Echo-Enabled Harmonics up to the 75Th Order from Precisely Tailored Electron Beams E

LETTERS PUBLISHED ONLINE: 6 JUNE 2016 | DOI: 10.1038/NPHOTON.2016.101 Echo-enabled harmonics up to the 75th order from precisely tailored electron beams E. Hemsing1*,M.Dunning1,B.Garcia1,C.Hast1, T. Raubenheimer1,G.Stupakov1 and D. Xiang2,3* The production of coherent radiation at ever shorter wave- phase-mixing transformation turns the sinusoidal modulation into lengths has been a long-standing challenge since the invention a filamentary distribution with multiple energy bands (Fig. 1b). 1,2 λ of lasers and the subsequent demonstration of frequency A second laser ( 2 = 2,400 nm) then produces an energy modulation 3 ΔE fi doubling . Modern X-ray free-electron lasers (FELs) use relati- ( 2) in the nely striated beam in the U2 undulator (Fig. 1c). vistic electrons to produce intense X-ray pulses on few-femto- Finally, the beam travels through the C2 chicane where a smaller 4–6 R(2) second timescales . However, the shot noise that seeds the dispersion 56 brings the energy bands upright (Fig. 1d). amplification produces pulses with a noisy spectrum and Projected into the longitudinal space, the echo signal appears as a λ λ h limited temporal coherence. To produce stable transform- series of narrow current peaks (bunching) with separation = 2/ limited pulses, a seeding scheme called echo-enabled harmonic (Fig. 1e), where h is a harmonic of the second laser that determines generation (EEHG) has been proposed7,8, which harnesses the character of the harmonic echo signal. the highly nonlinear phase mixing of the celebrated echo EEHG has been examined experimentally only recently and phenomenon9 to generate coherent harmonic density modu- at modest harmonic orders, starting with the 3rd and 4th lations in the electron beam with conventional lasers. Here, harmonics18,19, the 7th harmonic20 and most recently at the we report on a demonstration of EEHG up to the 75th harmonic, 15th harmonic21 of infrared lasers. These studies demonstrated where 32 nm light is produced from a 2,400 nm laser. We also that the EEHG harmonics are generated with small relative demonstrate that individual harmonic amplitudes are con- increases in the beam energy spread compared with high-gain trolled by simple adjustment of the phase mixing. Results harmonic-generation (HGHG) schemes22–24 and also that the show the potential of laser-based manipulations to achieve spectrum is much less sensitive to initial electron-beam phase- precise control over the coherent spectrum in future X-ray space distortions. However, to reach from ultraviolet seed FELs for new science10,11. lasers to the soft X-ray wavelengths where the most compelling The well-known echo effect is a highly nonlinear process that was scientific applications are found, harmonic numbers h ≥ 50 are originally described in 1950 by E.L. Hahn in the context of precessing required, which in turn requires exquisite preservation of the nuclear spins9. Echoes have been observed in many areas of physics, fine-scale phase-space memory. including cyclotron beams12, plasma waves13, photons14, hadron Here, we report the first results of EEHG experiments in the colliders15, molecular rotors in gas16 and in classical mechanical h = 60 and h = 75 harmonic regimes, which also highlight the fine systems17. Broadly described, echoes arise in a medium that is first and unique control the echo mechanism provides over the coherent excited by a perturbation that then damps completely due to dephas- emission spectrum. The results suggest the possibility to precisely ing. The inherent damping mechanism is non-dissipative, however, tailor the pulses in future X-ray FELs for new science applications10,11. and the perturbations remain deeply encoded as highly filamentary From EEHG theory, the optimal harmonic bunching bh is tuned h ≈ λ R(1) λ R(2) structures in the phase space. Following an excitation by a second and scales according to the ratio of dispersions, 2 56 / 1 56 . R(1) perturbation, the phase mixing is partially reversed as the system Accordingly, the C1 chicane was set to 56 = 12.5 mm, close to its evolves, and the echo signal appears as a recoherence effect. This is peak value. In the first experiment, the dispersion of the second R(2) μ the mechanism behind the proposed echo-enabled harmonic gener- chicane was approximately 56 = 600 m to produce bunching ation (EEHG) technique, used to produce fully coherent X-ray pulses near the 60th harmonic of the 2,400 