pith. sign in

arxiv: 2606.11567 · v1 · pith:MM6PZOHZnew · submitted 2026-06-10 · ⚛️ physics.optics

Nonlinearity Reversal in Epsilon-Near-Zero Indium Tin Oxide Driven by Few-Cycle Light Pulse

Mustafa Goksu Ozlu , Colton Fruhling , Ian Hoffman , Jae Ik Choi , Marcello Ferrera , Alexandra Boltasseva , Vladimir M. Shalaev This is my paper

Pith reviewed 2026-06-27 09:13 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords epsilon-near-zeroindium tin oxidetwo-photon absorptionnonlinearity reversalfew-cycle pulsestransparent conducting oxidesrefractive index modulationPauli blocking
0
0 comments X

The pith

Few-cycle pulses drive sign reversal of nonlinearity in epsilon-near-zero ITO at intensities above 5 TW/cm².

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

The paper demonstrates that sub-8 fs pump pulses can achieve peak intensities exceeding 5 TW/cm² in indium tin oxide while staying below the damage threshold. This reveals a reversal in the sign of transmission and reflection modulations, leading to a full-cycle oscillation in the refractive index within 300 fs. The reversal amplitude scales quadratically with intensity, which the authors attribute to a two-photon absorption process enabled when intraband excitations lift Pauli blocking in the conduction band. This interplay between interband and intraband transitions explains the observed dynamics and suggests applications in time-varying photonics.

Core claim

At the highest pump intensities, a complete change in the sign of the modulation for both transmission and reflection is obtained, producing a full-cycle oscillation of the refractive index modulation within 300 fs. The amplitude of the sign reversal scales quadratically with the intensity, explained by a simple two-photon absorption model enabled by intraband excitations that vacate states at the bottom of the conduction band, lifting Pauli blocking.

What carries the argument

Two-photon absorption model enabled by intraband excitations in the conduction band that lift Pauli blocking for interband transitions.

If this is right

  • The sign reversal occurs starting at optical pump intensities of approximately 5 TW/cm².
  • The model captures the essential trends and reveals dynamics of competing interband and intraband transitions.
  • This intensity-controlled mechanism could enable new applications of TCOs for time-varying photonics such as photonic time crystals.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Varying the pump pulse duration while holding fluence fixed would change the peak intensity and could suppress or enhance the observed reversal.
  • The same intraband-enabled TPA process may occur in other transparent conducting oxides with comparable conduction-band filling.
  • Extending measurements to still higher intensities could identify additional competing nonlinear channels.

Load-bearing premise

Intraband excitations from lower to upper states in the conduction band vacate bottom states, lifting Pauli blocking to allow interband two-photon absorption.

What would settle it

An experiment that measures conduction-band population dynamics and finds insufficient vacating of bottom states at these intensities would falsify the TPA model for the sign reversal.

read the original abstract

Recent breakthrough studies of nonlinearities at extreme pump intensities ($\sim$1 $\text{TW/cm}^2$) in transparent conducting oxides (TCOs) have rewritten our understanding of the dynamics in these materials. However, exploring TCO dynamics beyond these intensities is prohibited by the damage threshold of the material. In this work, we overcome this problem by using a few-cycle pump laser pulse (sub-8\,fs) to maximize the intensity while keeping the optical fluence below the damage threshold. We observe a reversal in the optical response trend starting at optical pump laser intensities of $\sim$5 $\text{TW/cm}^2$ similar to Segal et al. At the highest pump pulse intensities, we obtain a complete change in the sign of the modulation for both transmission and reflection, producing a full-cycle oscillation of the refractive index modulation within 300\,fs. The amplitude of the sign reversal scales quadratically with the intensity. We therefore propose a simple two-photon absorption (TPA) model to explain the observed behaviour. The TPA, which is normally forbidden by the Pauli blocking, is enabled here by intraband excitations from the lower to the upper non-equilibrium states of the conduction band (CB). Such excitations vacate the states at the bottom of the CB, lifting up the blocking and thus making interband TPA possible. The model is in good agreement with experimental results, capturing the essential trends in the observed data and revealing the dynamics of competing channels caused by the interplay between interband and intraband transitions. This intensity-controlled mechanism could be the key to unlocking new applications of TCOs for time-varying photonics such as photonic time crystals.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript reports the use of sub-8 fs pump pulses to access intensities above 5 TW/cm² in ENZ ITO without exceeding the damage threshold. It observes a reversal in the sign of transmission and reflection modulation at high intensities, producing a full-cycle refractive-index oscillation within 300 fs, with the reversal amplitude scaling quadratically with intensity. The authors propose a simple TPA model in which intraband excitations from lower to upper non-equilibrium CB states vacate states near the CB minimum, lifting Pauli blocking and enabling interband TPA; they state that this model captures the essential trends and the interplay between interband and intraband channels.

