{"id":"ca21d2aa-be23-404e-abc7-7d0166e6bec5","arxiv_id":"2607.06469","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":5,"one_line_summary":"Exploiting Fabry-Perot and symmetry-protected BICs in multilayered time-varying metasurfaces enables polarization-insensitive scattering anomalies and monochromatic nonreciprocal transmission at perturbative modulation amplitudes.","lead":"This paper shows that bound states in the continuum (BICs) in multilayered, time-varying metasurfaces can produce strong optical effects—like lasing, perfect absorption, and one-way light transmission—at very low modulation powers. A smart generalist might read it because it bridges high-Q nanophotonics with time-varying media, potentially enabling practical, low-power optical isolators and dynamic wave control for on-chip photonics.","discovery_kind":"unclear","skeptic_critique":{"model":"glm-5.2","headline":"Lasing/CPA thresholds and nonreciprocal divergence rely on a lossless, purely real permittivity; finite material absorption caps the BIC Q-factor and may eliminate the perturbative regime.","rationale":"The reader correctly identified the lossless, idealized modulation assumption as the weakest point. My analysis confirms this is indeed the single most load-bearing concern: the entire 'perturbative regime' claim depends on the diverging Q-factor of BICs, which is strictly a lossless-limit phenomenon. The thresholds reported (M ~ 10^-3 to 10^-4) are so small that even modest material absorption could increase them by orders of magnitude. However, I recommend UNCHANGED rather than a harsher verdict because: (1) the paper explicitly states the framework is general and the perturbative examples are illustrative; (2) the theoretical framework itself (T-matrix, S-matrix, pseudounitarity) is internally consistent and correctly derived; (3) the use of BICs to lower modulation thresholds is a valid and novel conceptual contribution regardless of the exact quantitative thresholds; (4) the paper does not claim experimental readiness, and the lossless assumption is standard for initial theoretical demonstrations of this type. The CONDITIONAL verdict is appropriate — the claim holds in principle but requires the loss analysis to confirm the perturbative regime survives realistic material constraints. The reader's assessment is accurate and well-calibrated.","tokens_in":23700,"tokens_out":898,"duration_ms":355598,"concrete_test":"Introduce a small imaginary part to the permittivity, ε(t) = 1 + (χ_st + iχ_abs)[1 + Mcos(Ωt+φ)], and recompute the S-matrix eigenvalues for the FP-BIC cavity (Fig. 2c-d) and the nonreciprocal device (Fig. 4c-e) as a function of χ_abs. Track how the CPA/lasing threshold M and the nonreciprocal pole position M shift. If for a realistic material loss tangent (e.g., Im[ε]/Re[ε] ~ 10^-3 to 10^-2 for TCOs or doped dielectrics at optical frequencies) the threshold M exceeds ~0.1, the 'perturbative regime' claim is substantially weakened. If M remains below ~0.01 for realistic loss values, the claim is robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that scattering anomalies (EP, CPA, lasing) and strong nonreciprocity occur at 'extremely small, perturbative modulation amplitudes' (M << 1). This relies entirely on the diverging radiative Q-factor of the BIC in the lossless limit. The entire framework uses a real, lossless permittivity ε(t) = 1 + χ_st[1 + Mcos(Ωt+φ)] with χ_st = 10.68. No imaginary part (material absorption) is included anywhere in the calculations. For the FP-BIC example, the CPA/lasing threshold is M = 6×10^-3; for the SP-BIC nonreciprocal device, the S-matrix pole appears at M = 1.319×10^-4. These thresholds scale as ~1/Q_rad in the lossless case. However, in any real material (TCOs, dielectrics), the total Q-factor is capped at Q_total = Q_rad * Q_abs / (Q_rad + Q_abs), where Q_abs is set by intrinsic material loss. If Q_abs is finite, the effective Q is bounded, and the modulation amplitude required to reach the lasing/CPA threshold or the nonreciprocal pole increases proportionally. Specifically, the threshold M scales as ~1/Q_total rather than ~1/Q_rad. If Q_abs is comparable to or smaller than the (detuned) Q_rad used in the simulations, the required M could shift from the perturbative regime (M << 1) to M ~ 1 or higher, invalidating the headline claim. The paper provides no quantitative analysis of how finite losses affect these thresholds. This is the load-bearing assumption: that the lossless BIC Q-factor is a meaningful proxy for achievable Q in experimentally realizable