Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Generalized superradiance for producing broadband coherent radiation with transversely modulated arbitrarily diluted bunches

Nature Physics volume 17, pages 99–104 (2021)Cite this article

Subjects

An Author Correction to this article was published on 17 May 2021

This article has been updated

Abstract

Superradiance is the anomalous radiance describing coherent photon emission from a gas. It plays a crucial role in atomic physics, quantum mechanics and astrophysics. Because the intensity of superradiant light beams is proportional to the number of particles squared, superradiance is also at the core of today’s most powerful light sources. Superradiant emission is intuitively expected when the distance between light-emitting particles is much smaller than the photon wavelength. Here, we break this assumption by predicting a never considered superradiance effect that holds even when the particle number per wavelength vanishes. We discover that a bunch of relativistic charged particles arranged in certain ways can generate an optical shock along the Vavilov–Cherenkov angle in vacuum, thereby concentrating broadband radiation in any spectral region into single light bullets. The process leaves clear experimental signatures, and we illustrate it in the form of a previously unrecognized nonlinear superradiant Thomson scattering. This concept may enable new forms of superradiant emission in advanced light sources, atomic physics systems, and unlock coherent emission in plasma accelerators.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Schematic of the conditions leading to generalized superradiance.
Fig. 2: Spatiotemporal profile of radiation emitted through generalized superradiance.
Fig. 3: Simulation results of the superradiant nonlinear Thomson scattering regime.
Fig. 4: Simulation results showing peak intensity scalings for generalized superradiance.

Data availability

All data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source Data are provided with this paper.

Code availability

All computer codes supporting the findings of this study are fully documented within the paper and its references. Reasonable requests for access to the codes should be directed to J.V. on behalf of the Osiris consortium.

Change history

References

  1. Gross, M. & Haroche, S. Superradiance: an essay on the theory of collective spontaneous emission. Phys. Rep. 93, 301–396 (1982).

    Article  ADS  Google Scholar 

  2. Dicke, R. Coherence in spontaneous radiation processes. Phys. Rev. 93, 99–110 (1954).

    Article  ADS  Google Scholar 

  3. Rehler, N. E. & Eberly, J. H. Superradiance. Phys. Rev. A 3, 1735–1751 (1971).

    Article  ADS  Google Scholar 

  4. Skribanowitz, N., Herman, I. P., MacGillivray, J. C. & Feld, M. S. Observation of Dicke superradiance in optically pumped HF gas. Phys. Rev. Lett. 30, 309–312 (1973).

    Article  ADS  Google Scholar 

  5. Scully, M. O. & Svidzinsky, A. A. The super of superradiance. Science 325, 1510–1511 (2009).

    Article  Google Scholar 

  6. Scully, M. O., Fry, E. S., Raymond Ooi, C. H. & Wódkiewicz, K. Directed spontaneous emission from an extended ensemble of N atoms: timing is everything. Phys. Rev. Lett. 96, 010501 (2006).

    Article  ADS  Google Scholar 

  7. Brito, R., Cardoso, V. & Pani, P. Superradiance 906 (Lecture Notes in Physics, Springer-Verlag, 2015).

  8. Madey, J. Stimulated emission of Bremsstrahlung in a periodic magnetic field. J. Appl. Phys. 42, 1906–1913 (1971).

    Article  ADS  Google Scholar 

  9. Bonifacio, R., McNeil, B. W. J. & Pierini, P. Superradiance in the high-gain free-electron laser. Phys. Rev. A 40, 4467–4475 (1989).

    Article  ADS  Google Scholar 

  10. Bonifacio, R., De Salvo, L., Pierini, P., Piovella, N. & Pellegrini, C. Spectrum, temporal structure and fluctuations in a high-gain free-electron laser starting from noise. Phys. Rev. Lett. 73, 70–73 (1994).

    Article  ADS  Google Scholar 

  11. Bonifacio, R., Pellegrini, C. & Narducci, L. Collective instabilities and high-gain regime in a free electron laser. Opt. Commun. 50, 373–378 (1984).

    Article  ADS  Google Scholar 

  12. Gover, A. et al. Superradiant and stimulated-superradiant emission of bunched electron beams. Rev. Mod. Phys. 91, 035003 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  13. Gover, A. Superradiant and stimulated-superradiant emission in prebunched electron-beam radiators. I. Formulation. Phys. Rev. ST Accel. Beams 8, 030701 (2005).

    Article  ADS  Google Scholar 

  14. Cherenkov, P. A. Visible luminescence of pure liquids under the influence of γ-radiation. Dokl. Akad. Nauk SSSR 2, 451–454 (1934).

