- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

High-order harmonic generation from ultrarelativistic s-polarized 400 nm laser-solid interactions

V. Flores1,*, H. Allison1, D. Attiyah1, N. Beier1,2, P. Efthimion3, K. A. Flippo4, L. Gao3, S. Hakimi1, K. Hill3 et al.

R. Hollinger5, M. Logantha1, Y. Musthafa1, R. Nedbailo5, V. Senthilkumaran2, R. Shepherd6, V. N. Shlyaptsev7, H. Song7, S. Wang6, J. J. Rocca5,7, A. E. Hussein2, and F. Dollar1,†

  • *Contact author: floresvr@uci.edu
  • †Contact author: fdollar@uci.edu
PDF

Phys. Rev. Research 8, L032019 – Published 4 August, 2026

DOI: https://doi.org/10.1103/2vys-hgwm

Abstract

Harmonic emission from s-polarized, 400 nm, ultrahigh-contrast laser-solid interactions is observed to exhibit a plasma-frequency cutoff at relativistic intensities (∼1020Wcm−2), with harmonics emerging beyond this cutoff in the ultrarelativistic regime (∼1021Wcm−2). Experimental conditions isolate J⃗×B⃗ heating as the dominant absorption mechanism, and particle-in-cell simulations show that its intensity-dependent evolution drives distinct harmonic generation mechanisms.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (70)

