{"id":"acd8a79b-8f92-479a-8f0f-cbf2e28580b4","arxiv_id":"2507.05253","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"In silicon photonic crystal slabs with stealthy-hyperuniform disorder, band linewidths jump sharply at k = K/2, and residual in-stealthy-region single scattering is quantitatively explained by the imaginary part of the effective mass from radiative loss.","lead":"Researchers fabricated large silicon photonic crystal slabs with specially designed stealthy-hyperuniform hole-size disorder and measured how light scattering broadens the photonic band lines. They observed the predicted transition at the stealthy cutoff, and showed that residual scattering inside the stealthy region comes from the slab's radiative losses, modeled as a complex effective mass.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Fabricated spectral density is never directly measured; the claim that the actual scattering kernel is stealthy rests on a simulated linear radius-to-potential mapping (Eqs. S34-S37), whose failure would invalidate the K/2 transition.","rationale":"After reconstructing the argument, the transition at |k|=K/2 follows from the support of the spectral density entering the leading-order self-energy (Eq. 2). The entire experimental program - the stealthy regime, the non-Hermitian residual scattering, and the multiple-scattering onset - is interpreted within the single-scattering formula Eq. (S7), so the identity of that spectral density with the fabricated dielectric structure is essential. The paper's own caveats (Supplemental Section 2 and Eq. S35) state that the relation between radius change and potential is only linear to leading order and that the 10^-2 threshold is an estimate; nevertheless, it is a simulated estimate on designed patterns, not a characterization of fabricated samples or of the k-dependent Bloch overlap matrix elements. This is a limitation, not a demonstrated error: the measured phase diagrams matching theory provide indirect evidence that the effective spectral density is stealthy, and the non-Hermitian effect's w0^2 scaling and K-dependence (Fig. 5) are nontrivial. The reader's CONDITIONAL verdict already encodes this addressability. The proposed SEM/mask-based spectral-density check would settle the concern without requiring new theory, so no verdict change is needed.","tokens_in":1016,"tokens_out":1089,"duration_ms":289709,"concrete_test":"Take the actual GDS/BEAMER pattern files (or high-resolution SEM images of the w0=0.2 and w0=0.4 samples), extract hole radii, and compute the ensemble-averaged spectral density S_eps(q)=<|int eps(r) exp(-iq dot r) dr|^2>/A from the real dielectric profile. Compare S_eps(q<K)/S_eps(q>K) with the F about 10^-3/10^-2 claim in Fig. S3; if the measured ratio exceeds these thresholds, recompute the predicted excess linewidth from Eq. (S7) with the measured S_eps(q) and check whether the transition at |k|=K/2 and the in-stealthy-region linewidth survive. A simpler variant: generate the designed patterns with added fabrication noise (sigma_r about 2-5% of r0) and repeat the Fig. S3 calculation; if the stealthy-region leakage grows above 1%, the radius-to-potential mapping is too fragile to support the central claim.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central observable is excess linewidth, and its interpretation as a probe of stealthy-hyperuniform scattering depends on the identity between the spectral density of the imposed local potential V (Eqs. S28/S31) and the actual scattering kernel of the fabricated photonic crystal. The only support for this identity is the analytic estimate in Supplemental Eqs. (S34)-(S37) and Fig. S3, which assumes each hole is an independent circular form factor whose radius is linearly related to the band-edge shift V0, and that higher-order leakage |eps~(q<K)|^2 is at most 10^-2 of the outside value. This estimate is made on the designed pattern, not on the fabricated samples; the paper never measures the spectral density of the actual dielectric profile. Fabrication disorder (acknowledged in Fig. 4 as significant near w0=0.05), etch bias, and nonlinearity of the radius-to-band-edge mapping (Fig. S2(d) is only linearized near r0) can each put spectral weight inside the exclusion circle. If the effective F in Eq. (S38) exceeds the claimed 10^-2, the residual linewidth in the stealthy regime attributed to the complex-mass mechanism (Eq. S57) would be contaminated by ordinary non-stealthy scattering, and the sharp transition at |k|=K/2 would not be a clean test of stealthy hyperuniformity. Because the non-Hermitian and multiple-scattering conclusions are all read through the same kernel, this unmeasured assumption is the most load-bearing.