Significance. If the proposed mechanism is quantitatively validated, the result would be significant for intensity-tunable nonlinearities in TCOs and for time-varying photonics applications such as photonic time crystals. The experimental strategy of using few-cycle pulses to reach high peak intensities at low fluence is a clear strength. However, the current manuscript supplies no rate-equation solutions, occupancy calculations, or transition-rate comparisons to confirm that the intraband depletion is large enough and fast enough to dominate and reverse both real and imaginary permittivity changes.

major comments (2)
  1. [Abstract] Abstract (final paragraph): the claim that intraband excitations 'vacate the states at the bottom of the CB, lifting up the blocking and thus making interband TPA possible' is presented without any Fermi-Dirac occupancy calculation, rate-equation solution, or estimate of the change in available final states on the ~300 fs timescale. This leaves the central attribution of the quadratic sign reversal to TPA unsupported by quantitative evidence.
  2. [Abstract] Abstract: the statement that 'the model is in good agreement with experimental results, capturing the essential trends' is made without reference to any specific data, error bars, or comparison of predicted versus measured amplitudes, undermining the assertion that the TPA channel dominates over Kerr, free-carrier, and heating contributions above 5 TW/cm².
minor comments (1)
  1. [Abstract] The abstract refers to 'competing channels caused by the interplay between interband and intraband transitions' but provides no explicit list or ordering of those channels.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting areas where the abstract could be strengthened with additional quantitative support. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract (final paragraph): the claim that intraband excitations 'vacate the states at the bottom of the CB, lifting up the blocking and thus making interband TPA possible' is presented without any Fermi-Dirac occupancy calculation, rate-equation solution, or estimate of the change in available final states on the ~300 fs timescale. This leaves the central attribution of the quadratic sign reversal to TPA unsupported by quantitative evidence.

    Authors: We agree that the abstract statement would be more robust with explicit quantitative backing. The main text presents a simple TPA model motivated by the observed quadratic intensity scaling of the sign reversal. In the revised manuscript we will add a short rate-equation estimate of intraband excitation and the resulting change in occupancy near the conduction-band minimum on the 300 fs timescale, showing that the depletion is sufficient to lift Pauli blocking and enable the interband channel. revision: yes

  2. Referee: [Abstract] Abstract: the statement that 'the model is in good agreement with experimental results, capturing the essential trends' is made without reference to any specific data, error bars, or comparison of predicted versus measured amplitudes, undermining the assertion that the TPA channel dominates over Kerr, free-carrier, and heating contributions above 5 TW/cm².

    Authors: We acknowledge that the abstract claim would be clearer if it pointed to the supporting data. The manuscript already contains direct comparisons between the model and measured transmission/reflection traces (including the quadratic scaling) in the results section and figures. We will revise the abstract to reference the relevant figures and to note that the model reproduces the observed trends and the intensity at which the TPA channel overtakes other contributions. revision: yes

Circularity Check

1 steps flagged

TPA model introduced to match observed quadratic scaling of sign reversal; agreement follows by construction of model choice

specific steps
  1. fitted input called prediction [Abstract]
    "The amplitude of the sign reversal scales quadratically with the intensity. We therefore propose a simple two-photon absorption (TPA) model to explain the observed behaviour. ... The model is in good agreement with experimental results, capturing the essential trends in the observed data and revealing the dynamics of competing channels caused by the interplay between interband and intraband transitions."

    Quadratic scaling is measured directly; TPA is selected precisely because it supplies quadratic intensity dependence. The claimed agreement and 'revelation of competing channels' therefore follow from the model's built-in functional form rather than from an a-priori prediction of the coefficient or the intensity at which reversal occurs.

full rationale

The paper reports an experimental observation of intensity-dependent sign reversal in modulation (with quadratic amplitude scaling) and then proposes a TPA model whose defining feature is quadratic intensity dependence. The model is stated to be 'in good agreement' and to 'capture the essential trends,' but no independent first-principles calculation of the reversal threshold, amplitude coefficient, or dominance over Kerr/free-carrier terms is supplied. The explanatory step therefore reduces to selecting a functional form that reproduces the measured scaling. The intraband-depletion mechanism enabling TPA is asserted without rate-equation or occupancy verification, leaving the central claim partially circular.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard semiconductor physics (Pauli blocking in conduction band) plus the paper-specific postulate that intraband excitations enable TPA; no new entities are introduced and no free parameters are explicitly listed in the abstract.

axioms (1)
  • domain assumption Pauli blocking prevents interband two-photon absorption in the conduction band of ITO under equilibrium conditions.
    Invoked in the final paragraph to explain why TPA is normally forbidden and how intraband excitations lift it.

pith-pipeline@v0.9.1-grok · 5862 in / 1372 out tokens · 22172 ms · 2026-06-27T09:13:44.253335+00:00 · methodology

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

49 extracted references · 36 canonical work pages · 4 internal anchors

  1. [1]

    In: 2025 Conference on Lasers and Electro- Optics (CLEO), pp

    Segal, O., Konforty, N., Saha, S., Fruhling, C., Ozlu, M., Cohen, O., Plotnik, Y., Boltasseva, A., Shalaev, V.M., Segev, M.: Complex Temporal Dynamics of Refractive Index Changes Induced by Modulation of Indium Tin Oxide. In: 2025 Conference on Lasers and Electro- Optics (CLEO), pp. 1–2 (2025)

    2025

  2. [2]

    Optics Communications55(6), 447–449 (1985) https://doi.org/10.1016/0030-4018(85)90151-8

    Strickland, D., Mourou, G.: Compression of amplified chirped optical pulses. Optics Communications55(6), 447–449 (1985) https://doi.org/10.1016/0030-4018(85)90151-8

    work page doi:10.1016/0030-4018(85)90151-8 1985

  3. [3]

    Intense Internal and External Fluorescence as Solar Cells Approach the Shockley-Queisser Efficiency Limit

    Lewenstein, M., Balcou, P., Ivanov, M.Y., L’Huillier, A., Corkum, P.B.: Theory of high- harmonic generation by low-frequency laser fields. Physical Review A49(3), 2117–2132 (1994) https://doi.org/10.1103/PhysRevA.49.2117 arXiv:1106.1603

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physreva.49.2117 1994

  4. [4]

    CLEO (2), 4–5 (2022)

    Tsur, M.E., Birk, M., Gorlach, A., Kr¨ uger, M., Kaminer, I., Cohen, O.: High Harmonic Generation Driven by Quantum Light : Strong-Field Approximation & Attosecond Pulses. CLEO (2), 4–5 (2022)

    2022

  5. [5]

    In: Molecular Spectroscopy and Quantum Dynamics, pp

    Baykusheva, D.R., W¨ orner, H.J.: Attosecond Molecular Dynamics and Spectroscopy. In: Molecular Spectroscopy and Quantum Dynamics, pp. 113–161. Elsevier, ??? (2021). https: //doi.org/10.1016/B978-0-12-817234-6.00009-X

    work page doi:10.1016/b978-0-12-817234-6.00009-x 2021

  6. [6]

    Quantum mechanical approach to probing the birth of attosecond pulses using a two-color field

    Krausz, F., Ivanov, M.: Attosecond physics. Reviews of Modern Physics81(1), 163–234 (2009) https://doi.org/10.1103/RevModPhys.81.163 arXiv:1102.1291

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/revmodphys.81.163 2009

  7. [7]

    Physical Review Letters43(4), 267– 270 (1979) https://doi.org/10.1103/PhysRevLett.43.267

    Tajima, T., Dawson, J.M.: Laser electron accelerator. Physical Review Letters43(4), 267– 270 (1979) https://doi.org/10.1103/PhysRevLett.43.267

    work page doi:10.1103/physrevlett.43.267 1979

  8. [8]

    SCIENCE377, 425–428 (2022)

    Lyubarov, M., Lumer, Y., Dikopoltsev, A., Lustig, E., Sharabi, Y., Segev, M.: Amplified emission and lasing in photonic time crystals. SCIENCE377, 425–428 (2022)

    2022

  9. [9]

    Physical Review Letters135(13), 133801 (2025) https://doi.org/10.1103/5v2w-yg7v

    Park, J., Lee, K., Zhang, R.-y., Park, H.-c., Ryu, J.-w., Cho, G.Y., Lee, M.Y., Zhang, Z., Park, N., Jeon, W., Shin, J., Chan, C.T., Min, B.: Spontaneous Emission Decay and 12 Excitation in Photonic Time Crystals. Physical Review Letters135(13), 133801 (2025) https://doi.org/10.1103/5v2w-yg7v

    work page doi:10.1103/5v2w-yg7v 2025

  10. [10]

    SPIE (2022)

    Galiffi, E., Tirole, R., Yin, S., Li, H., Vezzoli, S., Huidobro, P.A., Silveirinha, M.G., Sapienza, R., Al` u, A., Pendry, J.B.: Photonics of time-varying media. SPIE (2022). https://doi.org/10.1117/1.AP.4.1.014002

    work page doi:10.1117/1.ap.4.1.014002 2022

  11. [11]

    Engheta, B.N.: Four-dimensional optics using time-varying metamaterials379(6638), 1190–1192 (2023) https://doi.org/10.1126/science.adf1094

    work page doi:10.1126/science.adf1094 2023

  12. [12]

    Science352(6287), 795–797 (2016) https://doi.org/10.1126/ science.aae0330

    Alam, M.Z., De Leon, I., Boyd, R.W.: Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region. Science352(6287), 795–797 (2016) https://doi.org/10.1126/ science.aae0330

    2016

  13. [13]

    ACS Photonics2(11), 1584–1591 (2015) https://doi.org/10.1021/acsphotonics.5b00355

    Capretti, A., Wang, Y., Engheta, N., Dal Negro, L.: Comparative Study of Second- Harmonic Generation from Epsilon-Near-Zero Indium Tin Oxide and Titanium Nitride Nanolayers Excited in the Near-Infrared Spectral Range. ACS Photonics2(11), 1584–1591 (2015) https://doi.org/10.1021/acsphotonics.5b00355

    work page doi:10.1021/acsphotonics.5b00355 2015

  14. [14]

    Optica2(7), 616 (2015) https://doi.org/10.1364/optica.2.000616

    Kinsey, N., DeVault, C., Kim, J., Ferrera, M., Shalaev, V.M., Boltasseva, A.: Epsilon- near-zero Al-doped ZnO for ultrafast switching at telecom wavelengths. Optica2(7), 616 (2015) https://doi.org/10.1364/optica.2.000616

    work page doi:10.1364/optica.2.000616 2015

  15. [15]

    Optics Letters40(7), 1500 (2015) https://doi.org/10.1364/ol.40.001500

    Capretti, A., Wang, Y., Engheta, N., Dal Negro, L.: Enhanced third-harmonic generation in Si-compatible epsilon-near-zero indium tin oxide nanolayers. Optics Letters40(7), 1500 (2015) https://doi.org/10.1364/ol.40.001500

    work page doi:10.1364/ol.40.001500 2015

  16. [16]

    Physical Review Letters120(4), 43902 (2018) https://doi.org/10.1103/ PhysRevLett.120.043902 arXiv:1709.06972

    Vezzoli, S., Bruno, V., Devault, C., Roger, T., Shalaev, V.M., Boltasseva, A., Ferrera, M., Clerici, M., Dubietis, A., Faccio, D.: Optical Time Reversal from Time-Dependent Epsilon- Near-Zero Media. Physical Review Letters120(4), 43902 (2018) https://doi.org/10.1103/ PhysRevLett.120.043902 arXiv:1709.06972

    Pith/arXiv arXiv 2018

  17. [17]

    Optical Materials Express, Vol

    Cleary, J.W., Smith, E.M., Leedy, K.D., Grzybowski, G., Guo, J., Vasudev, A.P., Kang, J.H., Park, J., Liu, X., Brongersma, M.L., Zhao, H., Wang, Y., Capretti, A., Negro, L.D., Klamkin, J., Amin, R., Suer, C., Ma, Z., Sarpkaya, I., Khurgin, J.B., Agarwal, R., Sorger, V.J., Shi, K., Lu, Z., H Lee, H.W., Sokhoyan, R., Pala, R.A., Thyagarajan, K., Han, S., Ts...

    work page doi:10.1364/ome.8.001231 2018

  18. [18]

    Nano Letters10(6), 2111–2116 (2010) https://doi

    Feigenbaum, E., Diest, K., Atwater, H.A.: Unity-order index change in transparent con- ducting oxides at visible frequencies. Nano Letters10(6), 2111–2116 (2010) https://doi. org/10.1021/nl1006307 13

    work page doi:10.1021/nl1006307 2010

  19. [19]

    ACS Photonics10(8), 2467–2473 (2023) https://doi.org/10.1021/acsphotonics.3c00498

    Fan, Q., Shaltout, A.M., van de Groep, J., Brongersma, M.L., Lindenberg, A.M.: Ultrafast Wavefront Shaping via Space-Time Refraction. ACS Photonics10(8), 2467–2473 (2023) https://doi.org/10.1021/acsphotonics.3c00498

    work page doi:10.1021/acsphotonics.3c00498 2023

  20. [20]

    Nature Communications 2021 12:112(1), 1–6 (2021) https://doi.org/10.1038/ s41467-021-21332-y

    Bohn, J., Luk, T.S., Tollerton, C., Hutchings, S.W., Brener, I., Horsley, S., Barnes, W.L., Hendry, E.: All-optical switching of an epsilon-near-zero plasmon resonance in indium tin oxide. Nature Communications 2021 12:112(1), 1–6 (2021) https://doi.org/10.1038/ s41467-021-21332-y

    2021

  21. [21]

    Optica7(3), 226 (2020) https://doi.org/10.1364/optica.374788

    Khurgin, J.B., Clerici, M., Bruno, V., Caspani, L., DeVault, C., Kim, J., Shaltout, A., Boltasseva, A., Shalaev, V.M., Ferrera, M., Faccio, D., Kinsey, N.: Adiabatic frequency shifting in epsilon-near-zero materials: the role of group velocity. Optica7(3), 226 (2020) https://doi.org/10.1364/optica.374788

    work page doi:10.1364/optica.374788 2020

  22. [22]

    Nature Communications11(1), 1–7 (2020) https://doi.org/10.1038/ s41467-020-15682-2

    Zhou, Y., Alam, M.Z., Karimi, M., Upham, J., Reshef, O., Liu, C., Willner, A.E., Boyd, R.W.: Broadband frequency translation through time refraction in an epsilon- near-zero material. Nature Communications11(1), 1–7 (2020) https://doi.org/10.1038/ s41467-020-15682-2

    2020

  23. [23]

    ACS Photonics (2021) https://doi

    Liu, C., Alam, M.Z., Pang, K., Manukyan, K., Reshef, O., Zhou, Y., Choudhary, S., Patrow, J., Pennathurs, A., Song, H., Zhao, Z., Zhang, R., Alishahi, F., Fallahpour, A., Cao, Y., Almaiman, A., Dawlaty, J.M., Tur, M., Boyd, R.W., Willner, A.E.: Photon Acceleration Using a Time-Varying Epsilon-near-Zero Metasurface. ACS Photonics (2021) https://doi. org/10...