  1. A. Macchi, M. Borghesi, and M. Passoni, Ion acceleration by superintense laser-plasma interaction, Rev. Mod. Phys. 85, 751 (2013).
  2. M. Roth, D. Jung, K. Falk, N. Guler, O. Deppert, M. Devlin, A. Favalli, J. Fernandez, D. Gautier, M. Geissel, et al., Bright laser-driven neutron source based on the relativistic transparency of solids, Phys. Rev. Lett. 110, 044802 (2013).
  3. L. Disdier, J.-P. Garçonnet, G. Malka, and J.-L. Miquel, Fast neutron emission from a high-energy ion beam produced by a high-intensity subpicosecond laser pulse, Phys. Rev. Lett. 82, 1454 (1999).
  4. H.-S. Park, D. M. Chambers, H.-K. Chung, R. J. Clarke, R. Eagleton, E. Giraldez, T. Goldsack, R. Heathcote, N. Izumi, M. H. Key, et al., High-energy kα radiography using high-intensity, short-pulse lasers), Phys. Plasmas 13, 056309 (2006).
  5. N. H. Burnett, H. A. Baldis, M. C. Richardson, and G. D. Enright, Harmonic generation in CO2 laser target interaction, Appl. Phys. Lett. 31, 172 (1977).
  6. C. Thaury and F. Quéré, High-order harmonic and attosecond pulse generation on plasma mirrors: Basic mechanisms, J. Phys. B: At. Mol. Opt. Phys. 43, 213001 (2010).
  7. F. Quéré, C. Thaury, H. George, J. P. Geindre, E. Lefebvre, G. Bonnaud, P. Monot, and P. Martin, High-order harmonic generation using plasma mirrors, Plasma Phys. Controlled Fusion 50, 124007 (2008).
  8. B. Dromey, S. Kar, C. Bellei, D. C. Carroll, R. J. Clarke, J. S. Green, S. Kneip, K. Markey, S. R. Nagel, P. T. Simpson, L. Willingale, P. McKenna, D. Neely, Z. Najmudin, K. Krushelnick, P. A. Norreys, and M. Zepf, Bright multi-keV harmonic generation from relativistically oscillating plasma surfaces, Phys. Rev. Lett. 99, 085001 (2007).
  9. M. Zepf, B. Dromey, S. Kar, C. Bellei, D. C. Carroll, R. J. Clarke, J. S. Green, S. Kneip, K. Markey, S. R. Nagel, P. T. Simpson, L. Willingale, P. McKenna, D. Neely, Z. Najmudin, K. Krushelnick, and P. A. Norreys, High harmonics from relativistically oscillating plasma surfaces—A high brightness attosecond source at keV photon energies, Plasma Phys. Controlled Fusion 49, B149 (2007).
  10. M. Yeung, S. Rykovanov, J. Bierbach, L. Li, E. Eckner, S. Kuschel, A. Woldegeorgis, C. Rödel, A. Sävert, G. G. Paulus, M. Coughlan, B. Dromey, and M. Zepf, Experimental observation of attosecond control over relativistic electron bunches with two-colour fields, Nat. Photonics 11, 32 (2017).
  11. L. Chopineau, A. Denoeud, A. Leblanc, E. Porat, P. Martin, H. Vincenti, and F. Quéré, Spatio-temporal characterization of attosecond pulses from plasma mirrors, Nat. Phys. 17, 968 (2021).
  12. S. G. Rykovanov, M. Geissler, J. Meyer-ter Vehn, and G. D. Tsakiris, Intense single attosecond pulses from surface harmonics using the polarization gating technique, New J. Phys. 10, 025025 (2008).
  13. G. D Tsakiris, K. Eidmann, J. Meyer-ter Vehn, and F. Krausz, Route to intense single attosecond pulses, New J. Phys. 8, 19 (2006).
  14. J. A. Wheeler, A. Borot, S. Monchocé, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quéré, Attosecond lighthouses from plasma mirrors, Nat. Photonics 6, 829 (2012).
  15. A. Tarasevitch, A. Orisch, D. Von Der Linde, P. Balcou, G. Rey, J. P. Chambaret, U. Teubner, D. Klöpfel, and W. Theobald, Generation of high-order spatially coherent harmonics from solid targets by femtosecond laser pulses, Phys. Rev. A 62, 023816 (2000).
  16. M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, Role of the plasma scale length in the harmonic generation from solid targets, Phys. Rev. E 58, R5253 (1998).
  17. M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Attosecond metrology, Nature (London) 414, 509 (2001).