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports experiments on large-area silicon photonic crystal slabs in which stealthy-hyperuniform disorder is imposed by Fourier-filtered, site-dependent hole-radius variations on a square lattice. Using angle-resolved reflection spectroscopy, the authors extract the linewidths of a quadratic photonic band and define an excess linewidth relative to a clean periodic sample. They observe a sharp increase in excess linewidth at |k| = K/2, which they identify as the transition from the stealthy to the non-stealthy scattering regime. They further report a finite excess linewidth inside the stealthy region, which they attribute to the imaginary part of the complex effective mass arising from out-of-plane radiative loss, and a super-quadratic disorder dependence, which they attribute to multiple scattering. The theoretical framework is a leading-order self-energy expression using the spectral density of the imposed potential, evaluated for Hermitian and non-Hermitian quadratic bands, with closed-form analytical results verified against numerical summation and compared with the experimental phase diagrams.","tokens_in":32111,"tokens_out":7003,"duration_ms":80672,"significance":"If the central interpretation holds, this is a valuable experimental advance: it uses photonic linewidths as a direct probe of the scattering kernel in stealthy-hyperuniform media, provides an analytic formula for the K/2 transition, and demonstrates a non-Hermitian contribution to disorder scattering through a parameter-free prediction based on the clean-sample imaginary effective mass. The large system sizes (10^6-10^7 sites), the closed-form self-energy results, and the explicit quantitative comparison between theory and experiment are notable strengths. The manuscript is also unusually candid about its assumptions, particularly in Supplemental Section 2, where the authors state that the photonic crystal is only 'effectively stealthy' and quantify the leakage by a simulated estimate. However, the load-bearing premise -- that the fabricated samples have negligible spectral density inside the exclusion circle -- is never directly measured, and this same unmeasured quantity competes with both the non-Hermitian and multiple-scattering attributions.","major_comments":[{"comment":"The premise that the fabricated samples are effectively stealthy is not directly tested. The only support for the in-stealthy-region leakage factor F <= 10^-2 is a calculation on the designed dielectric profile that assumes independent circular holes and a linear radius-to-potential mapping (Eqs. S34-S37), not a measurement of the fabricated samples. Etch bias, sidewall roughness, and radius errors (acknowledged in Fig. 4 for w0 < 0.05) can only add spectral weight inside the exclusion circle. Because the transition at |k| = K/2, the non-Hermitian residual, and the multiple-scattering term are all interpreted through this scattering kernel, the paper should either measure the spectral density of the actual fabricated patterns (for example, from SEM images) or demonstrate robustness of the conclusions to F at fabrication-realistic levels. As it stands, the central 'effectively stealthy' premise is an unverified assumption.","section":"Supplemental Section 2, Eqs. (S34)-(S38) and Fig. S3"},{"comment":"The attribution of the O(w0^4) excess linewidth in the stealthy regime to multiple scattering is not uniquely supported. The authors' own estimate in Supplemental Section 2 gives F proportional to w0^2, and Eq. (S51) for k < K/2 yields an excess linewidth proportional to F * w0^2, i.e., O(w0^4) -- the same scaling as the fitted higher-order term in Fig. 5(c). Thus the observed super-quadratic growth is equally consistent with residual non-stealthy single scattering from imperfect stealthiness. The paper needs a diagnostic that separates these two mechanisms, such as measuring F for each fabricated sample or comparing samples with intentionally different F, before the multiple-scattering