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.

Analytical solutions for the emitted nonlinear Thomson scattering spectrum with radiation reaction (RR) included are provided for a single electron colliding with a high intensity laser pulse. Further expressions are derived for the peak intensity for a given harmonic order and the downshift of the frequency when RR is included. Controlling the spectrum with shaping of the laser pulse frequency (chirp) has been investigated. It is shown that chirping of the laser pulse gives a distinct fingerprint of the effect of RR in the spectrum.

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.

Relative narrow bandwidth-high energy radiation can be produced through Thomson scattering, where highly relativistic electrons collide with a laser pulse. The bandwidth of such a source is determined, among others factors, by the bandwidth of the laser pulse and the energy spread of the electrons. Here we investigate how the bandwidth of such a source can be minimized, with a particular emphasis on electron bunches with a correlated energy spread of several percent, that are typical for plasma based accelerator schemes. We show that by introducing a chirp on the laser pulse it is possible to compensate the broadening effect due to the energy spread of the electrons, and obtain the same bandwidth as a quasi-monochromatic plane wave laser pulse colliding with a monoenergetic electron bunch. Ultimately, the bandwidth of a Thomson source is limited by the acceptance angle and the initial transverse momentum of electrons (emittance).

We present a scheme to generate synchronised THz and soft X-ray radiation pulses by using a free-electron laser oscillator driven by a high repetition rate (of order 10–100 MHz) energy recovery linac. The backward THz radiation in the oscillator cavity interacts with a successive electron bunch, thus producing few ${10}^5$ soft/hard X-ray photons per shot (namely ${10}^{12}$–${10}^{13}$ photons/s) via Thomson/Compton back-scattering, synchronised with the mJ-class THz pulse within the temporal jitter of electron beams accelerated in the superconducting cavities of the linac (less than 100 fs). Detailed simulations have been performed in order to assess the capability of the scheme for typical wavelengths of interest, between 10 and 50 $\mathsf{\mu }$m for the TeraHertz radiation and 0.5–3 nm for the X-rays.

High-energy radiation can be generated by colliding a relativistic electron bunch with a high-intensity laser pulse—a process known as Thomson scattering. In the nonlinear regime the emitted radiation contains harmonics. For a laser pulse whose length is comparable to its wavelength, the carrier envelope phase changes the behavior of the motion of the electron and therefore the radiation spectrum. Here we show theoretically and numerically the dependency of the spectrum on the intensity of the laser and the carrier envelope phase. Additionally, we also discuss what experimental parameters are required to measure the effects for a beamed pulse.