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REVIEW 4 major objections 5 minor 59 references

Semi-analytical modeling of receive transfer function and thermal noise of integrated photonic ultrasound transducers

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that the receive transfer function and thermal-noise noise equivalent pressure of integrated photonic ultrasound transducers can be predicted semi-analytically by pairing time-domain finite-element simulation with…

desk verdict A genuinely new time-domain FEM pipeline for IPUT RTF and thermal NEP, but the central 'close match' validation fails by a factor 2–3 on the only RTF point; the framework is worth refereeing, not the current claim. read the letter →

arxiv 2506.02817 v1 pith:LP5Z6MFK submitted 2025-06-03 physics.app-ph physics.ins-det

Sabiju Valiya Valappil , Peter Harmsma , Maurits van der Heiden , Martin Verweij , Paul van Neer This is my paper · ORCID
classification physics.app-phphysics.ins-det
keywords integratedphotonicultrasoundtransducerreceivetransferfunctionthermalnoiseequivalentpressurephotoelasticeffectringresonatortime-domainfiniteelementanalysismembrane
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

The paper sets out to show that the receive transfer function and the thermal-noise noise equivalent pressure of integrated photonic ultrasound transducers can be obtained from a semi-analytical procedure: a time-domain finite-element simulation of the incident ultrasound wave, the membrane, and the attached optical waveguide, followed by closed-form optical and thermal formulas. If the claim holds, designers can predict sensitivity and noise floor from geometry and material properties before spending a fabrication run. The paper validates the procedure against a published ring-resonator IPUT: resonance frequency and Q factor agree closely, the modeled RTF is -33.6 fm/Pa against a measured 67 fm/Pa, and the modeled thermal NEP is 0.03 Pa against a measured total NEP of 0.4 Pa. The remaining RTF gap is assigned to prestress and fabrication-induced geometry changes, which the paper leaves out of the model. The paper concludes that the gap should close once prestress is included, since the reference device is known to be buckled.

What carries the argument

The load-bearing object is the coupled time-domain finite-element model of acoustic and elastic wave propagation in a 2D axisymmetric, and a 3D quarter-symmetric, water-membrane-waveguide domain, together with two closed-form expressions: Eq. (18) for the receive transfer function and Eq. (36) for the thermal-noise noise equivalent pressure. The finite-element step supplies the radial displacement $u$ and the stress tensor $\boldsymbol{\sigma}$ that enter the optical calculation; the effective mass $m_{\mathrm{eff}}$ absorbs the fluid loading through a mass factor, and the equipartition theorem converts the resonator's mechanical susceptibility into the thermal force spectral density $4k_B T\omega_0 m_{\mathrm{eff}}/Q$. This machinery splits the RTF into an elongation contribution and a photoelastic contribution, and it shows that both act in the same direction for the validated ring-resonator design.

What would settle it

Measure the initial stress of a fabricated IPUT membrane, for example from its resonance-frequency shift or from a separate stress characterization, include that stress as an initial condition in the same time-domain finite-element model, and check whether the predicted RTF moves from about -33 fm/Pa toward the measured 67 fm/Pa; if it does not, the prestress explanation is wrong and the model is not quantitatively predictive for real devices.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central claim is that an IPUT's receive response can be written as a mechanical part, the membrane deformation under an incident pressure wave, times an optical part, the resonance-wavelength shift caused by that deformation. Equation (18) expresses the receive transfer function as $(d\lambda/dP)=\frac{\lambda}{n_g L}(n_{\mathrm{eff}}\,dL/dP + L\,dn_{\mathrm{eff}}/dP)$, where the first term is the ring-waveguide elongation and the second is the photoelastic change of the effective index; both are evaluated from the stress and displacement fields produced by a time-domain finite-element simulation of the coupled water-membrane-waveguide system. Equation (36) then multiplies this RTF by the thermal-pressure spectral density from an equipartition-based single-oscillator model to give the noise equivalent pressure in wavelength units. In the validation against the reference sensor, the modeled resonance frequency is 0.615 MHz versus 0.76 MHz measured, the modeled Q is 11.75 versus about 10 measured, the modeled RTF is -33.6 fm/Pa versus 67 fm/Pa measured in the 2D model and -22 fm/Pa in the 3D model, and the modeled thermal NEP is 0.03 Pa versus a total experimental NEP of 0.4 Pa. The paper attributes the RTF gap to prestress and fabrication-induced geometry, which it leaves out of the scope.