    work page doi:10.1021/acsphotonics.0c01929 2021

  24. [24]

    Optica8(12), 1532–1537 (2021) https://doi.org/10.1364/OPTICA.436324

    Bohn, J., Luk, T.S., Horsley, S., Hendry, E.: Spatiotemporal refraction of light in an epsilon-near-zero indium tin oxide layer: Frequency shifting effects arising from interfaces. Optica8(12), 1532–1537 (2021) https://doi.org/10.1364/OPTICA.436324

    work page doi:10.1364/optica.436324 2021

  25. [25]

    Journal of the Optical Society38(11) (2021) https://doi.org/10.1364/JOSAB.427682

    Pendry, J.B., Galiffi, E., Huidobro, P.A.: Gain in time-dependent media-a new mechanism. Journal of the Optical Society38(11) (2021) https://doi.org/10.1364/JOSAB.427682

    work page doi:10.1364/josab.427682 2021

  26. [26]

    Advanced Optical Materials12(1) (2024) https://doi.org/10.1002/adom.202301232

    Jaffray, W., Clerici, M., Heijnen, B., Boltasseva, A., Shalaev, V.M., Ferrera, M.: Nonlinear Loss Engineering in Near-Zero-Index Bulk Materials. Advanced Optical Materials12(1) (2024) https://doi.org/10.1002/adom.202301232

    work page doi:10.1002/adom.202301232 2024

  27. [27]

    Nature Photonics 2026 20:220(2), 163–169 (2026) https://doi.org/10.1038/s41566-025-01833-8

    Galiffi, E., Harwood, A.C., Vezzoli, S., Tirole, R., Al` u, A., Sapienza, R.: Optical coherent perfect absorption and amplification in a time-varying medium. Nature Photonics 2026 20:220(2), 163–169 (2026) https://doi.org/10.1038/s41566-025-01833-8

    work page doi:10.1038/s41566-025-01833-8 2026

  28. [28]

    Khurgin, J.B., Clerici, M., Kinsey, N.: Fast and Slow Nonlinearities in Epsilon-Near-Zero Materials (2020) https://doi.org/10.1002/lpor.202000291

    work page doi:10.1002/lpor.202000291 2020

  29. [29]

    Controlling hybrid nonlinearities in transparent conducting oxides via two-colour excitation

    Clerici, M., Kinsey, N., DeVault, C., Kim, J., Carnemolla, E.G., Caspani, L., Shaltout, A., Faccio, D., Shalaev, V., Boltasseva, A., Ferrera, M.: Controlling hybrid nonlinearities in transparent conducting oxides via two-colour excitation. Nature communications8(1), 15829 (2017) https://doi.org/10.1038/ncomms15829 arXiv:1606.05824

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/ncomms15829 2017

  30. [30]

    Beyond the perturbative description of the nonlinear optical response of low-index materials

    Reshef, O., Giese, E., Zahirul Alam, M., De Leon, I., Upham, J., Boyd, R.W.: Beyond the 14 perturbative description of the nonlinear optical response of low-index materials. Optics Letters42(16), 3225 (2017) https://doi.org/10.1364/ol.42.003225 arXiv:1702.04338

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1364/ol.42.003225 2017

  31. [31]

    Nonperturbative Nonlinearities

    Khurgin, J.B., Kinsey, N.: “Nonperturbative Nonlinearities”: Perhaps Less than Meets the Eye. ACS Photonics11(8), 2874–2887 (2024) https://doi.org/10.1021/ACSPHOTONICS. 4C00645

    work page doi:10.1021/acsphotonics 2024

  32. [32]

    Nature Physics19(7), 999–1002 (2023) https://doi.org/10.1038/s41567-023-01993-w

    Tirole, R., Vezzoli, S., Galiffi, E., Robertson, I., Maurice, D., Tilmann, B., Maier, S.A., Pendry, J.B., Sapienza, R.: Double-slit time diffraction at optical frequencies. Nature Physics19(7), 999–1002 (2023) https://doi.org/10.1038/s41567-023-01993-w

    work page doi:10.1038/s41567-023-01993-w 2023

  33. [33]

    arXiv (2024)

    Pendry, J.B.: An Avalanche Model for Femtosecond Optical Response. arXiv (2024). https: //doi.org/10.48550/arXiv.2407.08391

    work page doi:10.48550/arxiv.2407.08391 2024

  34. [34]

    Nanophotonics12(12), 2221–2230 (2023) https://doi.org/10.1515/ NANOPH-2023-0126;JOURNAL:JOURNAL:21928614;ISSUE:ISSUE:DOI

    Lustig, E., Segal, O., Saha, S., Bordo, E., Chowdhury, S.N., Sharabi, Y., Fleischer, A., Boltasseva, A., Cohen, O., Shalaev, V.M., Segev, M.: Time-refraction optics with sin- gle cycle modulation. Nanophotonics12(12), 2221–2230 (2023) https://doi.org/10.1515/ NANOPH-2023-0126;JOURNAL:JOURNAL:21928614;ISSUE:ISSUE:DOI

    2023

  35. [35]

    Accessed 2026-05-08

    Narimanov, E.E.: Electromagnetic response for modulation at an optical timescale113(3), 033501 https://doi.org/10.1103/ppwc-jcrp . Accessed 2026-05-08

    work page doi:10.1103/ppwc-jcrp 2026

  36. [36]

    org/10.1364/ome.471672

    Hayran, Z., Khurgin, J.B., Monticone, F.:ℏωversusℏk: Dispersion and energy constraints on time-varying photonic materials and time crystals [Invited]12(10), 3904 https://doi. org/10.1364/ome.471672

    work page doi:10.1364/ome.471672

  37. [37]

    Fruhling, C., Ozlu, M.G., Segal, O., Jaffray, W., Stengel, S., Ferrera, M., Boltasseva, A., Segev, M., Shalaev, V.M.: Time-refraction near the critical angle and angular streaking with attosecond resolution15(5), 1065–1075

  38. [38]

    116.233901

    Caspani, L., Kaipurath, R.P.M., Clerici, M., Ferrera, M., Roger, T., Kim, J., Kinsey, N., Pietrzyk, M., Falco, A.D., Shalaev, V.M., Boltasseva, A., Faccio, D.: Enhanced Nonlinear Refractive Index inε-Near-Zero Materials (2016) https://doi.org/10.1103/PhysRevLett. 116.233901

    work page doi:10.1103/physrevlett 2016

  39. [39]

    Laser Physics Letters4(1), 38–43 (2007) https://doi.org/10.1002/lapl.200610070

    Dietzek, B., Pascher, T., Sundstr¨ om, V., Yartsev, A.: Appearance of coherent artifact signals in femtosecondtransient absorption spectroscopy in dependence on detector design. Laser Physics Letters4(1), 38–43 (2007) https://doi.org/10.1002/lapl.200610070

    work page doi:10.1002/lapl.200610070 2007

  40. [40]

    Physical Review Applied19(1), 1 (2023) https://doi.org/10.1103/PhysRevApplied.19.014005 arXiv:2207.14528

    Sarkar, S., Un, I.W., Sivan, Y.: Electronic and Thermal Response of Low-Electron-Density Drude Materials to Ultrafast Optical Illumination. Physical Review Applied19(1), 1 (2023) https://doi.org/10.1103/PhysRevApplied.19.014005 arXiv:2207.14528

    work page doi:10.1103/physrevapplied.19.014005 2023

  41. [41]

    Physical Review Applied18(5), 054067 (2022) https://doi.org/10.1103/PhysRevApplied.18.054067

    Tirole, R., Galiffi, E., Dranczewski, J., Attavar, T., Tilmann, B., Wang, Y.-T., Huidobro, P.A., Al´ u, A., Pendry, J.B., Maier, S.A., Vezzoli, S., Sapienza, R.: Saturable Time-Varying Mirror Based on an Epsilon-Near-Zero Material. Physical Review Applied18(5), 054067 (2022) https://doi.org/10.1103/PhysRevApplied.18.054067

    work page doi:10.1103/physrevapplied.18.054067 2022

  42. [42]

    Physical Review B - Condensed Matter and Materials Physics 78(7) (2008) https://doi.org/10.1103/PHYSREVB.78.075211

    Walsh, A., Da Silva, J.L.F., Wei, S.H.: Origins of band-gap renormalization in degenerately 15 doped semiconductors. Physical Review B - Condensed Matter and Materials Physics 78(7) (2008) https://doi.org/10.1103/PHYSREVB.78.075211

    work page doi:10.1103/physrevb.78.075211 2008

  43. [43]

    Physical Review Letters100(16) (2008) https://doi.org/10.1103/PHYSREVLETT.100

    Walsh, A., Da Silva, J.L.F., Wei, S.H., K¨ orber, C., Klein, A., Piper, L.F.J., Demasi, A., Smith, K.E., Panaccione, G., Torelli, P., Payne, D.J., Bourlange, A., Egdell, R.G.: Nature of the band gap of In2O3 revealed by first-principles calculations and X-ray spectroscopy. Physical Review Letters100(16) (2008) https://doi.org/10.1103/PHYSREVLETT.100. 167402

    work page doi:10.1103/physrevlett.100 2008

  44. [44]

    Pending Publication (2025)

    Jaffray, W., Stengel, S., Boltasseva, A., Shalaev, V.M., Rizza, C., Ceglia, D., Vin- centi, M.A., Scalora, M., Clerici, M., Ferrera, M.: Single-pump hybrid nonlinearities in transparent conductors. Pending Publication (2025)

    2025

  45. [45]

    arXiv preprint arXiv:2605.21432 (2026)

    Harwood, A.C., Lim, S.Z.J., Raziman, T.V., Li, Y., Stones, J., Tisch, J.W.G., Horsley, S.A.R., Vezzoli, S., Pendry, J.B., Sapienza, R.: Intraband and interband competition drives ultrafast modulations of indium tin oxide. arXiv preprint arXiv:2605.21432 (2026)

    Pith/arXiv arXiv 2026

  46. [46]

    Physical Review Applied11(6), 064062 (2019) https://doi.org/10.1103/PhysRevApplied.11.064062

    Wang, H., Du, K., Jiang, C., Yang, Z., Ren, L., Zhang, W., Chua, S.J., Mei, T.: Extended Drude Model for Intraband-Transition-Induced Optical Nonlinearity. Physical Review Applied11(6), 064062 (2019) https://doi.org/10.1103/PhysRevApplied.11.064062

    work page doi:10.1103/physrevapplied.11.064062 2019

  47. [47]

    ScienceAdvances9,eadf8537

    Gurung, S., Bej, S., Dang, Q., Sahoo, A., Anopchenko, A., Yi, Z., Sokolov, A.V., Marini, A., Lee, H.W.H.: Control of ultrafast hot electron dynamics in epsilon-near-zero conductive oxide thin films. Science Advances11(21), 8850 (2025) https://doi.org/10.1126/SCIADV. ADU8850;CTYPE:STRING:JOURNAL

    work page doi:10.1126/sciadv 2025

  48. [48]

    https://arxiv.org/abs/2512.24641

    Choi, J.I., Mkhitaryan, V., Fruhling, C., Khurgin, J.B., Kildishev, A.V., Shalaev, V.M., Boltasseva, A.: Pathway to Optical-Cycle Dynamic Photonics: Extreme Electron Temper- atures in Transparent Conducting Oxides (2025). https://arxiv.org/abs/2512.24641

    arXiv 2025

  49. [49]

    Applied Physics Letters105(18), 42 (2014) https://doi.org/10

    Liu, X., Park, J., Kang, J.H., Yuan, H., Cui, Y., Hwang, H.Y., Brongersma, M.L.: Quan- tification and impact of nonparabolicity of the conduction band of indium tin oxide on its plasmonic properties. Applied Physics Letters105(18), 42 (2014) https://doi.org/10. 1063/1.4900936/132914 16 Supplementary Information Nonlinearity Reversal in Epsilon-Near-Zero I...

    2014