materials.","agreement_with_reader":"agree"},"referee_report":{"model":"glm-5.2","summary":"This manuscript presents the first application of bound states in the continuum (BICs) to multilayered time-varying metasurfaces. The authors develop a theoretical framework based on T-matrix and S-matrix methods for spatio-temporal metamaterials and demonstrate two main results: (1) polarization-insensitive scattering anomalies (exceptional points, coherent perfect absorption, and lasing) at extremely small modulation amplitudes using Fabry-Perot BICs in a metasurface cavity, and (2) strong nonreciprocal one-way monochromatic transmission using symmetry-protected BICs with a traveling-wave modulation phase profile. The framework builds on the authors' prior work on T-matrix methods for time-varying metasurfaces (Refs. 20, 21, 30, 55) and applies it to the BIC setting. The derivations in the supplementary sections appear consistent, and the convergence parameters are documented.","tokens_in":24511,"tokens_out":1432,"duration_ms":169424,"significance":"The paper addresses a timely question at the intersection of BIC physics and time-varying metamaterials. The core idea—that diverging radiative Q-factors of BICs can lower the modulation threshold for scattering anomalies and nonreciprocity—is physically reasonable and, if valid, represents a useful contribution. The framework is general and not limited to perturbative modulation amplitudes. The demonstration of monochromatic nonreciprocal transmission (avoiding the frequency-conversion sidebands typical of time-modulated nonreciprocal devices) is a notable conceptual advance. The pseudounitarity and reciprocity conditions (Eqs. 11–12) provide a rigorous foundation for the S-matrix analysis. However, the central quantitative claims about 'extremely small' and 'perturbative' modulation amplitudes are derived entirely in the lossless limit, and the paper does not provide a quantitative analysis of how finite material losses affect these thresholds. This gap is load-bearing for the headline claims and must be addressed.","major_comments":[{"comment":"The central quantitative claims—that scattering anomalies and nonreciprocity occur at 'extremely small, perturbative modulation amplitudes' (M << 1)—rely entirely on the diverging radiative Q-factor of the BIC in the lossless limit. The permittivity is taken as purely real: ε(t) = 1 + χ_st[1 + Mcos(Ωt+φ)] with χ_st = 10.68, with no imaginary part anywhere in the calculations. For the FP-BIC example, the CPA/lasing threshold is M = 6×10⁻³ (Fig. 2(d)); for the SP-BIC nonreciprocal device, the S-matrix pole appears at M = 1.319×10⁻⁴ (Fig. 4(c)). These thresholds scale as ~1/Q_rad in the lossless case. However, in any real material (TCOs, dielectrics), the total Q-factor is capped at Q_total = Q_rad·Q_abs/(Q_rad + Q_abs), where Q_abs is set by intrinsic material absorption. If Q_abs is finite, the effective Q is bounded, and the modulation amplitude required to reach the lasing/CPA threshold","section":null},{"comment":"The paper claims to be the 'first exploitation of BICs in multilayered time-varying metasurfaces' and states that 'BICs in multilayered time-varying metasurfaces...have never been considered.' However, Ref. 31 (Garg et al., 'Photonic time crystals assisted by quasi-bound states in the continuum,' Sci. Adv., accepted 2026) appears to be by the same group and directly addresses qBICs in time-varying metasurfaces. The relationship between the present manuscript and Ref. 31 should be clarified: what is genuinely new here beyond what was already reported in Ref. 31? The novelty claim should be scoped precisely, particularly regarding the multilayered aspect and the nonreciprocal device.","section":null}],"minor_comments":[{"comment":"In the caption of Fig. 2(c), the lasing point L_x is described as 'not shown' in the eigenvalue plot, yet |λ_L_x| is plotted in Fig. 2(d). The caption should clarify what is and is not shown.","section":null},{"comment":"The phase profile φ_n = 2.85nπ/4 (Section on Nonreciprocal transmission) is stated to be 'chosen so that the nonreciprocity of the resulting structure is significant,' but no systematic optimization or sensitivity analysis is provided. A brief discussion of how this choice was arrived at, or how robust the nonreciprocal response is to variations in φ_n, would help reproducibility.","section":null},{"comment":"The static susceptibility χ_st = 10.68 is used throughout but its physical origin (material, wavelength regime) is not specified. Given that the paper claims relevance to TCOs and dielectrics, specifying