To explore the production of structured light beams in the soft or even hard x-ray regimes it is necessary to reach a substantial advance in theoretical modelling.

Although  the presence of scalar sub-attosecond waveforms using long wavelength ~9 μm drivers has been already predicted, coherent zeptosecond pulses have not been yet found. Theory must play a guiding role to propose generation scenarios and characterization schemes for potential experiments. 

Theoretical treatment of coherent structured hard X-rays and subattosecond pulses represents a breakthrough that has yet to be addressed. For this, a pioneering application of HPC was developed for similar HHG in complex beams.

This will allow the development of bulk computation algorithms, in combination with existing big data manipulation techniques, which will represent a revolutionary advance in the description of micro and macroscopic HHG.

The highly specialized numerical tools developed will be disseminated and made available to the scientific community dedicated to the field of attosecond physics in the EU.

• #O1.1. To design HHG models towards the generation of structured hard x-ray sub-attosecond pulses.
• #O1.2. To seek scenarios of light angular momentum control from HHG in molecules.
• #O1.3. To explore and exploit the effects of the propagation of the driving field, looking for schemes where the photon energy, flux and pulse duration of the structured harmonics can be controlled and optimized.
• #O1.4. To propose complete characterization techniques of ultrafast structured sources.
• #O1.5. To implement a multiplatform user-friendly HHG code to be freely used by the EU community.

For more information: 

C. Hernández-García, J. A. Pérez-Hernández, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, A. Jaron-Becker, A. Becker, and L. Plaja, “Zeptosecond High Harmonic keV X-Ray Waveforms Driven by Midinfrared Laser Pulses”, Phys. Rev. Lett. 111, 033002 (2013).

USAL repository Gredos: http://hdl.handle.net/10366/146633

A. Sanchez-Gonzalez, et al. “Accurate prediction of X-ray pulse properties from a free-electron laser using machine learning”, Nat. Commun. 8, 15461 (2017).

The generation of high-order harmonics from solid targets have been demonstrated by different publications, and opens exciting opportunities to tailor structured XUV fields.

Two-dimensional (2D) solids represent an extraordinary opportunity to explore HHG induced by structured light in absence of degrading propagation effects. However, there are different considerations to take into account such as the constraints imposed by conservation rules of angular momentum in HHG in solids or the feasibility of tailor structured XUV fields through HHG in 2D materials, as in atoms or molecules.

We shall develop theoretical tools to monitor and control the electron dynamics in 2D materials when interacting with structured beams carrying SAM and/or OAM. In addition, in contrast to atomic or molecular gases, solid targets can be sculpted to tailor the OAM and flux properties of the emitted high-frequency radiation. 

The development of solid targets to generate structured XUV/x-ray light through HHG conveys a unique opportunity not only to increase the flux of such light sources, but to engineer a novel on-source generation of structured light. This represents a major breakthrough for the application of structured sources to applications at the nanoscale, such as microscopy, imaging or nanomagnetism.

Three sub objetives have been defined in order to reach principal objetive:

• #O2.1. To unveil the electron dynamics of the nonlinear interaction of circularly polarized light with 2D solids.
• #O2.2. To determine the conservation rules of angular momenta in HHG in solids driven by structured pulses.
• #O2.3. To pioneer the design of solid targets to imprint angular momentum to XUV sources through HHG.

For more information: 

S. Ghimire, A. D. Di Chiara, E. Sistrunk, P. Agostini, L. Di Mauro, and D. Reis, “Observation of high-order harmonic generation in a bulk cristal”, Nat. Phys. 7, 138 (2011).

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids”, Nature 522, 462 (2015).

N. Yoshikawa, T. Tamaya, and K. Tanaka, “High-harmonic generation in graphene enhanced by elliptically polarized light excitation”, Science 356, 736 (2017).

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. Reis, “Solid-state harmonics beyond the atomic limit”, Nature 534, 520 (2017).

When propagating through inhomogeneous media, light beams can exchange SAM and OAM at the nanoscale.

