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REVIEW 2 major objections 5 minor 95 references

Combined tools for Particle-In-Cell simulations performed with transversely asymmetric chirped lasers

T0 review · 2 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read The ACE toolbox reconstructs chirped, transversely asymmetric laser fields from measured fluence images and spectral phase, and when loaded into a particle-in-cell simulation it reproduces the optimized electron spectrum of an experiment to

desk verdict Practical toolbox extends GSA-MD to chirped asymmetric pulses; single-point validation and no code/data are the main soft spots. read the letter →

arxiv 2607.19121 v1 pith:QSBV4VA4 submitted 2026-07-21 physics.plasm-ph physics.comp-ph

I. Moulanier , F. Massimo , T. L. Steyn , B. Cros This is my paper · ORCID
classification physics.plasm-phphysics.comp-ph PACS 52.38.Kd52.65.Rr
keywords laserwakefieldaccelerationchirpedpulsetransverseasymmetryGerchberg-Saxtonalgorithmmodedecompositionparticle-in-cellsimulationspectralphaseelectronbunchenergyspectrum
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper introduces the Asymmetric Chirped Electric field reconstruction (ACE) toolbox, which combines a transverse laser profile reconstructed from multiple fluence images with a temporally chirped envelope built from spectral phase coefficients. The central claim is that, under the assumption of negligible spatio-temporal couplings, these two independent reconstructions can be multiplied together to form a realistic 3D laser field suitable for particle-in-cell simulations. When applied to a laser wakefield acceleration experiment in which the electron bunch had been optimized by spectral chirping, the simulated electron spectrum matched the measured one: 90 MeV versus 92 MeV peak energy and 0.18 pC/MeV versus 0.16 pC/MeV peak spectral charge. This matters because it allows simulations to capture both transverse asymmetry and temporal chirp from routine experimental diagnostics, and it enables Bayesian-optimization loops that tune chirp coefficients against simulated electron properties.

What carries the argument

The central object is the factorized electric field E = Re{ E_perp(r,z_f) * T(t) }, where E_perp is a sum of paraxial modes (Hermite-Gauss for reconstruction, Laguerre-Gauss for the cylindrical PIC code) and T(t) is a chirped Gaussian temporal envelope obtained by applying the spectral phase polynomial. The reconstruction uses GSA-MD, which iterates between measured fluence planes, enforcing the measured modulus while propagating modes analytically, to retrieve the transverse complex phase. The temporal chirp is applied in the frequency domain via a Taylor expansion of the spectral phase up to fourth order. The work also introduces an energy ratio alpha that quantifies the fraction of the la

What would settle it

Measure the full spatio-temporal field of the laser (e.g., with a spatially resolved spectral interference technique such as SEA TADPOLE) at a plane not used in the reconstruction and compare it to the ACE-predicted field. A mismatch beyond experimental uncertainty, or an observed change in the electron spectrum when STCs are deliberately introduced, would falsify the factorization assumption and invalidate the reconstructed simulation field.

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Extended reading notes

Core claim

The ACE toolbox reconstructs the electric field of a chirped, transversely asymmetric laser by factorizing it as the product of a transverse spatial distribution and a temporal profile: E(r,z_f,t) = Re{ E_perp(r,z_f) * T(t) }. The transverse part is obtained with the Gerchberg-Saxton Algorithm with Mode Decomposition (GSA-MD) from fluence images at several planes along the propagation axis, yielding a sum of Hermite-Gauss modes. The temporal part is obtained by inverse Fourier transforming a Gaussian spectrum with the experimentally set polynomial spectral phase coefficients. These are combined and translated into a Laguerre-Gauss basis for quasi-3D cylindrical particle-in-cell simulations.

Load-bearing premise

The laser's electric field must factor cleanly into a transverse spatial part times a temporal chirp, with no space-time coupling; if real pulses have significant spatio-temporal couplings, the independent reconstructions cannot be combined into a valid 3D field.

Editorial extensions

If this is right

  • If the factorization holds, the ACE toolbox provides a direct path from routine diagnostics (fluence images and spectral phase settings) to realistic PIC simulations of chirped asymmetric laser-driven accelerators.
  • The parametric study of the second-order chirp coefficient reproduces the experimental transition from a broad electron spectrum to a single peaked spectrum, and yields scaling laws for maximum energy, charge, and energy spread as functions of phi_2.
  • Because the reconstruction is separable, it can be used in both Cartesian and cylindrical PIC geometries with only a basis conversion step.
  • The modular structure allows the same measured transverse distribution to be combined with arbitrary temporal profiles, enabling studies of chirp effects while holding the transverse field fixed.
  • The method is compatible with Bayesian optimization workflows, since each simulation is initialized from measured laser parameters and the electron outputs can be used as objective functions.

