Skip to main content

Thank you for visiting 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.

High-order multiphoton Thomson scattering


Electron–photon scattering, or Thomson scattering, is one of the most fundamental mechanisms in electrodynamics, underlying laboratory and astrophysical sources of high-energy X-rays. After a century of studies, it is only recently that sufficiently high electromagnetic field strengths have been available to experimentally study the nonlinear regime of Thomson scattering in the laboratory. Making use of a high-power laser and a laser-driven electron accelerator, we made the first measurements of high-order multiphoton scattering, in which more than 500 near-infrared laser photons were scattered by a single electron into a single X-ray photon. Both the electron motion and the scattered photons were found to depend nonlinearly on field strength. The observed angular distribution of scattered X-rays permits independent measurement of absolute intensity, in situ, during interactions of ultra-intense laser light with free electrons. Furthermore, the experiment's potential to generate attosecond-duration hard X-ray pulses can enable the study of ultrafast nuclear dynamics.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Schematic of the experimental set-up used to study multiphoton TS.
Figure 2: Spatial characteristics of X-rays generated by multiphoton Thomson back-scattering.
Figure 3: Origin of diamond-shaped spatial profile of the scattered X-rays from multiphoton TS.
Figure 4: Angular dependence of X-ray energy distribution for low-order and high-order TS.
Figure 5: Dependence of the Thomson X-ray spectrum on the nonlinearity of the laser–electron interaction.
Figure 6: Scaling of total radiated power and on-axis solid-angle radiated power dP/dΩ.


  1. 1

    Thomson, J. J. On electrical oscillations and the effects produced by the motion of an electrified sphere. Proc. Lond. Math. Soc. 1, 197–219 (1883).

    MathSciNet  Article  Google Scholar 

  2. 2

    Evans, D. E. & Katzenstein, J. Laser light scattering in laboratory plasmas. Rep. Prog. Phys. 32, 207–271 (1969).

    ADS  Article  Google Scholar 

  3. 3

    Longair, M. S. High-Energy Astrophysics (Cambridge Univ. Press, 2011).

    Google Scholar 

  4. 4

    Prunty, S. A primer on the theory of Thomson scattering for high-temperature fusion plasmas. Phys. Scripta 89, 128001 (2014).

    Article  Google Scholar 

  5. 5

    Glenzer, S. H. & Redmer, R. X-ray Thomson scattering in high energy density plasmas. Rev. Mod. Phys. 81, 1625–1663 (2009).

    ADS  Article  Google Scholar 

  6. 6

    Leemans, W. et al. X-ray based subpicosecond electron bunch characterization using 90° Thomson scattering. Phys. Rev. Lett. 77, 4182–4185 (1996).

    ADS  Article  Google Scholar 

  7. 7

    Powers, N. D. et al. Quasi-monoenergetic and tunable X-rays from a laser-driven Compton light source. Nat. Photon. 8, 28–31 (2014).

    ADS  Article  Google Scholar 

  8. 8

    Chen, S. et al. MeV-energy X rays from inverse Compton scattering with laser-wakefield accelerated electrons. Phys. Rev. Lett. 110, 155003 (2013).

    ADS  Article  Google Scholar 

  9. 9

    Schwoerer, H., Liesfeld, B., Schlenvoigt, H., Amthor, K. & Sauerbrey, R. Thomson-backscattered X rays from laser-accelerated electrons. Phys. Rev. Lett. 96, 014802 (2006).

    ADS  Article  Google Scholar 

  10. 10

    Albert, F. & Thomas, A. G. Applications of laser wakefield accelerator-based light sources. Plasma Phys. Control. Fusion 58, 103001 (2016).

    ADS  Article  Google Scholar 

  11. 11

    Corde, S. et al. Femtosecond X rays from laser-plasma accelerators. Rev. Mod. Phys. 85, 1–48 (2013).

    ADS  Article  Google Scholar 

  12. 12

    Rousse, A. et al. Production of a keV X-ray beam from synchrotron radiation in relativistic laser-plasma interaction. Phys. Rev. Lett. 93, 135005 (2004).

    ADS  Article  Google Scholar 

  13. 13

    Terzić, B., Deitrick, K., Hofler, A. S. & Krafft, G. A. Narrow-band emission in Thomson sources operating in the high-field regime. Phys. Rev. Lett. 112, 074801 (2014).

    ADS  Article  Google Scholar 

  14. 14

    Nakano, T. et al. Multi-GeV laser-electron photon project at SPring-8. Nucl. Phys. A 684, 71–79 (2001).

    ADS  Article  Google Scholar 

  15. 15

    Strickland, D. & Mourou, G. Compression of amplified chirped optical pulses. Opt. Commun. 55, 447–449 (1985).