  18. A. Pukhov, X-rays in a flash, Nat. Phys. 2, 439 (2006).
  19. R. Neutze, R. Wouts, D. Van der Spoel, E. Weckert, and J. Hajdu, Potential for biomolecular imaging with femtosecond x-ray pulses, Nature (London) 406, 752 (2000).
  20. F. Quéré, C. Thaury, P. Monot, S. Dobosz, P. Martin, J.-P. Geindre, and P. Audebert, Coherent wake emission of high-order harmonics from overdense plasmas, Phys. Rev. Lett. 96, 125004 (2006).
  21. S. V. Bulanov, N. M. Naumova, and F. Pegoraro, Interaction of an ultrashort, relativistically strong laser pulse with an overdense plasma, Phys. Plasmas 1, 745 (1994).
  22. R. Lichters, J. Meyer‐ter‐Vehn, and A. Pukhov, Short‐pulse laser harmonics from oscillating plasma surfaces driven at relativistic intensity, Phys. Plasmas 3, 3425 (1996).
  23. P. Gibbon, Harmonic generation by femtosecond laser-solid interaction: A coherent “water-window” light source? Phys. Rev. Lett. 76, 50 (1996).
  24. A. Jullien, O. Albert, F. Burgy, G. Hamoniaux, J.-P. Rousseau, J.-P. Chambaret, F. Augé-Rochereau, G. Chériaux, J. Etchepare, N. Minkovski, and S. M. Saltiel, 10−10 temporal contrast for femtosecond ultraintense lasers by cross-polarized wave generation, Opt. Lett. 30, 920 (2005).
  25. H. C. Kapteyn, M. M. Murnane, A. Szoke, and R. W. Falcone, Prepulse energy suppression for high-energy ultrashort pulses using self-induced plasma shuttering, Opt. Lett. 16, 490 (1991).
  26. A. Lévy, T. Ceccotti, P. D’Oliveira, F. Réau, M. Perdrix, F. Quéré, P. Monot, M. Bougeard, H. Lagadec, P. Martin, J.-P. Geindre, and P. Audebert, Double plasma mirror for ultrahigh temporal contrast ultraintense laser pulses, Opt. Lett. 32, 310 (2007).
  27. G. Doumy, F. Quéré, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J. C. Gauthier, J.-P. Geindre, and T. Wittmann, Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses, Phys. Rev. E 69, 026402 (2004).
  28. G. Doumy, S. Dobosz, P. D’Oliveira, P. Monot, M. Perdrix, F. Quéré, F. Réau, P. Martin, P. Audebert, J. Gauthier, et al., High order harmonic generation by non-linear reflection of a pedestal-free intense laser pulse on a plasma, Appl. Phys. B 78, 901 (2004).
  29. P. Monot, G. Doumy, S. Dobosz, M. Perdrix, P. D’Oliveira, F. Quéré, F. Réau, P. Martin, P. Audebert, J.-C. Gauthier, and J.-P. Geindre, High-order harmonic generation by nonlinear reflection of an intense high-contrast laser pulse on a plasma, Opt. Lett. 29, 893 (2004).
  30. C. Thaury, F. Quere, J.-P. Geindre, A. Levy, T. Ceccotti, P. Monot, M. Bougeard, F. Réau, P. d’Oliveira, P. Audebert, et al., Plasma mirrors for ultrahigh-intensity optics, Nat. Phys. 3, 424 (2007).
  31. P. Gibbon, Cleaner petawatts with plasma optics, Nat. Phys. 3, 369 (2007).
  32. B. Dromey, D. Adams, R. Hörlein, Y. Nomura, S. Rykovanov, D. Carroll, P. Foster, S. Kar, K. Markey, P. McKenna, et al., Diffraction-limited performance and focusing of high harmonics from relativistic plasmas, Nat. Phys. 5, 146 (2009).
  33. S. Kohlweyer, G. Tsakiris, C.-G. Wahlström, C. Tillman, and I. Mercer, Harmonic generation from solid-vacuum interface irradiated at high laser intensities, Opt. Commun. 117, 431 (1995).
  34. U. Teubner, G. Pretzler, T. Schlegel, K. Eidmann, E. Förster, and K. Witte, Anomalies in high-order harmonic generation at relativistic intensities, Phys. Rev. A 67, 013816 (2003).
  35. U. Teubner, K. Eidmann, U. Wagner, U. Andiel, F. Pisani, G. D. Tsakiris, K. Witte, J. Meyer-ter Vehn, T. Schlegel, and E. Förster, Harmonic emission from the rear side of thin overdense foils irradiated with intense ultrashort laser pulses, Phys. Rev. Lett. 92, 185001 (2004).
