# Two-Beam Free-Electron Lasers and Self-Injected Nonlinear Harmonic Generation
## 4 Final Comments
In these studies, a chemical reaction, an excitation or a structural change on the surface of a solid, is triggered by a first pulse with a fixed frequency and, after a delay, a second pulse, at a different frequency, records the previous event. In this way, following its time evolution, information on pathways, barriers and transition states of the phenomenon can be accessed. X-ray FEL beams, consisting of colored (not necessarily harmonics) pair pulses, are suited to conduct experiments on structural dynamics, designed to probe the ultrafast evolution of atomic, electronic and magnetic structures [39; 40; 41]. The control of the polarization offers a further degree of freedom for selective excitation of species. The use of two-color laser pulses, with orthogonal polarizations of comparable intensities, allows the selective excitation of the molecular fluorescence and opens the possibility of controlling the internal organization and space orientation of molecules, thus providing a significant improvement of techniques based on fluorescence anisotropy and dichroism [42; 43]. FEL schemes capable of producing dual frequency beams have been tested in the past [44; 45; 46; 47; 48; 49; 50]. Other interesting proposals to generate two-color FEL emission in the X-ray region have been discussed in the literature [51; 52; 53]. Along with these efforts, further research work has been focused on the study of X-FEL beams with tunable polarization [54; 55; 26; 56; 57]. Within this respect different schemes have been proposed and developed, they include crossed-planar undulators [26; 54] and elliptical permanent undulators in after-burner [55; 56]. The drawback of the first scheme is associated with the relatively low degree of polarization, the elliptical undulators, on the other side, produce FEL pulses with well-defined polarizations. This is indeed the case of the Delta-like undulator, installed at LCLS and at SPARC [58]. Experiments have shown that the radiation from the Delta undulator exhibits an extremely high degree of circular polarization compared to crossed-planar undulators. Even though the switching of the polarization at KHz rate appears problematic. We have mentioned that the schemes we have proposed are by no means straightforward regarding either the electron beam (s) handling and the undulator construction. The effective implementation of a bi-harmonic device is not straightforward, cheap and the relevant magnetic characterization is by no means an easy task, but largely within the present technology. The same comment applies to the production and use of beams with different energies. The proposal of high repetition rate X-ray FELs driven by superconducting Linacs, and the significant improvements of fast kickers and pulses timing open the possibility of designing systems producing \"bunch-to-bunch energy-changed beams\". The proposal of multi-beam energy operation [59] at SHINE [60] is extremely promising. Without commenting on the relevant specific issues, we report the sketch of Figure 8. It exhibits an achromatic and isochronous delay system, inserted before the last accelerating section. Consequently, the arrival time of the electron beam at the last accelerating section is changed, which means a different accelerating phase and eventually beams with different energies. Thisdevice combined with undulators of bi-orthogonal type can produce high repetition rate multicolor/variable polarization pulses. Conceptualization, E.D.P., E.S., G.D.; methodology, E.D.P., E.S., G.D.; software, E.D.P., E.S., G.D.; validation, E.D.P., E.S., G.D.; formal analysis, E.D.P., E.S., G.D.; data curation, E.D.P., E.S., G.D.; writing original draft preparation, E.D.P., E.S., G.D.; writing review and editing, E.D.P., E.S., G.D.; visualization, E.D.P., E.S., G.D.; supervision, E.D.P., E.S., G.D.; project administration, E.D.P., E.S., G.D. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The authors declare no conflict of interest.