The free-electron laser (FEL) FERMI is a unique facility, providing users with laser-like pulses in the XUV spectral range. At FERMI, the generation of highly coherent pulses, with tunable spectro-temporal properties, relies on the so-called high-gain harmonic generation (HGHG) technique. In the latter, a (single) infrared seed laser is used to shape the electron-beam properties and trigger the amplification process. Amplification occurs at one selected harmonic, h, of the seed. However, in HGHG, the seed energy required to prepare the electron beam for FEL emission becomes larger and larger for higher harmonics (i.e., shorter FEL wavelengths). For high harmonics, the resulting strong electron-beam energy modulation reduces the FEL gain, limiting the scheme to h<15 (wavelengths of about 10-20 nm) for a single HGHG scheme, or to h of the order of 60-70 (i.e., 4-5 nm), in case of two-stage HGHG. Moreover, at such high h, the sensitivity to the shape of the electron-beam phase space becomes critical and may severely affect the FEL radiation in terms of longitudinal coherence, pulse energy, and shot-to-shot stability. In addition, the HGHG scheme cannot cover the whole harmonic range, as the final harmonic number is a product between the harmonic numbers of the individual stages. Last, but not least, the two-stage setup uses a relatively large portion of the e-beam to accommodate the double seeding process, which makes the implementation double-pulse operation difficult.
The drawbacks of the two-stage HGHG can be overcome by using a recently proposed technique called echo-enabled harmonic generation (EEHG), where the electron-beam is shaped using two seed lasers to enable FEL emission at high harmonics. The method requires a much weaker energy modulation compared to HGHG and is also intrinsically less sensitive to the initial electron-beam imperfections, making it a strong candidate for producing highly stable, nearly fully coherent, and intense FEL pulses, down to soft x-ray wavelengths.
Image: The EEHG scheme together with the e-beam phase space at different stages of the evolution. The 1st seed laser with a wavelength λ1 imprints a sinusoidal energy modulation with an amplitude ΔE<3σE, σE is the initial uncorrelated energy spread, onto the relativistic e-beam in the 1st modulator. After passing through a strong 1st chicane, the electrons with different energies move relative to each other, resulting in a striated phase space with multiple energy bands. Importantly, the energy spread within a single band is much smaller than σE. The electrons then pass through the 2nd modulator, where their energy is again periodically modulated using a 2nd seed laser with λ2= λ1 and ΔE2≈ΔE1. After traversing a weaker 2nd chicane, the e-beam phase space is rotated, transforming the sinusoidal energy modulation into a periodic density modulation, with high-frequency components. As the energy spread within a single band is much smaller than σE, only a moderate ΔE2 is required to reach very high harmonics. The e-beam is then injected into the radiator, tuned to emit light at a high harmonic of the 2nd seed laser.