    Google Scholar 

  15. Tamm, I. E. & Frank, I. M. Coherent in-medium fast-electron radiation. Dokl. Akad. Nauk USSR 14, 109–114 (1937).

    MATH  Google Scholar 

  16. Vieira, J., Mendonça, J. T. & Quéré, F. Optical control of the topology of laser-plasma accelerators. Phys. Rev. Lett. 121, 054801 (2018).

    Article  ADS  Google Scholar 

  17. Kinkaid, B. A short period helical wiggler as an improved source of synchrotron radiation. J. Appl. Phys. 48, 2684–2691 (1977).

    Article  ADS  Google Scholar 

  18. Chen, S. Y., Maksimchuk, A. & Umstadter, D. Experimental observation of relativistic nonlinear Thomson scattering. Nature 396, 653–655 (1998).

    Article  ADS  Google Scholar 

  19. Ta Phuoc, K. et al. All-optical compton gamma-ray source. Nat. Photon. 6, 308–311 (2012).

    Article  ADS  Google Scholar 

  20. Yan, W. et al. High-order multiphoton Thomson scattering. Nat. Photon. 11, 514–520 (2017).

    Article  Google Scholar 

  21. Vranic, M., Martins, J. L., Vieira, J., Fonseca, R. A. & Silva, L. O. All-optical radiation reaction at 1021 W/cm2. Phys. Rev. Lett. 113, 134801 (2014).

    Article  ADS  Google Scholar 

  22. Cole, J. M. et al. Experimental evidence of radiation reaction in the collision of a high-intensity laser pulse with a laser-wakefield accelerated electron beam. Phys. Rev. X 8, 011020 (2018).

    Google Scholar 

  23. Poder, K. et al. Experimental signatures of the quantum nature of radiation reaction in the field of an ultraintense laser. Phys. Rev. X 8, 031004 (2018).

    Google Scholar 

  24. Vranic, M., Grismayer, T., Fonseca, R. A. & Silva, L. O. Quantum radiation reaction in head-on laser-electron beam interaction. New J. Phys. 18, 073035 (2016).

    Article  ADS  Google Scholar 

  25. Esarey, E., Ride, S. K. & Sprangle, P. Nonlinear Thomson scattering of intense laser pulses from beams and plasmas. Phys. Rev. E 48, 3003–3021 (2002).

    Article  ADS  Google Scholar 

  26. Zhao, L. et al. Terahertz oscilloscope for recording time information of ultrashort electron beams. Phys. Rev. Lett. 122, 144801 (2019).

    Article  ADS  Google Scholar 

  27. Froula, D. H. et al. Spatiotemporal control of laser intensity. Nat. Photon. 12, 262–265 (2018).

    Article  ADS  Google Scholar 

  28. Sainte-Marie, A., Gobert, O. & Quéré, F. Controlling the velocity of ultrashort light pulses in vacuum through spatio-temporal couplings. Optica 4, 1298–1304 (2017).

    Article  ADS  Google Scholar 

  29. Weingartner, R. et al. Ultralow emittance electron beams from a laser-wakefield accelerator. Phys. Rev. ST Accel. Beams 15, 111302 (2012).

    Article  ADS  Google Scholar 

  30. Prat, E. et al. Generation and characterization of intense ultralow-emittance electron beams for compact X-ray free-electron lasers. Phys. Rev. Lett. 123, 234801 (2019).

    Article  ADS  Google Scholar 

  31. Borrelli, S. et al. Generation and measurement of sub-micrometer relativistic electron beams. Commun. Phys. 1, 52 (2018).

    Article  Google Scholar 

  32. Lu, W., Huang, C., Zhou, M., Mori, W. B. & Katsouleas, T. Nonlinear theory for relativistic plasma wakefields in the blowout regime. Phys. Rev. Lett. 96, 165002 (2006).

    Article  ADS  Google Scholar 

  33. Tajima, T. & Dawson, J. M. Laser electron accelerator. Phys. Rev. Lett. 43, 267–270 (1979).

    Article  ADS  Google Scholar 

  34. Shaw, J. L. et al. Role of direct laser acceleration of electrons in a laser wakefield accelerator with ionization injection. Phys. Rev. Lett. 118, 064801 (2017).

    Article  ADS  Google Scholar 

  35. Zhang, X., Khudik, V. N. & Shvets, G. Synergistic laser-wakefield and direct-laser acceleration in the plasma-bubble regime. Phys. Rev. Lett. 114, 184801 (2015).

    Article  ADS  Google Scholar 

  36. Cipiccia, S. et al. Gamma-rays from harmonically resonant betatron oscillations in a plasma wake. Nat. Phys. 7, 867–871 (2011).

    Article  Google Scholar 

  37. Ayllon, R., Mendonça, J. T., Gisbert, A. T., Piovella, N. & Robb, G. R. M. Multimode collective scattering of light in free space by a cold atomic gas. Phys. Rev. A 100, 023630 (2019).