the corresponding material and wavelength would strengthen the connection to experimental feasibility.","section":null},{"comment":"In Eq. (6c), the branch cut structure for ω_j < 0 involves k_jgαd with a negated in-plane wavevector (-k_∥ + g). While the supplementary material provides derivation details, a brief physical interpretation in the main text of why the in-plane wavevector is negated for negative frequencies would aid readability.","section":null},{"comment":"Fig. 4(f) shows T↓↓ = 1.01, which is slightly above unity. While this is consistent with the parametric gain mechanism (time modulation-induced gain compensating radiative loss), the text could explicitly note that T > 1 is expected and does not violate energy conservation in the time-varying context, to prevent confusion.","section":null},{"comment":"The term 'scattering anomalies' is used throughout but is not formally defined. A brief definition or reference to the standard terminology (e.g., from Ref. 48) in the introduction would help readers from adjacent communities.","section":null}],"recommendation":"major_revision","confidential_remarks":"The overlap with Ref. 31 (same group, qBICs in time-varying metasurfaces) is worth noting for novelty assessment. The present paper's distinctive contributions appear to be the multilayered S-matrix framework and the nonreciprocal device concept, but the authors should make this explicit. The loss issue is the more serious concern: the thresholds M ~ 10⁻⁴ to 10⁻² are impressive in the lossless limit but their experimental relevance hinges on whether Q_abs for real materials at optical frequencies is sufficiently large. A back-of-envelope estimate for a specific material (e.g., Si with Q_abs ~ 10⁴–10⁵ at telecom wavelengths) would go a long way toward establishing credibility of the 'perturbative' claim."},"author_rebuttal":{"model":"glm-5.2","summary":"We thank the referee for a careful reading and for identifying two substantive issues. On the first (material losses), the referee is correct that our quantitative thresholds are derived in the lossless limit and that finite absorption will raise them. We will add a quantitative analysis with finite imaginary permittivity and revise the headline language accordingly. On the second (relationship to Ref. 31), we will clarify the scope of the novelty claim to distinguish the present work precisely from our prior results.","responses":[{"response":"The referee raises a valid and important point. We agree that the absence of material loss is a load-bearing assumption for the specific numerical thresholds reported (M = 6×10⁻³ for CPA/lasing in the FP-BIC example; M = 1.319×10⁻⁴ for the S-matrix pole in the SP-BIC nonreciprocal device). The referee's physical reasoning is correct: when Q_abs is finite, the total Q-factor saturates and the modulation amplitude required to reach a scattering anomaly or an S-matrix pole increases relative to the lossless value. We will address this in the revised manuscript in three ways. First, we will add simulations with a finite imaginary part of the permittivity (Im(ε) > 0) for both the FP-BIC and SP-BIC examples, showing quantitatively how the CPA/lasing threshold and the S-matrix pole position shift as a function of Q_abs. Second, we will include an analytical scaling argument: in the regime Q_rad >> Q_abs (which is the regime where the BIC physics is most relevant), the effective Q is approximately Q_abs, and the modulation threshold scales as M_thresh ~ 1/Q_abs rather than 1/Q_rad. This means the advantage over a non-BIC resonant structure (where Q_rad is bounded) persists as long as Q_abs exceeds the radiative Q-factor of a comparable non-BIC resonance. Third, we will revise the language throughout the manuscript—particularly in the abstract and the discussion—to qualify that the reported thresholds correspond to the lossless limit and that finite material losses will raise them, with the revised text providing the quantitative relationship. We note that even for realistic TCO materials with moderate loss (e.g., Im(ε) ~ 10⁻²–10⁻¹), the thresholds remain well within the perturbative regime (M << 1), though they are no longer as extreme as in the lossless case. We will present具体","revision_made":"yes","referee_comment":"The central quantitative claims—that scattering anomalies and nonreciprocity occur at 'extremely small, perturbative modulation amplitudes' (M << 1)—rely entirely on the diverging radiative Q-factor of the BIC in the lossless limit. The permittivity is taken as purely real... In any real material (TCOs, dielectrics), the total Q-factor is capped at Q_total = Q_rad·Q_abs/(Q_rad + Q_abs)... If Q_abs is finite, the effective Q is bounded, and the modulation amplitude required to reach the lasing/CPA threshold [is raised]."