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Final Report Summary - X-HARM (New frontiers for coherent X-ray generation)

There is great interest in extending coherent light into the x-ray regime from both fundamental and technological point of view. Coherent x-rays open a new regime in quantum nonlinear optics, allow us to probe electron dynamics in (inner shells of) molecules and materials, and enable advanced metrologies and wavelength-limited imaging schemes. Advances in the understanding of macroscopic phase-matching of high-order harmonic generation (HHG) have made it possible to generate bright, coherent, high harmonic beams in the UV to keV region using mid-IR driving lasers. More interestingly, this new source of coherent x-rays is emitted with attosecond bandwidths (1 as = 10-18 s). As a consequence, there is a strong interest to fully characterize and control the temporal emission of HHG soft x-rays. In the work that has been done within this project, we perform the most advanced theoretical analysis, to unveil the characteristics of extreme HHG (spectral, temporal and polarization) and the generation of soft x-ray attosecond pulses.

This project was extended over three years, and it was structured in a two-year outgoing stage at JILA, University of Colorado at Boulder (Outgoing Host), followed by a third year of return to University of Salamanca (Returning Host). The main objectives of the project can be categorized in the following main lines:
L1. New frontiers in keV harmonic generation.
L2. Theoretical analysis of interaction of ultrashort coherent keV sources with matter.
L3. Novel scenarios for UV harmonic generation.

The project was completed with excellent results. During the outgoing phase the experienced researcher (ER) has collaborated actively in the theoretical support of the results of the experimental groups at the outgoing host (OH), obtaining results beyond the initial expectations. These works have been performed under the supervision of the ultrafast atomic, molecular and optical theory groups at JILA and in collaboration with the group at the returning host (RH). During the third year, the ER was established in the group at the RH, leading new theoretical projects and collaborating actively with the experimental group. In addition, he was able to continue the strong collaboration with the experimental team at the OH, and to establish new collaborations with several international groups. The main deliverables consist of 17 publications in peer-reviewed international journals (one of them in the review process and six of them in high impact factor journals like Science, Nature Photonics, PNAS or Physical Review Letters), with a relevant impact in the scientific community. The ER was able to present his results at several international conferences. The researcher’s training activities, transfer of knowledge activities, and integration activities were developed as it was planned in the project. In the following, we summarize the main results of the project.

First, we have investigated the properties of HHG-X-ray radiation by using midinfrared laser sources, and, particularly, we have focused in the properties arising in the temporal domain to reach the zeptosecond (1 zs = 10-21 s) timescale. We have demonstrated theoretically that the temporal structure of high harmonic x-ray pulses generated with midinfrared lasers differs substantially from those generated with near-infrared pulses, especially at high photon energies. In particular, we showed that, although the total width of the x-ray bursts spans femtosecond time scales, the pulse exhibits a zeptosecond structure due to the interference of high harmonic emission from multiple reencounters of the electron wave packet with the ion (see Figure 1, “Zeptosecond X-ray waveform generation”). Properly filtered and without any compensation of the chirp, regular subattosecond keV waveforms can be produced [Phys. Rev. Lett. 111, 033002 (2013)].

We have then concentrated on extending our theoretical studies towards performing 3D simulations including propagation effects. To that end we have developed a code for the simulation of HHG and propagation with long wavelength driving lasers. The HHG-propagation code has been optimized implementing MPI (Message Passing Interface) in order to use all the capabilities of the Janus supercomputer at the University of Colorado, Boulder. Thanks to the use of these unique computational capabilities, and in collaboration with the experimental group at JILA, we have shown that when mid-IR lasers are used to drive HHG, the conditions for optimal soft x-ray generation naturally coincide with the generation of isolated attosecond pulses (see Figure 2, “Isolated soft x-ray attosecond pulses”) [PNAS 111, E2361, (2014)]. Our theoretical results, which are in very good agreement with experimental data, predict that in contrast to attosecond pulse generation in the extreme-ultraviolet regime, long-duration, multi-cycle, driving laser pulses are more suitable for generating bright isolated soft x-ray bursts, to mitigate group velocity walk-off between the laser and the x-ray fields that otherwise limit the conversion efficiency [New Journal of Physics, 18, 073031 (2016)].

