- Open Access
Anomalous effects in single-slit diffraction of light at relativistic intensities
Phys. Rev. Research 7, 043163 – Published 12 November, 2025
DOI: https://doi.org/10.1103/f4yl-r4qd
Abstract
High-order harmonic generation via single-slit diffraction of relativistic laser pulses is investigated. Using fully kinetic two-dimensional (2D) and three-dimensional (3D) particle-in-cell simulations, we show that interesting optical phenomena emerge, including the generation of harmonic beams that are anomalously polarized orthongal to the driver, harmonic spectrum variation depending on the incident laser polarization, and a deflection of transmitted lights that leads to a tilted harmonic intensity pattern due to total angular momentum conservation. It is shown that these anomalous effects are associated with complex peripheral electron dynamics on the plasma vacuum interface. To account for these effects, a new theoretical model is developed that can calculate harmonic fields from arbitrary 2D electron motion within the diffraction plane based on the “relativistic oscillating window” mechanism; the results agree well with the simulations. Our model indicates that the optical properties of the harmonic beams are determined by the 2D in-plane electron motion, which can be leveraged to provide immense opportunities for manipulating light-matter interaction at relativistic intensities.
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References (43)
- D. Strickland and G. Mourou, Compression of amplified chirped optical pulses, Opt. Commun. 55, 447 (1985).
- G. Mourou, T. Tajima, and S. V. Bulanov, Optics in the relativistic regime, Rev. Mod. Phys. 78, 309 (2006).
- 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).
- 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).
- T. Baeva, S. Gordienko, and A. Pukhov, Theory of high-order harmonic generation in relativistic laser intensity with overdense plasma, Phys. Rev. E 74, 046404 (2006).
- F. Krausz and M. Ivanov, Attosecond physics, Rev. Mod. Phys. 81, 163 (2009).
- P. Heissler, R. Horlein, J. M. Mikhailova, L. Waldecker, P. Tzallas, A. Buck, K. Schmid, C. M. S. Sears, F. Krausz, L. Veisz, M. Zepf, and G. D. Tsakiris, Few-cycle driven relativistically oscillating plasma mirrors: A source of intense isolated attosecond pulse, Phys. Rev. Lett. 108, 235003 (2012).
- A. S. Pirozhkov, S. V. Bulanov, T. Z. Esirkepov, M. Mori, A. Sagisaka, and H. Daido, Attosecond pulse generation in the relativistic regime of the laser-foil interaction: The sliding mirror model, Phys. Plasmas 13, 013107 (2006).
- G. Ma, W. Dallari, A. Borot, F. Krausz, W. Yu, G. D. Tsakiris, and L. Veisz, Intense isolated attosecond pulse generation from relativistic laser plasmas using few-cycle laser pulses, Phys. Plasmas 22, 033105 (2015).
- L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes, Phys. Rev. A 45, 8185 (1992).
- Y. Shi, B. F. Shen, L. G. Zhang, X. M. Zhang, W. P. Wang, and Z. Z. Xu, Light fan driven by a relativistic laser pulse, Phys. Rev. Lett. 112, 235001 (2014).
- J. Vieira, R. M. G. M. Trines, E. P. Alves, R. A. Fonseca, J. T. Mendonca, P. Norreys, and L. O. Silva, Amplification and generation of ultra-intense twisted laser pulse via stimulated Raman scattering, Nat. Commun. 7, 10371 (2016).
- X. M. Zhang, B. F. Shen, Y. Shi, X. F. Wang, L. G. Zhang, W. P. Wang, J. C. Xu, L. Yi, and Z. Z. Xu, Generation of intense high-order vortex harmonics, Phys. Rev. Lett. 114, 173901 (2015).
- A. Denoeud, L. Chopineau, A. Leblanc, and F. Quéré, Interaction of ultraintense laser vortices with plasma mirrors, Phys. Rev. Lett. 118, 033902 (2017).
- L. G. Zhang, B. F. Shen, X. M. Zhang, S. Huang, Y. Shi, C. Liu, W. P. Wang, J. C. Xu, Z. K. Pei, and Z. Z. Xu, Deflection of a reflected intense vortex laser beam, Phys. Rev. Lett. 117, 113904 (2016).
- J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Terabit free-space data transmission employing orbital angular momentum multiplexing, Nat. Photon. 6, 488 (2012).
- G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, Free-space information transfer using light beams carrying orbital angular momentum, Opt. Express 12, 5448 (2004).
- K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis, Nature (London) 440, 935 (2006).
- C. Thaury, F. Quéré, J.-P. Geindre, A. Levy, T. Ceccotti, P. Monot, M. Bougeard, F. Réau, P. d’Oliveira, P. Audebert, R. Marjoribanks, and P. Martin, Plasma mirror for ultrahigh-intensity optics, Nat. Phys. 3, 424 (2007).
- A. Jullien, S. Kourtev, O. Albert, G. Cheriaux, J. Etchepare, N. Minkovski, and S. M. Saltiel, Highly efficient temporal cleaner for femtosecond pulses based on cross-polarized wave generation in a dual crystal scheme, Appl. Phys. B 84, 409 (2006).
- B. Gonzalez-Izquierdo, R. J. Gray, M. King, R. J. Dance, R. Wilson, J. McCreadie, N. M. H. Butler, R. Capdessus, S. Hawkes, J. S. Green, M. Borghesi, D. Neely, and P. McKenna, Optically controlled dense current structures driven by relativistic plasma aperture-induced diffraction, Nat. Phys. 12, 505 (2016).
- B. Gonzalez-Izquierdo, M. King, R. J. Gray, R. Wilson, R. J. Dance, H. Powell, D. A. Maclellan, J. McCreadie, N. M. H. Butler, S. Hawkes, J. S. Green, C. D. Murphy, L. C. Stockhausen, D. C. Carroll, N. Booth, G. G. Scott. M. Borghesi, D. Neely, and P. McKenna, Towards optical polarization control of laser-driven proton acceleration in foils undergoing relativistic transparency, Nat. Commun. 7, 12891 (2016).
- M. J. Duff, R. Wilson, M. King, B. Gonzalez-Izquierdo, A. Higginson, S. D. R. Williamson, Z. E. Davidson, R. Capdessus, N. Booth, S. Hawkes, D. Neely, R. J. Gray, and P. McKenna, High order mode structure of intense light fields generation via a laser-driven relativistic plasma aperture, Sci. Rep. 10, 105 (2020).
- L. Yi, High-harmonic generation and spin-orbital interaction of light in a relativistic oscillating window, Phys. Rev. Lett. 126, 134801 (2021).
- R. Trines, H. Schmitz, M. King, P. McKenna, and R. Bingham, Laser harmonic generation with independent control of frequency and orbital angular momentum, Nat. Commun. 15, 6878 (2024).
- M. Jirka, O. Klimo, and M. Matys, Relativistic plasma aperture for laser intensity enhancement, Phys. Rev. Res. 3, 033175 (2021).
- E. F. J. Bacon, M. King, R. Wilson, T. P. Frazer, R. J. Gray, and P. McKenna, High order modes of intense second harmonic light produced from a plasma aperture, Matter Radiat. Extremes 7, 054401 (2022).
- K. Hu and L. Yi, Generation of isolated subfemtosecond electron bunches by the diffraction of a polarization-tailored intense laser beam, Phys. Rev. Lett. 133, 045001 (2024).
- T. D. Arber, K. Bennett, C. S. Brady, A. Lawrence-Douglas, M. G. Ramsay, N. J. Sircombe, P. Gillies, R. G. Evans, H. Schmitz, A. R. Bell, and C. P. Ridgers, Contemporary particle-in-cell approach to laser-plasma modelling, Plasma Phys. Controlled Fusion 57, 113001 (2015).
- J. D. Jackson, Classic Electrodynamics, 3rd ed. (Wiley, New York, 1999).
- Y. Tian, J. S. Liu, W. T. Wang, C. Wang, A. H. Deng, C. Q. Xia, W. T. Li, L. H. Cao, H. Y. Lu, H. Zhang, Y. Hu, Y. X. Leng, R. X. Li, and Z. Z. Xu, Electron emission at locked phases from the laser-driven surface plasma wave, Phys. Rev. Lett. 109, 115002 (2012).
- M. Thévenet, A. Leblanc, S. Kahaly, H. Vincenti, A. Vernier, F. Quéré, and J. Faure, Vacuum laser acceleration of relativistic electrons using plasma mirror injectors, Nat. Phys. 12, 355 (2016).
- L. Yi and T. Fülöp, Coherent diffraction radiation of relativistic terahertz pulses from a laser-driven microplasma waveguide, Phys. Rev. Lett. 123, 094801 (2019).
- U. Happek, A. J. Sievers, and E. B. Blum, Observation of coherent transition radiation, Phys. Rev. Lett. 67, 2962 (1991).
- C. B. Schroeder, E. Esarey, J. van Tilborg, and W. P. Leemans, Theory of coherent transition radiation generated at a plasma-vacuum interface, Phys. Rev. E 69, 016501 (2004).
- G. Q. Liao, Y. T. Li, H. Liu, G. G. Scott, D. Neely, Y. H. Zhang, B. J. Zhu, Z. Zhang, C. Armstrong, E. Zemaityte, P. Bradford, P. G. Huggard, D. R. Rusby, P. McKenna, C. M. Brenner, N. C. Woolsey, W. M. Wang, Z. M. Sheng, and J. Zhang, Multimillijoule coherent terahertz bursts from picosecond laser-irradiated metal foils, Proc. Natl. Acad. Sci. USA 116, 3994 (2019).
- N. Naumova, I. Sokolov, J. Nees, A. Maksimchuk, V. Yanovsky, and G. Mourou, Attosecond electron bunches, Phys. Rev. Lett. 93, 195003 (2004).
- M. King, R. Wilson, E. F. J. Bacon, E. J. Dolier, T. P. Frazer, J. Goodman, R. J. Gray, and P. McKenna, Perspectives on laser-plasma physics in the relativistic transparency regime, Eur. Phys. J. A 59, 132 (2023).
- C. Rosales-Guzmán, B. Ndagano, and A. Forbes, A review of complex vector light fields and their applications, J. Opt. 20, 123001 (2018).
- Z. Chen, R. Hu, S. Zhang, and T. Yuan, Relativistic high-order harmonic generation of spatiotemporal optical vortices, Phys. Rev. A 106, 013516 (2022).
- K. Bliokh and F. Nori, Transverse and longitudinal angular momenta of light, Phys. Rep. 592, 1 (2015).
- Y. Meng, R. Li, and L. Yi, Relativistic oscillating window driven by an intense Laguerre-Gaussian laser pulse, Phys. Rev. Lett. 135, 165001 (2025).
- K. Hu, X. Guo, and L. Yi, High-harmonic generation and optical torque interaction via relativistic diffraction of a spatiotemporal vortex light, arXiv:2505.03215.