},{"response":"We thank the referee for flagging this. Ref. 31 is indeed by our group, and we should have been more precise in scoping the novelty claim. The two works address related but distinct problems. In Ref. 31, qBICs in a single-layer time-varying metasurface are used to expand the momentum bandgap of a photonic time crystal; the focus is on the bandgap width as a function of the qBIC's radiative Q-factor. The present manuscript addresses two problems that are not covered in Ref. 31: (1) scattering anomalies (EPs, CPA, lasing) in a multilayered time-varying FP cavity exploiting FP-BICs, with polarization-insensitive operation—Ref. 31 does not study scattering anomalies, CPA, lasing, or FP-BICs; and (2) nonreciprocal monochromatic one-way transmission using SP-BICs in a multilayered metasurface with a traveling-wave modulation phase profile—Ref. 31 does not address nonreciprocity, SP-BICs, or multilayered structures. Additionally, the present manuscript develops the S-matrix framework for multilayered time-varying metasurfaces (including the star product and pseudounitarity/reciprocity conditions), which is not present in Ref. 31. We will revise the manuscript to scope the novelty claim precisely: rather than stating that 'BICs in multilayered time-varying metasurfaces have never been considered,' we will state that the exploitation of BICs for scattering anomalies and nonreciprocal transmission in multilayered time-varying metasurfaces is new, and we will explicitly state the relationship to Ref. 31.","revision_made":"yes","referee_comment":"The paper claims to be the 'first exploitation of BICs in multilayered time-varying metasurfaces' and states that 'BICs in multilayered time-varying metasurfaces...have never been considered.' However, Ref. 31 (Garg et al., 'Photonic time crystals assisted by quasi-bound states in the continuum,' Sci. Adv., accepted 2026) appears to be by the same group and directly addresses qBICs in time-varying metasurfaces. The relationship between the present manuscript and Ref. 31 should be clarified: what is genuinely new here beyond what was already reported in Ref. 31? The novelty claim should be scoped precisely, particularly regarding the multilayered aspect and the nonreciprocal device."}],"tokens_in":23756,"tokens_out":1209,"duration_ms":177371,"standing_objections":[]},"desk_editor":{"model":"glm-5.2","letter":"Short version: this paper combines bound states in the continuum (BICs) with time-varying multilayered metasurfaces for the first time, and the combination is genuinely new. The T-matrix/S-matrix framework is well-built and the scattering-anomaly results (EPs, CPA, lasing at M ~ 10^-3; nonreciprocal one-way transmission at M ~ 10^-4) are internally consistent. The main soft spot is that the entire 'perturbative regime' argument rests on lossless materials, and the paper never quantifies what finite absorption does to those thresholds. It deserves a serious referee who pushes on exactly that question. I think the reader's CONDITIONAL verdict is about right, maybe slightly harsh — the theoretical contribution is solid even if the experimental claims need tempering. The stress-test concern about material losses is real and load-bearing. The permittivity is purely real everywhere (ε = 1 + χ_st[1 + Mcos(Ωt+φ)], χ_st = 10.68, no imaginary part). The BIC Q-factors diverge only in the lossless limit, and the reported thresholds (M = 6×10^-3 for CPA/lasing, M = 1.319×10^-4 for the nonreciprocal pole) scale as ~1/Q_rad. With finite Q_abs, the effective Q is capped and the required M increases proportionally. For the SP-BIC nonreciprocal device operating at M ~ 10^-4, even modest absorption could push the threshold well into M ~ 1 territory, which would invalidate the headline claim. The paper should have included at least a back-of-envelope estimate: pick a realistic material (ITO, silicon), plug in its Q_abs, and show whether the thresholds stay perturbative. That said, I disagree with the reader's soundness score of 6.0 being driven entirely by this gap. The T-matrix and S-matrix derivations are careful, the symmetry relations for negative frequencies are properly derived in the supplementary, and the pseudounitarity framework is used correctly. The convergence parameters are documented. The framework itself is general — the authors note it works for large M too — so adding a loss term is a parameter extension, not a fundamental limitation. What is genuinely new: the specific combination of BIC physics with temporal modulation in a multilayer platform, the polarization-insensitive scattering anomalies (a nice consequence of C_4 symmetry), and the monochromatic one-way transmission design. The nonreciprocal device keeping the transmitted field at the same frequency as the input despite time modulation is a clean result. The self-citations (Refs 20, 21, 30, 55) are to the authors' prior T-matrix/S-matrix framework, which is the appropriate tool here — not circular. Who this is for: researchers in time-varying photonics and BIC physics who want to understand how resonant enhancement lowers modulation thresholds. The theoretical framework is reusable. Recommendation: accept for peer review. The referee should require a quantitative loss analysis — even a simple model showing how Q_abs maps to increased M thresholds — before the 'perturbative regime' claims are fully credible. The theoretical contribution stands on its own; the experimental claims need the caveat.","headline":"BICs in time-varying metasurfaces: novel combination, but lossless idealization is load-bearing for the 'perturbative regime' claim","tokens_in":24715,"tokens_out":753,"would_cite":true,"duration_ms":149368,"reading_group":"no","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["42.25.Bs","42.25.Gy","78.67.Pt"],"model":"glm-5.2","headline":"BICs unlock strong light modulation at extremely low power","keywords":["bound states in the continuum","time-varying metasurfaces","nonreciprocal transmission","exceptional points","coherent perfect absorption","Floquet scattering","photonic time crystals","S-matrix"],"falsifier":"Measure the S-matrix eigenvalues of a fabricated two-layer BIC metasurface under temporal modulation. If material losses prevent eigenvalues from approaching zero (CPA) or diverging (lasing) at M ~ 10⁻³, or if the nonreciprocal transmission contrast collapses below two orders of magnitude at M ~ 10⁻⁴ in a four-layer sample, the perturbative-regime claim is experimentally falsified.","tokens_in":23796,"feed_emoji":"🔦","tokens_out":1395,"duration_ms":161885,"temperature":0.7,"pith_summary":"This paper demonstrates that bound states in the continuum (BICs) — electromagnetic modes that are trapped inside a structure despite being energetically able to radiate away — can be harnessed in multilayered metasurfaces whose material properties are rapidly modulated in time. The central idea is that the diverging quality factors of BICs dramatically prolong the interaction between light and the time-varying medium, so that effects normally requiring large modulation amplitudes become achievable at perturbatively small ones (M well below 1%). Using Fabry-Perot BICs in a two-layer cavity, the authors show that polarization-insensitive exceptional points, coherent perfect absorption, and lasing emerge at modulation amplitudes of roughly 5×10⁻³. Using symmetry-protected BICs in a four-layer structure with a staggered temporal modulation phase that breaks time-reversal symmetry, they demonstrate strong nonreciprocal transmission — light passes in one direction but not the other — at modulation amplitudes near 1.3×10⁻⁴, with the transmitted field remaining monochromatic despite the time modulation. The analytical and computational framework combines T-matrix and S-matrix methods extended to Floquet (time-periodic) scattering, including symmetry relations for negative-frequency harmonics and the S-matrix star product for stacking layers.","feed_headline":"BICs let time-modulated metasurfaces steer light at tiny power","feed_subtitle":"Bound states in the continuum amplify time-modulation effects enough to enable lasing, perfect absorption, and one-way optical transmission—","key_machinery":"Bound states in the continuum (BICs): electromagnetic resonances with vanishing radiative linewidth in the lossless limit. Fabry-Perot BICs arise in a cavity formed by two identical metasurfaces when each layer is perfectly reflecting at the BIC frequency. Symmetry-protected BICs arise at high-symmetry points in k-space where radiative coupling is forbidden by mirror symmetry. Quasi-BICs (qBICs) are obtained by slightly detuning from the exact BIC condition, yielding a finite but very high Q-factor that permits external excitation. The Floquet S-matrix relates incident and outgoing field amplitudes across a frequency comb ω_j = ω + jΩ; its pseudounitarity (Eq. 11) and reciprocity (Eq. 12)条件","core_discovery":"The paper's central discovery is that the diverging radiative Q-factors of BICs act as a resonance amplifier for time-modulation effects, collapsing the modulation amplitude required to reach scattering singularities (EPs, CPA, lasing) and nonreciprocal one-way transmission by orders of magnitude compared to non-resonant time-varying media. In the Fabry-Perot BIC example, the pseudounitarity of the Floquet S-matrix forces eigenvalues into inverse-conjugate pairs, so that once a pair coalesces at an exceptional point, one eigenvalue necessarily flows to zero (CPA) while its partner diverges (lasing) — all at M ≈ 6×10⁻³. In the symmetry-protected BIC example, the extremely low radiative lossof","pith_inferences":["Material absorption in real dielectrics and TCOs will cap the BIC Q-factor at a finite value, which should raise the modulation amplitude at which EPs, CPA, and nonreciprocity occur — but the enhancement over non-resonant schemes may still be substantial if the material Q is high enough. A quantitative study of how absorption degrades the perturbative regime would establish the practical ceiling.","The staggered phase profile φ_n = Kz_n discretizes a traveling-wave modulation; using more layers could approximate the continuous profile more faithfully, potentially strengthening nonreciprocity or reducing the required M further, but at the cost of fabrication complexity.","The choice Ω = 2ω_qbic places two Floquet harmonics at the qBIC resonance; other harmonic-to-resonance alignments (e.g., Ω = ω_qbic coupling j=0 and j=1) might access different scattering anomalies or nonreciprocal configurations, broadening the design space."],"forward_implications":["If BIC-enhanced time modulation works as described, on-chip optical isolators and circulators could be built without magnets or large modulation powers, using standard dielectric or TCO metasurface fabrication.","The CPA and lasing thresholds at M ~ 10⁻³ suggest that practical parametric oscillation and coherent absorption could be driven by modest pump intensities in BIC-based cavities.","The monochromatic nonreciprocal transmission — where the output frequency equals the input frequency despite time modulation — would simplify integration of nonreciprocal elements into existing optical communication systems that cannot tolerate frequency conversion.","The framework is general and valid for large M, so the same platform could access regimes beyond the perturbative limit, potentially uncovering additional scattering anomalies or topological features in the Floquet spectrum."],"fun_headline_variants":["BICs cut power needed for nonreciprocal light steering in metasurfaces","Time-modulated metasurfaces achieve one-way light flow at low power via BICs","Bound states collapse power needed for lasing in time-varying metasurfaces","BICs drive low-power lasing and one-way light in time-modulated metasurfaces","Low-power perfect absorption and lasing in time-varying metasurfaces via BICs"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The analytical framework assumes lossless materials and perfectly sinusoidal temporal modulation. Real materials have intrinsic absorption, which caps the diverging BIC quality factors and would raise the modulation amplitude needed to observe the reported effects, potentially pushing them out of the perturbative regime.","fun_headline_variants_meta":{"raw":{"variants":["BICs cut power needed for nonreciprocal light steering in metasurfaces","Time-modulated metasurfaces achieve one-way light flow at low power via BICs","Bound states collapse power needed for lasing in time-varying metasurfaces","BICs drive low-power lasing and one-way light in time-modulated metasurfaces","Low-power perfect absorption and lasing in time-varying metasurfaces via BICs"]},"model":"glm-5.2","effort":"high","cost_usd":0.0,"raw_usage":{"total_tokens":1293,"prompt_tokens":613,"completion_tokens":680,"prompt_tokens_details":null},"tokens_in":613,"tokens_out":680,"duration_ms":40635,"temperature":1.0,"reasoning_tokens":547,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-08T04:38:47.094022+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"Measure the S-matrix eigenvalues of a fabricated two-layer BIC metasurface under temporal modulation. If material losses prevent eigenvalues from approaching zero (CPA) or diverging (lasing) at M ~ 10⁻³, or if the nonreciprocal transmission contrast collapses below two orders of magnitude at M ~ 10⁻⁴ in a four-layer sample, the perturbative-regime claim is experimentally falsified.","supporting_citations":[],"review_version":1}