The HHG-3D propagation code has been further extended to include combinations of driving fields with different wavelengths and polarization states. For many years, it was believed that it is impossible to generate bright circularly polarized light by HHG, due to the efficiency reduction in the rescattering process if driven by an elliptically polarized driving field. However, it has been shown that a particular combination of bi-chromatic (800 nm and 400 nm) counter-rotating electric fields can be used to produce circularly polarized EUV light enabling the first tabletop implementation of X-ray magnetic circular dichroism (XMCD) measurements. In collaboration with the experimental group at the OH, we have performed simulations to temporally and spectrally characterize this new HHG source [Science Advances, 2, 1501333 (2016)], and to extend this technique to the production of bright circularly polarized light in the soft X-ray regime [PNAS 112, 14206 (2015)]. In addition, also in collaboration with the experimental group at the OH, we have introduced an alternative technique to produce circularly polarized harmonics, through non-collinear mixing of counter-rotating, circularly polarized driving lasers of the same color [Nature Photonics, 9, 743 (2015)]. Further theoretical analysis of this technique allowed us to predict, for the first time, the generation of isolated circularly polarized attosecond pulses (see Fig. 3, “Generation of circularly polarized attosecond pulses”) [Phys. Rev. A, 93, 043855 (2016)].

We have also studied different universal scaling laws of HHG for UV harmonic generation. First, we have studied the scaling of the harmonic yield when using HHG driven by UV lasers sources. Surprisingly we have found, in collaboration with the experimental group at the OH, that highly ionized species play a relevant role in HHG driven by 267 nm light. This led us propose a new and unprecedented route to obtain soft-x-ray radiation from ionized species in the HHG process (see Fig. 4, “The ultraviolet surprise: generation of soft x-ray harmonics from UV lasers”) [Science, 350, 1225 (2015)]. Second, we have studied the role of orbital angular momentum in HHG using our HHG-3D propagation code. We have driven HHG by helical phased beams, also called optical vortices. The combination of the properties of optical vortices carrying OAM with the spatiotemporal coherent characteristics of HHG and propagation opened a new and promising perspective in ultrafast science. Our calculations demonstrate that EUV harmonic vortices can be generated, and survive to the propagation effects, producing coherent attosecond pulses with helical pulse structure (see Fig. 5, “Helical extreme-ultraviolet attosecond beam driven by HHG”) [Phys. Rev. Lett. 111, 083602 (2013)]. Recently, we have unveiled the non-perturbative nature of HHG in the production of XUV vortex beams, generating new and unprecedented orbital angular momentum contributions [manuscript submitted]. This work merges two distant topics in Optical Science, a joint venture with promising perspectives for non-linear and attosecond physics, optical and quantum communications, ultrafast micromanipulation, microscopy, and spectroscopy, among others.

Finally, we have used our HHG and propagation code to study the effects of propagation in the interference of the electronic quantum paths that lead to the harmonic generation. In collaboration with the experimental group at the RH, we demonstrated theoretically and experimentally that phase-matching in the transverse direction can have a leading influence when generating XUV continuum harmonic radiation for different carrier-envelope-phase configurations [Opt. Exp. 23, 21497 (2015), Phys. Rev. A, 93, 13816 (2016)].

In conclusion, the ER has obtained relevant results in the rapidly emerging field of coherent soft x-ray and attosecond pulse generation through HHG driven by midinfrared laser fields. These results substantially advance the understanding of the underlying physics beyond the HHG process, and will facilitate new notable progress in this area of research. This work is of broad interest in view of the importance of these light sources for other areas of research, including atomic, molecular and optical as well as solid state physics, chemistry, and material engineering.

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