Summary :

At LOA, we study relativistic plasma-mirrors, a dense surface-plasma created in the laboratory on a liquid-sheet target [1], which reflects ultra-intense laser pulses of <4 fs duration [2]. This corresponds to less than two light-wave oscillation cycles, such that their phase with respect to the pulse envelope strongly affects the driving laser waveform. This setup is a beautiful model system for studying relativistic laser-plasma interactions at the attosecond timescale [3].

The experimental observables are notably a beam of electrons accelerated off the target to relativistic energies, and the reflected laser pulses, which get compressed to attosecond duration in the nonlinear reflection, their spectrum spanning the whole visible range and into the XUV. In recent experiments with very thin targets, we detected the same observables on the target front and back side.

We propose a numerical and theoretical M2 project accompanying these experiments. The student will run particle-in-cell simulations using either the Smilei or the WarpX code on a local multi-GPU system and analyse the numerical results to extract observables to be compared to experimental results, and to propose physical interpretations. Notably the variation of the front and back face electron and XUV yield/spectra will be studied as function of the laser carrier-envelope-phase.

We are looking for a student with good practical experience in python programming, eagerness to learn, and a keen interest in laser-plasma interaction at extreme relativistic conditions. Existing knowledge in plasma physics and (ultrafast) optics will be highly appreciated.

The student will be advised by experimentalists (Jaismeen Kaur and Stefan Haessler) and an experienced laser-plasma theoretician (Igor Andriyash). She/he will gain experience working with state-of-the-art high-performance-computing soft- and hardware, gain insight into both theoretical and experimental aspects of ultra-high intensity laser-plasma interactions.

Financial support for the internship : Yes

Financial support for the PhD thesis : Yes

Internship proposal : Yes

PhD thesis proposal : No

Contact : stefan.haessler@ensta.fr

[1] A. Cavagna et al., Continuous relativistic high-harmonic generation from a kHz liquid-sheet plasma mirror, Opt. Lett. 50, 165 (2025)

[1] M. Ouillé et al., Relativistic-Intensity near-Single-Cycle Light Waveforms at kHz Repetition Rate, Light Sci. Appl. 9, 1 (2020)

[3] M. Ouillé et al., Lightwave-controlled relativistic plasma mirrors, Opt. Lett. 49, 4847 (2024).

Figure: Schematic diagram of a collision experiment between a relativistic electron beam generated by laser-plasma acceleration and a laser beam boosted in intensity using a plasma mirror with the aim of reaching the strong field QED regime with signatures such as the generation of gamma photons or positrons.

Theme:
Quantum Electrodynamics, or QED, is the physical theory that unifies electromagnetism and quantum physics to describe how light and matter interact. It is considered one of the best-proven theories in its linear regime thanks to the measurement of the fine-structure constant with unparalleled precision. However, it is when light intensity becomes extreme, in the so-called “strong-field” regime, that “Strong Field QED” (or SF-QED) reveals its most astonishing predictions, such as the generation of matter from the vacuum in the form of electron/positron pairs. These extreme regimes have been studied theoretically for over a century but have never been achieved experimentally.
The recent development of a new generation of lasers that deliver femtosecond pulses with a power of several petawatts makes it possible to develop experimental strategies to reach the strong-field regime of QED. The most commonly considered strategy to achieve this is to collide a relativistic electron beam with an ultra-intense laser field [1]. This strategy should soon make it possible to achieve SF-QED in its perturbative regime.
The strategy that will be studied during this doctoral program is the so-called “Doppler boost” [2]: instead of directly using an ultra-intense laser pulse for the collision, its intensity will be increased tenfold beforehand in order to overcome the perturbative regime of SF-QED and reach its highly nonlinear regime, where even the theory remains unknown today.
The Doppler boost consists of converting the ultra-intense laser pulse to the extreme ultraviolet (XUV) by the relativistic Doppler effect when it is reflected off a plasma mirror. The XUV beam, of much shorter wavelength, can then be focused on a much smaller surface than the laser, which has the effect of increasing the light intensity by three orders of magnitude. The interaction of any type of matter (gas, solid, relativistic electrons) with this XUV pulse is then in the highly nonlinear regime of SF-QED [3], see figure.

Objective:
The objective of the thesis is to generate “Doppler-boosted” pulses to obtain the highest light intensities ever achieved on Earth, of the order of 1025W/cm2, and to use them to carry out the very first SF-QED experiments. The first experiment of the thesis is planned for October 2026 on the 100 TW laser of the Applied Optics Laboratory, in order to demonstrate the robustness of the experimental design. If this experiment is successful, it will lead to experiments on the largest laser infrastructures in the world: APOLLON (CEA), BELLA (Berkeley), ELI-NP (Romania).
The objective of the internship, starting in February 2026, is to gain a theoretical and experimental understanding of the plasma mirror mechanism and XUV pulse generation, as well as to prepare for the October experiment, with numerical simulations and the design of several experimental devices, such as an XUV spectrometer, a mechanism for enhancing the temporal contrast of the laser pulse, and the preparation of the experimental chamber. The intern will participate in other laser-plasma interaction experiments during the spring of 2026 to familiarize themselves with the environment and devices.
The doctoral student must be able to plan, organize, and successfully conduct complex experiments with high scientific stakes, supervised and supported by the thesis supervisor and the LOA technical support team.

Profile of the desired candidate:
The proposed thesis aims to conduct high-impact experiments in the field of physics, including the first experimental observation of strong-field QED phenomena. To achieve such objectives, the desired candidate must be passionate about research and possess a strong work ethic and autonomy. Pragmatism is also a key quality for an experimental thesis. A good understanding of optics is required, and knowledge of plasma physics would be a plus.
A certain proficiency in numerical simulations is also required (but experience in the field is not necessary), as numerical studies are key tools for preparing experiments and validating results.
You must obviously be prepared to occasionally travel abroad for several weeks. Finally, a dose of humor for long evenings in the experimental rooms is always welcome by all colleagues.

Degree: Master’s degree in physics/optics, or equivalent
Knowledge of: Python/Matlab
Thesis Opportunity: Yes, preferred
Probable Funding Contract: Yes

Contact: Adrien Leblanc (adrien.leblanc@ensta.fr)

Bibliography:

[1] Lobet, M, et al. « Generation of high-energy electron-positron pairs in the collision of a laser-accelerated electron beam with a multipetawatt laser. » Physical Review Accelerators and Beams 20.4 (2017): 043401.

[2] Vincenti, H. « Achieving extreme light intensities using optically curved relativistic plasma mirrors. » Physical review letters 123.10 (2019): 105001.

[3] Fedeli, L, et al. « Probing strong-field QED with Doppler-boosted petawatt-class lasers. » Physical review letters 127.11 (2021): 114801.  

When an intense laser pulse of femtosecond duration propagates through air, it gives rise to filamentation, a spectacular process where the beam contracts spatially to form a thin channel of light in which the intensity is maintained at ~1013 W / cm2. Filamentation is accompanied by the formation of a long column of short-lived plasma generated in the wake of the laser pulse. This column notably has the capacity to initiate and guide electric arcs of several meters with great reproducibility [1]. In recent years several applications based on plasma filaments have been proposed such as the laser lightning rod [2] and the radio frequency virtual antenna [3].

A crucial parameter for these applications (in particular for lightning triggering) is the lifetime of the plasma created by filamentation, which must be as long as possible. The aim of this internship will therefore be to characterize the parameters of the plasma produced by the femtosecond laser and to test different methods to increase this lifespan. To do this, different time-resolved spectroscopy, interferometry and imaging techniques [4] will be implemented. In particular, we will seek to develop a measurement of plasma temperature by Raman spectroscopy.

The candidate must have basic knowledge of optics or plasma physics, a good level of English and present solid academic references.
This internship will be paid and may lead to an extension into the thesis

Contact: aurelien.houard@ensta.fr

[1] B. Forestier, et al., “Triggering, guiding and deviation of long air spark discharges with femtosecond laser filament”, AIP Advances 2, 012151-13 (2012)
[2] A. Houard et al. Laser-guided lightning, Nature Photonics 17, 231 (2023)
[3] Y. Brelet, et al., Radiofrequency plasma antenna generated by femtosecond laser filaments in air”, Applied Physics Letters 101, 264106 (2012)

When an intense femtosecond laser pulse propagates in air, it gives rise to filamentation, a spectacular process in which the beam contracts spatially to form a thin channel of light in which the intensity is maintained at ~1013 W/cm2. Filamentation is accompanied by the formation of a long column of short-lived plasma generated in the wake of the laser pulse. This column is capable of guiding lightning [1] and producing secondary radiation from THz [2] to UV [3], which can be used for remote sensing applications in the atmosphere [4].

The recent development of laser technologies based on amplification in Yb:YAG crystals has made it possible to significantly increase the power of femtosecond lasers [5]. This type of very promising laser source was used by our team for the first demonstration of lightning guidance by laser filamentation [1], but the significant thermal effects that appear at this power are still poorly understood and very few studies of filaments have been carried out at this wavelength.

This internship will focus on the detailed characterization of the plasma produced in air by a 200 mJ, 800 fs laser pulse at 1.03 µm and 515 nm. We will also evaluate the effect of the laser repetition rate on the filamentation and characterize the different radiation produce by the filament at 1.03 µm.

Candidates should have a basic knowledge of optics or plasma physics, a good level of English and solid academic references.
This internship will be remunerated and may lead to an extension into a Ph.D thesis.

Contact: aurelien.houard@ensta.fr

Publications by the team related to the subject
[1] Laser-guided lightning, Nature Photonics 17, 231 (2023)
[2] White-Light Filaments for Atmospheric Analysis, Science 301, 61 (2003)
[3] Conical Forward THz Emission from Femtosecond-Laser-Beam Filamentation in Air, Phys. Rev. Lett. 98, 235002 (2007)
[4] Lasing of ambient air with microjoule pulse energy pumped by a multi terawatt IR femtosecond laser, Opt. Lett. 39,1725 (2014)
[5] Ultrafast thin-disk multipass amplifier with 720 mJ operating at kilohertz repetition rate for applications in atmospheric research, Optics Express 28, 30164 (2020)

Abstract : Laser-plasma acceleration makes it possible to reduce the size of electron accelerators
by 3 to 4 orders of magnitude, for societal and scientific applications. This acceleration concept is
based on focusing an intense laser pulse in a light gas that turns into a plasma. The laser pulse
expels the electrons out of its path and creates an ion cavity in its wake. Due to the complete
separation of charges, the fields in the cavity have amplitudes out of reach of other technologies.
Electrons injected in the cavity can thus gain very high energies on short distances.

Tremendous efforts have been made over the past three decades to master this approach and
produce electrons with energies up to about 10 GeV, but little attention has been paid to the
utility of relatively low-energy electrons. However, laser-plasma accelerators can efficiently
produce beams of low energy, high charge, high divergence, and micrometer source size that are
of great interest for industrial and medical applications. We recently optimized the accelerator for
these applications and observed that the beam divergence increases sharply with the charge.
While a broad divergence is beneficial for many applications, the use of the beam becomes too
complex beyond a certain level. We recently had an idea to reduce the divergence, while
retaining the charge: temporally or spatially separate the laser pulse into multiple pulses of lower
energy that each individually accelerates an electron beam. The electron beam thus produced has
the same charge as the beam generated with a single laser pulse but a lower divergence and a
longer total duration.

The objective of the internship is to carry out the first demonstration of this approach. This will
involve installing the device to create the pulse train, carrying out the experiment, and comparing
the results to the reference case. Numerical simulations could complete this work. The internship
could continue with a Ph.D. during which the student will continue to improve the source for
societal applications (testing new approaches). Depending on the student’s taste, the Ph.D. could
also address the theory.

