTV6}},
  note         = {Machine review of arXiv:2512.00594}
}

read the original abstract

AlGaAs/GaAs coatings are being considered as coating candidates for gravitational-wave detectors. In this paper we investigate the birefringence properties of this crystalline semiconductor material by modulating the optical illumination on the mirror coating and monitoring the induced birefringence. While the measured low-frequency birefringence values align with previous studies, we observed a frequency-dependent behavior in the illumination-to-birefringence coupling, characterized by a pole increasing with illumination intensity and a DC gain decreasing with illumination intensity. We developed a theoretical mode based on a master equation to characterize the measurement results by considering photon-induced electric fields and electro-optical effects. This model reproduces the frequency and intensity dependencies of the induced birefringence. Additionally, this model predicts a generation-recombination noise (GR noise) will be observable in the coatings birefringence. While the presented measurement cannot predict the exact level of GR noise, for the frequency band and spot sizes relevant for gravitational-wave detectors we expect GR noise to be white below the pole frequency, scale with power the same way laser shot noise does, and for fixed power be independent of spot size.

Figures

Figures reproduced from arXiv: 2512.00594 by the authors.

**Figure 3.** FIG. 3: Fitting results at different illumination intensity [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 5.** FIG. 5: Transfer functions from 430 nm LED intensity to [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗

Figures from the paper (4 more)

**Figure 6.** Figure 6: FIG. 6: Single global fit for two sets of data with different [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

**Figure 7.** Figure 7: FIG. 7: Block diagram of the experimental setup. [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: FIG. 8: LED calibration. For the 700 nm LED, we [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 9.** Figure 9: FIG. 9: Frequency response of the 700 nm LED measured [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

LIGO A$^\sharp$: Detector Design and Science Prospects Beyond A+
astro-ph.IM 2026-08 conditional novelty 6.0 of 10

LIGO A#, a room-temperature upgrade of the LIGO detectors proposed for the 2030s, would broaden sensitivity and increase projected compact-binary detection rates by factors of four to eight relative to A+.
Photo-birefringent effects in crystalline AlGaAs mirror coatings
physics.optics 2026-02 conditional novelty 6.0 of 10

Crystalline AlGaAs coating birefringence changes follow a unified intensity scaling with fitted per-wavelength coefficients, and LED illumination can cancel power-induced frequency noise at low cavity power.

Reference graph

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

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Thus, each contributes a shot noise (δRandδGrespectively) with (1-sided) amplitude spectral density equal top 2G( ¯N , Ii)

The generationGand recombinationReach are probabilistic processes that can only generate or destroy a whole charge carrier. Thus, each contributes a shot noise (δRandδGrespectively) with (1-sided) amplitude spectral density equal top 2G( ¯N , Ii). The literature refers to this noise as Generation-Recombination noise, abbreviated as GR noise. To calculate ...

[2] [2]

We will refer to this coupling as photo-optic noise

Intensity fluctuations in the drive fieldsI i will couple to the birefringence with the transfer function derived in appendix A (equation 26 and 36). We will refer to this coupling as photo-optic noise. First, we note that we can write the (1-sided) amplitude spectral density for the source termsδRand δGas q 2G( ¯N , Ii) = q 2R( ¯N , Ii) = q 2Γ ¯N+ 2r( ¯N...

[3] [3]

LED Illumination Calibration The LED conversion from drive voltage to illumination intensity is shown in Fig. 8. The external illumination sources at 700 nm and 430 nm were incident under approximately 45 degrees to the mirror surface. Throughout this paper we report the illumination intensity without correcting for the angle cosine or for the effective c...

[4] [4]

The slope of the error signal linear range corresponds to the sensing gain

PDH Locking Loops for the Two Polarizations The laser locking sensing responsesS s andS p can be obtained from the error signal in the PDH locking process. The slope of the error signal linear range corresponds to the sensing gain. It varied between 6 V/GHz and 18 V/GHz, depending on the laser input power. The measurement was repeated for every data run

[5] [5]

The transfer function from illumination to birefringence, which is written asIin the block diagram, can then be calculated from the following measurement results

Transfer Functions The LED drive (X) is first converted to the LED light intensity and then induces a birefringent frequency shift for the two orthogonal modes, in a different direction.H p andH s in the diagram denote the locking loop gains of two orthogonal modes.H b denotes the gain of the PLL. The transfer function from illumination to birefringence, ...

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Stefan W. Ballmer. Photothermal transfer function of dielectric mirrors for precision measurements.Phys. Rev. D, 91:023010, 1 2015

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2023