interpretation can be accepted.","section":"Fig. 4 and Supplemental Eq. (S51)"},{"comment":"The headline claim that residual single scattering inside the stealthy region is an intrinsically non-Hermitian effect is not uniquely established by the data. A Hermitian quadratic band with a non-zero stealthiness leakage F already produces a finite, roughly k-independent excess linewidth for k < K/2 (Eq. S51), with magnitude proportional to F. Therefore the observed finite excess linewidth in the stealthy region can be explained without any complex effective mass if F is large enough. The quantitative match in Fig. 5(b) is encouraging, but it relies on the simulated F ~ 10^-3; without a fabricated-sample measurement of F or a control experiment, the non-Hermitian attribution is not fully separated from imperfect stealthiness.","section":"Main text Fig. 5 and Supplemental Eq. (S51)"}],"minor_comments":[{"comment":"The color maps for the excess linewidth in Figs. 3 and 4 are presented without colorbars or explicit units; adding a shared colorbar would make the phase diagrams substantially easier to interpret.","section":"Main text Figs. 3 and 4"},{"comment":"The sum over q in Eq. (2) would benefit from stating explicitly that it runs over the first Brillouin zone and that the spectral density is the disorder-averaged quantity defined in Supplemental Section 1.","section":"Main text Eq. (2)"},{"comment":"The caption of Fig. 2(f) states that arrows marked with an x denote forbidden scattering events, but no x marks appear in the panel; please clarify the caption or the figure.","section":"Main text Fig. 2(f)"},{"comment":"The quadratic fit used to extract Im(1/2m) and Im(E0) is described only by its resulting values; reporting the number of fitted k points and a residual or goodness-of-fit measure would strengthen confidence in these extracted parameters.","section":"Supplemental Section 6, Fig. S12(e)"},{"comment":"The second transition at kx = pi/(3a) - K/2 is demonstrated with a single sample and only in the Supplemental Material; the main text should either mention this second transition explicitly or point the reader to the supplement more prominently.","section":"Supplemental Section 5, Fig. S9(e)"},{"comment":"The manuscript does not include a data availability statement; given the large experimental dataset and the centrality of the extracted linewidths, a statement about data and code availability would be helpful.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"To the editor: This is a strong experimental paper with a clear theoretical framework, and the analytical self-energy results are a genuine contribution. However, the central interpretation rests on an unmeasured property of the fabricated samples -- the spectral density inside the exclusion circle -- and the same unmeasured leakage term competes with both the multiple-scattering and the non-Hermitian attributions. I recommend major revision with a request for either direct spectral-density characterization of the fabricated patterns or a correspondingly weakened set of claims, so that the stealthiness premise and the mechanism attributions are placed on firmer ground."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"I read this as a genuinely useful paper. The new thing is not stealthy-hyperuniform disorder itself but the observable: they use photonic band linewidth as a self-energy probe, which lets them see the K/2 transition directly in fabricated slabs, and then identify a non-Hermitian mechanism—complex effective mass from radiative loss—that produces residual single scattering inside the stealthy region. The period-tripling second transition is a nice addition, and the main analytic formula is checked against numerical summation and experiment with real band parameters. That is real progress, not just a new sample of an old idea.\n\nThe strongest piece is the non-Hermitian claim. They extract Im(1/2m) from a clean sample and use it to predict the in-stealthy-region linewidth, and it matches the disordered-sample data without a fit parameter for that part. That is a clean falsifiable step and it works. I also think the central transition at |k| = K/2 is well supported: the phase diagram has the right shape, and the Hermitian single-scattering formula plus the non-Hermitian correction explains the residual linewidth quantitatively.