    Article  ADS  Google Scholar 

  38. van Steenbergen, A., Gallardo, J., Sandweiss, J. & Fang, J.-M. Observation of energy gain at the BNL inverse free-electron-laser accelerator. Phys. Rev. Lett. 77, 2690 (1996).

    Article  ADS  Google Scholar 

  39. Duris, J. et al. High-quality electron beams from a helical inverse free-electron laser accelerator. Nat. Commun. 5, 4928 (2014).

    Article  ADS  Google Scholar 

  40. Jackson, J. D. Classical Electrodynamics 3rd edn (Wiley, 2001).

  41. Fonseca, R. A. et al. OSIRIS: A Three-dimensional, Fully Relativistic Particle in Cell Code for Modeling Plasma Based Accelerators Vol. 2331, 342–351 (Lecture Notes in Computer Science, Springer, 2002).

  42. Fonseca, R. A. et al. Exploiting multi-scale parallelism for large scale numerical modelling of laser wakefield accelerators. Plasma Phys. Controlled Fusion 55, 124011 (2013).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge stimulating discussions with A. Gover, who provided a significant contribution towards the clarification of the concept. We also acknowledge use of Marenostrum at the Barcelona Supercomputing Center, Piz Daint in Switzerland and SuperMUC at the Leibniz Research Center in Munich, Germany, under PRACE awards. This work was partially supported by the EU Accelerator Research and Innovation for European Science and Society (EU ARIES) under grant agreement no. 730871 (H2020-INFRAIA-2016-1) and by the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 871124 (Laserlab-Europe). J.V. and M.P. acknowledge the support of FCT (Portugal) grants no. SFRH/IF/01635/2015 and PD/BD/150411/2019.

Author information

Authors and Affiliations

  1. GoLP/Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

    J. Vieira, M. Pardal, J. T. Mendonça & R. A. Fonseca

  2. ISCTE, Lisbon University Institute, Lisbon, Portugal

    R. A. Fonseca

Authors
  1. J. Vieira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Pardal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. T. Mendonça
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. A. Fonseca
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to all aspects of this work.

Corresponding author

Correspondence to J. Vieira.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Avraham Gover and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 The role of the bunch transverse size on generalised superradiance.

(a-c), show the time-integrated radiation profile from co-propagating nonlinear Thomson scattering in a spherical detector in the far field. The angular coordinates in the spherical detectors are θ and φ. The colour scale is normalised to the maximum intensity in the left and right sides of each frame. The left side of each frame represents the radiation for a single electron, where most of the radiation is directed into an angle φw = a0/γ ≃ 0.0447rad. Here, a0 = eA/mec2 ≃ 4.47 is the normalised laser vector potential at the radial position of the particle and γ = 100 is the particle relativistic factor. The right side of each frame represents the radiation from the modulated electron bunch. The Vavilov–Cherenkov angle corresponds, in this case, to the angle of maximum emission for a single electron, φw. In (a) the bunch transverse size is δrβ = 3.1c/ω0 and ω0 is the laser frequency. In (b), δrβ = 1.0c/ω0, and in (c) δrβ = 0.31c/ω0. The right panels show that the integrated angular radiation profile becomes sharper as the bunch transverse size decreases. This is a result of superradiant emission in generalised superradiance. d, shows the temporal intensity profile of the superradiant light bursts. The different lines were obtained by integrating the spatiotemporal radiation profiles along any of the angular coordinates. Each line was normalised to its corresponding peak intensity. Each curve corresponds to the right half of panels (a-c), where black is for δrβ = 3.1c/ω0, yellow corresponds to δrβ = 1c/ω0 and red to δrβ = 0.3c/ω0.

Source data

Extended Data Fig. 2 The role of the bunch divergence (or emittance) on generalised superradiance.

The figure shows the time-integrated radiation profile from co-propagating nonlinear Thomson scattering in a spherical detector in the far field. The angular coordinates in the spherical detectors are θ and φ. The colour scale is normalised to the maximum intensity in the left and right sides of each frame. The left side of each frame represents the radiation for a single particle, where most of the radiation is directed into an angle φw = a0/γ ≃ 0.047, where a0 = eA/mec2 ≃ 4.47 is the normalised laser vector potential at the position of the particle and γ = 100 is the particle relativistic factor. The right side of each frame represents the radiation from the modulated electron bunch. The Vavilov–Cherenkov angle φVC ≃ 0.06rad is higher than φw. Color scales were normalised to the peak values in all plots. In (a) δp⊥ = 1.0mec and in (b) δp⊥ = 0.1mec, where δp⊥ corresponds to the bunch transverse momentum spread. As a result of generalised superradiance, both frames (a) and (b) show that the maximum emission angle for the bunch does not coincide with the single-particle maximum emission angle, even though individual bunch particles in the right side of each frame execute the same trajectory as the single particle (shown in the left side). The time-integrated radiation profile becomes sharper for lower δp⊥, approaching the ideal case of a zero emittance bunch with δp⊥ = 0.

Extended Data Fig. 3 The role of the bunch energy spread on generalised superradiance.

The role of the bunch energy spread on generalised superradiance. a-b, show the time-integrated radiation profile from co-propagating nonlinear Thomson scattering in a spherical detector in the far field. The angular coordinates in the spherical detectors are θ and φ. The colour scale is normalised to the maximum intensity in the left and right sides of each frame. The left side of each frame represents the radiation for a single particle, where most of the radiation is directed into an angle φw = a0/γ ≃ 0.047, where a0 = eA/mec2 ≃ 4.47 is the normalised laser vector potential at the position of the particle and γ = 100 is the particle relativistic factor. The right side of each frame represents the radiation from the modulated electron bunch. The Vavilov–Cherenkov angle φVC ≃ 0.06rad is higher than φw. Color scales were normalised to the peak values in all plots. In (a), δp∥ = 10.0mec, and in (b) δp∥ = 1.0mec, where δp∥ is the bunch longitudinal momentum spread. As a result of generalised superradiance, both frames (a) and (b) show that the maximum emission angle for the bunch does not coincide with the single particle maximum emission angle, even though individual bunch particles in the right side of each frame execute the same trajectory as the single particle (shown in the left side). The time-integrated radiation profile becomes sharper for lower δp∥, approaching the ideal case of a zero energy-spread bunch with δp∥ = 0. c, shows the temporal intensity profile of the superradiant light bursts. The different lines were obtained by integrating the spatiotemporal radiation profiles along any of the angular coordinates. Each line was normalised to its corresponding peak intensity. Each curve then corresponds to the right half of frames (a-b), where black corresponds to δp∥ = 10mec, and red to δp∥ = 1mec. The dashed black line is a scaled version of the solid black curve. Although the peak intensity is higher for δp∥ = 1mec than for δp∥ = 10mec, the duration of the superradiant light pulse remains identical in both cases. This indicates robustness of generalised superradiance to large (10% in this case) bunch energy spreads.

Source data

Extended Data Fig. 4 Generalised superradiance in the context of spontaneous undulator radiation theory.

Generalised superradiance in the context of spontaneous undulator radiation theory. The figure shows the spectral linewidth functions of a single electron [F(ω), in red] and of the electron bunch [\({F}^{\prime}(\omega )\), in black] as a function of the emitted frequency ω. (a-b), illustrate an example of generalised superradiance with unmatched linewidth functions. The red line shows the spectral linewidth function of a long electron bunch with duration σt. The spectral width of the function \({F}^{\prime}(\omega )\) is Δω = 2/σt. The bunch is transversely modulated at a frequency ωm, and the bunch spectral function is maximum at frequencies ω = nωm. The black line represents the spectral linewidth function of a single electron bunch, F(ω). The corresponding spectral width of F(ω) is Δω = ωn/(nNw), where Nw is the number of electron oscillations during the interaction length. The single electron resonant emission frequency is ω = ωn. Here, the bunch and single electron linewidth functions are not matched, ωn ≠ nωm. As a result, emission will not be in a superradiant regime. c, Example of regular superradiance. The red line illustrates the spectral linewidth of a short electron bunch where σt ≲ 1/ωn. The bunch spectral linewidth functionthus overlaps with the single electron spectral linewidth. d, Illustration of generalised superradiance with matched linewidth functions. Here the bunch modulation respects nωm = ωn. Emission will be in a superradiant regime even though the bunch is long such that σt ≫ 1/ωn.

Supplementary information

Supplementary Information

Supplementary Figs. 1–5, Discussion and Tables 1 and 2.

Source data

Source Data Fig. 2e

Numerical data used to generate Fig. 2e.

Source Data Fig. 3d-f

Numerical data used to generate Fig. 3d–f.

Source Data Fig. 4

Numerical data used to generate Fig. 4a and the yellow squares in Fig. 4b.

Source Data Extended Data Fig. 1d

Numerical data used to generate Extended Data Fig. 1d.

Source Data Extended Data Fig. 3c

Numerical data used to generate Extended Data Fig. 3c.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vieira, J., Pardal, M., Mendonça, J.T. et al. Generalized superradiance for producing broadband coherent radiation with transversely modulated arbitrarily diluted bunches. Nat. Phys. 17, 99–104 (2021). https://doi.org/10.1038/s41567-020-0995-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-020-0995-5

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing