In this paper, we present the generalities of the Compton interaction process; we analyse the different paradigms of Inverse Compton Sources, implemented or in commissioning phase at various facilities, or proposed as future projects. We present an overview of the state of the art, with a discussion of the most demanding challenges.

In this work, we propose to design a liquid crystal–based modular and extendable platform of cutting-edge optical technologies for studying materials based on the analysis of polarization and wavefront of light in the wavelength range of 10–50 μm, which is considered to work even in the longer wavelengths range. This platform will be driven by the future THz-FEL source TerRa@BriXSinO that produces high power radiation in THz-range from 6 THz up to 30 THz (Mid-/Far-IR). The lack of optical infrastructures in this range has been tackled by fabricating liquid crystal–based geometric phase components that have been specifically designed for this purpose. This is in order to optimally exploit all the source’s potential for maximum accuracy and efficiency in determining polarization- and wavefront-sensitive properties of materials. We present an overview of a few experiments for characterizing bulk inhomogeneities, dielectric anisotropy, surface roughness, cracks, impact damages, and stress and strain effects with special emphasis on non-destructive tests on composite structures. The tools for wavefront shaping developed within our platform will be exploited to add a further degree of freedom, i.e., orbital angular momentum, to nonlinear optics techniques, such as Terahertz Hyper-Raman spectroscopy, for investigating chiral agents’ properties.

Fine time-resolved analysis of matter—that is, spectroscopy and photon scattering—in the linear response regime requires fs-scale pulsed, high repetition rate, fully coherent X-ray sources. A seeded Free-Electron Laser, driven by a linac based on Super Conducting cavities, generating ${10}^8$–${10}^{10}$ coherent photons at 2–5 keV with 0.2–1 MHz of repetition rate, can address this need. The scheme proposed is a Free-Electron Laser Oscillator at 3 keV, working with a cavity based on X-ray mirrors. The whole chain of the X-ray generation is here described by means of start-to-end simulations.

Fine time-resolved analysis of matter—i.e., spectroscopy and photon scattering—in the linear response regime requires a fs-scale pulsed, high repetition rate, fully coherent x-ray source. A seeded free-electron laser (FEL) driven by a super-conducting linac, generating ${10}^8–{10}^{10}$ coherent photons at 2–5 keV with about 0.5 MHz of repetition rate, can address this need. The seeding scheme proposed is the echo-enabled harmonic generation, alimented by a FEL oscillator working at 13.6 nm with a cavity based on Mo-Si mirrors. The whole chain of the x-ray generation is here described by means of start-to-end simulations. Comparisons with the self-amplified spontaneous emission and a fresh-bunch harmonic cascade performed with similar electron beams show the validity of this scheme.

EuPRAXIA@SPARC_LAB is a new Free Electron Laser (FEL) facility that is currently under construction at the Laboratori Nazionali di Frascati of the INFN. The electron beam driving the FEL will be delivered by an X-band normal conducting LINAC followed by a plasma wakefield acceleration stage. It will be characterized by a small footprint and will deliver ultra-bright photon pulses for experiments in the water window to the user community. In addition to the soft-X-rays beamline already planned in the project, we propose the installation of a second photon beamline with seeded FEL pulses in the range between 50 and 180 nm. Here, we will present the FEL generation scheme, the layout of the dedicated beamline and the potential applications of the FEL radiation source in this low energy range.

In this paper, we show that an electron beam produced by a super-conducting linac, driven in a sequence of two undulator modules of different periods, can generate two-color Terahertz radiation with wavelengths ranging from 100 $\mathsf{\mu }$m to 2 $\mathsf{\mu }$m. The generated pulses are synchronized, both MW-class, and highly coherent. Their specific properties and generation will be discussed in detail. Besides the single-spike pulse structure, usually observed in oscillators, we show that both the THz pump and probe can be modulated in a coherent comb of pulses, enabling periodic excitation and stroboscopic measurements.