    ADS  Article  Google Scholar 

  16. 16

    Bahk, S. et al. Generation and characterization of the highest laser intensities (1022 W/cm2). Opt. Lett. 29, 2837–2839 (2004).

    ADS  Article  Google Scholar 

  17. 17

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

    ADS  Article  Google Scholar 

  18. 18

    Babzien, M. et al. Observation of the second harmonic in Thomson scattering from relativistic electrons. Phys. Rev. Lett. 96, 054802 (2006).

    ADS  Article  Google Scholar 

  19. 19

    Sarri, G. et al. Ultrahigh brilliance multi-MeV γ-ray beams from nonlinear relativistic Thomson scattering. Phys. Rev. Lett. 113, 224801 (2014).

    ADS  Article  Google Scholar 

  20. 20

    Khrennikov, K. et al. Tunable all-optical quasimonochromatic Thomson X-ray source in the nonlinear regime. Phys. Rev. Lett. 114, 195003 (2015).

    ADS  Article  Google Scholar 

  21. 21

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

    ADS  Article  Google Scholar 

  22. 22

    Sakai, Y. et al. Observation of red shifting and harmonic radiation in inverse Compton scattering. Phys. Rev. Spec. Top. Accel. Beams 18, 060702 (2015).

    ADS  Article  Google Scholar 

  23. 23

    Lau, Y. Y., He, F., Umstadter, D. P. & Kowalczyk, R. Nonlinear Thomson scattering: a tutorial. Phys. Plasmas 10, 2155–2162 (2003).

    ADS  Article  Google Scholar 

  24. 24

    Wiedemann, H. Particle Accelerator Physics (Springer, 2015).

    Book  Google Scholar 

  25. 25

    Sarachik, E. S. & Schappert, G. T. Classical theory of the scattering of intense laser radiation by free electrons. Phys. Rev. D 1, 2738–2753 (1970).

    ADS  Article  Google Scholar 

  26. 26

    Esarey, E., Ride, S. K. & Sprangle, P. Nonlinear Thomson scattering of intense laser pulses from beams and plasmas. Phys. Rev. E 48, 3003–3021 (1993).

    ADS  Article  Google Scholar 

  27. 27

    Koga, J., Esirkepov, T. Z. & Bulanov, S. V. Nonlinear Thomson scattering in the strong radiation damping regime. Phys. Plasmas 12, 093106 (2005).

    ADS  Article  Google Scholar 

  28. 28

    Rykovanov, S., Geddes, C., Schroeder, C., Esarey, E. & Leemans, W. Controlling the spectral shape of nonlinear Thomson scattering with proper laser chirping. Phys. Rev. Accel. Beams 19, 030701 (2016).

    ADS  Article  Google Scholar 

  29. 29

    Di Piazza, A., Müller, C., Hatsagortsyan, K. Z. & Keitel, C. H. Extremely high-intensity laser interactions with fundamental quantum systems. Rev. Mod. Phys. 84, 1177–1228 (2012).

    ADS  Article  Google Scholar 

  30. 30

    Quesnel, B. & Mora, P. Theory and simulation of the interaction of ultraintense laser pulses with electrons in vacuum. Phys. Rev. E 58, 3719–3732 (1998).

    ADS  Article  Google Scholar 

  31. 31

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

    ADS  Article  Google Scholar 

  32. 32

    Esarey, E., Schroeder, C. & Leemans, W. Physics of laser-driven plasma-based electron accelerators. Rev. Mod. Phys. 81, 1229–1285 (2009).

    ADS  Article  Google Scholar 

  33. 33

    Har-Shemesh, O. & Di Piazza, A. Peak intensity measurement of relativistic lasers via nonlinear Thomson scattering. Opt. Lett. 37, 1352–1354 (2012).

    ADS  Article  Google Scholar 

  34. 34

    Pariente, G., Gallet, V., Borot, A., Gobert, O. & Quéré, F. Space–time characterization of ultra-intense femtosecond laser beams. Nat. Photon. 10, 547–553 (2016).

    ADS  Article  Google Scholar 

  35. 35

    Heinzl, T., Seipt, D. & Kaempfer, B. Beam-shape effects in nonlinear Compton and Thomson scattering. Phys. Rev. A 81, 022125 (2010).

    ADS  Article  Google Scholar 

  36. 36

    Chen, M. et al. Modeling classical and quantum radiation from laser-plasma accelerators. Phys. Rev. Spec. Top. Accel. Beams 16, 030701 (2013).