Reading between the lines

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

  • A natural extension is to include first-order spatio-temporal coupling corrections in the mode decomposition; the current factorization is the zero-coupling limit, and the modal basis could in principle absorb a mild coupling if measured.
  • The strong correlation between ionization volume and charged particle output suggests a fast surrogate model based on the chirped amplitude and duration could replace expensive PIC simulations in early optimization scans.
  • The same reconstruction pipeline could apply to other laser-plasma configurations, such as plasma mirrors or radiation pressure acceleration, whenever fluence images and spectral phase are available and STCs are weak.
  • A skeptic could test the method's limits by applying it to a laser with intentionally induced STCs and comparing the simulated electron spectrum to an experiment; the agreement should degrade predictably as STCs grow.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper introduces the ACE toolbox for reconstructing a transversely asymmetric, spectrally chirped laser pulse from measured fluence images and DAZZLER chirp coefficients, under the explicit assumption of negligible spatio-temporal couplings (STC). The transverse field is retrieved with GSA-MD in an HG basis and converted to an LG basis for FBPIC quasi-3D PIC simulations; the temporal profile is synthesized from a Gaussian with polynomial spectral phase. The method is applied to the LLC laser-wakefield experiment at the Bayesian-optimization working point: the simulated electron spectrum peaks at 90 MeV with 0.18 pC/MeV versus 92 MeV and 0.16 pC/MeV experimentally. A scan over phi_2 is used to interpret the low-energy-spread working point as dominated by envelope shaping rather than by the instantaneous frequency chirp, supported by a TCS-vs-TAS comparison and an estimate of the chirp term in the pulse-duration evolution equation.

Significance. If the claims hold, the paper provides a modular and well-documented workflow for injecting realistic chirped laser profiles into cylindrical-geometry PIC codes, extending the GSA-MD transverse reconstruction in a way that is potentially useful for Bayesian optimization with spectral shaping. The appendices contain the numerical parameters and the TCS-vs-TAS comparison is a clean numerical experiment supporting the envelope-shaping interpretation. However, no code or data archive is provided, the validation rests on a single averaged spectrum at one working point, and the central no-STC factorization is asserted rather than demonstrated. These issues currently limit the strength of the central claim.

major comments (2)
  1. [Section II, Eq. (1); Section III.C, Fig. 8] The entire reconstruction rests on the factorization E⊥(r,z_f,t)=Re{Ẽ⊥(r,z_f) T̃(t)}. The manuscript explicitly restricts the toolbox to regimes with negligible STC but provides no evidence that the LLC laser satisfies this condition. The DAZZLER and the downstream amplifier/compressor chain are known sources of spatial chirp and pulse-front tilt [41–43]. The measured fluence images are wavelength-integrated, so in the presence of residual STC the GSA-MD transverse distribution is not the field at any single time or frequency, and the product field in Eq. (1) is not a valid representation. The single-spectrum agreement in Fig. 8 (90 vs 92 MeV; 0.18 vs 0.16 pC/MeV) is an integrated observable and is not a sensitive test of the factorization. Please either add a direct STC characterization for the LLC system or revise the validation claim to a conditional statement ('consistent with the mo
  2. [Section II.C, Eqs. (13)–(14); Table I] The laser-energy normalization is internally inconsistent. In Eq. (13), α is defined as sqrt(∫|ẽ⊥|² / ∫f), where f and |ẽ⊥|² are each normalized by their own maximum. If the modelled peak intensity is matched to the measured one, the ratio of laser energies is (∫|ẽ⊥|²)/(∫f) = α², not α. Equation (14) and Table I set Elaser,sim = α Elaser = 0.85×0.87 J = 0.74 J, whereas the same-peak-intensity energy fraction gives α² Elaser ≈ 0.63 J. This overestimates the modelled energy by roughly 15% (about 8% in field amplitude) and propagates into all electron-spectrum results. Please correct the definition/use of α, or re-run the simulations with the correct normalization.
minor comments (5)
  1. [Section III.C and Appendix 5] The statement 'Both fits predict that … no bunch would be injected for values of φ2 ∼ 600 fs²' is an extrapolation beyond the simulated range φ2 ∈ [0, 501] fs². The R² values (0.98 and 0.95) describe the fitted data; they do not validate the zero-charge prediction at 600 fs². Please remove this prediction or explicitly label it as an unverified extrapolation.
  2. [General] No code, data, or repository is provided. For a toolbox paper, releasing the implementation (GSA-MD, basis swap, temporal synthesis) or at least an archived dataset would materially improve reproducibility and allow the community to adopt the method.
  3. [Section III.A, Eq. (15)] The sign convention in Eq. (15) should be checked against the definition ξ = z − ct and the Wigner-transform plots in Fig. 5. The plotted negative slope in the TCS panel appears to be consistent with a positive φ2 only under a particular convention for ξ; a short derivation or sign clarification would help.
  4. [General] Minor editorial issues: 'Kroenecker' should be 'Kronecker'; the integral sign in Eq. (7) is typeset as a stray 'x'; the notation for the reconstructed field alternates between Ẽ⊥ and ẽ⊥ without being defined uniformly; Fig. 8 would benefit from showing the shot-to-shot spread of the 10-shot experimental average.
  5. [Section III.C, Fig. 8] The experimental spectrum is an average of 10 consecutive shots, but no shot-to-shot variance is shown. Since the simulation is compared to this single averaged curve, indicating the experimental spread would calibrate how significant the 90-vs-92 MeV and 0.18-vs-0.16 pC/MeV differences are.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: reconstruction uses measured fluence and chirp coefficients; validation is a forward simulation.