  36. K. Eidmann, T. Kawachi, A. Marcinkevičius, R. Bartlome, G. D. Tsakiris, K. Witte, and U. Teubner, Fundamental and harmonic emission from the rear side of a thin overdense foil irradiated by an intense ultrashort laser pulse, Phys. Rev. E 72, 036413 (2005).
  37. A. Tarasevitch, K. Lobov, C. Wünsche, and D. von der Linde, Transition to the relativistic regime in high order harmonic generation, Phys. Rev. Lett. 98, 103902 (2007).
  38. Y. Wang, S. Wang, A. Rockwood, B. M. Luther, R. Hollinger, A. Curtis, C. Calvi, C. S. Menoni, and J. J. Rocca, 0.85 PW laser operation at 3.3 Hz and second-harmonic beamline, Opt. Lett. 42, 3828 (2017).
  39. E. G. Gamaly, A. V. Rode, B. Luther-Davies, and V. T. Tikhonchuk, Ablation of solids by femtosecond lasers: Ablation mechanism and ablation thresholds for metals and dielectrics, Phys. Plasmas 9, 949 (2002).
  40. U. Teubner, J. Bergmann, B. van Wonterghem, F. P. Schäfer, and R. Sauerbrey, Angle-dependent x-ray emission and resonance absorption in a laser-produced plasma generated by a high intensity ultrashort pulse, Phys. Rev. Lett. 70, 794 (1993).
  41. S. C. Wilks, W. L. Kruer, M. Tabak, and A. B. Langdon, Absorption of ultra-intense laser pulses, Phys. Rev. Lett. 69, 1383 (1992).
  42. S. C. Wilks, Simulations of ultraintense laser–plasma interactions, Phys. Fluids B 5, 2603 (1993).
  43. P. Mulser and D. Bauer, High Power Laser-Matter Interaction (Springer Science & Business Media, Berlin, Heidelberg, 2010), Vol. 238, Chap. 4, pp. 153–191.
  44. F. Brunel, Not-so-resonant, resonant absorption, Phys. Rev. Lett. 59, 52 (1987).
  45. W. L. Kruer and K. Estabrook, J × B heating by very intense laser light, Phys. Fluids 28, 430 (1985).
  46. A. V. Mitrofanov, D. A. Sidorov-Biryukov, M. V. Rozhko, S. V. Ryabchuk, A. A. Voronin, and A. M. Zheltikov, High-order harmonic generation from a solid-surface plasma by relativistic-intensity sub-100-fs mid-infrared pulses, Opt. Lett. 43, 5571 (2018).
  47. N. F. Beier, H. Allison, P. Efthimion, K. A. Flippo, L. Gao, S. B. Hansen, K. Hill, R. Hollinger, M. Logantha, Y. Musthafa, R. Nedbailo, V. Senthilkumaran, R. Shepherd, V. N. Shlyaptsev, H. Song, S. Wang, F. Dollar, J. J. Rocca, and A. E. Hussein, Homogeneous, micron-scale high-energy-density matter generated by relativistic laser-solid interactions, Phys. Rev. Lett. 129, 135001 (2022).
  48. D. Neely, D. Chambers, C. Danson, P. Norreys, S. Preston, F. Quinn, M. Roper, J. Wark, and M. Zepf, A multi-channel soft x-ray flat-field spectrometer, AIP Conf. Proc. 426, 479 (1998).
  49. H. Takabe, Relativistic laser and solid target interactions, in The Physics of Laser Plasmas and Applications, Vol. 1: Physics of Laser Matter Interaction (Springer International Publishing, Cham, 2020), Chap. 7, pp. 239–285.
  50. S. Wilks, W. Kruer, and W. Mori, Odd harmonic generation of ultra-intense laser pulses reflected from an overdense plasma, IEEE Trans. Plasma Sci. 21, 120 (1993).
  51. A. Macchi, A Superintense Laser-Plasma Interaction Theory Primer, 1st ed., Springer Briefs in Physics (Springer, Dordrecht, 2013), Chap. 4, pp. 59–79.
  52. S. Kahaly, S. Monchocé, H. Vincenti, T. Dzelzainis, B. Dromey, M. Zepf, P. Martin, and F. Quéré, Direct observation of density-gradient effects in harmonic generation from plasma mirrors, Phys. Rev. Lett. 110, 175001 (2013).
  53. F. Quéré, C. Thaury, J.-P. Geindre, G. Bonnaud, P. Monot, and P. Martin, Phase properties of laser high-order harmonics generated on plasma mirrors, Phys. Rev. Lett. 100, 095004 (2008).
  54. A. Kramida, Y. Ralchenko, J. Reader, and NIST ASD Team, NIST Atomic Spectra Database (version 5.12) [Online], National Institute of Standards and Technology, Gaithersburg, MD, 2024, https://physics.nist.gov/asd, accessed 12 December 2025.