\n\nSoft spots, in proportion. The most load-bearing assumption is that the fabricated dielectric profile actually has a stealthy spectral density. They never measure it; they estimate from the designed pattern that the in-stealthy-region spectral density is below 10^-2 of the outside value (F ~ 10^-3 for typical samples). The estimate assumes a linear radius-to-potential mapping and ignores fabrication disorder, which they acknowledge is significant near w0 = 0.05. If F were larger than claimed, part of the residual linewidth attributed to Im(m) would be ordinary non-stealthy scattering. That would weaken, but not necessarily destroy, the non-Hermitian conclusion—the quantitative agreement with the clean-sample prediction argues the contamination is not dominant. Still, this is exactly the measurement that would make the paper bulletproof.\n\nThe multiple-scattering evidence is softer: it rests on a fitted O(w0^4) term, not a derived next-order calculation. That is fine as evidence, but I would not call it a quantitative test. The 8-parameter Fano fits and the phase diagrams also lack full error budgets, and no data or code are shipped. These are addressable rather than fatal.\n\nWho is this for? Anyone working on correlated disordered photonics, wave transport in hyperuniform media, or non-Hermitian band physics. It deserves a serious referee, and with a few revisions—ideally a measured or at least more carefully bounded spectral density, an error budget on the fits, and a clearer statement about the multiple-scattering fit—it will be worth citing. I would not desk reject it.","headline":"A strong experimental-theory paper on linewidth as a probe of stealthy-hyperuniform scattering; the central K/2 transition holds up, and the main weakness is the unmeasured fabricated spectral density.","tokens_in":32719,"tokens_out":1463,"would_cite":true,"duration_ms":20448,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["42.70.Qs","42.25.Dd"],"model":"deepseek-v4-flash","headline":"Photonic band linewidths directly measure scattering by stealthy-hyperuniform disorder, with a sharp transition at |k| = K/2 and residual scattering from the complex effective mass.","keywords":["stealthy hyperuniformity","photonic crystal slab","linewidth","disorder scattering","bound state in the continuum","complex effective mass","Fourier filtering","multiple scattering"],"falsifier":"Measure the excess linewidth inside the stealthy region ($|\\mathbf{k}|<K/2$) for a slab whose band is purely guided below the light line, where radiative loss and hence $\\mathrm{Im}(m)$ vanish; if a finite residual excess linewidth remains, the non-Hermitian explanation is wrong. Alternatively, directly characterize the dielectric profile of a fabricated sample and compute $\\tilde{\\rho}(\\mathbf{q})$ to verify that the exclusion region is genuinely empty.","tokens_in":31524,"feed_emoji":"💡","tokens_out":9118,"duration_ms":86776,"temperature":0.7,"pith_summary":"Photonic crystal slabs whose hole radii carry stealthy-hyperuniform disorder should suppress single scattering for wavevectors whose iso-frequency contour lies entirely inside the momentum exclusion region. The paper uses the excess linewidth of a quadratic photonic band—the difference in linewidth between disordered and clean samples—as a direct, angle-resolved experimental measure of that scattering. It reports a sharp transition at $|\\mathbf{k}| = K/2$, where $K$ is the exclusion-region cutoff, with steeply rising linewidth above and almost none below. It also finds that residual linewidth inside the stealthy region is not an artifact of imperfect stealthiness but an intrinsic non-Hermitian effect: the band's complex effective mass, caused by radiative loss out of the slab, allows scattering to states with different real energy. If correct, this makes photonic-crystal linewidths a quantitative probe of hyperuniform wave transport and identifies non-Hermiticity as essential to interpreting 'transparent' stealthy systems.","feed_headline":"Band linewidths expose stealthy disorder's scattering cutoff","feed_subtitle":"In silicon photonic slabs, scattering switches on exactly when the mode contour exits the disorder's exclusion zone.","key_machinery":"The machinery is the leading-order self-energy of a quadratic band under a weak random potential whose spectral density $\\tilde{\\rho}(\\mathbf{q})$ vanishes in the exclusion region $|\\mathbf{q}|<K$. Its imaginary part, $\\mathrm{Im}\\,\\Sigma_{\\mathbf{k}} = (1/N)\\sum_{\\mathbf{q}} \\mathrm{Im}[\\tilde{\\rho}(\\mathbf{q})/(\\mathrm{Re}\\,E_{\\mathbf{k}} - E_{\\mathbf{k}+\\mathbf{q}} + i0^+)]$, equals the excess linewidth and is evaluated analytically by integration over the iso-frequency contour; the contour geometry yields the $k=K/2$ transition. The second load-bearing element is the complex effective mass $m$ inherited from the symmetry-protected bound state in the continuum: the radiative decay rate $O(k^2)$ appears as $\\mathrm{Im}(1/2m)$, which converts the infinitely thin iso-frequency contour into a ring of finite $\\mathbf{k}$-space width, producing the non-Hermitian residual scattering. Period-tripling of the disorder pattern (correlating hole radii over $3\\times 3$ plaquettes, $b=3a$) enlarges the effective stealthiness parameter and creates nine exclusion circles that produce a second transition at $k_x = \\pi/(3a) - K/2$ along $k_y=0$.","core_discovery":"The central claim is that the transition between stealthy and non-stealthy scattering behavior is directly observable in the linewidths of photonic bands of large silicon slab samples, and that the transition condition is geometric: single scattering is forbidden below $|\\mathbf{k}| = K/2$ because no allowed scattering vector can connect two points on the same iso-frequency contour while staying inside the excluded spectral-density region. Above that threshold the excess linewidth grows from zero as an arccos function of $K/2|\\mathbf{k}|$, in quantitative agreement with a leading-order self-energy calculation. The same measurements show that the excess linewidth in the stealthy regime is finite and proportional to the imaginary part of the effective mass times the square of the disorder, establishing that out-of-plane radiative loss—through a symmetry-protected bound state in the continuum at the band tip—qualitatively changes the scattering phase diagram: it broadens the iso-frequency contour in $\\mathbf{k}$-space and permits scattering that a Hermitian theory forbids. Higher-order disorder scaling reveals additional multiple-scattering contributions in the stealthy regime.","pith_inferences":["If the linewidth probe is as direct as claimed, the same method could be inverted: angle-resolved excess-linewidth data could reconstruct the spectral density $\\tilde{\\rho}(\\mathbf{q})$ of other correlated-disorder patterns, effectively imaging the scattering kernel.","The complex-mass scattering mechanism is generic for any open wave system with a BIC-pinned quadratic band, so similar residual scattering should appear in acoustic, plasmonic, or polaritonic analogs with radiative loss.","A multiple-scattering theory beyond $\\tilde{\\rho}^2$ is the clear next step; linewidth measurements already show the need for it at $w_0>0.2$.","The fixed-effective-mass assumption could be relaxed by letting disorder renormalize $\\mathrm{Im}(m)$; this likely explains part of the quantitative mismatch at the largest disorder values."],"forward_implications":["Excess linewidth can serve as a general experimental observable for scattering by correlated disorder in photonic systems, complementing direct transmission measurements.","The transition at $|\\mathbf{k}| = K/2$ is a direct spectroscopic signature of stealthy-hyperuniformity: below it, leading-order single scattering is suppressed; above it, scattering grows sharply.","Residual transparency in the stealthy regime is set by non-Hermitian radiative loss, not by fabrication imperfections, so suppressing out-of-plane loss would sharpen the transition and reduce residual linewidth.","Multiple scattering sets in as disorder increases even inside the stealthy region, meaning the suppression of scattering holds only to leading order.","Period-tripling provides a practical way to reach large stealthiness parameters at small accessible wavevectors, with a predictable second transition from the nine-fold exclusion geometry."],"supporting_citations":[{"why":"Defines hyperuniformity through vanishing low-wavenumber density fluctuations, the foundational concept of the paper.","marker":"[1]"},{"why":"Comprehensive survey of hyperuniform states of matter, providing the theoretical context for stealthy-hyperuniformity.","marker":"[2]"},{"why":"Claims