Typically spin-orbit optical interactions have been considered to generate negligible effects, however it has been recently demonstrated, that at the nanoscale, they can be considerable relevant, with potential applications for manipulating small particles and controlling light propagation. Structured XUV/x-ray sources offer a unique opportunity to explore spin-orbit interaction at the nanoscale –i.e. with single atomic or molecular systems–, however some theoretical and numerical development and tools have to be done since the paraxial approximation of the structured x-rays fails.

Is to be expected that when generated in the XUV or x-ray domain, ultrafast structured light beams will change the rules of the game in laser-matter interaction, where novel conservation rules of angular momentum will be obtained.

As result of the development carried out in the frame of this objective, an entirely new form of interaction of x-ray light with matter at the nanoscale is going to be defined, where the angular momentum becomes a relevant parameter, opening a door to an entirely new set of applications and fundamental investigations 

Two sub objetives have been defined in order to reach principal objetive:

• #O3.1. To perform a full 3D description of structured light beams focused down to the nanometer scale.
• #O3.2. To describe electron dynamics and conservation rules in the spin-orbit interaction between ultrafast structured light pulses and single atoms and molecules.

For more information:

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light”, Nat. Photonics 9, 796 (2015).

F. Cardano and L. Marrucci, “Spin-orbit photonics”, Nat. Photonics 9, 776 (2015).

Current avances and developments on nanotechnology related with the accurately control of the material properties have expanded the frontiers of electronic devices, magnetic storage or the use of photovoltaic energy. 

The possibility of generating fs and attosecond light pulses with tailored angular momentum properties provide unique tools to create transient ultrafast electric currents and the modification of nonmaterial magnetic properties at fs and sub-fs time scales.

Since the pioneering work on ultrafast laser induced demagnetization, fs laser pulses have been widely used in theoretical and experimental studies of femtomagnetism. Magnetic effects in such short time-scales have been proved and due not only to thermal relaxation processes, but also to coherent almost instantaneous interactions between photons and spins, which can only be tested using ultrashort laser pulses. There is an interaction of laser pulses with magnetic materials is its strong dependence with the polarization of light. 

This project an unique opportunity to scale down the dynamics of ultrafast magnetization and to tailor magnetic nanodomains in the fs and attosecond timescales using ultrafast structured XUV/x-ray pulses. 

Three sub objetives have been defined in order to reach principal objetive:

• #O4.1. To propose the generation of intense, structured, magnetic fields in the femto and attosecond scales.
• #O4.2. To explore the generation of ultrafast electronic currents in nanostructures using XUV/x-ray beams carrying SAM and/or OAM
• #O4.3. To unveil the magnetization dynamics driven by femto and attosecond magnetic pulses.

For more information:

E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. Bigot, “Ultrafast Spin Dynamics in Ferromagnetic Nickel”, Phys. Rev. Lett. 76, 4250 (1996).

J.-Y. Bigot, M. Vomir, E. Beaurepaire, “Coherent ultrafast magnetism induced by femtosecond laser pulses”, Nat. Phys. 5, 515–520 (2009).

Boeglin, C. et al., “Distinguishing the ultrafast dynamics of spin and orbital moments in solids,” Nature 465, 458 (2010).

P. Tengdin, W. You, C. Chen, X. Shi, D. Zusin, Y. Zhang, C. Gentry, A. Blonsky, M. Keller, P. M. Oppeneer, H. C. Kapteyn, Z. Tao, M. M. Murnane, “Critical behavior within 20 fs drives the out-ofequilibrium laser-induced magnetic phase transition in nickel”, Sci. Adv. 4, 9744 (2018).

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, “Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses”, Nature 435, 655 (2005).

T. Fan, P. Grychtol, R. Knut, C. Hernández-García, D. Hickstein, D. Zusin, C. Gentry, F. Dollar, C. Mancuso, C. W. Hogle, O. Kfir, D. Legut, K. Carva, J. Ellis, K. Dorney, C. Chen, O. G. Shpyrko, E. E. Fullerton, O. Cohen, P. M. Oppeneer, D. B. Milosevic, A. Becker, A. Jaron-Becker, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, “Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism”, Proc. Natl. Acad. Sci. U.S.A. 112, 14206 (2015).