  55. S. Augst, D. D. Meyerhofer, D. Strickland, and S. L. Chin, Laser ionization of noble gases by Coulomb-barrier suppression, J. Opt. Soc. Am. B 8, 858 (1991).
  56. B. M. Penetrante and J. N. Bardsley, Residual energy in plasmas produced by intense subpicosecond lasers, Phys. Rev. A 43, 3100 (1991).
  57. J. Li, A. V. Arefiev, S. S. Bulanov, D. Kawahito, M. Bailly-Grandvaux, G. M. Petrov, C. McGuffey, and F. N. Beg, Ionization injection of highly-charged copper ions for laser driven acceleration from ultra-thin foils, Sci. Rep. 9, 666 (2019).
  58. R. Hollinger, S. Wang, Y. Wang, A. Moreau, M. G. Capeluto, H. Song, A. Rockwood, E. Bayarsaikhan, V. Kaymak, A. Pukhov, et al., Extreme ionization of heavy atoms in solid-density plasmas by relativistic second-harmonic laser pulses, Nat. Photon. 14, 607 (2020).
  59. J. J. Rocca, M. G. Capeluto, R. C. Hollinger, S. Wang, Y. Wang, G. R. Kumar, A. D. Lad, A. Pukhov, and V. N. Shlyaptsev, Ultra-intense femtosecond laser interactions with aligned nanostructures, Optica 11, 437 (2024).
  60. C. Rödel, D. an der Brügge, J. Bierbach, M. Yeung, T. Hahn, B. Dromey, S. Herzer, S. Fuchs, A. G. Pour, E. Eckner, et al., Harmonic generation from relativistic plasma surfaces in ultrasteep plasma density gradients, Phys. Rev. Lett. 109, 125002 (2012).
  61. R. J. L. Timmis, C. R. J. Fitzpatrick, J. P. Kennedy, H. M. Huddleston, E. Denis, A. James, C. Baird, D. Symes, D. McGonegle, E. Atonga, et al., Efficiency-optimized relativistic plasma harmonics for extreme fields, Nature (London) 652, 1153 (2026).
  62. F. Dollar, P. Cummings, V. Chvykov, L. Willingale, M. Vargas, V. Yanovsky, C. Zulick, A. Maksimchuk, A. G. R. Thomas, and K. Krushelnick, Scaling high-order harmonic generation from laser-solid interactions to ultrahigh intensity, Phys. Rev. Lett. 110, 175002 (2013).
  63. T. Baeva, S. Gordienko, and A. Pukhov, Theory of high-order harmonic generation in relativistic laser interaction with overdense plasma, Phys. Rev. E 74, 046404 (2006).
  64. J. Derouillat, A. Beck, F. Pérez, T. Vinci, M. Chiaramello, A. Grassi, M. Flé, G. Bouchard, I. Plotnikov, N. Aunai, J. Dargent, C. Riconda, and M. Grech, SMILEI: A collaborative, open-source, multi-purpose particle-in-cell code for plasma simulation, Comput. Phys. Commun. 222, 351 (2018).
  65. A. Bourdier, Oblique incidence of a strong electromagnetic wave on a cold inhomogeneous electron plasma. Relativistic effects, Phys. Fluids 26, 1804 (1983).
  66. P. Gibbon and A. R. Bell, Collisionless absorption in sharp-edged plasmas, Phys. Rev. Lett. 68, 1535 (1992).
  67. P. Gibbon, A. Andreev, E. Lefebvre, G. Bonnaud, H. Ruhl, J. Delettrez, and A. R. Bell, Calibration of one-dimensional boosted kinetic codes for modeling high-intensity laser–solid interactions, Phys. Plasmas 6, 947 (1999).
  68. U. Teubner, D. Altenbernd, P. Gibbon, E. Förster, A. Mysyrowicz, P. Audebert, J.-P. Geindre, J. Gauthier, R. Lichters, and J. M. ter Vehn, Observation of VUV radiation at wavelengths in the ωp- and 2ωp-wavelength range emitted from femtosecond laser-plasmas, Opt. Commun. 144, 217 (1997).
  69. T. Kunzl, R. Lichters, and J. Meyer-Ter-Vehn, Large-amplitude plasma waves and 2ωp emission driven by laser-generated electron jets in overdense plasma layers, Laser Part. Beams 21, 583 (2003).
  70. R. Ondarza-Rovira and T. J. M. Boyd, Plasma effects on harmonic spectra generated from moderately relativistic laser-plasma interactions, Phys. Rev. E 86, 026407 (2012).

Outline

Information

Phys. Rev. Research 8, L032019– Published 4 August, 2026
  • Received 13 January 2026
  • Accepted 1 July 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation