Pith. sign in

REVIEW 3 major objections 8 minor 64 references

Terahertz four-wave mixing at glass surfaces reveals hidden medium-range structure

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · glm-5.2

2026-07-08 06:24 UTC pith:TDWDGPRR

load-bearing objection Solid new technique applied to amorphous glasses; structural claims are plausible but need tightening on the TPA-detuning confound. the 3 major comments →

arxiv 2607.06417 v1 pith:TDWDGPRR submitted 2026-07-07 physics.optics cond-mat.mtrl-sci

Terahertz-driven four-wave mixing at glass surfaces: Probing vibrational resonances and structural regimes

Mathias Hedegaard Kristensen , J\'er\^ome Degert , Theo Guillaume , Emmanuel Abraham , Laetitia Dalstein , Eric Freysz This is my paper
classification physics.optics cond-mat.mtrl-sci PACS 78.47.jb78.47.jh61.43.Fs63.50.Lm
keywords structuralvibrationalevolutionterahertz-drivencollectivecompositionalcorrelationsdirect
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper demonstrates that terahertz-driven four-wave mixing (FWM) at glass surfaces can probe low-frequency vibrational modes and structural evolution in amorphous solids, a class of materials that has resisted clean spectroscopic dissection by linear infrared, Raman, and terahertz time-domain techniques. The method works in reflection geometry, where wavevector mismatch naturally confines the signal to the top ~50 nm of the bulk, making it a near-surface probe without requiring thin samples or transmission geometries. Applied to a compositional series of PbO-silicate glasses (20-54 mol% PbO), the technique resolves distinct contributions from collective Boson-peak excitations and Pb-O/Si-O network stretching modes, and tracks how these modes shift as lead content increases. The dominant vibrational frequency blueshifts monotonically with PbO content, crossing from the Si-O-Si network band into the composite Pb-O/Qn stretch band, directly reflecting the progressive transformation of Pb2+ from a silicate-network modifier toward a network former. The central structural claim concerns a pronounced, non-monotonic peak in both the FWM signal intensity and the in-plane-to-out-of-plane polarization ratio (ISS/IPS) at 44 mol% PbO. At this composition, NMR finds no change in local Pb-O coordination and Pb-O-Pb free-oxide linkages are negligible, yet the FWM observables spike. The authors interpret this as direct evidence that a collective reorganization of Pb2+ lone-pair spatial correlations occurs in the medium-range structure (correlations extending 5-20 angstroms, beyond nearest-neighbor bonding) independently of changes in local coordination geometry. The polarization ratio is particularly diagnostic because it tracks the anisotropy of the third-order susceptibility tensor chi^(3), which is dominated by the highly polarizable Pb2+ lone-pair electrons; a peak in this ratio signals a change in the directionality of the electronic charge distribution, not merely an increase in the number of polarizable units. The paper also develops a perturbative third-order nonlinear response model with two effective Lorentzian vibrational modes (a bosonic mode and a network stretching mode) that reproduces the strongly Stokes-shifted spectra and the absent anti-Stokes signal across all six compositions, with R-squared values between 0.94 and 0.99.

Core claim

The paper's central discovery is that a non-monotonic peak in both FWM signal intensity and the ISS/IPS polarization ratio at 44 mol% PbO in lead silicate glasses provides direct spectroscopic evidence that Pb2+ lone-pair electrons undergo a collective spatial reorganization at the medium-range structural scale (5-20 angstrom correlations) that is decoupled from any change in nearest-neighbor Pb-O bonding. This is a structural transition invisible to diffraction-derived coordination numbers and NMR chemical shifts, but directly accessible through the anisotropy of the third-order nonlinear optical susceptibility chi^(3), which is governed by the spatial organization of the polarizable lone-p

What carries the argument

The key machinery is terahertz-driven four-wave mixing in reflection geometry: a near-infrared pulse and an intense terahertz pulse interact at the glass surface to generate a signal at 2*omega +/- Omega, confined to ~50 nm by wavevector mismatch. The signal is enhanced by resonant coupling to low-frequency vibrational modes (Boson peak, Pb-O stretching, Si-O network deformations). The Stokes/anti-Stokes asymmetry arises from proximity to a two-photon absorption resonance. The ISS/IPS ratio probes chi^(3) tensor anisotropy, which tracks lone-pair spatial correlations. A perturbative model with two effective Lorentzian vibrational modes fits the spectra across all compositions.

Load-bearing premise

The structural interpretation of the FWM signal depends on representing the broad vibrational continua of the amorphous network using only two discrete effective Lorentzian modes, with the vibrational linewidth fixed at 1.5 THz because it cannot be independently resolved under broadband femtosecond excitation. If this two-mode parameterization does not adequately capture the true vibrational density of states, the extracted mode frequencies and their compositional trends may,

What would settle it

If the FWM signal intensity and ISS/IPS ratio at 44 mol% PbO were found to correlate with a surface-specific effect (e.g., lead leaching producing a Pb-depleted surface layer) rather than bulk medium-range structure, the central structural claim would be undermined. The paper addresses this by arguing that Pb depletion should suppress rather than enhance Pb-related signatures, but a direct depth-profiling measurement would be the decisive test.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • THz-driven FWM in reflection geometry could be applied to other amorphous or disordered systems where medium-range structural order governs macroscopic properties, including chalcogenide glasses, phase-change materials, and metal-organic framework glasses.
  • The technique's ~50 nm depth confinement could be deliberately exploited to study surface-localized phenomena such as leaching, weathering, or polishing-induced alteration layers in glasses, where depth-resolved sensitivity is the primary asset.
  • The sensitivity of the chi^(3) tensor anisotropy to lone-pair organization suggests the method could disambiguate structural-role debates in other lone-pair or polarizable-cation glass systems where diffraction and NMR give ambiguous or conflicting pictures.
  • Replacing the femtosecond optical probe with narrowband picosecond pulses would lift the convolution limit on spectral resolution, enabling independent determination of vibrational dephasing rates and potentially resolving overlapping contributions such as the Boson peak and Pb2+ rattling modes below 7.5 THz.
  • The finding that medium-range lone-pair reorganization occurs independently of local coordination changes could inform glass engineering strategies where medium-range structure, rather than local bonding, is the design parameter for tuning nonlinear optical or mechanical properties.

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 demonstrates THz-driven four-wave mixing (FWM) at the surfaces of PbO–silicate glasses (20–54 mol% PbO) in a reflection geometry, confining the nonlinear signal to a ~50 nm near-surface layer. The authors observe Stokes-shifted FWM spectra that they attribute to coupling between the NIR/THz fields and low-frequency vibrational modes (Boson peak, Pb–O stretching, Si–O network modes). Across the compositional series, they track the FWM intensity, spectral centroid, and the ISS/IPS polarization ratio, finding a non-monotonic peak in both intensity and ISS/IPS at 44 mol% PbO. They interpret this as evidence for collective reorganization of Pb2+ lone-pair spatial correlations in the medium-range structure, independent of nearest-neighbor coordination changes. A third-order perturbative response model with two effective Lorentzian vibrational modes is used to fit the spectra, yielding mode frequencies and coupling parameters that are compared against literature IR/Raman/NMR assignments.

Significance. The application of THz-driven FWM to amorphous systems in a depth-confined reflection geometry is a genuine methodological advance. The perturbative scaling test (Fig. 3, R²=0.986), the polarization selection-rule verification, and the systematic exclusion of cascaded χ(2) contributions are well-executed controls. The correlation of FWM observables with independent structural probes (NMR, diffraction, Raman) across six compositions provides a useful cross-validation framework. The technique's accessibility with table-top sources and its ~50 nm depth sensitivity position it as a complementary tool to linear spectroscopies for near-surface glass characterization.

major comments (3)
  1. §1.4 and Table 2: The central structural claim rests on the non-monotonic peak in ISS/IPS at 44 mol% PbO being attributed to lone-pair spatial reorganization. However, §1.2 explicitly acknowledges that the ISS/IPS ratio deviates from the Kleinman value of ~9 because the excitation is near the TPA resonance (~2.3 eV), making the ratio 'material- and frequency-dependent.' Table 2 shows that the fitted TPA detuning δ varies from −19.0 to −26.0 THz across compositions — a ~7 THz range. If δ varies with composition, the near-resonant dispersion of χ(3)xxxx/χ(3)xyyx will also vary, potentially producing a non-monotonic ISS/IPS trend purely from electronic resonance effects. The manuscript does not present a calculation or argument isolating the resonance-driven contribution to the ratio from the structurally-driven contribution. This is load-bearing for the claim that the ISS/IPS peak reflects
  2. lone-pair reorganization rather than composition-dependent TPA dispersion. The authors should either (a) show that the δ variation across compositions is too small to account for the observed ISS/IPS variation, or (b) explicitly decompose the ratio into resonance-driven and structure-driven components. Without this, the structural interpretation of Pillar (2) of the central claim is not adequately supported.
  3. §1.5 and Table 2: The spectral model fits six free parameters per composition to the FWM spectra, with the vibrational linewidth γ_vib fixed at 1.5 THz because it is 'not independently resolvable.' The authors acknowledge that parameter compensation redistributes amplitude between μ_V/μ_B and μ_VB. Given this compensation, the extracted mode frequencies ν_B and ν_V (Fig. 5B) and their compositional trends — which are used to support the structural regime interpretation — may not be uniquely determined. The manuscript should demonstrate that ν_V is robustly constrained by the fits (e.g., by showing fit residuals or confidence intervals for ν_V across a range of fixed γ_vib values), or else qualify the structural claims that depend on the specific extracted frequency values.
minor comments (8)
  1. Abstract: 'toward network-former' contains a stray space ('to ward').
  2. §1.3: 'Pb-right network' appears to be a typo for 'Pb-rich network.'
  3. Figure 4A: The R² values are displayed on the figure but the six compositions are listed in a non-monotonic order (20, 29, 39, 44, 50, 54). Consider noting this explicitly or sorting consistently.
  4. Table 2: The μ_VB parameter hits the upper bound (10.0) for the 20 and 29 mol% compositions. This should be noted as a potential boundary artifact in the fit, and its implications for the low-composition regime interpretation discussed.
  5. §1.1: 'absorption lenghth' should be 'absorption length.'
  6. Figure 5A: The color scale for the six compositions is not clearly distinguishable. Consider using more distinct colors or labeling individual curves.
  7. The Discussion section (unnumbered, beginning after §1.5) mixes conclusions, limitations, and future work. Consider separating these into distinct subsections for clarity.
  8. Table S1: SF57 and SF58 are listed with identical n(ω) and n(2ω) values (1.8235 and 1.9172), giving identical L_coh = 53 nm. If this is correct it should be noted; if not, one set of values should be corrected.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for a careful and constructive report. Both major comments identify legitimate concerns about whether the central structural claims are adequately isolated from confounding effects (TPA dispersion in Comment 1; parameter degeneracy in Comment 2). We address each below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: §1.4 and Table 2: The central structural claim rests on the non-monotonic peak in ISS/IPS at 44 mol% PbO being attributed to lone-pair spatial reorganization. However, §1.2 explicitly acknowledges that the ISS/IPS ratio deviates from the Kleinman value of ~9 because the excitation is near the TPA resonance (~2.3 eV), making the ratio 'material- and frequency-dependent.' Table 2 shows that the fitted TPA detuning δ varies from −19.0 to −26.0 THz across compositions — a ~7 THz range. If δ varies with composition, the near-resonant dispersion of χ(3)xxxx/χ(3)xyyx will also vary, potentially producing a non-monotonic ISS/IPS trend purely from electronic resonance effects. The manuscript does not present a calculation or argument isolating the resonance-driven contribution to the ratio from the structurally-driven contribution. This is load-bearing for the claim that the ISS/IPS peak reflects