    ADS  Article  Google Scholar 

  37. 37

    Jochmann, A. et al. High resolution energy-angle correlation measurement of hard X rays from laser-Thomson backscattering. Phys. Rev. Lett. 111, 114803 (2013).

    ADS  Article  Google Scholar 

  38. 38

    Thomas, A., Ridgers, C., Bulanov, S., Griffin, B. & Mangles, S. Strong radiation-damping effects in a gamma-ray source generated by the interaction of a high-intensity laser with a wakefield-accelerated electron beam. Phys. Rev. X 2, 041004 (2012).

    Google Scholar 

  39. 39

    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).

    ADS  Article  Google Scholar 

  40. 40

    Hartemann, F. V. et al. High-intensity scattering processes of relativistic electrons in vacuum and their relevance to high-energy astrophysics. Astrophys. J. Suppl. Ser. 127, 347–356 (2000).

    ADS  Article  Google Scholar 

  41. 41

    Bednarek, W., Kirk, J. & Mastichiadis, A. Production of gamma-rays by inverse Compton scattering in jets. Astron. Astrophys. Suppl. Ser. 120, 571–574 (1996).

    ADS  Google Scholar 

  42. 42

    Sambruna, R. M. et al. The high-energy continuum emission of the gamma-ray blazar PKS 0528 134. Astrophys. J. 474, 639–649 (1997).

    ADS  Article  Google Scholar 

  43. 43

    Stewart, P. & Sweeney, G. Collective relaxation of ultra-relativistic plasmas. Astron. Astrophys. 44, 1–7 (1975).

    ADS  Google Scholar 

  44. 44

    Li, J., Hatsagortsyan, K. Z., Galow, B. J. & Keitel, C. H. Attosecond gamma-ray pulses via nonlinear Compton scattering in the radiation-dominated regime. Phys. Rev. Lett. 115, 204801 (2015).

    ADS  Article  Google Scholar 

  45. 45

    Luo, W. et al. Generation of bright attosecond X-ray pulse trains via Thomson scattering from laser-plasma accelerators. Opt. Express 22, 32098–32106 (2014).

    ADS  Article  Google Scholar 

  46. 46

    Chung, S., Yoon, M. & Kim, D. E. Generation of attosecond X-ray and gamma-ray via Compton backscattering. Opt. Express 17, 7853–7861 (2009).

    ADS  Article  Google Scholar 

  47. 47

    Wu, H. & Meyer-ter-Vehn, J. Giant half-cycle attosecond pulses. Nat. Photon. 6, 304–307 (2012).

    ADS  Article  Google Scholar 

  48. 48

    Hartemann, F. V. et al. Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field at focus. Phys. Rev. E 51, 4833–4843 (1995).

    ADS  Article  Google Scholar 

  49. 49

    Umstadter, D. Method of aligning a laser-based radiation source. US patent 9,485,847 (2016).

  50. 50

    Harvey, C., Heinzl, T. & Ilderton, A. Signatures of high-intensity Compton scattering. Phys. Rev. A 79, 063407 (2009).

    ADS  Article  Google Scholar 

Download references


The authors thank K. Brown, J. Mills, C. Petersen, N. Glasco, A. Okelberry, P. Mood and B. Nordell for their contributions. This work was supported primarily by the Air Force Office for Scientific Research, award number FA9550-14-1-0345. Additional support provided by the National Science Foundation, grant no. PHY-1535700 (ultra-low emittance electron beams); the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), award no. DE-FG02-05ER15663 (ultrafast X-ray science); and the Department of Homeland Security Domestic Nuclear Detection Office, competitively awarded contract HSHQDC-13-C-B0036 (low-dose X-ray radiography). This support does not constitute an express or implied endorsement on the part of the Government. M.C. acknowledges the support from the National Science Foundation of China (grant no. 11374209,11421064). Simulations were performed on the Π super computer at Shanghai Jiao Tong University. The authors also thank M. Fuchs from the University of Nebraska, Lincoln and Z.-M. Sheng from Shanghai Jiao Tong University and University of Strathclyde for useful discussions.

Author information




The experiments were conceived and designed by D.U., W.Y., S.B. and S.C. Experiments were performed by W.Y., C.F., D.H., G.G., P.Z., J.Z., B.Z. and C.L. Data was analysed by G.G., W.Y., D.H. and C.F. Simulation effort was provided by M.C., J.L., C.F. and S.C. The manuscript was written by D.U., W.Y., S.B., G.G., S.C. and M.C.

Corresponding author

Correspondence to Donald Umstadter.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 596 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yan, W., Fruhling, C., Golovin, G. et al. High-order multiphoton Thomson scattering. Nature Photon 11, 514–520 (2017).

Download citation

Further reading


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