Introduction
We are synthesizing XUV attosecond beams with original properties, in particular carrying various angular momentum, and developing specific associated applications.
As with matter, two forms of angular momentum are traditionally distinguished when associated with light: spin angular momentum, associated with the circular polarization of light, and orbital angular momentum, associated with the helical shape of the wavefront.
Attosecond physics has been built on the use of angular momentum-free beams: essentially Gaussian, with a flat wavefront, uniform polarization and generally linear.
We are exploring the possibility of breaking out of this straitjacket, by creating a variety of structurations of attosecond XUV light and developing their applications.
Research hypotheses
At the heart of our research is the upconversion process whereby an intense femtosecond infrared laser field is converted into a series of odd harmonics of its fundamental frequency. We focus on the High Harmonic Generation (HHG) process in gases.
It produces a very broad harmonic comb that extends into the XUV region of the spectrum. Firstly, we use it to synthesize attosecond pulses, i.e. light pulses with durations of between 10 and 18 seconds. Secondly, these harmonic combs or attosecond pulses are used to study photoionization or transient reflectivities in pump/probe schemes, where one of the beams is the remaining IR from the upconversion process.
Our research hypothesis is that the HHG is an ideal playground for studying angular momentum behavior in nonlinear processes, and will offer unprecedented capabilities to these state-of-the-art attosecond sources for applications.
XUV beams with orbital angular momentum
Like any massive particle, photons can carry both spin and orbital angular momentum.
The former is associated with the circular polarization of a light beam, while the latter is associated with a helical wavefront (see, for example, the review by A. M. Yao and M. J. Padgett).
Laguerre’s Gaussian beams form a basis for light beams with orbital angular momentum (see, for example, D. Dounas-Frazer’s review). These two types of beam find applications in different situations.
In particular, while the spin projection along the propagation axis for paraxial beams is limited to two values, the orbital angular momentum can take any positive or negative integer value.
This allows much denser encoding of light beam information. For spectroscopic and imaging perspectives in particular, it would be invaluable to have XUV beams with orbital angular momentum at hand.
It’s also an ideal situation for testing conservation laws derived from quantum mechanics.
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We have successfully transferred orbital angular momentum from a visible light beam to the XUV using the high harmonic generation process.
These beams have a helical wavefront associated with an azimuthal phase. The phase singularity at the center of the beam leads to zero intensity, which explains their “doughnut” shape.
We could also measure their “topological charge” and verify the conservation law: the q harmonic carries q times the orbital angular momentum of the driving laser. Finally, we could measure their space-time structure, showing a double-helix pattern.
Thanks to a collaboration with Giovanni de Ninno‘s group, we were able to generalize this transfer law to the case of two-beam HHGs.
See also the press release on the CEA website Géneaux et al.
Géneaux et al,Nature Communications, Aug, 2016. Vol. 7, 12583
Gauthier et al, Nature Communications, 2017, Vol. 8, 14971
Géneaux et al.,Phys. Rev. A, 2017, Vol. 95, 051801
Camper et al,Optics Letters, 2017, Vol. 42, 3769
In a parallel experiment with Lou Di Mauro’s group, we were able to generate very intense MidIR ultrashort laser pulses containing OAM, directly in an OPA stage. This could pave the way for the direct synthesis of very high harmonics carrying OAM.
More recently, on the FERMI-FEL, we have demonstrated the enhanced capabilities of OAM beams for imaging. Using a ptychographic approach, a 30% increase in image resolution compared with a regular Gaussian beam was achieved at λ=18.9 nm, reaching a resolution of 85 nm.
Further information: Ligne de lumière nanolite, High-resolution ptychographic imaging at a seeded free-electron laser source using OAM beams
Möbius strip polarization
Beyond OAM and SAM, it has recently been noticed that light beams can exhibit a topologically non-trivial structure, in which the two types of angular momentum (SAM and OAM) are intertwined: the photon state is no longer an eigenvector of the spin or orbital angular momentum operators (SAM and OAM), but of a new operator, a linear combination of SAM and OAM, called generalized angular momentum (GAM).
Interestingly, while the eigenvalues of SAM and OAM are integer, GAM, a combination of (OAM 1/2 SAM), has half-integer eigenvalues.
The unresolved question was the role of this new quantity in light-matter interactions: a mere mathematical construct, or a quantity as fundamental as spin and orbital angular momentum?
Experimentally, laser beams with a Möbius strip polarization structure and a GAM of ℏ/2 were generated in LIDYL’s ATTOLab facility, and used to produce high-order harmonics (HHG).
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A detailed study of the structure of the generated harmonics shows that the fractional angular momentum of the fundamental infrared beam is transferred to these harmonics in the extreme ultraviolet, and that the structure of the Möbius strip is preserved during conversion.
Photons in the q-order harmonic carry a GAM of qℏ/2, and their OAM and SAM are entangled. As a result, the GAM appears as a perfectly valid angular momentum of light, just like the OAM and SAM. It can now be manipulated in the same way in non-linear light-matter interaction experiments.
We are currently building on this first demonstration to further develop our shaping capabilities and find applications for these beams.
To find out more: Non-linear optics with a light beam carrying a half-integer angular momentum (Möbius strip polarization)
Related publication:
“Nonlinear up-conversion of a polarization Möbius strip with half-integer optical angular momentum“
Helical magnetic dichroism
Although available for over 20 years, beams carrying orbital angular momentum have rarely been used for spectroscopy.
We wondered whether, in the linear regime, they could provide a specific signature when reflected off a magnetic structure.
These are widely studied by exploiting the polarization of light, via the magneto-optic Kerr effect, or the Faraday effect.
We have extended the formalism describing these effects to the case of beams carrying an orbital angular momentum, and identified a “helical magnetic dichroism”.
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A collaboration involving researchers from eight institutions, which we coordinated, demonstrated this effect in 2021.
The permalloy magnetic sample selected has a vortex-shaped magnetization whose direction of rotation is fixed by the direction of the magnetic field during the initial magnetization of the layer.
It is placed at the focus of the DIPROI experimental device, receiving the beam from the FERMI(Elettra) XUV free-electron laserin Trieste , Italy. The laser pulse duration is of the order of a few tens of femtoseconds, and the reflected beam forms a far-field image featuring chiral asymmetry, a signature of the presence of polarized vortices.
The direction of the image (right or left) depends on the direction of the vortexes and that of the MAO (see figure).
This first demonstration is currently being extended, both theoretically and on an ATTOLab harmonic source.
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Further information: First observation of magnetic helical dichroism in vortex structures
Related publications :
“Electromagnetic theory of helicoidal dichroism in reflection from magnetic structures“,
M. Fanciulli, D. Bresteau, M. Vimal, M. Luttmann, M. Sacchi, and T. Ruchon, Physical Review A, 103 (1) (2021) 013501.
“Observation of magnetic helicoidal dichroism with extreme ultraviolet light vortices“,
M. Fanciulli, M. Pancaldi, E. Pedersoli, M. Vimal, D. Bresteau, M. Luttmann, D. De Angelis, P. R. Ribič, B. Rösner, C. David, C. Spezzani, M. Manfredda, R. Sousa, I.-L. Prejbeanu, L. Vila, B. Dieny, G. De Ninno, F. Capotondi, M. Sacchi, and T. Ruchon, Physical Review Letters, 128 (2022) 077401.
Multi-beam high-order harmonic generation
Our efforts to control the angular momentum of beams produced by HHG (High Harmonic Generation) led us to use several conducting beams, crossing each other at an angle in the HHG medium.
It was known that in this situation, multiple harmonic sub-beams are emitted. For the q harmonic, these correspond to the absorption of q-n photons from the first beam and n photons from the second beam.
Thus, the energy of the outgoing photon is still qℏω, but its direction of propagation is (q-n) k1 n k2; k1 and k2 being the wave vectors of the two driving beams. We first showed that, in addition to the conservation of energy and momentum, the orbital angular momentum was also conserved in this process (see above). However, the efficiency of each sub-beam as a function of the relative intensity of the two driving beams could not be interpreted.
To recombine this photon picture with the more standard field-based HHG approach, we carried out a series of experiments demonstrating that the generation of a given harmonic results from the coherent addition of several interfering processes: beyond the minimum number of photons required to produce a given harmonic, each channel involves one or more additional photon pairs, associated with the combination of an equal number of stimulated absorptions and emissions.
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A very simple model, counting the various contributing channels, has enabled us to account for the experimental results. This result offers a new perspective on the HHG process, from the photon point of view, to be exploited in attosecond quantum optics.
Related publications :
“Photon pathways and the non-perturbative scaling law of high harmonic generation“
Mekha Vimal, Martin Luttmann, Titouan Gadeyne, Matthieu Guer, Romain Cazali, David Bresteau, Fabien Lepetit, Olivier Tcherbakoff, Jean-François Hergott, Thierry Auguste, and Thierry Ruchon, Phys. Rev. Lett. 131 (2023) 203402.
“Nonperturbative transverse mode coupling in high-order harmonic generation“
Martin Luttmann, Mekha Vimal, Matthieu Guer, Titouan Gadeyne, Céline Chappuis, Jean-François Hergott, and Thierry Ruchon, Phys. Rev. A 108 (2023), 053509.
“Photonic Picture of High Harmonics“
Further information: Photonic decomposition of high-order harmonics in strong fields