Load-bearing premise

The membrane is modeled with no initial stress and with nominal dimensions; the paper itself says that prestress and fabrication-induced geometry changes are beyond its scope, and invokes them to explain why the predicted receive transfer function is two to three times lower than the measured value.

Editorial extensions

If this is right

  • The receive transfer function separates cleanly into an elongation term and a photoelastic term, so designers can estimate which effect dominates from the stress state of the waveguide alone.
  • Because the thermal-noise NEP in wavelength units is the RTF times the thermal pressure, any error in the modeled RTF directly corrupts the predicted noise floor; an accurate acoustic model is a prerequisite for noise-limited design.
  • For the validated device the modeled thermal NEP is 0.03 Pa, more than an order of magnitude below the 0.4 Pa experimental NEP, so the measured sensor's floor is set by the read-out chain rather than by thermal acoustic noise.
  • The 2D axisymmetric model captures resonance frequency and Q factor well, but the 3D quarter-symmetric model is needed for the true racetrack waveguide geometry, where the RTF is about 35% lower than in 2D.
  • The same semi-analytical chain can be extended to multilayer or geometrically complex membranes through a numerically computed mode shape, enabling optimization before fabrication.

Reading between the lines

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

  • If prestress and fabrication-induced buckling were added as initial conditions in the same finite-element model, the modeled RTF would likely rise from -33.6 fm/Pa toward the measured 67 fm/Pa; this is a direct, testable extension of the paper's own hypothesis.
  • The same mechanical-plus-optical decomposition should transfer to Mach-Zehnder IPUTs by replacing the ring-resonator wavelength shift with a phase shift, since the paper's mechanical model is not specific to ring resonators.
  • The finding that thermal noise sits far below the measured NEP implies that near-term performance gains for IPUTs in medical ultrasound will come from lower-noise optical read-out, not from further reducing thermal acoustic noise.
  • One could invert the model: because prestress shifts the resonance frequency upward, matching the modeled frequency to a measured one could serve as a non-destructive estimate of membrane tension.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript presents a semi-analytical modeling framework for integrated photonic ultrasound transducers (IPUTs). The mechanical response is computed with time-domain finite element simulations in 2D axisymmetric and 3D configurations, including a water domain with radiation boundary conditions; the optical response is added analytically through Eq. (18), which combines waveguide elongation and photoelastic index changes into a wavelength-shift receive transfer function (RTF). A thermal-noise equivalent pressure is derived in Section 5 from equipartition, an effective-mass oscillator model, and the RTF, giving Eq. (36). The model is applied to a silicon ring-resonator IPUT from Refs. [15,59] and compared with published values of resonance frequency, Q-factor, RTF, and NEP. The paper claims a close match with literature.

Significance. The derivation is genuinely forward: no parameters are fitted to the experimental RTF or NEP, the optical indices n_eff and n_g come from a mode solver, the fluid domain is included in the time-domain simulation rather than modeled as a harmonic source, and the thermal noise is derived from the same resonator parameters as the RTF. If the validation were successful, the model would be a useful quantitative design tool for IPUT sensitivity and noise. These are real strengths. However, the central validation claim fails at the only available RTF comparison point: the modeled RTF is a factor of 2–3 below experiment, and the NEP comparison in Section 6.5 does not independently constrain the model. The disagreement is therefore not a minor presentation issue; it undermines the quantitative predictive claim made in the abstract.