Possibilité de thèse : Oui Pursuing into PhD : Yes
Contrat-financement probable / Expected contract-funding : CIFRE grant

Contact : Cedric Thaury

Abstract: As ionized media, plasmas are not subject to electrical breakdown and can thus withstand very high amplitude
electric fields. This property is at the basis of laser-plasma accelerators. An intense laser pulse is focused into a light gas
that turns into a plasma. The laser pulse then expels the plasma electrons out of its path and creates an ion cavity in its
wake. The electric fields in this cavity are 3 to 4 orders of magnitude stronger than those obtained in conventional
accelerators. Therefore, we can accelerate electrons to energies of a few giga-electronvolts (v>0.9999999c) in just a few
centimeters, whereas this would require hundreds of meters with conventional techniques.

The maximum energy of these so-called wakefield accelerators is ultimately limited by the dephasing between the electron
beam and the accelerating field. This dephasing comes from the velocity difference between the accelerating field and the
electron beam, which causes the latter to leave the accelerator field after an acceleration of typically a few centimeters. This
limitation could, in principle, be removed by controlling the velocity of the accelerating plasma wave, which requires the
generation of an intense laser pulse that propagates in a vacuum at a superluminal velocity (> c). We recently produced
such a pulse experimentally and numerically showed that it could dramatically increase the energy of the electrons produced
through laser-plasma acceleration. However, many questions remain open: how to inject electrons into this accelerator, how
to ensure that the laser keeps its unique properties in the plasma over long distances, and what is the energy efficiency of
this accelerator…?

The internship objective is to study the propagation of a superluminal and ultra-intense pulse in a plasma using a numerical
code developed in the laboratory. The results could be, at least partially, compared to analytical calculations. The internship
could continue with a PhD during which the student will study superluminal laser-plasma acceleration using Particle-In-Cell
simulations. Complex spatiotemporal couplings will be introduced to optimize the propagation of the laser or to locally slow
down the pulse and thus control the injection of electrons into the accelerator. The student will also study the energy
efficiency of this new accelerator concept using analytical and numerical approaches. Finally, he/she may explore the
potential of ultra-intense superluminal pulses for other applications.

Contrat-financement probable / Expected contract-funding : IPP grant

Contact : Cedric Thaury

Abstract :

Relativistic electron beams have many potential societal applications, particularly in medicine. Today two types of accelerators are used to generate them: either linear accelerators, very bulky and expensive, or laser acceleration in a plasma, more compact and less expensive but not yet directly applicable for the general public. This has been a very active area of research for two decades with several challenges to overcome such as (i) increasing the charge (number of electrons), and (ii) improving the mono-energetic aspect of the beams.

Using a very high power femtosecond laser (a few 100TW) focused at Ultra-High Intensity (UHI), two types of acceleration were demonstrated:

• 1) by reflection of the laser on a solid target: thanks to the high density, a strong charge of several tens of nanocoulombs (nC) is accelerated but quite weakly, a few MeV, because on a small dimension (some 10-100 μm);
• 2) by propagation of the laser in a gas, a plasma bubble is formed in the wake of the pulse. It traps and accelerates electrons over several centimeters to reach very high energies, around 100MeV, but with a more modest charge of around ~1nC (low density gas). Gas cells with shocks were developed to inject electrons into the bubble in a very localized manner in order to make the beam quasi-monoenergetic.

At the Applied Optics Laboratory, we have demonstrated a new type of injection by combining a plasma mirror and a gas jet in order to combine the forces of the two systems, see figure, panel a.

• Step 1, injection: the laser reflects on a solid target in order to remove a large charge from the high density and this in a very localized manner, just on the surface of the target.
• Step 2, acceleration: then, the laser propagates a few millimeters in the gas to accelerate the electron bunch to high energies and monoenergetically. Experimental proof of such has been achieved very recently.

Objectives:

The electron beams generated by this new type of accelerator increase the performance of these laser-plasma accelerators tenfold and make it possible to consider medium-term applications. On the one hand, medical applications using lower energy but high cadence lasers, and on the other hand, the drastic increase in the electronic charge available on the largest laser installations in the world (PetaWatt laser) could allow to demonstrate for the first time experimentally the effects of Quantum ElectroDynamics (which predicts, for example, the creation of matter in a vacuum). These two axes will be studied during the thesis.

