Echo-enabled harmonics up to the 75th order from precisely tailored electron beams

The production of coherent radiation at ever shorter wavelengths has been a long-standing challenge since the invention of lasers(1,2) and the subsequent demonstration of frequency doubling(3). Modern X-ray free-electron lasers (FELs) use relativistic electrons to produce intense X-ray pulses on few-femtosecond timescales(4-6). However, the shot noise that seeds the amplification produces pulses with a noisy spectrum and limited temporal coherence. To produce stable transformlimited pulses, a seeding scheme called echo-enabled harmonic generation (EEHG) has been proposed(7,8), which harnesses the highly nonlinear phase mixing of the celebrated echo phenomenon(9) to generate coherent harmonic density modulations in the electron beam with conventional lasers. Here, we report on a demonstration of EEHG up to the 75th harmonic, where 32 nm light is produced from a 2,400 nm laser. We also demonstrate that individual harmonic amplitudes are controlled by simple adjustment of the phase mixing. Results show the potential of laser-based manipulations to achieve precise control over the coherent spectrum in future X-ray FELs for new science(10,11).