nm laser. The bunched beam in a free-electron laser (FEL)7,8. EEHG exploits the fact that the was boosted to 192 MeV in a short linac (Fig. 1) such that the fine phase-coherent echo structures have much higher frequency λ ≈ 40 nm harmonic wavelengths were radiated at the 3rd harmonic content than the original perturbations, so the temporal coherence of the U3 emission spectrum (see Methods). Figure 2a shows the of modulations imprinted by conventional lasers can be passed to characteristic undulator radiation pattern seen in the quadratic shorter wavelengths, with the electrons serving as the harmonic dependence of the wavelength on the vertical forward angle (see upconversion medium. Methods), and the bright peaks are the coherent harmonic echo The EEHG concept is illustrated in the schematic of our exper- signals. The image is the average of over 200 consecutive shots, imental layout in Fig. 1. The E = 120 MeV relativistic electron but is representative of typical single shots. The spectrum of each λ beam co-propagates with a laser pulse ( 1 = 800 nm) in a magnetic shot, taken from the vertical projection, is shown in Fig. 2b. undulator, U1 (see Methods). The resonant interaction imprints a Analysis of the spectral stability over all shots gives a 0.025 nm ΔE sinusoidal energy modulation with amplitude 1 in the electron (r.m.s.) variation of the central wavelength of the 59th harmonic beam phase space (Fig. 1a). Linear longitudinal dispersion signal (0.063% relative). The observed bandwidth of each harmonic through the magnetic chicane C1, given by the transport matrix peak for each shot is equal to the measured 0.15 nm resolution of R(1) element 56 , allows electrons with different energies to move the extreme ultraviolet (EUV) spectrometer (see Methods), but relative to one another as they traverse different path lengths. This simulations indicate the true bandwidth to be 0.011 nm (full-width 1SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA. 2Key Laboratory for Laser Plasmas (Ministry of Education), Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China. 3Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240, China. *e-mail: [email protected]; [email protected] 512 NATURE PHOTONICS | VOL 10 | AUGUST 2016 | www.nature.com/naturephotonics © 2016 Macmillan Publishers Limited. All rights reserved NATURE PHOTONICS DOI: 10.1038/NPHOTON.2016.101 LETTERS e 4.0 3.5 3.0 Laser 1 2.5 2.0 1.5 U1 C1 Laser 2 Current (a.u.) 1.0 0.5 U2 0.0 C2 0.0 0.2 0.4 0.6 0.8 1.0 Electron z λ / 1 beam Linac U3 a 10 b 5 10 c E σ / 0 5 E 10 d Δ −5 0 5 10 −10 −5 0 5 0.0 0.2 0.4 0.6 0.8 1.0 −10 −5 0 z λ / 1 0.0 0.2 0.4 0.6 0.8 1.0 −10 −5 z λ / 1 0.0 0.2 0.4 0.6 0.8 1.0 −10 z/λ 1 0.0 0.2 0.4 0.6 0.8 1.0 z λ / 1 Figure 1 | Schematic layout of the echo beam line and evolution of the electron-beam phase space after successive transformations. a–c, The electron beam is first modulated in energy by a laser (a), dispersed by transit through a magnetic chicane (b) and modulated again by a second laser (c). d,e,The final phase space distribution (d) has a series of vertical energy stripes that project to sharp peaks in the electron beam current distribution (e). a 3 1,600 b 200 1,400 14 2 180 1,200 160 12 1 140 1,000 10 120 0 800 100 8 Shot (mm) y 600 80 6 −1 60 400 4 −2 40 200 20 2 −3 0 39 40 41 42 43 44 45 39 40 41 42 43 44 45 λ (nm) λ (nm) c Harmonics 61 60 59 58 57 56 55 54 14 12 10 8 6 Intensity (a.u.) 4 2 39 40 41 42 43 44 45 λ (nm) Figure 2 | Echo harmonics of the 2,400 nm laser in the 60th harmonic range. a, Undulator emission. b, Individual spectra over multiple consecutive shots. c, Spectrum of the incoherent spontaneous radiation (single shots in light red, average in dark red) and the coherent echo signal (single shots in light blue, average in dark blue). NATURE PHOTONICS | VOL 10 | AUGUST 2016 | www.nature.com/naturephotonics 513 © 2016 Macmillan Publishers Limited. All rights reserved LETTERS NATURE PHOTONICS DOI: 10.1038/NPHOTON.2016.101 a Harmonics b Harmonics 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 1,000 400 Measured 900 Simulated bunching 350 800 300 700 600 250 200 Intensity (a.u.) Intensity (a.u.) 500 400 150 300 100 200 50 100 0 31 32 33 34 35 36 37 31 32 33 34 35 36 37 λ (nm) λ (nm) Figure 3 | Echo in the 75th harmonic range. a,Measuredelectronbeamemissionspectrumwithecholaserson(singleshotsinlightblue,averageindark blue) and with lasers off (single shots in light red, average in dark red).

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