Internship/thesis objectives :

90% experimental, 10% theory/simulations. (i) The main objective is to adapt the experimental schemes developed at 100TW towards both 10TW lasers and PW lasers. Numerous experiments on the largest laser infrastructures in the world (APOLLON (Fr), ELI (Romania), BELLA (California)) will take place. (ii) Design the hybrid target with hydrodynamic simulations in order to minimize shocks during the expansion of the gas against the solid target. (iii) Carry out numerical simulations of the interaction in order to understand the different injection parameters and to determine which configuration makes it possible to optimize the acceleration conditions. (iv) Experiments on biological samples are planned on 10TW lasers.

Environment :

The experimental implementation and development parts of the hybrid target are carried out within the Ultra-fast Sources of Particles and X-rays (UPX) team at the LOA. Experiments on different lasers (Bordeaux, Marseille, California, Romania) will be carried out. A dynamic team that is at the world forefront in laser electron acceleration. The theory/numerical part is done in collaboration with CEA Saclay.

Possibility of thesis Yes
Probable contract-financing / Expected contract-funding? IPP Doctoral School

Contact :

Adrien Leblanc / Cedric Thaury

State-of-the-art multi-PW lasers, such as APOLLON (France), and km-scale accelerators such as FACET-II at Stanford (USA) [1], allow to create on Earth the extreme conditions for fundamental interactions between particles and fields. Such interactions follow the laws of strong-field quantum electrodynamics (QED) that has emerged as a promising discovery science area with exciting opportunities. Strong-field QED effects appear when the electric field experienced by the electron in its rest frame approaches the Schwinger field E_S=m²c³/(eℏ), and their most spectacular manifestations include the production of electron-positron pairs through the inverse-Compton scattering and the nonlinear Breit-Wheeler processes. At multi-PW laser facilities such as APOLLON, strong-field QED experiments can be performed by colliding high-energy electrons produced by a novel type of particle accelerator, namely a laser-driven plasma accelerator, with a high-intensity counterpropagating laser pulse or another source of strong fields. Several avenues will be explored in the ANR g4QED project (Gamma photon sources as a path for strong-field QED experiments), specifically including two promising concepts: (i) the use of a plasma mirror to reflect the laser pulse and enable the collision between the high-energy electrons and the laser pulse [2], and (ii) the use of multiple foils to focus the electron beam to very small size, and use the focused electron beam itself as the source of strong fields [3,4].

The internship and the PhD will aim to model, theoretically and numerically, these two concepts and to provide the best strategies to implement them experimentally on APOLLON and FACET-II. The work will involve a rich variety of physics: the interaction between laser pulses and plasmas, between particle beams and plasma, as well as the strong-field QED physics that we aim to unveil experimentally. The development of advanced numerical modeling for this project will also be key to provide accurate physical interpretation for the experiments. During the internship, the student will work more specifically on the first concept with the modeling of the plasma channel formation, the laser focusing and compression in the plasma, the laser-driven plasma acceleration, the generation of the plasma mirror for the laser reflection, and finally the strong-field QED collision. The goal is to understand its potential for strong-field QED experiments, as well as possible limitations or paths for further improvements.

[1] V. Yakimenko et al., Phys. Rev. Accel. Beams 22, 101301 (2019).

[2] K. Ta Phuoc et al., Nature Photonics 6, 308 (2012).

[3] A. Sampath et al., Phys. Rev. Lett. 126, 064801 (2021).

[4] A. Matheron et al., Comm. Phys. 6, 141 (2023).

PhD conditions: The M2 internship can be continued by a PhD with co-supervision by CEA and LOA, which will be funded by CEA through the ANR g4QED (collaborative project between CEA, LOA and LULI). In addition, the PhD student can apply to be Teaching Assistant at Ecole Polytechnique and other graduate schools.

Contact : Igor Andriyash / Sebastien Corde