    Authors: The referee raises a valid and important concern. We agree that the compositional variation of the TPA detuning δ could, in principle, modulate the ISS/IPS ratio through near-resonant electronic dispersion of the χ(3) tensor, and that the manuscript does not currently isolate this effect from the structurally driven contribution. This is a genuine gap in the argument. We will address it in the revised manuscript through the following approach. First, we will present a quantitative estimate of the expected resonance-driven variation of |χ(3)xxxx/χ(3)xyyx|² across the fitted δ range (−19 to −26 THz) using the standard two-level dispersion model for the tensor ratio near an electronic resonance (following the framework of Levenson and Bloembergen, Ref. 50). This calculation will show whether the ~7 THz variation in δ is sufficient to account for the observed non-monotonic ISS/IPS trend (which rises from ~5 to ~13 and then drops back to ~9). Second, we note that the ISS/IPS peak at 44 mol% PbO is non-monotonic — it rises and then falls — whereas δ does not follow a corresponding non-monotonic trend (it goes from −21.6 to −24.2 to −19.0 to −19.1 to −26.0 to −19.0 THz). The lack of correlation between the δ trajectory and the ISS/IPS trajectory is itself suggestive, but we agree this qualitative observation is not a substitute for a quantitative calculation. Third, we will add an explicit discussion of this confound, including a figure or table comparing the δ-predicted ratio variation to the measured ISS/IPS values. If the calculation shows that the δ variation is too small to account for the observed ISS/IPS variation, this will strengthen our structural interpretation; if it shows a non-negligible contribution, we will explicitly decompose the ratio and qualify the claim. revision: yes

  2. Referee: §1.5 and Table 2: The spectral model fits six free parameters per composition to the FWM spectra, with the vibrational linewidth γ_vib fixed at 1.5 THz because it is 'not independently resolvable.' The authors acknowledge that parameter compensation redistributes amplitude between μ_V/μ_B and μ_VB. Given this compensation, the extracted mode frequencies ν_B and ν_V (Fig. 5B) and their compositional trends — which are used to support the structural regime interpretation — may not be uniquely determined. The manuscript should demonstrate that ν_V is robustly constrained by the fits (e.g., by showing fit residuals or confidence intervals for ν_V across a range of fixed γ_vib values), or else qualify the structural claims that depend on the specific extracted frequency values.

    Authors: The referee is correct that the parameter compensation between μ_V/μ_B and μ_VB, combined with the fixed γ_vib, could affect the uniqueness of the extracted mode frequencies. We appreciate this point and will address it in two ways. First, we will perform and include a sensitivity analysis in which γ_vib is varied over a physically plausible range (e.g., 0.5–3.0 THz) and show the resulting confidence intervals on ν_V and ν_B. We expect that ν_V, which is primarily constrained by the spectral position of the Stokes-shifted peak and the assignment-boundary crossings, will be robust to γ_vib variation, while the coupling amplitudes (μ_V/μ_B and μ_VB) absorb the compensating changes — but this needs to be demonstrated explicitly rather than asserted. Second, we will include fit residuals (or a residual analysis) for all six compositions in the revised manuscript or Supplementary Material. Third, we acknowledge that even if ν_V is robustly determined, the structural regime interpretation rests partly on the specific frequency values crossing assignment boundaries (e.g., the Si–O–Si to Pb–O/Qn stretch transition). We will qualify the claims that depend on the precise extracted frequency values, particularly where the fitted ν_V lies near an assignment boundary, and will frame the structural regime interpretation in terms of the monotonic blueshift trend rather than the exact frequency values at each composition. We note that the monotonic blueshift of ν_V from ~11 THz (20 mol%) to ~22 THz (54 mol%) spans a range far exceeding the assignment boundary uncertainties, so the overall trend — which is the primary structural claim — should be robust even if individual frequency values carry larger uncertainties than the fit quality alone suggests. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claims rest on direct experimental observables correlated with external literature data

full rationale

The paper's central claims are supported by two pillars: (1) the non-monotonic FWM intensity peak at 44 mol% PbO, which is a direct, model-independent experimental measurement; and (2) the non-monotonic ISS/IPS ratio, also a direct experimental measurement (ratio of maximum intensities in two polarization configurations). Neither is derived from the spectral model. The spectral model (Section 3.3) is used to fit the FWM spectra and extract vibrational mode frequencies (ν_B, ν_V), but the paper is transparent that these are fit parameters, not predictions: 'Fits to the SS spectra yield coefficients of determination R² between 0.94 and 0.99.' The extracted frequencies are then compared against external literature assignments (Table 1, citing [43, 44, 23, 17]) and structural data from independent techniques (NMR [28], diffraction [25, 27], EXAFS [26]). The structural interpretation of the ISS/IPS ratio invokes external results on Kleinman symmetry breaking near TPA resonance (Levenson and Bloembergen [50], Yablonovitch et al. [49]) and Pb²⁺ lone-pair chemistry (Watson and Parker [59], Alderman et al. [25, 58]). The one self-citation present is to reference [4] (Dalstein, Kristensen, Abraham, Degert, Freysz), cited only for the experimental setup schematic and the silicon FWM precedent — it is methodological, not load-bearing for the structural claims. The skeptic's concern about composition-dependent TPA detuning δ confounding the ISS/IPS ratio is a valid correctness risk (uncontrolled confound), but it is not circularity: δ is a fit parameter in the spectral model, while ISS/IPS is measured independently, and the structural claim is not defined in terms of δ. No step in the derivation chain reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

6 free parameters · 3 axioms · 0 invented entities

The model relies on six free parameters fitted per composition to represent the nonlinear response. The core structural interpretation depends on the ad-hoc modeling choice of representing the amorphous vibrational density of states with two discrete Lorentzian modes and fixing the linewidth.

free parameters (6)
  • delta (TPA detuning) = varies by composition, e.g., -21.6 THz at 20 mol%
    Fitted to match the spectral position relative to the TPA resonance.
  • gamma_el (electronic dephasing rate) = varies, e.g., 4.54 THz at 20 mol%
    Fitted to match the electronic response linewidth.
  • nu_B (bosonic mode frequency) = varies, e.g., 4.50 THz at 20 mol%
    Fitted to capture the low-frequency collective mode contribution.
  • nu_V (vibrational mode frequency) = varies, e.g., 11.2 THz at 20 mol%
    Fitted to capture the higher-frequency network stretching contribution.
  • mu_V/mu_B (relative coupling strength) = varies, e.g., 0.49 at 20 mol%
    Fitted to set the relative amplitude of the vibrational to bosonic channel.
  • mu_VB (cross-manifold coupling) = varies, constrained to [0.1, 10]
    Fitted to set the cross-manifold coupling amplitude.
axioms (3)
  • ad hoc to paper The broad continua of vibrational excitations in the amorphous network can be represented by two discrete effective Lorentzian modes.
    Invoked in Section 1.5 and 3.3 to make the numerical fitting tractable.
  • ad hoc to paper The vibrational linewidth gamma_vib is not independently resolvable and can be fixed at 1.5 THz.
    Invoked in Section 1.5 to address parameter compensation due to convolution-limited spectral resolution.
  • domain assumption Cascaded chi(2) contributions to the FWM response are negligible.
    Invoked in Section 1.2 to justify interpreting the ISS/IPS ratio as reflecting the intrinsic bulk chi(3) tensor.

pith-pipeline@v1.1.0-glm · 35980 in / 2210 out tokens · 393986 ms · 2026-07-08T06:24:35.615377+00:00 · methodology

0 comments
read the original abstract

Disordered materials such as glasses exhibit complex structural dynamics that are challenging to probe with conventional spectroscopies. We demonstrate that terahertz-driven four-wave mixing (FWM) at glass surfaces provides direct access to low-frequency vibrational modes and structural evolution in amorphous solids. Applied to a compositional series of PbO-silicate glasses (20-54 mol% PbO), this technique resolves distinct contributions from collective Boson-peak excitations and Pb-O / Si-O network stretching modes, and tracks their systematic evolution across structurally distinct compositional regimes. The dominant vibrational frequency blueshifts with PbO content, reflecting the progressive evolution of the Pb$^{2+}$ network role from silicate-modifier to ward network-former. A pronounced enhancement of the FWM signal near 44 mol% PbO coincides with the emergence of medium-range Pb-Pb correlations, while in-plane-to-out-of-plane FWM intensity ratio ($I_{\rm SS}/I_{\rm PS}$) tracks $\chi^{(3)}$ tensor anisotropy tied to Pb$^{2+}$ lone-pair spatial correlations. The non-monotonic peak in both observables at 44 mol% PbO - a composition where NMR finds no change in local Pb-O coordination and Pb-O-Pb free-oxide linkages are negligible - provides direct evidence that a collective lone-pair reorganization occurs in the medium-range structure independently of nearest-neighbor bonding. These results establish terahertz-driven FWM as a bulk-sensitive, near-surface depth-confined ($\sim$50 nm) nonlinear spectroscopy sensitive to vibrational and electronic structural fingerprints inaccessible to linear infrared, Raman, and terahertz time-domain probes.

Figures

Figures reproduced from arXiv: 2607.06417 by Emmanuel Abraham, Eric Freysz, J\'er\^ome Degert, Laetitia Dalstein, Mathias Hedegaard Kristensen, Theo Guillaume.

Figure 1
Figure 1. Figure 1: THz-driven FWM at a lead oxide silicate glass sur￾face. The incident THz electric field ETHz(Ω) and optical laser field Elas(ω) interact within the near-surface region to generate a FWM signal EFWM(2ω ± Ω) at the corresponding Stokes (difference) and anti-Stokes (sum) frequencies. Spring-shaped bonds represent local￾ized vibrational modes within the disordered lattice contributing to the nonlinear response… view at source ↗
Figure 2
Figure 2. Figure 2: FWM and SHG characterization of a lead glass sample with 44 mol% PbO content. Only polarization configurations that exhibit nonzero responses are shown; combinations yielding no measurable signal are omitted for clarity. The absence of signal in these configurations is consistent with the symmetry of the third-order nonlinear susceptibility tensor for isotropic, centrosymmetric media. (A) Temporal evolutio… view at source ↗
Figure 3
Figure 3. Figure 3: FWM signal dependence on optical peak fluence in a lead glass sample with 44 mol% PbO content. Each data point (circles) represents the mean field strength (square root of the intensity) across the full recorded spectrum at a given NIR laser peak fluence in the SS polarization configuration. The mean field strength is normalized to the maximum value, and error bars represent the weighted standard deviation… view at source ↗
Figure 4
Figure 4. Figure 4: PbO-dependent FWM response in lead glass samples. (A) FWM spectra in the SS polarization configuration of samples with varying PbO content plotted as a function of frequency shift relative to the SHG carrier frequency. The circles show the experimental data, with error bars indicating the standard deviation from three consecutive measurements. Solid lines represent modeled spectra (see Section 2.5) fitted … view at source ↗
Figure 5
Figure 5. Figure 5: Fitted vibrational response functions and extracted mode frequencies across PbO compositions. (A) Imaginary parts of the bosonic (dashed) and vibrational (solid) Lorentzian response functions extracted from fits to the SS FWM spectra, plotted as a function of frequency for each composition (color scale, 20–54 mol% PbO). Each mode is normalized to its peak amplitude. The green curve shows the spectral ampli… view at source ↗
Figure 6
Figure 6. Figure 6: Pathway-resolved decomposition of the fitted third￾order polarization P (3)(Ω′ ) for the 44 mol% PbO glass. The to￾tal fitted response [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Liouville pathways contributing to the THz-driven FWM response. The eighteen signal-active third-order pathways are grouped into excited-state (ES, A1–A6), ground-state (GS, B1–B6), and resonant (R, C1–C6) classes, distinguished by whether the THz interaction (Ω, purple arrows) occurs on the ket-side within |e ⋆⟩ (ES) or |g ⋆⟩ (GS) after the optical TPA transition; or whether it drives a resonant ground-st… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

64 extracted references · 64 canonical work pages

  1. [1]

    Nicoletti, A

    D. Nicoletti, A. Cavalleri, Nonlinear light–matter interaction at terahertz frequencies, Advances in Optics and Photonics 8 (3) (2016) 401–464. doi:10.1364/AOP.8.000401

    work page doi:10.1364/aop.8.000401 2016

  2. [2]

    Y . Lu, Y . Huang, J. Cheng, R. Ma, X. Xu, Y . Zang, Q. Wu, J. Xu, Nonlinear optical physics at terahertz frequency, Nanophotonics 13 (18) (2024) 3279–3298. doi:10.1515/nanoph-2024-0109

    work page doi:10.1515/nanoph-2024-0109 2024

  3. [3]

    F. Selz, J. K ¨olbel, F. Paries, G. von Freymann, D. Molter, D. M. Mittleman, Terahertz-induced nonlinear response in ZnTe, Opt. Express 33 (5) (2025) 9575–9586. doi:10.1364/OE.546261

    work page doi:10.1364/oe.546261 2025

  4. [4]

    Dalstein, M

    L. Dalstein, M. Tondusson, M. H. Kristensen, E. Abraham, J. Degert, E. Freysz, Near-infrared–terahertz hyper-Raman spectroscopy of an excited silicon surface, The Journal of Chem- ical Physics 161 (15) (2024) 154708. doi:10.1063/5.0230655

    work page doi:10.1063/5.0230655 2024

  5. [5]

    Paparo, A

    D. Paparo, A. Martinez, A. Rubano, Coherent terahertz hyper- Raman spectroscopy, Journal of Raman Spectroscopy 56 (9) (2025) 920–932. doi:10.1002/jrs.6787

    work page doi:10.1002/jrs.6787 2025

  6. [6]

    Frenzel, M

    M. Frenzel, M. Cherasse, J. M. Urban, F. Wang, B. Xiang, L. Nest, L. Huber, L. Perfetti, M. Wolf, T. Kampfrath, X.- Y . Zhu, S. F. Maehrlein, Nonlinear terahertz control of the lead halide perovskite lattice, Science Advances 9 (21) (2023) eadg3856. doi:10.1126/sciadv.adg3856

    work page doi:10.1126/sciadv.adg3856 2023

  7. [7]

    Vaswani, J

    C. Vaswani, J. H. Kang, M. Mootz, L. Luo, X. Yang, C. Sun- dahl, D. Cheng, C. Huang, R. H. J. Kim, Z. Liu, Y . G. Collantes, E. E. Hellstrom, I. E. Perakis, C. B. Eom, J. Wang, Light quan- tum control of persisting higgs modes in iron-based supercon- ductors, Nature Communications 12 (1) (2021) 258

    work page 2021

  8. [8]

    Grasset, K

    R. Grasset, K. Katsumi, P. Massat, H.-H. Wen, X.-H. Chen, Y . Gallais, R. Shimano, Terahertz pulse-driven collective mode in the nematic superconducting state of Ba 1−xKxFe2As2, npj Quantum Materials 7 (1) (2022) 4

    work page 2022

  9. [9]

    T. D. Bennett, S. Horike, J. C. Mauro, M. M. Smedskjaer, L. Wondraczek, Looking into the future of hybrid glasses, Na- ture Chemistry 16 (11) (2024) 1755–1766

    work page 2024

  10. [10]

    S. S. Sørensen, C. A. N. Biscio, M. Bauchy, L. Fajstrup, M. M. Smedskjaer, Revealing hidden medium-range order in amor- phous materials using topological data analysis, Science Ad- vances 6 (37) (2020) eabc2320. doi:10.1126/sciadv.abc2320

    work page doi:10.1126/sciadv.abc2320 2020

  11. [11]

    Y . Shi, B. Deng, J. Neuefeind, Q. Zhou, M. M. Smedskjaer, S. R. Elliott, M. Bauchy, Revealing the effect of medium-range structure on silicate glass hardness, Phys. Rev. Mater. 7 (2023) 013602. doi:10.1103/PhysRevMaterials.7.013602

    work page doi:10.1103/physrevmaterials.7.013602 2023

  12. [12]

    S. S. Sørensen, P. P. Cielecki, H. Johra, M. Bockowski, E. Skovsen, Y . Yue, M. M. Smedskjaer, Thermal conduc- tion in a densified oxide glass: Insights from lattice dy- namics, Materials Today Communications 32 (2022) 104160. doi:10.1016/j.mtcomm.2022.104160. 15

    work page doi:10.1016/j.mtcomm.2022.104160 2022

  13. [13]

    Christensen, Y

    R. Christensen, Y . Bokor Bleile, S. S. Sørensen, C. A. N. Biscio, L. Fajstrup, M. M. Smedskjaer, Medium-range order structure controls thermal stability of pores in zeolitic imidazolate frame- works, The Journal of Physical Chemistry Letters 14 (33) (2023) 7469–7476

    work page 2023

  14. [14]

    Baldi, V

    G. Baldi, V . M. Giordano, G. Monaco, B. Ruta, Sound attenuation at terahertz frequencies and the boson peak of vitreous silica, Phys. Rev. Lett. 104 (2010) 195501. doi:10.1103/PhysRevLett.104.195501

    work page doi:10.1103/physrevlett.104.195501 2010

  15. [15]

    Gelin, H

    S. Gelin, H. Tanaka, A. Lemaˆıtre, Anomalous phonon scattering and elastic correlations in amorphous solids, Nature Materials 15 (11) (2016) 1177–1181

    work page 2016

  16. [16]

    Shintani, H

    H. Shintani, H. Tanaka, Universal link between the boson peak and transverse phonons in glass, Nature Materials 7 (11) (2008) 870–877

    work page 2008

  17. [17]

    O. Wada, D. Ramachari, C.-S. Yang, T. Uchino, C.-L. Pan, Ab- sorption dispersion below boson peak frequency in oxide glasses studied by THz-time domain spectroscopy, Journal of Applied Physics 135 (8) (2024) 085108. doi:10.1063/5.0191384

    work page doi:10.1063/5.0191384 2024

  18. [18]

    M. F. Ando, S. Fuhrmann, Z. Pan, B. P. Rodrigues, T. Mori, S. G. Ebbinghaus, K. Wondraczek, S. Kitani, L. Wondraczek, Boson peak and structural heterogeneity in ternary SiO 2-Al2O3-B2O3 glasses, Journal of the American Ceramic Society 104 (10) (2021) 4991–5000. doi:10.1111/jace.17771

    work page doi:10.1111/jace.17771 2021

  19. [19]

    N. J. Tostanoski, S. K. Sundaram, Universal power-law of ter- ahertz optical properties of borosilicate, tellurite, and chalco- genide glass families, Scientific Reports 13 (1) (2023) 2260

    work page 2023

  20. [20]

    Radica, M

    F. Radica, M. Cassetta, G. Iezzi, A. Pisello, F. Vet- ere, A. Del Vecchio, M. Cestelli Guidi, B. T. Poe, Short-range order and chemical compositions of glasses along the basaltic-rhyolite sub-alkaline join by Raman and FTIR spectroscopies, Chemical Geology 648 (2024) 121938. doi:10.1016/j.chemgeo.2024.121938

    work page doi:10.1016/j.chemgeo.2024.121938 2024

  21. [21]

    Gautam, A

    C. Gautam, A. K. Yadav, A. K. Singh, A review on infrared spectroscopy of borate glasses with effects of different addi- tives, International Scholarly Research Notices 2012 (1) (2012) 428497. doi:10.5402/2012/428497

    work page doi:10.5402/2012/428497 2012

  22. [22]

    J. W. E. Drewitt, L. Hennet, D. R. Neuville, From short to medium range order in glasses and melts by diffraction and Ra- man spectroscopy, Reviews in Mineralogy and Geochemistry 87 (1) (2022) 55–103. doi:10.2138/rmg.2022.87.02

    work page doi:10.2138/rmg.2022.87.02 2022

  23. [23]

    I. B. Kacem, L. Gautron, D. Coillot, D. R. Neuville, Structure and properties of lead silicate glasses and melts, Chemical Geol- ogy 461 (2017) 104–114. doi:10.1016/j.chemgeo.2017.03.030

    work page doi:10.1016/j.chemgeo.2017.03.030 2017

  24. [24]

    A. K. Yadav, P. Singh, A review of the structures of oxide glasses by Raman spectroscopy, RSC Adv. 5 (2015) 67583– 67609. doi:10.1039/C5RA13043C

    work page doi:10.1039/c5ra13043c 2015

  25. [25]

    O. L. G. Alderman, A. C. Hannon, D. Holland, R. Dupree, G. Lehr, A. Vitale, S. Feller, Lead silicate glass structure: new insights from diffraction and modeling of probable lone pair lo- cations, Journal of the American Ceramic Society 105 (2022) 938–957. doi:10.1111/jace.18125

    work page doi:10.1111/jace.18125 2022

  26. [26]

    Rybicki, A

    J. Rybicki, A. Rybicka, A. Witkowska, G. Bergmanski, A. D. Cicco, M. Minicucci, G. Mancini, The structure of lead- silicate glasses: molecular dynamics and exafs studies, Jour- nal of Physics: Condenced Matter 13 (2001) 9781–9797. doi:10.1088/0953-8984/13/43/309

    work page doi:10.1088/0953-8984/13/43/309 2001

  27. [27]

    Takaishi, M

    T. Takaishi, M. Takahashi, J. Jin, T. Uchino, T. Yoko, M. Taka- hashi, Structural study on PbO–SiO2 glasses by X-ray and neu- tron diffraction and 29Si MAS NMR measurements, Journal of the American Ceramic Society 88 (6) (2005) 1591–1596. doi:https://doi.org/10.1111/j.1551-2916.2005.00297.x

    work page doi:10.1111/j.1551-2916.2005.00297.x 2005

  28. [28]

    S. Sen, R. F. Lancelotti, I. Hung, Z. Gan, Characterization of the Pb coordination environment and its connectivity in lead sil- icate glasses: Results from 2D 207Pb NMR spectroscopy, The Journal of Physical Chemistry B 128 (11) (2024) 2811–2820. doi:10.1021/acs.jpcb.3c08307

    work page doi:10.1021/acs.jpcb.3c08307 2024

  29. [29]

    J. E. Graebner, B. Golding, L. C. Allen, Phonon local- ization in glasses, Phys. Rev. B 34 (1986) 5696–5701. doi:10.1103/PhysRevB.34.5696

    work page doi:10.1103/physrevb.34.5696 1986

  30. [30]

    S. R. Elliott, A unified model for the low-energy vibrational be- haviour of amorphous solids, Europhysics Letters 19 (3) (1992)

    work page 1992

  31. [31]

    doi:10.1209/0295-5075/19/3/009

    work page doi:10.1209/0295-5075/19/3/009

  32. [32]

    A. P. Sokolov, Vibrations at the boson peak: random- and coherent-phase contributions, Journal of Physics: Con- densed Matter 11 (10A) (1999) A213. doi:10.1088/0953- 8984/11/10A/017

    work page doi:10.1088/0953- 1999

  33. [33]

    Lubchenko, P

    V . Lubchenko, P. G. Wolynes, The origin of the boson peak and thermal conductivity plateau in low-temperature glasses, Pro- ceedings of the National Academy of Sciences 100 (4) (2003) 1515–1518. doi:10.1073/pnas.252786999

    work page doi:10.1073/pnas.252786999 2003

  34. [34]

    Zhang, J

    L. Zhang, J. Zheng, Y . Wang, L. Zhang, Z. Jin, L. Hong, Y . Wang, J. Zhang, Experimental studies of vibrational modes in a two-dimensional amorphous solid, Nature Communications 8 (1) (2017) 67

    work page 2017

  35. [35]

    Baggioli, A

    M. Baggioli, A. Zaccone, Unified theory of vibrational spectra in hard amorphous materials, Phys. Rev. Res. 2 (2020) 013267. doi:10.1103/PhysRevResearch.2.013267

    work page doi:10.1103/physrevresearch.2.013267 2020

  36. [36]

    J.; Li, J.; Edgar, J

    M. Gonz ´alez-Jim´enez, T. Barnard, B. A. Russell, N. V . Tukachev, U. Javornik, L.-A. Hayes, A. J. Farrell, S. Guinane, H. M. Senn, A. J. Smith, M. Wilding, G. Mali, M. Nakano, Y . Miyazaki, P. McMillan, G. C. Sosso, K. Wynne, Understand- ing the emergence of the boson peak in molecular glasses, Na- ture Communications 14 (1) (2023) 215. doi:10.1038/s414...

    work page doi:10.1038/s41467- 2023

  37. [37]

    Kyotani, S

    D. Kyotani, S. H. Oh, S. Kitani, Y . Fujii, H. Hijiya, H. Mizuno, S. Kohara, A. Koreeda, A. Masuno, H. Kawaji, S. Kojima, Y . Yamamoto, T. Mori, Relationship between the boson peak and first sharp diffraction peak in glasses, Scientific Reports 15 (1) (2025) 9617. doi:10.1038/s41598-025-94454-8

    work page doi:10.1038/s41598-025-94454-8 2025

  38. [38]

    Moriel, E

    A. Moriel, E. Lerner, E. Bouchbinder, Boson peak in the vi- brational spectra of glasses, Phys. Rev. Res. 6 (2024) 023053. doi:10.1103/PhysRevResearch.6.023053

    work page doi:10.1103/physrevresearch.6.023053 2024

  39. [39]

    Akirmak-Yamac, S

    E. Akirmak-Yamac, S. S. Sørensen, R. S. Welch, M. M. Smedskjaer, C. J. Wilkinson, Comparing the vibrational properties of common glass interatomic potentials, Journal of the American Ceramic Society 108 (8) (2025) e20517. doi:10.1111/jace.20517

    work page doi:10.1111/jace.20517 2025

  40. [40]

    Clerici, L

    M. Clerici, L. Caspani, E. Rubino, M. Peccianti, M. Cassataro, A. Busacca, T. Ozaki, D. Faccio, R. Morandotti, Counterpropa- gating frequency mixing with terahertz waves in diamond, Opt. Lett. 38 (2) (2013) 178–180. doi:10.1364/OL.38.000178

    work page doi:10.1364/ol.38.000178 2013

  41. [41]

    Noskovicova, M

    E. Noskovicova, M. Koys, M. Jerigova, D. Velic, D. Lorenc, Resonantly enhanced terahertz four-wave mixing in fluorides, Opt. Lett. 49 (15) (2024) 4370–4372. doi:10.1364/OL.530693

    work page doi:10.1364/ol.530693 2024

  42. [42]

    R. P. McDonnell, D. D. Kohler, J. C. Wright, Coher- ent IR-hyper-Raman four wave mixing spectroscopy, The Journal of Chemical Physics 161 (21) (2024) 214201. doi:10.1063/5.0231422

    work page doi:10.1063/5.0231422 2024

  43. [43]

    N. S. Mueller, A. P. Fellows, B. John, A. E. Nacle- rio, C. Carbogno, K. Gharagozloo-Hubmann, D. Bal ´aˇz, R. A. Kowalski, H. H. Heenen, C. Scheurer, K. Reuter, J. D. Caldwell, M. Wolf, P. R. Kidambi, M. Th ¨amer, A. Paarmann, Full crystallographic imaging of hexagonal boron nitride monolayers with phonon-enhanced sum-frequency microscopy, Advanced Materi...

    work page doi:10.1002/adma.202510124 2026

  44. [44]

    Feller, G

    S. Feller, G. Lodden, A. Riley, T. Edwards, J. Croskrey, A. Schue, D. Liss, D. Stentz, S. Blair, M. Kelley, G. Smith, S. Singleton, M. Affatigato, D. Holland, M. Smith, E. Kamit- 16 sos, C. Varsamis, E. Ioannou, A multispectroscopic structural study of lead silicate glasses over an extended range of compo- sitions, Journal of Non-Crystalline Solids 356 (6...

    work page 2010

  45. [45]

    doi:10.1016/j.jnoncrysol.2009.12.003

    work page doi:10.1016/j.jnoncrysol.2009.12.003 2009

  46. [46]

    Zagrai, R

    M. Zagrai, R. C. Gavrea, S. Macavei, A. A. Dehelean, A. Popa, M. L. Soran, R. A. Mereu, Glass-forming ability, chemical dura- bility, and structural properties of lead dioxide-silicate glass sys- tem, Crystals 14 (5) (2024). doi:10.3390/cryst14050436

    work page doi:10.3390/cryst14050436 2024

  47. [47]

    Hehlen, E

    B. Hehlen, E. Courtens, A. Yamanaka, K. Inoue, Nature of the boson peak of silica glasses from hyper-Raman scatter- ing, Journal of Non-Crystalline Solids 307–310 (2002) 87–91. doi:10.1016/S0022-3093(02)01444-8

    work page doi:10.1016/s0022-3093(02)01444-8 2002

  48. [48]

    Tanaka, Two-photon optical absorption in amorphous materi- als, Journal of Non-Crystalline Solids 338-340 (2004) 534–538

    K. Tanaka, Two-photon optical absorption in amorphous materi- als, Journal of Non-Crystalline Solids 338-340 (2004) 534–538. doi:10.1016/j.jnoncrysol.2004.03.036

    work page doi:10.1016/j.jnoncrysol.2004.03.036 2004

  49. [49]

    Y . R. Shen, Principles of nonlinear optics, Wiley-Interscience, New York, NY , USA, 1984

    work page 1984

  50. [50]

    R. W. Boyd, Nonlinear Optics, fourth edition Edition, Academic Press, 2020

    work page 2020

  51. [51]

    Yablonovitch, N

    E. Yablonovitch, N. Bloembergen, J. J. Wynne, Dispersion of the nonlinear optical susceptibility inn−InSb, Phys. Rev. B 3 (1971) 2060–2062. doi:10.1103/PhysRevB.3.2060

    work page doi:10.1103/physrevb.3.2060 1971

  52. [52]

    M. D. Levenson, N. Bloembergen, Dispersion of the nonlinear optical susceptibility tensor in centrosymmetric media, Phys. Rev. B 10 (1974) 4447–4463. doi:10.1103/PhysRevB.10.4447

    work page doi:10.1103/physrevb.10.4447 1974

  53. [53]

    Flytzanis, N

    C. Flytzanis, N. Bloembergen, Infrared dispersion of third-order susceptibilities in dielectrics: Retardation effects, Progress in Quantum Electronics 4 (1976) 271–399. doi:10.1016/0079- 6727(76)90003-3

    work page doi:10.1016/0079- 1976

  54. [54]

    S. K. Lee, E. J. Kim, Probing metal-bridging oxygen and configurational disorder in amorphous lead silicates: In- sights from 17O solid-state nuclear magnetic resonance, The Journal of Physical Chemistry C 119 (1) (2015) 748–756. doi:10.1021/jp509780f

    work page doi:10.1021/jp509780f 2015

  55. [55]

    Kohara, H

    S. Kohara, H. Ohno, M. Takata, T. Usuki, H. Morita, K. Suzuya, J. Akola, L. Pusztai, Lead silicate glasses: Binary network- former glasses with large amounts of free volume, Phys. Rev. B 82 (2010) 134209. doi:10.1103/PhysRevB.82.134209

    work page doi:10.1103/physrevb.82.134209 2010

  56. [56]

    V . V . Dimitrov, S.-N. Kim, T. Yoko, S. Sakka, Third har- monic generation in PbO-SiO 2 and PbO-B 2O3 glasses, Jour- nal of the Ceramic Society of Japan 101 (1169) (1993) 59–63. doi:10.2109/jcersj.101.59

    work page doi:10.2109/jcersj.101.59 1993

  57. [57]

    Dimitrov, S

    V . Dimitrov, S. Sakka, Electronic oxide polarizability and opti- cal basicity of simple oxides. i, Journal of the Applied Physics 79 (3) (1996) 1736–1740. doi:10.1063/1.360962

    work page doi:10.1063/1.360962 1996

  58. [58]

    Dimitrov, S

    V . Dimitrov, S. Sakka, Linear and nonlinear optical properties of simple oxides. ii, Journal of the Applied Physics 79 (3) (1996) 1741–1745. doi:10.1063/1.360963

    work page doi:10.1063/1.360963 1996

  59. [59]

    Adair, L

    R. Adair, L. L. Chase, S. A. Payne, Nonlinear refractive in- dex of optical crystals, Phys. Rev. B 39 (1989) 3337–3350. doi:10.1103/PhysRevB.39.3337

    work page doi:10.1103/physrevb.39.3337 1989

  60. [60]

    O. L. G. Alderman, A. C. Hannon, D. Holland, S. Feller, G. Lehr, A. J. Vitale, U. Hoppe, M. v. Zimmerman, A. Wa- tenphul, Lone-pair distribution and plumbite network formation in high lead silicate glass, 80PbO·20SiO 2, Phys. Chem. Chem. Phys. 15 (2013) 8506–8519. doi:10.1039/C3CP51348C

    work page doi:10.1039/c3cp51348c 2013

  61. [61]

    G. W. Watson, S. C. Parker, Origin of the lone pair ofα-PbO from density functional theory calculations, J. Phys. Chem. B 103 (8) (1999) 1258–1262. doi:10.1021/jp9841337

    work page doi:10.1021/jp9841337 1999

  62. [62]

    Schultz-M ¨unzenberg, W

    C. Schultz-M ¨unzenberg, W. Meisel, P. G¨utlich, Changes of lead silicate glasses induced by leaching, Journal of Non-Crystalline Solids 238 (1) (1998) 83–90. doi:https://doi.org/10.1016/S0022- 3093(98)00580-8

    work page doi:10.1016/s0022- 1998

  63. [63]

    P. W. Wang, L. Zhang, Structural role of lead in lead silicate glasses derived from xps spectra, Jour- nal of Non-Crystalline Solids 194 (1) (1996) 129–134. doi:https://doi.org/10.1016/0022-3093(95)00471-8

    work page doi:10.1016/0022-3093(95)00471-8 1996

  64. [64]

    De Sousa Meneses, M

    D. De Sousa Meneses, M. Malki, P. Echegut, Struc- ture and lattice dynamics of binary lead silicate glasses investigated by infrared spectroscopy, Jour- nal of Non-Crystalline Solids 352 (8) (2006) 769–776. doi:https://doi.org/10.1016/j.jnoncrysol.2006.02.004. 17 Supplementary Materials for Terahertz-driven four-wave mixing at glass surfaces: Probing vibr...

    work page doi:10.1016/j.jnoncrysol.2006.02.004 2006