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Characterizing Photonic Ring Resonator Filters for OH Suppressed Near-infrared Astronomy

T0 review · 3 major / 8 minor · reviewed 2026-07-07 · glm-5.2

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Pith's one-line read Quadratic law predicts where ring resonator filters suppress light

desk verdict Honest prototype characterization with a reasonable qualitative finding but statistically fragile quantitative claims. The quadratic model for suppressed-wavelength progression is probably directionally correct, but the evidence is thin. read the letter →

arxiv 2607.05351 v1 pith:MTDMHWBC submitted 2026-07-06 astro-ph.IM

A. Hermann , J. Lasker , R. Vaisakh , R. Kehoe , R. Staten , A. Wallace , S. Ellis , K. Kuehn
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S. Kuhlmann
This is my paper · ORCID
classification astro-ph.IM
keywords photonicringresonatorOHsuppressionnear-infraredastronomyfreespectralrangegrouprefractiveindexH-bandsupernovacosmologyatmosphericemission
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

Photonic ring resonators (PRRs) are tiny circular waveguides that can filter out specific wavelengths of light, making them attractive for suppressing bright atmospheric OH emission lines that plague ground-based near-infrared astronomy. This paper tests a prototype PRR device (ANT-07) across the lower H-band (1480–1620 nm) and attempts to predict its performance in the upper H-band (1620–1800 nm) by fitting polynomial models to the suppressed wavelengths, depths, and linewidths (FWHM) measured at four lower orders. The central finding is that the suppressed wavelength of a PRR progresses with resonance order according to a quadratic function, rather than a linear one. This quadratic behavior is consistent with the theoretical free spectral range formula when the group refractive index of the waveguide material is allowed to vary linearly with wavelength, rather than being held constant as in the simplest theory. The quadratic-linear model yields lower chi-squared values than a pure linear fit across all five dips, and the one experimentally measured upper H-band data point (the third dip at order 6, measured at 1634.00 nm) matches the quadratic-linear prediction (1633.48 nm) more closely than the linear prediction (1624.93 nm). No reliable trends were established for how dip depth or FWHM evolve with order.

What carries the argument

The free spectral range (FSR) of a ring resonator, which governs the spacing between consecutive resonance wavelengths; the group refractive index n_g, which determines phase delay in the waveguide and is shown to vary linearly with wavelength for this silicon device; and the resonance condition (φ = 2πm), which selects which wavelengths are suppressed at each integer order m.

What would settle it

If the suppressed wavelength at order 6 for dips other than the third were measured with a calibrated dip-fitter and deviated from the quadratic-linear prediction by more than the ~1 nm agreement seen for the third dip, the quadratic model would be undermined.

Watch

Extended reading notes

Core claim

The suppressed wavelengths of photonic ring resonator filters follow a quadratic dependence on resonance order, arising from the wavelength-dependence of the group refractive index in the waveguide material. By replacing the constant group refractive index assumption with a linear wavelength-dependent term (n_g = n_0 + n_1·λ), the free spectral range acquires quadratic corrections that explain the observed curvature in the progression of suppressed wavelengths across orders. This provides a predictive model for placing suppression dips at target OH emission wavelengths across a broader spectral range than the device was originally fabricated for.

Load-bearing premise

The quadratic model for suppressed wavelength is established from only four lower-order data points per dip and corroborated by a single experimental measurement at order 6 for one dip; the remaining four upper H-band dip locations were read by eye from an unflattened spectrum where dips overlap, so the model's validity across all dips and orders rests on limited evidence.

Editorial extensions

If this is right

  • If the quadratic model holds across more orders and devices, PRR filters fabricated for one wavelength band could be predictably characterized and tuned for OH suppression across adjacent bands without fabricating entirely new chips.
  • The wavelength-dependence of the group refractive index is a critical parameter that must be measured or modeled for each PRR material and geometry; assuming it constant leads to large prediction errors (chi-squared values of 10,000+).
  • The broadening and blending of dips at higher orders (FWHM grows roughly as λ²) sets a practical upper limit on how many OH lines a single PRR can suppress before adjacent dips become unresolvable.
  • Reliable extraction of dip depth and FWHM at higher orders remains an unsolved problem; without accurate predictions of these metrics, total OH suppression cannot be guaranteed.

Reading between the lines

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

  • The quadratic model is fitted to only four data points per dip and validated against a single upper H-band measurement; a denser sampling of orders (e.g., m = 5 and m = 7) would more rigorously test whether the quadratic term suffices or a cubic correction is needed, as the Taylor expansion of the FSR with linear n_g(λ) actually contains cubic terms.
  • If the linear wavelength-dependence of n_g can be independently measured (e.g., via ellipsometry or interferometry on the same silicon wafer), the quadratic-linear model could become fully predictive rather than fitted, reducing the number of free parameters and strengthening extrapolation confidence.
  • The dip broadening problem at higher orders suggests that future PRR designs for upper H-band suppression may need smaller ring circumferences or different waveguide materials with lower dispersion to keep FWHM within the ~0.2 nm target for effective OH line suppression.
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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

3 major / 8 minor

Summary. This manuscript characterizes a prototype photonic ring resonator (PRR) filter (ANT-07) for OH suppression in near-infrared astronomy, extending prior lower H-band (1480–1620 nm) measurements into the upper H-band (1620–1665 nm). The authors measure suppressed wavelengths, FWHM, and depth for the first four orders of five dips, fit polynomial models to these data, and extrapolate to the sixth order. They conclude that suppressed wavelengths progress quadratically with order, consistent with a wavelength-dependent group refractive index, while depth and FWHM show no reliable trend. The sixth-order predictions are compared against visual-inspection measurements from an unflattened upper H-band spectrum.

Significance. The paper addresses a practical instrumentation problem—extending PRR-based OH suppression to the upper H-band—and provides a transparent, falsifiable comparison of linear versus quadratic-linear models for wavelength progression. The theoretical motivation via a linear wavelength-dependent group refractive index (Eqs. 5–6) is a reasonable physical extension of the standard FSR formula. The work is incremental but appropriate for a prototype characterization study. The target venue (JAAVSO) appears suitable for this type of instrumentation development paper.

major comments (3)
  1. §4, Eq. (4) and surrounding text: The chi-squared statistic uses σ = 10 pm for suppressed wavelengths, described as the laser resolution. However, the actual uncertainty on the DF suppressed wavelengths extracted by the dip-fitting script is not established. The script is documented to fail for depth and FWHM on most dips (§4), and DF vs. VI suppressed wavelengths differ by up to ~0.3 nm in some cases (Table 1 vs. Table 5). If the true fitting uncertainty is ~0.1–0.5 nm rather than 0.01 nm, the absolute chi-squared values in Table 2 (ranging from 3.8 to 14,184) cannot be interpreted for goodness-of-fit. The ratio between linear and quadratic-linear chi-squared is preserved, so the model selection direction is unaffected, but the claim that the quadratic-linear model provides an acceptable fit (as opposed to merely a better-than-linear fit) is not currently supported. The authors should (
  2. §4, Table 3 and Fig. 5: The sixth-order experimental validation relies entirely on visually inspected dip centers from an unflattened, blended spectrum with no quantified uncertainty. The quadratic-linear predictions agree with these measurements to within 0.1–1.9 nm (Table 3), which is clearly better than the linear model's 7–11 nm errors. However, without any uncertainty estimate on the visual inspection, the statistical significance of this agreement cannot be assessed. The authors should provide at minimum a rough uncertainty estimate for the visual measurements (e.g., based on dip width and blending).
  3. §5, Eqs. (5)–(6): The theoretical derivation introduces n0 and n1 as parameters in ng(λ) = n0 + n1λ, but these are never fitted or constrained from the data. The quadratic-linear fit to suppressed wavelengths is a purely empirical polynomial fit; it is not derived from or constrained by Eqs. (5)–(6). The claim that the quadratic progression is 'consistent with the theoretical dependence' (§7) would be strengthened if the authors could extract n0 and n1 from their fit and check whether the values are physically reasonable for silicon waveguides, or at least clarify that the theoretical derivation provides qualitative motivation rather than quantitative prediction.
minor comments (8)
  1. §1: The abstract and introduction motivate the work with supernova cosmology and OH suppression, but the connection between the specific prototype measurement (orders 1–6 of one device) and the broader astronomical application could be stated more directly.
  2. §2, Eq. (2): The notation λres,m = mλres = mLng is slightly ambiguous; the relationship between λres and Lng should be stated more explicitly.
  3. §4, Table 2: The caption refers to 'quad-lin. fit' while the text uses 'quadratic-linear' and §5 uses 'linear-quadratic'. Consistent naming would help.
  4. §4, Table 5 footnote: The footnote text is garbled ('1585 a · · ·3.3· · ·1.10'). This should be corrected.
  5. §5: The phrase 'linear-quadratic fit' is used where 'quadratic-linear' is used elsewhere. Consistent naming would help.
  6. Fig. 5: The green lines indicating dip centers are helpful but the dip numbering in blue could be larger or placed more clearly to improve readability.
  7. §6: The future work items are reasonable but somewhat lengthy; the licensing/construction paragraph could be shortened or removed as it is not directly relevant to the scientific findings.
  8. Table 4: Predicted depths for dips 4 and 5 are negative (-0.72 and -0.39 dB), which is unphysical. This should be noted and discussed, or the predictions should be presented without comment.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive report. All three major comments identify legitimate weaknesses that we can and should address in revision. We agree fully with Comments 1 and 2 and will revise accordingly. For Comment 3, we agree that the theoretical derivation should be clarified as qualitative motivation rather than quantitative prediction, and will revise the text; extracting physically constrained values of n0 and n1 from our data is not straightforward with the current four-point fits, and we explain why below.

read point-by-point responses

  1. Referee: §4, Eq. (4): The chi-squared statistic uses σ = 10 pm (laser resolution), but the actual uncertainty on DF suppressed wavelengths extracted by the dip-fitting script is not established. The script fails for depth and FWHM on most dips, and DF vs. VI suppressed wavelengths differ by up to ~0.3 nm. If the true fitting uncertainty is ~0.1–0.5 nm, absolute chi-squared values cannot be interpreted for goodness-of-fit. The model selection direction is preserved, but the claim that the quadratic-linear model provides an acceptable fit is not supported.

    Authors: The referee is correct on all points. The 10 pm value reflects the laser step size and spectrum granularity, not the uncertainty on the dip-fitting script's extracted suppressed wavelength. The discrepancies between DF and VI suppressed wavelengths (up to ~0.3 nm in Table 1 vs. Table 5) make clear that the true fitting uncertainty is larger than 10 pm, likely in the 0.1–0.5 nm range as the referee suggests. We agree that the absolute chi-squared values in Table 2 therefore cannot be interpreted for goodness-of-fit; only the ratio between linear and quadratic-linear chi-squared is meaningful for model selection. We will revise the manuscript to (1) explicitly state that σ = 10 pm represents the measurement granularity rather than the fitting uncertainty, (2) acknowledge that the true fitting uncertainty is not yet established and is likely orders of magnitude larger, (3) remove or qualify the claim that the quadratic-linear model provides an acceptable fit, replacing it with the more limited claim that the quadratic-linear model is strongly preferred over the linear model, and (4) note that proper goodness-of-fit assessment awaits improved characterization of the dip-fitting script's uncertainties. revision: yes

  2. Referee: §4, Table 3 and Fig. 5: The sixth-order experimental validation relies entirely on visually inspected dip centers from an unflattened, blended spectrum with no quantified uncertainty. The quadratic-linear predictions agree to within 0.1–1.9 nm, but without any uncertainty estimate on the visual inspection, the statistical significance of this agreement cannot be assessed. The authors should provide at minimum a rough uncertainty estimate.

    Authors: We agree. The visual inspection measurements were made on an unflattened spectrum with significant blending, and we did not assign uncertainties to these measurements. We will provide a rough uncertainty estimate in the revised manuscript. Based on the dip widths (FWHM ~2.5 nm for the third dip at sixth order, and broader for other dips) and the degree of blending visible in Fig. 5, we estimate that the visual inspection uncertainty on suppressed wavelength is approximately ±1–2 nm for the third dip (which is relatively isolated) and approximately ±2–4 nm for the more blended dips. We will add these estimates to Table 3 and discuss their implications: the quadratic-linear predictions for the third dip (0.5 nm agreement) are within this uncertainty, while for the more blended dips the agreement (0.1–1.9 nm) is comparable to the estimated uncertainty. We will also note explicitly that the sixth-order validation is qualitative rather than statistically rigorous, and that a proper test requires an improved spectrum (flattened, higher SNR) and automated dip-fitting. revision: yes

  3. Referee: §5, Eqs. (5)–(6): n0 and n1 are introduced as parameters in ng(λ) = n0 + n1λ but are never fitted or constrained from the data. The quadratic-linear fit is purely empirical. The claim that the quadratic progression is 'consistent with the theoretical dependence' would be strengthened if the authors could extract n0 and n1 and check whether they are physically reasonable, or at least clarify that the theoretical derivation provides qualitative motivation rather than quantitative prediction.

    Authors: The referee is correct that the quadratic-linear fit is purely empirical and is not derived from or constrained by Eqs. (5)–(6). We will revise the manuscript to clarify this distinction explicitly: the theoretical derivation in §5 provides qualitative motivation for expecting a quadratic component in the wavelength progression, but the fit itself is an empirical polynomial. We agree that extracting n0 and n1 from the fit and checking their physical reasonableness would strengthen the paper. However, doing so rigorously is not straightforward with our current data. The empirical quadratic-linear fit has three free parameters fitted to four data points per dip, leaving only one degree of freedom. Mapping these empirical coefficients back to n0 and n1 requires knowledge of the ring circumference L (which is set during fabrication but has manufacturing tolerances) and the relationship between the empirical fit parameters and the physical model parameters, which involves the Taylor expansion in Eq. (6). With only four data points and uncertain fitting errors, the resulting constraints on n0 and n1 would be too weak to be physically meaningful. We will state this limitation transparently and frame the theoretical derivation as qualitative motivation. We will also soften the claim in §7 from 'consistent with the theoretical dependence' to 'qualitatively consistent with the expectation from a wavelength-dependent group refractive index.' revision: partial

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity. The central claim is an empirical extrapolation with independent experimental verification; the theoretical justification is post-hoc but not self-referential.

full rationale

The paper's derivation chain is: (1) measure suppressed wavelengths at m=1–4 in the lower H-band, (2) fit linear and quadratic-linear polynomial models to those four points per dip, (3) extrapolate to m=6, (4) measure m=6 experimentally in the upper H-band, (5) compare predictions to experiment (Table 3). This is standard empirical extrapolation with an independent check. The chi-squared comparison (Table 2) is a goodness-of-fit measure on the training data, not a prediction, but the paper does not present it as such—it presents the m=6 experimental comparison as the independent validation. The theoretical justification (Eq. 5–6) introduces n_g(λ) = n_0 + n_1·λ motivated by a private communication from a collaboration member, and shows via Taylor expansion that this produces quadratic terms in the FSR. This is post-hoc qualitative motivation, not a derivation that feeds its own outputs back as inputs; n_0 and n_1 are never quantified or fitted, so there is no self-definitional loop. The citation to Ellis et al. 2023 (co-author S. Ellis) for standard results (FWHM ∝ λ², n_g not constant with wavelength) is a minor self-citation for well-known physics, not a load-bearing uniqueness theorem. The paper's weaknesses—few data points, visual inspection uncertainties, overstated claims about 'quantifying coefficients in Eq. 3'—are correctness and statistical concerns, not circularity.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

No new entities are postulated. The device ANT-07 is a physical chip fabricated by Applied Nanotools, Inc., not an invented entity.

free parameters (4)
  • Polynomial fit coefficients (linear and quadratic-linear models for suppressed wavelength) = Not explicitly tabulated; determined by least-squares minimization on 4 data points per dip
    These coefficients are fitted to lower-H-band data (orders 1–4) and used to extrapolate to order 6. They are the primary free parameters of the predictive model.
  • n0 (base group refractive index) = Not explicitly given; implicitly determined through polynomial fits
    Introduced in Eq. 5 as the base index of refraction. Its value is never independently measured or stated; it enters the theoretical justification (Eq. 6) but is not separately constrained.
  • n1 (linear wavelength-dependent dispersion term) = Not explicitly given; sourced from private communication (P. Liu)
    Introduced in Eq. 5 as a linear dispersion correction. Its value is not independently published or measured in this paper; it comes from unpublished work by a collaboration member.
  • Sigma assumptions for chi-squared (10 pm for wavelength, 0.25 dB for depth/FWHM) = 10 pm and 0.25 dB
    These uncertainty values are chosen based on projected laser resolution and visual estimation ability, not independently calibrated. They directly affect the chi-squared values in Table 2.
assumptions (4)
  • domain assumption The group refractive index n_g varies linearly with wavelength (Eq. 5)
    Section 5: This is stated to come from work by a PhD student in the collaboration via private communication. It is not independently verified in the paper. The quadratic model for suppressed wavelength depends on this assumption.
  • standard math The FSR formula (Eq. 3) accurately describes the PRR's resonance spacing
    Section 2: Standard ring resonator theory from Heebner et al. (2007). Used as the basis for the theoretical derivation in Eq. 6.
  • ad hoc to paper Measurement uncertainties are constant across all orders
    Section 4: 'All measurement uncertainties are assumed to be constant and not varying with order.' This simplifies the chi-squared calculation but may not hold given that dip broadening and blending increase with order.
  • ad hoc to paper Visual inspection provides reliable estimates of dip depth and FWHM
    Section 4: VI metrics are used in lieu of DF metrics because the dip-fitting script failed. The paper assumes visual estimates with 0.25 dB uncertainty are sufficient, but this is not validated.

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Cite this review

Pith. "Pith review of Characterizing Photonic Ring Resonator Filters for OH Suppressed Near-infrared Astronomy." pith.science (2026). https://pith.science/paper/MTDMHWBC

@misc{pith2026260705351,
  author       = {Pith},
  title        = {Pith review of: Characterizing Photonic Ring Resonator Filters for OH Suppressed Near-infrared Astronomy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MTDMHWBC}},
  note         = {Machine review of arXiv:2607.05351}
}
read the original abstract

Supernova cosmology relies on accurate measurement of the absolute magnitudes of Type Ia supernovae. Observation in the visible incurs significant systematic uncertainties in these measurements due to their high degree of interstellar dust extinction. Observing in the near-infrared (750-2500 nm) mitigates this issue by decreasing attenuation, decreasing dispersion, and increasing supernova observation distances. However, ground-based observations in the near-infrared suffer from sky background caused by atmospheric OH emission lines. Advancements in photonic ring resonator filter devices make it feasible to suppress these lines. In this paper, we evaluate the performance of a prototype photonic ring resonator device developed for use in the lower H-band (1480-1620 nm). Specifically, we characterize the progression of suppressed wavelengths into the upper H-band (1620-1800 nm) enabling the suppression of emission lines over a broader wavelength range.

Figures

Figures reproduced from arXiv: 2607.05351 by the authors.

Figure 1
Figure 1. Diagram provides an abstract representation of the evanescent coupling between the ring resonator and the source fiber. Solid arrows indicate signals, while dashed ar￾rows indicate coupling coefficients. As a result of evanescent coupling, the entire spec￾trum of input light cross-couples into the ring. Within the ring, each wavelength undergoes repeated TIR. For the case of negligible attenuation from coupling, wav… view at source ↗
Figure 2
Figure 2. (1) tunable laser with wavelength range of 1620 to 1665 nm, (2) adjustable polarization controller, (3) pho￾tonic ring resonator device ANT-07, (4) InGaAs detector, (5) digitizer. All components are connected via fiber coupling. Additionally, the upper H-band experimental setup included a protractor to measure the angle of the in-line polarization controller, which we varied incrementally to determine the angle at w… view at source ↗
Figure 4
Figure 4. indicates that, as a dip’s order increases, its FWHM also increases such that consecutive dips begin to blend together and become unresolvable. This is ex￾pected, as FWHM of a dip is proportional to the sup￾pressed wavelength squared (Ellis et al. 2023). The dips also become more shallow with increasing wavelength, likely a result of increased attenuation due to de-tuning (Heebner et al. 2007). As seen in [PITH_FUL… view at source ↗
Figures from the paper (4 more)
Figure 3
Figure 3. Figure 3: Unflattened spectra of ANT-07 in the upper H￾band. All dips are in their sixth order. The relative polar￾ization angles are (a) -45° (b) -90° (c) -120°. Spectrum (c) was selected for subsequent upper H-band analysis. Green lines indicate the visually inspected dip loca…
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: The fits and extrapolations for the third dip with increasing order. Dashed lines indicate extrapolations for m > 4. Black is the linear fit, red is the quadratic-linear model, and blue is the cubic-quadratic-linear model. χ 2 s are tabulated in the bottom right. The r…
Figure 7
Figure 7. Figure 7: Plots showing the linear fits and extrapolations for VI depth (top) and FWHM (bottom) of the third PRR’s dips with order. Dashed lines indicate extrapolations for m > 4. The red points at the 6th order are the experimental VI measurements for depth and FWHM, respective…

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