high-density hyperuniform materials can be transparent, the transparency prediction this experiment probes at the level of linewidth.","marker":"[3]"},{"why":"Open-source guided-mode expansion package used for band-structure simulation and for calibrating the radius-to-potential mapping.","marker":"[22]"},{"why":"Gives the $O(k^2)$ radiative-loss scaling of BIC-governed resonances, the origin of the complex effective mass.","marker":"[24]"},{"why":"Provides the Fourier filtering method used to generate the stealthy-hyperuniform disorder configurations.","marker":"[25]"},{"why":"Supplies the self-energy formalism for disordered systems, from which the excess-linewidth observable is derived.","marker":"[27]"},{"why":"Guided-resonance reflection model used to fit reflection spectra and extract linewidths.","marker":"[28]"}],"fun_headline_variants":["Stealthy disorder's quiet zone ends at geometric cutoff in photonic bands","Radiative loss causes residual scattering in stealthy photonic slabs","Sharp linewidth jump marks stealthy-to-scattering transition in photonic bands","Non-Hermitian effect lets light scatter inside stealthy exclusion zone"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that a hole-radius change acts as a weak local potential that shifts only the band-edge energy while leaving the quadratic dispersion and the complex effective mass fixed, and that the fabricated dielectric pattern is effectively stealthy because its in-region spectral density is below $10^{-2}$ of the out-of-region value, as estimated by simulation rather than direct measurement of the fabricated samples.","fun_headline_variants_meta":{"raw":{"variants":["Stealthy disorder's quiet zone ends at geometric cutoff in photonic bands","Radiative loss causes residual scattering in stealthy photonic slabs","Sharp linewidth jump marks stealthy-to-scattering transition in photonic bands","Non-Hermitian effect lets light scatter inside stealthy exclusion zone"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000411,"raw_usage":{"total_tokens":2174,"prompt_tokens":1037,"completion_tokens":1137,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":653,"completion_tokens_details":{"reasoning_tokens":1058}},"tokens_in":653,"tokens_out":1137,"duration_ms":10065,"temperature":1.0,"reasoning_tokens":1058,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T19:29:59.623171+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the excess linewidth inside the stealthy region ($|\\mathbf{k}|<K/2$) for a slab whose band is purely guided below the light line, where radiative loss and hence $\\mathrm{Im}(m)$ vanish; if a finite residual excess linewidth remains, the non-Hermitian explanation is wrong. Alternatively, directly characterize the dielectric profile of a fabricated sample and compute $\\tilde{\\rho}(\\mathbf{q})$ to verify that the exclusion region is genuinely empty.","supporting_citations":[{"cited_title":"intrinsic loss","cited_arxiv_id":null,"evidence_quote":"Defines hyperuniformity through vanishing low-wavenumber density fluctuations, the foundational concept of the paper."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Comprehensive survey of hyperuniform states of matter, providing the theoretical context for stealthy-hyperuniformity."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Claims high-density hyperuniform materials can be transparent, the transparency prediction this experiment probes at the level of linewidth."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Open-source guided-mode expansion package used for band-structure simulation and for calibrating the radius-to-potential mapping."},{"cited_title":"F., Gopalakrishnan, S","cited_arxiv_id":null,"evidence_quote":"Gives the $O(k^2)$ radiative-loss scaling of BIC-governed resonances, the origin of the complex effective mass."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Fourier filtering method used to generate the stealthy-hyperuniform disorder configurations."},{"cited_title":"& Dal Negro, L","cited_arxiv_id":null,"evidence_quote":"Supplies the self-energy formalism for disordered systems, from which the excess-linewidth observable is derived."},{"cited_title":"K., Kim, J., Steinhardt, P","cited_arxiv_id":null,"evidence_quote":"Guided-resonance reflection model used to fit reflection spectra and extract linewidths."}],"review_version":1}