major comments (4)
  1. [§6.2 and §6.3] The modeled RTF is -33.6 fm/Pa in the 2D axisymmetric model and -22 fm/Pa in the 3D model, while the experimental value reported in [59] is 67 fm/Pa. This is a factor of 2–3 discrepancy, and the 3D model, which uses the actual racetrack geometry, gives the larger error. These numbers do not support the abstract's statement of a 'close match'. This comparison is the load-bearing validation of the paper's central claim.
  2. [§6.4] The RTF discrepancy is attributed to prestress and fabrication-induced geometric variations, which are explicitly declared 'beyond the scope'. Reference [22] states that the validation device buckled under prestress. A model that excludes the stress state of the very device used for validation cannot establish quantitative predictive power. To support the validation claim, the model would need to include prestress or the claim would need to be restricted to a forward-methodology description without a quantitative validation statement.
  3. [§6.5] The NEP comparison does not independently validate the thermal-noise model. The measured NEP of 0.4 Pa is dominated by readout-system noise, so it does not test the predicted thermal-noise contribution of 0.03 Pa. Furthermore, Eq. (36) multiplies p_s by the RTF, so an RTF error of a factor of 2–3 translates directly into a corresponding error in the wavelength-domain NEP. The observation that the experimental NEP is above the thermal floor may be consistent with the model, but it does not confirm Eq. (36).
  4. [§5.1 and Eq. (22)] The effective mass is set as m_eff = 0.3 x (1 + beta) m_s, with the coefficient 0.3 adopted without derivation for this specific geometry and without sensitivity analysis. Since p_s scales as sqrt(m_eff), the NEP values in Fig. 13 depend on this choice. Because Section 6.5 provides no independent experimental confirmation of the thermal-noise prediction, this parameter should either be derived from Eq. (39) or varied to show its influence on the conclusions.
minor comments (5)
  1. [Eq. (16)] The expression for C2 appears to contain a typesetting error: as printed, the bracket contains a term '/2E' and the whole bracket is again divided by 2E, which is dimensionally inconsistent. Please correct and verify the stress-optic constants against Ref. [48].
  2. [Eqs. (33) and (34)] The first term in the denominator is written as (omega - omega_0)^2, while the second term is (omega omega_0 / Q)^2. These two terms have incompatible units; the intended expression is presumably (omega_0^2 - omega^2)^2, as in Eq. (30). Please correct this in both equations.
  3. [§6.2] The predicted RTF values are negative while the experimental value is quoted as positive. If the experimental value is a magnitude only, the sign convention should be stated explicitly in the comparison.
  4. [§6.2] The 2D axisymmetric representation uses a circular ring whose radius equals R1^WG of the racetrack, which the authors note overestimates the elongation contribution. This makes the 2D and 3D RTF values not directly comparable for validation; a brief explanation of why the 2D result is still relevant would help.
  5. [Abstract and Section 6.4] The phrase 'close match' in the abstract is contradicted by the factor-of-2–3 RTF discrepancy reported in Sections 6.2 and 6.3. The abstract and conclusions should be reworded to describe the results as a forward model with quantitative limitations rather than a validated close match.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the semi-analytical RTF and NEP models are forward derivations with independently sourced parameters, and the validation data disagree with the model rather than being fitted.

full rationale

The derivation chain is forward and self-contained. The RTF, Eq. (18), is assembled from the wavelength–length relation of Eq. (7), FEM-computed displacements and stresses, and literature photoelastic constants; n_eff and n_g are obtained from an optical mode solver, and C1, C2 come from external literature, so no parameter is fitted to the target RTF or NEP. The NEP, Eqs. (32)–(36), follows from the equipartition theorem and a harmonic-oscillator representation whose effective mass and fluid loading are taken from standard references, again not fitted to the measured noise. The experimental values used for validation come from [15,59], which share some co-authors, but the model's own outputs disagree with those experiments (RTF a factor of 2–3 lower, resonance frequency ~19% higher, Q-factor ~15% different), demonstrating that the model was not constructed to reproduce the measured result. The reference to [22] about buckling/prestress in Section 6.4 is used only to explain the observed discrepancy and is not a load-bearing part of the derivation. Thus no predicted quantity reduces by construction to its inputs, and no self-citation chain forces the claimed result. The validation mismatch and the fact that the experimental NEP is dominated by readout noise are legitimate correctness or evidence-strength concerns, but they are not circularity.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The model rests on standard wave equations, a single-mode harmonic oscillator approximation with literature-based effective mass, and several simplifying assumptions (thin structures, no prestress, isotropic photoelasticity, circular waveguide in 2D). No parameters are fitted to the validation data, and no new physical entities are introduced. The most consequential assumption is the neglect of prestress, which the paper itself identifies as the likely cause of the 2-3x discrepancy between modeled and measured RTF.