full rationale

The derivation chain is not circular. The temporal profile is obtained from measured DAZZLER chirp coefficients via Eqs. (2)-(3); the transverse field is retrieved from measured fluence images by GSA-MD; the two are combined under the explicitly stated no-STC factorization of Eq. (1). The factorizability is an untested premise but not a reduction of the output to the input. The comparison in Fig. 8 is a forward FBPIC simulation: the experimental electron spectrum was not used to fit the reconstruction (parameters such as alpha, n0, and modal truncation are independently determined). The Appendix 5 statement that 'Both fits predict... no bunch would be injected for values of phi2 ~ 600 fs^2' is an extrapolation of fitted curves to simulation data, but it is peripheral and clearly derived from the fits; it does not support the central ACE reconstruction claim. The citation of [40] to note prior TCS/ACE agreement is a self-citation, but the present paper also provides a fresh comparison, so the central claim does not rest solely on that citation. Overall, no load-bearing step reduces by construction to its inputs.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

No new physical entities are introduced. The ACE toolbox is a data-processing and simulation-initialization method that rests on standard paraxial optics, the no-STC factorization assumption, imported GSA-MD convergence, and a small number of calibration/numerical parameters (w0, alpha, eta) plus fit constants for the phi2 parametric study.

free parameters (5)
  • GSA-MD numerical waist and mode counts = w0=30 µm; Nm=Nn=30 (HG); Np=30, Nl=3 (LG)
    User-chosen parameters controlling radial extent and resolution of the modal basis; chosen larger than the physical waist to avoid overfitting (Appendix 1), and they affect the reconstructed field and electron spectra.
  • Energy ratio alpha = 0.85 (85%) at z* - zf = -250 µm
    Measured ratio of reconstructed to experimental fluence; used to set Elaser,sim = 0.74 J and scale the field amplitude by sqrt(alpha) (Eqs. 13-14).
  • Plasma compression factor eta = 0.81
    Estimated from TCS/TGS duration evolution at z - z_cell = 300 µm and used as an input to the charge and energy-spread fits (Appendix 5, Eq. 28-29).
  • Fit constants for Emax(phi2) = A1=223.7 MeV, C1=-262.8 MeV
    Nonlinear least-squares fit to 11 simulation points, R^2=0.99 (Appendix 4, Eq. 26).
  • Fit constants for Q(phi2) and sigma_E(phi2) = Q: A2=2.39 pC s^-1, C2=-76.2 pC; sigma_E: A2=1.63 MeV s^-1, C2=-42.3 MeV
    Fits to simulated charge and energy spread as functions of phi2, R^2=0.98 and 0.95 (Appendix 5, Eq. 27-29).
assumptions (6)
  • domain assumption Paraxial approximation and slowly varying envelope are valid for the laser field
    Used to represent the field as a modal sum and to propagate via HG/LG modes and Fresnel transforms; justified in Section II by w0=12.1 µm >> lambda0=0.8 µm.
  • domain assumption No spatio-temporal couplings; the field factorizes as E_perp = Re{ E_tilde_perp(r,zf) * T_tilde(t) } with modes temporally synchronized
    Explicitly stated in the abstract and Section II, Eq. (1). If false, temporal and transverse reconstruction cannot be performed independently.
  • domain assumption The unchirped temporal profile is Gaussian with known duration tau and carrier frequency omega0
    Used in Section II A, Eq. (2), to construct the chirped profile via Fourier transform and chirp phase coefficients.
  • domain assumption GSA-MD converges to the correct phase from a set of measured fluence planes
    The GSA-MD procedure is imported from prior references [15,16]; the paper reports reconstruction agreement (Fig. 3, 0.5 µm waist error) but does not prove convergence for this dataset.
  • domain assumption Ionization injection threshold for nitrogen is a(t) ~ 1.5
    Taken from Chen et al. [46] and used in Appendix 5 to model the ionization volume in the charge and energy-spread fits.
  • domain assumption Bunch maximum energy scales linearly with laser amplitude a0 in this near-bubble regime
    Used in Appendix 4, Eq. (26), to fit Emax(phi2); based on Refs. [69,70] for the 3D nonlinear bubble regime.

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Cite this review

Pith. "Pith review of Combined tools for Particle-In-Cell simulations performed with transversely asymmetric chirped lasers." pith.science (2026). https://pith.science/paper/QSBV4VA4

@misc{pith2026260719121,
  author       = {Pith},
  title        = {Pith review of: Combined tools for Particle-In-Cell simulations performed with transversely asymmetric chirped lasers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QSBV4VA4}},
  note         = {Machine review of arXiv:2607.19121}
}
read the original abstract

We introduce the Asymmetric Chirped Electric field reconstruction (ACE) toolbox, a suite of algorithms enabling the reconstruction of a laser transverse distribution coupled to a chirped temporal profile. This suite includes the implementation of the reconstructed distribution in Particle In-Cell simulations in cylindrical and Cartesian geometry. Under the assumption of negligible spatio-temporal couplings, the ACE toolbox extends a previously established method for realistic simulations of the transverse distribution by adding spectral chirping to the modal decomposition of the electric field. The relevance of the ACE toolbox is demonstrated through the modelling of a Laser Wakefield Acceleration experiment where the produced electron bunch was optimized via spectral chirping of the laser pulse.

Figures

Figures reproduced from arXiv: 2607.19121 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
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Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
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Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
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Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
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Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 3
Figure 3. Figure 3: from [73]. Evolution of [PITH_FULL_IMAGE:figures/full_fig_p010_3.png]
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Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
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Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
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Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]
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Figure 13. Figure 13: FIG. 13 [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]
Figure 7
Figure 7. Figure 7: (c) for the energy spread σE. The bunch injected charge, Q, grows with the volume in which the laser en￾velope is sufficiently high for the ionization of N5+. Since the input chirp coefficients only affect T˜(t) [Eq. (2)] and normalized amplitude a0,c [Eq. (29)], the v…

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Reference graph

Works this paper leans on

95 extracted references · 1 linked inside Pith

  1. [40]

    Valenta, T

    P. Valenta, T. Z. Esirkepov, J. Ludwig, S. Wilks, and S. Bulanov, Physical Review Accelerators and Beams28, 094601 (2025)

    2025

  2. [1]

    GSA-MD parameters In this appendix, the motivations behind the choice of the main parameters used for the ACE transverse recon- struction are discussed. Specifically, we explain how the transverse fluctuations and variations along the propaga- tion axis of the reconstructed distribution are controlled by the numerical waist and higher orders of the mode b...

  3. [2]

    Basis Swap

    Modelling of the transverse distribution in PIC simulations This appendix details the modelling of the ACE trans- verse distribution in PIC simulation, and the benefits of using a realistic distribution obtained via GSA-MD over a standard Gaussian fit in a PIC simulation. To perform the “Basis Swap” referred in Fig. 1, con- version operations between HG a...

  4. [3]

    Simulation parameters This appendix details the reasoning behind the choice of several numerical parameters of simulations shown in Table I of Sec. III A. In the quasi-3D cylindrical geometry, the choice of the number of azimuthal modes in the Pseudo-Spectral An- alytical Time-Domain (PSATD) solver of Maxwell equa- tions [81, 82] depends on two competing ...

  5. [4]

    7.(a) for the bunch maximum energyE max

    Fitting the bunch maximum energy withϕ 2 This appendix describes the equations used to fit the data points plotted in Fig. 7.(a) for the bunch maximum energyE max. The linear scaling between the electron en- ergy gain and the laser electric field amplitude is observed in the bubble regime which arises fora 0 ≥2 [69]. It is characterized by a spherical pla...

  6. [5]

    7.(b) for the chargeQ, and Fig

    Fitting the bunch charge and energy spread withϕ 2 This appendix describes the equations used to fit the data points plotted in Fig. 7.(b) for the chargeQ, and Fig. 7.(c) for the energy spreadσ E. The bunch injected charge,Q, grows with the volume in which the laser en- velope is sufficiently high for the ionization ofN 5+. Since the input chirp coefficie...

  7. [6]

    Tajima and J

    T. Tajima and J. M. Dawson, Phys. Rev. Lett.43, 267 (1979)

    1979

  8. [7]

    Esarey, C

    E. Esarey, C. B. Schroeder, and W. P. Leemans, Rev. Mod. Phys.81, 1229 (2009)

    2009

Show all 95 references
  1. [8]

    Assmann, M

    R. Assmann, M. Weikum, T. Akhter, D. Alesini, A. Alexandrova, M. Anania, N. Andreev, I. Andriyash, M. Artioli, A. Aschikhin,et al., The European Physical Journal Special Topics229, 3675 (2020)

    2020

  2. [9]

    Andr´ e, I

    T. Andr´ e, I. Andriyash, A. Loulergue, M. Labat, E. Rous- sel, A. Ghaith, M. Khojoyan, C. Thaury, M. Vall´ eau, F. Briquez,et al., Nature communications9, 1334 (2018)

    2018

  3. [10]

    A. Popp, J. Vieira, J. Osterhoff, Z. Major, R. H¨ orlein, M. Fuchs, R. Weingartner, T. Rowlands-Rees, M. Marti, R. Fonseca,et al., Physical review letters105, 215001 (2010)

    2010

  4. [11]

    Ferri, X

    J. Ferri, X. Davoine, S. Fourmaux, J. Kieffer, S. Corde, K. Ta Phuoc, and A. Lifschitz, Scientific reports6, 27846 (2016)

    2016

  5. [12]

    A. R. Maier, N. M. Delbos, T. Eichner, L. H¨ ubner, S. Jalas, L. Jeppe, S. W. Jolly, M. Kirchen, V. Leroux, P. Messner,et al., Physical Review X10, 031039 (2020)

    2020

  6. [13]

    L. T. Dickson, C. I. D. Underwood, F. Filippi, R. J. Shalloo, J. B. Svensson, D. Gu´ enot, K. Svendsen, I. Moulanier, S. D. Dufr´ enoy, C. D. Murphy, N. C. Lopes, P. P. Rajeev, Z. Najmudin, G. Cantono, A. Persson, O. Lundh, G. Maynard, M. J. V. Streeter, and B. Cros, Phys. Rev...

    2022

  7. [14]

    Dickson,Laser wakefield acceleration of electrons, Ph.D

    L. Dickson,Laser wakefield acceleration of electrons, Ph.D. thesis, Paris-Saclay University (2023)

    2023

  8. [15]

    Moulanier, L

    I. Moulanier, L. Dickson, C. Ballage, O. Vasilovici, A. Gremaud, S. Dobosz Dufr´ enoy, N. Delerue, L. Bernardi, A. Mahjoub, A. Cauchois,et al., Physics of Plasmas30(2023)

    2023

  9. [16]

    C. K. Birdsall and A. B. Langdon,Plasma physics via computer simulation(Taylor and Francis, New York, 2005)

    2005

  10. [17]

    Zemzemi,High-performance computing and numerical simulation for laser wakefield acceleration with realistic laser profiles, Ph.D

    I. Zemzemi,High-performance computing and numerical simulation for laser wakefield acceleration with realistic laser profiles, Ph.D. thesis, Polytechnic Institute of Paris (2020)

    2020

  11. [18]

    A. F. Lifschitz, X. Davoine, E. Lefebvre, J. Faure, C. Rechatin, and V. Malka, Journal of Computational Physics228, 1803 (2009)

    2009

  12. [19]

    R. W. Gerchberg, Optik35, 237 (1972)

    1972

  13. [20]

    Moulanier, L

    I. Moulanier, L. T. Dickson, F. Massimo, G. Maynard, and B. Cros, JOSA B40, 2450 (2023)

    2023

  14. [21]

    Massimo, I

    F. Massimo, I. Moulanier, A. Guerente, O. Khomyshyn, M. Masckala, T. L. Steyn, U. Schramm, A. Irman, and B. Cros, Phys. Rev. E113, 055211 (2026)

    2026

  15. [22]

    Th´ evenet, I

    M. Th´ evenet, I. A. Andriyash, L. Fedeli, A. Ferran Pousa, A. Huebl, S. Jalas, M. Kirchen, R. Lehe, R. J. Shalloo, A. Sinn,et al., inJournal of Physics: Conference Series, Vol. 3124 (IOP Publishing, 2025) p. 012014

    2025

  16. [23]

    Sainte-Marie, O

    A. Sainte-Marie, O. Gobert, and F. Quere, Optica4, 1298 (2017)

    2017

  17. [24]

    Leroux, T

    V. Leroux, T. Eichner, and A. R. Maier, Optics express 28, 8257 (2020)

    2020

  18. [25]

    Leemans, P

    W. Leemans, P. Catravas, E. Esarey, C. Geddes, C. Toth, R. Trines, C. Schroeder, B. Shadwick, J. Van Tilborg, and J. Faure, Physical review letters89, 174802 (2002)

    2002

  19. [26]

    Schroeder, E

    C. Schroeder, E. Esarey, C. Geddes, C. Toth, B. Shad- wick, J. Van Tilborg, J. Faure, and W. Leemans, Physics of Plasmas10, 2039 (2003)

  20. [27]

    T´ oth, J

    C. T´ oth, J. Faure, J. Van Tilborg, C. Geddes, C. Schroeder, E. Esarey, and W. Leemans, Optics let- ters28, 1823 (2003)

    2003

  21. [28]

    S. Y. Kalmykov, A. Beck, X. Davoine, E. Lefebvre, and B. A. Shadwick, New Journal of Physics14, 033025 (2012)

    2012

  22. [29]

    H. T. Kim, V. Pathak, K. Hong Pae, A. Lifschitz, F. Sylla, J. H. Shin, C. Hojbota, S. K. Lee, J. H. Sung, H. W. Lee,et al., Scientific reports7, 10203 (2017)

    2017

  23. [30]

    Pathak, A

    N. Pathak, A. Zhidkov, T. Hosokai, and R. Kodama, Physics of Plasmas25(2018)

    2018

  24. [31]

    Grigoriadis, G

    A. Grigoriadis, G. Andrianaki, I. Tazes, V. Dimitriou, M. Tatarakis, E. Benis, and N. Papadogiannis, Scientific Reports13, 2918 (2023)

    2023

  25. [32]

    D. R. Jones, M. Schonlau, and W. J. Welch, Journal of Global Optimization13, 455 (1998)

    1998

  26. [33]

    P. I. Frazier, A tutorial on bayesian optimization (2018), arXiv:1807.02811 [stat.ML]

    2018 arXiv

  27. [34]

    Kirchen, S

    M. Kirchen, S. Jalas, P. Messner, P. Winkler, T. Eich- ner, L. H¨ ubner, T. H¨ ulsenbusch, L. Jeppe, T. Parikh, M. Schnepp,et al., Physical review letters126, 174801 (2021)

    2021

  28. [35]

    Jalas, M

    S. Jalas, M. Kirchen, P. Messner, P. Winkler, L. H¨ ubner, J. Dirkwinkel, M. Schnepp, R. Lehe, and A. R. Maier, Physical review letters126, 104801 (2021)

    2021

  29. [36]

    Ferran Pousa, S

    A. Ferran Pousa, S. Jalas, M. Kirchen, A. Martinez de la Ossa, M. Th´ evenet, S. Hudson, J. Larson, A. Huebl, J.- 16 L. Vay, and R. Lehe, Physical Review Accelerators and Beams26, 084601 (2023)

    2023

  30. [37]

    Jalas, M

    S. Jalas, M. Kirchen, C. Braun, T. Eichner, J. Gonza- lez, L. H¨ ubner, T. H¨ ulsenbusch, P. Messner, G. Palmer, M. Schnepp,et al., Physical Review Accelerators and Beams26, 071302 (2023)

    2023

  31. [38]

    Irshad, S

    F. Irshad, S. Karsch, and A. D¨ opp, Physical Review Re- search5, 013063 (2023)

    2023

  32. [39]

    Irshad, C

    F. Irshad, C. Eberle, F. Foerster, K. v. Grafenstein, F. Haberstroh, E. Travac, N. Weisse, S. Karsch, and A. D¨ opp, Physical review letters133, 085001 (2024)

    2024

  33. [41]

    Shalloo, S

    R. Shalloo, S. Dann, J.-N. Gruse, C. Underwood, A. An- toine, C. Arran, M. Backhouse, C. Baird, M. Balcazar, N. Bourgeois,et al., Nature communications11, 6355 (2020)

    2020

  34. [42]

    Loughran, M

    B. Loughran, M. J. Streeter, H. Ahmed, S. Astbury, M. Balcazar, M. Borghesi, N. Bourgeois, C. Curry, S. Dann, S. DiIorio,et al., High Power Laser Science and Engineering11, e35 (2023)

    2023

  35. [43]

    Glenn, F

    G. Glenn, F. Treffert, H. Ahmed, S. Astbury, M. Borgh- esi, N. Bourgeois, C. Curry, S. J. Dann, S. DiIorio, N. Dover,et al., Physical Review Research8, 013101 (2026)

    2026

  36. [44]

    Zeraouli, D

    G. Zeraouli, D. Mariscal, E. Grace, K. Swanson, B. Djordjevic, M. Hill, S. Jiang, R. Daskalova, G. Tis- careno, D. Hanggi,et al., Physics of Plasmas33(2026)

    2026

  37. [45]

    M. P. Backhouse, L. T. Dickson, I. Moulanier, F. Mas- simo, C. C. Cobo, F. Filippi, C. Gustafsson, E. Lofquist, K. Svendsen, M. J. V. Streeter, R. J. Shalloo, O. Vasilovici, C. Ballage, S. J. D. Dann, C. D. Mur- phy, Z. Najmudin, S. Dobosz Dufr´ enoy, O. Lundh, and B. Cros, Ph...

    2025

  38. [46]

    Akturk, X

    S. Akturk, X. Gu, P. Bowlan, and R. Trebino, Journal of Optics12, 093001 (2010)

    2010

  39. [47]

    Pariente, V

    G. Pariente, V. Gallet, A. Borot, O. Gobert, and F. Qu´ er´ e, Nature Photonics10, 547 (2016)

    2016

  40. [48]

    Jeandet, S

    A. Jeandet, S. W. Jolly, A. Borot, B. Bussi` ere, P. Du- mont, J. Gautier, O. Gobert, J.-P. Goddet, A. Gonsalves, A. Irman, W. P. Leemans, R. Lopez-Martens, G. Men- nerat, K. Nakamura, M. Ouill´ e, G. Pariente, M. Pittman, T. P¨ uschel, F. Sanson, F. Sylla, C. Thaury, K. Zeil,...

    2022

  41. [49]

    A. Pak, K. Marsh, S. Martins, W. Lu, W. Mori, and C. Joshi, Physical Review Letters104, 025003 (2010)

    2010

  42. [50]

    McGuffey, A

    C. McGuffey, A. Thomas, W. Schumaker, T. Matsuoka, V. Chvykov, F. Dollar, G. Kalintchenko, V. Yanovsky, A. Maksimchuk, K. Krushelnick,et al., Physical Review Letters104, 025004 (2010)

    2010

  43. [51]

    M. Chen, E. Esarey, C. Schroeder, C. Geddes, and W. Leemans, Physics of Plasmas19, 033101 (2012)

    2012

  44. [52]

    Mirzaie, S

    M. Mirzaie, S. Li, M. Zeng, N. Hafz, M. Chen, G. Li, Q. Zhu, H. Liao, T. Sokollik, F. Liu,et al., Scientific reports5, 1 (2015)

    2015

  45. [53]

    R. Lehe, M. Kirchen, I. A. Andriyash, B. B. Godfrey, and J.-L. Vay, Computer Physics Communications203, 66 (2016)

    2016

  46. [54]

    J. R. Pierce, J. P. Palastro, F. Li, B. Malaca, D. Ram- sey, J. Vieira, K. Weichman, and W. B. Mori, Physical Review Research5, 013085 (2023)

    2023

  47. [55]

    Svelto and D

    O. Svelto and D. C. Hanna,Principles of lasers, Vol. 1 (Springer, 2010)

    2010

  48. [56]

    Quesnel and P

    B. Quesnel and P. Mora, Physical Review E58, 3719 (1998)

    1998

  49. [57]

    Tournois, Optics communications140, 245 (1997)

    P. Tournois, Optics communications140, 245 (1997)

    1997

  50. [58]

    Verluise, V

    F. Verluise, V. Laude, Z. Cheng, C. Spielmann, and P. Tournois, Optics letters25, 575 (2000)

    2000

  51. [59]

    Huijts, I

    J. Huijts, I. A. Andriyash, L. Rovige, A. Vernier, and J. Faure, Physics of Plasmas28(2021)

    2021

  52. [60]

    Borzsonyi, A

    A. Borzsonyi, A. P. Kovacs, and K. Osvay, Applied Sci- ences3, 515 (2013)

    2013

  53. [61]

    Mohseni, C

    M. Mohseni, C. Polzer, and T. Hellerer, Optics express 26, 10230 (2018)

    2018

  54. [62]

    J. W. Cooley and J. W. Tukey, Mathematics of compu- tation19, 297 (1965)

    1965

  55. [63]

    Diels and W

    J.-C. Diels and W. Rudolph,Ultrashort laser pulse phe- nomena(Elsevier, 2006)

    2006

  56. [64]

    S. W. Jolly, N. H. Matlis, F. Ahr, V. Leroux, T. Eichner, A.-L. Calendron, H. Ishizuki, T. Taira, F. X. K¨ artner, and A. R. Maier, Nature communications10, 2591 (2019)

    2019

  57. [65]

    Kaplan and P

    D. Kaplan and P. Tournois, Journal de Physique IV12, 69 (2002)

    2002

  58. [66]

    C. E. Shannon, Proceedings of the IRE37, 10 (2006)

    2006

  59. [67]

    A. E. Siegman, Journal of the Optical society of America 63, 1093 (1973)

    1973

  60. [68]

    Allen, M

    L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Wo- erdman, Physical review A45, 8185 (1992)

    1992

  61. [69]

    Born and E

    M. Born and E. Wolf,Principles of optics: electromag- netic theory of propagation, interference and diffraction of light(Elsevier, 2013)

    2013

  62. [70]

    Sroor, C

    H. Sroor, C. Moodley, V. Rodr ´ ıguez-Fajardo, Q. Zhan, and A. Forbes, J. Opt. Soc. Am. A38, 1443 (2021)

    2021

  63. [71]

    Paye and A

    J. Paye and A. Migus, Journal of the Optical Society of America B12, 1480 (1995)

    1995

  64. [72]

    Hong, J.-H

    K.-H. Hong, J.-H. Kim, Y. H. Kang, and C. H. Nam, Applied Physics B74, s231 (2002)

    2002

  65. [73]

    V. B. Pathak, J. Vieira, R. Fonseca, and L. Silva, New Journal of Physics14, 023057 (2012)

    2012

  66. [74]

    W. Lu, M. Tzoufras, C. Joshi, F. Tsung, W. Mori, J. Vieira, R. Fonseca, and L. Silva, Physical Review Spe- cial Topics—Accelerators and Beams10, 061301 (2007)

    2007

  67. [75]

    Couperus, R

    J. Couperus, R. Pausch, A. K¨ ohler, O. Zarini, J. Kr¨ amer, M. Garten, A. Huebl, R. Gebhardt, U. Helbig, S. Bock, et al., Nature communications8, 1 (2017)

    2017

  68. [76]

    Djordjevi´ c, C

    B. Djordjevi´ c, C. Benedetti, A. McNaughton, R. Lehe, H.-E. Tsai, S. Wilks, B. Reagan, G. Williams, J. van Tilborg, and C. Schroeder, arXiv preprint arXiv:2512.09125 (2025)

    2025

  69. [77]

    A. E. Siegman,Lasers(University Science Books, 1986)

    1986

  70. [78]

    Moulanier,Mod´ elisation r´ ealiste de l’acc´ el´ eration laser- plasma, Ph.D

    I. Moulanier,Mod´ elisation r´ ealiste de l’acc´ el´ eration laser- plasma, Ph.D. thesis, Universit´ e Paris-Saclay (2024)

    2024

  71. [79]

    Dominici, Journal of Difference Equations and Appli- cations13, 1115 (2007)

    D. Dominici, Journal of Difference Equations and Appli- cations13, 1115 (2007)

    2007

  72. [80]

    Kimel and L

    I. Kimel and L. R. Elias, IEEE Journal of quantum elec- tronics29, 2562 (2002)

    2002

  73. [81]

    Temme, Zeitschrift f¨ ur angewandte Mathematik und Physik ZAMP41, 114 (1990)

    N. Temme, Zeitschrift f¨ ur angewandte Mathematik und Physik ZAMP41, 114 (1990)

    1990

  74. [82]

    Deano, E

    A. Deano, E. J. Huertas, and F. Marcell´ an, Journal of Mathematical Analysis and Applications403, 477 (2013)

    2013

  75. [83]

    Abramowitz, I

    M. Abramowitz, I. A. Stegun, and J. E. Romain, Hand- book of mathematical functions, with formulas, graphs, and mathematical tables (1966)

    1966

  76. [84]

    J. L. Powell, Journal of econometrics25, 303 (1984)

    1984

  77. [85]

    Dickson, inJournal of Physics: Conference Series, 17 Vol

    L. Dickson, inJournal of Physics: Conference Series, 17 Vol. 3124 (IOP Publishing, 2025) p. 012013

    2025

  78. [86]

    J.-L. Vay, I. Haber, and B. B. Godfrey, Journal of Com- putational Physics243, 260 (2013)

    2013

  79. [87]

    B. B. Godfrey, J.-L. Vay, and I. Haber, Journal of Com- putational Physics258, 689 (2014)

    2014

  80. [88]

    Audet, P

    T. Audet, P. Lee, G. Maynard, S. D. Dufr´ enoy, A. Maitrallain, M. Bougeard, P. Monot, and B. Cros, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment909, 383 (2018)

    2018

  81. [89]

    Vay, Physical review letters98, 130405 (2007)

    J.-L. Vay, Physical review letters98, 130405 (2007)

    2007

  82. [90]

    P. Yu, X. Xu, A. Davidson, A. Tableman, T. Dalichaouch, F. Li, M. D. Meyers, W. An, F. S. Tsung, V. K. Decyk,et al., Journal of Computational Physics316, 747 (2016)

    2016

  83. [91]

    Massimo, A

    F. Massimo, A. Beck, J. D´ erouillat, I. Zemzemi, and A. Specka, Physical Review E102, 033204 (2020)

    2020

  84. [92]

    Kostyukov, A

    I. Kostyukov, A. Pukhov, and S. Kiselev, Physics of Plas- mas11, 5256 (2004)

    2004

  85. [93]

    C. L. Lawson and R. J. Hanson,Solving least squares problems(SIAM, 1995)

    1995

  86. [94]

    R. G. D. Steel and J. H. Torrie,Principles and procedures of statistics.(McGraw Hill, Inc, 1960)

    1960

  87. [95]

    L. C. Andrews,Special functions of mathematics for en- gineers, Vol. 49 (Spie Press, 1998)

    1998

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