free parameters (3)
  • Effective mass coefficient (0.3) = 0.3
    Multiplicative factor from [53] for the fundamental mode of a clamped circular plate; chosen by hand (not fitted) and directly scales the thermal NEP in Eq. (35).
  • Stress-optic constants C1, C2 = C1=-1.25e-11 Pa^-1, C2=4.66e-12 Pa^-1
    Taken from [48] for silicon; used in Eqs. (16)-(17) to compute the photoelastic contribution to the RTF. Literature inputs, not fitted to ultrasound data.
  • Optical mode indices n_eff, n_g = n_eff=2.228, n_g=4.386
    Computed with FIMMWAVE for the waveguide geometry; inputs from an optical mode solver, not fitted to the experimental RTF.
assumptions (6)
  • standard math Acoustic and elastic wave equations (Eqs. 1-5) govern the coupled fluid-structure response.
    Standard continuum mechanics used to derive the membrane displacement and stress fields.
  • domain assumption The membrane and waveguide are thin, linear structures; rotary inertia and shear deformation are neglected (Section 4).
    Needed to derive simple RTF expressions; may break for thick membranes or high frequencies.
  • domain assumption The membrane's dynamic response is dominated by its fundamental mode, modeled as a weakly damped single harmonic oscillator with effective mass from [53] (Section 5).
    Needed for the equipartition NEP derivation; not valid if higher modes contribute significantly.
  • domain assumption The IPUT is modeled without prestress and with nominal dimensions; prestress and fabrication variations are outside scope (Section 6.4).
    The paper explains the 2-3x RTF discrepancy by this omission, making it load-bearing for the model's predictive accuracy.
  • domain assumption The photoelastic tensor is approximated as isotropic using only p11 and p12, since the full anisotropic tensor is unavailable (Section 4.2).
    Underlies Eqs. (14)-(16); may introduce error for crystalline silicon waveguides.
  • domain assumption The waveguide is treated as a perfect ring; in the 2D axisymmetric model a circular ring with radius R1_WG is used instead of the racetrack (Section 6.3).
    The 3D model shows this approximation overestimates the RTF by about 35%.

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Cite this review

Pith. "Pith review of Semi-analytical modeling of receive transfer function and thermal noise of integrated photonic ultrasound transducers." pith.science (2026). https://pith.science/paper/LP5Z6MFK

@misc{pith2026250602817,
  author       = {Pith},
  title        = {Pith review of: Semi-analytical modeling of receive transfer function and thermal noise of integrated photonic ultrasound transducers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LP5Z6MFK}},
  note         = {Machine review of arXiv:2506.02817}
}
read the original abstract

Ultrasound transducers (UTs) are extensively used in several applications across a multitude of disciplines. A new type of UTs namely integrated photonic ultrasound transducers (IPUTs) possess superior performance due to the presence of optical interrogation systems, avoiding electric crosstalk and thermal electronic noise of the sensor. However, a major component of the IPUT's noise floor is its thermal acoustic noise. Several studies have been proposed to characterize IPUTs' behavior; nevertheless, these are either incomplete (model only the thermal noise) or targeted to characterize specific responses such as static behavior, in which the modeled receive transfer function (RTF) is about two orders lower than the experiments. In this study, we develop semi-analytical models based on time-domain finite element analysis and analytical expressions to characterize the RTF and thermal noise-induced noise equivalent pressure of IPUTs. We validate the models by comparing them with the literature, where we obtain a close match between them.

Figures

Figures reproduced from arXiv: 2506.02817 by the authors.

Figure 1
Figure 1. Schematic representation of an IPUT constituting an optical waveguide (blue ring) and a mechanical membrane (gray disc). In this study, we define the IPUT, as shown in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Transfer function and noise contribution representation in IPUT. M and O, respectively, describe the mechanical and optical components of the IPUT. 𝛿𝑃 , 𝛿𝑢, 𝛿𝜎, 𝛿𝑙, and 𝛿𝑛, respectively, represent the changes in pressure, membrane displacement (axial), stresses in the membrane, waveguide’s length change, and its refractive index change. 𝑃𝑇 𝐷 is the pressure due to the thermal displacement noise at the membrane. wave… view at source ↗
Figure 3
Figure 3. Axisymmetric representation of wave propagation through IPUT when the incoming ultrasound signal is coming from water (light green region). 𝑃 (𝒍, 𝑡) represents the plane Gaussian pressure pulse applied on the top edge of the water domain 𝒍 marked using a brown dashed line. Radiation BCs are provided to the boundaries of the water domain to limit the reflections. frequencies (MHz) is computationally intensive when us… view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Deformation of the membrane resulting in the displacement and stress of the waveguide. (a) Membrane deformed in its fundamental mode, (b) the axial displacement experienced by the waveguide due to bending of the membrane, (c) and (d), respectively, are the free body di…
Figure 5
Figure 5. Figure 5: IPUT with the surrounding fluid represented as a single harmonic oscillator (a) Membrane deformation (with the fluid on top) dominated by its fundamental mode, (b) Motion of the IPUT in the presence of surrounding fluid medium represented as a weakly damped single harm…
Figure 6
Figure 6. Figure 6: The IPUT design from [59] where (a) is the isometric view and (b) shows the side view of the IPUT only considering the racetrack waveguide (excluding all ports) with the substrate backing. Here the waveguide width 𝑤𝑊 𝐺 = 400 nm, its height ℎ𝑊 𝐺 = 220 nm, the diameter o…
Figure 7
Figure 7. Figure 7: The output displacement signal is represented as functions of (a) time and (b) frequency. The frequencies that correspond to the peak displacement (𝑓𝑐 = 0.615 MHz), and the lower (𝑓1 = 0.59 MHz) and upper (𝑓2 = 0.642 MHz) bounds of −3 dB BW are also marked in (b). 6.1.…
Figure 8
Figure 8. Figure 8: Radial displacement extracted along the thickness of the waveguide. The inset shows the schematic of the waveguide and membrane region where the arrow goes through the center of the waveguide and represents the abscissa. 𝑟 𝜃 𝑧 𝑦 𝑥 𝑧 (a) 0 0.22 -1 0 0.2 Thickness of the…
Figure 9
Figure 9. Figure 9: Normal stresses on the waveguide measured along the vertical edge of the waveguide. (a) coordinate transformation from cylindrical to Cartesian coordinate system and (b) corresponding stresses extracted along the waveguide thickness, where the axial stress is acting in…
Figure 10
Figure 10. Figure 10: Schematic representation of the 3D IPUT model, where the blue region represents the fluid domain while the gray and teal (embedded in gray) regions, respectively, are the membrane and waveguide. Since the RR is quarter-symmetric, symmetry BCs are provided on the two f…
Figure 11
Figure 11. Figure 11: The output displacement signal computed for the 3D model is represented as functions of (a) time and (b) frequency. The frequencies correspond to the peak displacement (𝑓 ∗ 𝑐 = 0.623 MHz), the lower (𝑓 ∗ 1 = 0.594 MHz) and upper (𝑓 ∗ 2 = 0.648 MHz) bounds of the −3 dB…
Figure 12
Figure 12. Figure 12: (a) Radial displacement extracted along the waveguide. The inset shows the schematic of the quarter waveguide where the arrow represents the direction along which the displacement is extracted. (b) Different stresses of the waveguide extracted along its thickness (the…
Figure 13
Figure 13. Figure 13: Plots of 𝑁𝐸𝑃𝑡ℎ as a function of (a) frequency and (b) Q factor for the operational ranges of medical ultrasound applications. The red triangles in both plots indicate the experimentally obtained 𝑁𝐸𝑃 from [15]. It can be seen that the IPUT is still limited by the noise…

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Pith tools

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