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Floquet-Bloch lattices are systems in which wave packets are subjet to periodic modulations both in time and space, showing rich dynamics. While this type of lattice is difficult to implement in solid-state physics, optical systems have provided excellent platforms to probe their physics: among other effects, they have revealed genuine phenomena such as the anomalous Floquet topological insulator and the funnelling of light into localised interface modes. Despite the crucial importance of the band dispersion in the photon dynamics and the topological properties of the lattice, the direct experimental measurement of the Floquet-Bloch bands has remained elusive. Here we report the direct measurement of the Floquet-Bloch bands of a photonic lattice with a single shot method. We use a system of two coupled fibre rings that implements a time-multiplexed Floquet-Bloch lattice. By Fourier transforming the impulse response of the lattice we obtain the band structure together with an accurate characterization of the lattice eigenmodes, i. e. the amplitudes and the phases of the Floquet-Bloch eigenvectors over the entire Brillouin zone. Our results open promising perspectives for the observation of topological effects in the linear and nonlinear regime in Floquet systems. Floquet-Bloch lattices are systems that are relatively difficult to implement in solid-state physics. Here, using a photonic lattice as an alternative, the authors experimentally observe Floquet-Bloch bands using a single-shot method which allows them to fully characterise the lattice eigenmode structure.

The engineering of synthetic materials characterised by more than one class of topological invariants is one of the current challenges of solid-state based and synthetic materials. Using a synthetic photonic lattice implemented in a two-coupled ring system we engineer an anomalous Floquet metal that is gapless in the bulk and shows simultaneously two different topological properties. On the one hand, this synthetic lattice presents bands characterised by a winding number. The winding emerges from the breakup of inversion symmetry and it directly relates to the appearance of Bloch suboscillations within its bulk. On the other hand, the Floquet nature of the lattice results in well-known anomalous insulating phases with topological edge states. The combination of broken inversion symmetry and periodic time modulation studied here enrich the variety of topological phases available in lattices subject to Floquet driving and suggest the possible emergence of novel phases when periodic modulation is combined with the breakup of spatial symmetries., Comment: Published version. Includes supplementary information

Relativistic electron bunches used in synchrotron light sources are complex media, in which patterns might form spontaneously. These spatial structures were studied over the past decades for very practical reasons. The patterns, which spontaneously appear during an instability, increase the terahertz radiation power by factors exceeding 10,0001,2. However, their irregularity1–7 largely prevented applications of this powerful source. Here we show that principles from chaos control theory8–10 allow us to generate regular spatio-temporal patterns, stabilizing the emitted terahertz power. Regular unstable solutions are expected to coexist with the undesired irregular solutions, and may thus be controllable using feedback control. We demonstrate the stabilization of such regular solutions in the Synchrotron SOLEIL storage ring. Operation of these controlled unstable solutions enables new designs of high-charge and stable synchrotron radiation sources. A feedback loop based on chaos control theory permits the generation of stable and coherent terahertz radiation from relativistic electron bunches in synchrotron light sources.

We report new oscillations of wave packets in quantum walks subjected to electric fields, that decorate the usual Bloch-Zener oscillations of insulators. The number of turning points (or suboscillations) within one Bloch period of these oscillations is found to be governed by the winding of the quasienergy spectrum. Thus, this provides a new physical manifestation of a topological property of periodically driven systems that can be probed experimentally. Our model, based on an oriented scattering network, is readily implementable in photonic and cold atomic setups.

We present a method allowing THz pulses to be recorded in single-shot at tens of MHz repetition rates and long record lengths, using a combination of the time-stretch data acquisition and electro-optic sampling techniques.

We present recent results on the characterization and control of the coherent terahertz pulses emitted by synchrotron radiation facilities. We first show novel ultrafast single-shot measurements techniques now allow these sources to be fully characterized in a pulse-by-pulse basis [1]. Then we present a novel feedback method that enables the dynamics of these sources to be fully controlled [2]. This opens the way to novel sources of stable THz radiation, and to high repetition-rate spectroscopic applications.

International audience; Abstract:Optical probes are among the most important techniques for characterizing new physical states induced by changes of temperature and/or pressure. In link with its high brightness and wide spectral coverage, infrared synchrotron radiation is ideally suited for such studies when the quantity of material to investigate is limited or when the system needs to be probed down to the sub mm domain.

With gigaelectron-volts per centimetre energy gains and femtosecond electron beams, laser wakefield acceleration (LWFA) is a promising candidate for applications, such as ultrafast electron diffraction, multistaged colliders and radiation sources (betatron, compton, undulator, free electron laser). However, for some of these applications, the beam performance, for example, energy spread, divergence and shot-to-shot fluctuations, need a drastic improvement. Here, we show that, using a dedicated transport line, we can mitigate these initial weaknesses. We demonstrate that we can manipulate the beam longitudinal and transverse phase-space of the presently available LWFA beams. Indeed, we separately correct orbit mis-steerings and minimise dispersion thanks to specially designed variable strength quadrupoles, and select the useful energy range passing through a slit in a magnetic chicane. Therefore, this matched electron beam leads to the successful observation of undulator synchrotron radiation after an 8 m transport path. These results pave the way to applications demanding in terms of beam quality., Electron beam quality in accelerators is crucial for light source application. Here the authors demonstrate beam conditioning of laser plasma electrons thanks to a specific transport line enabling the control of divergence, energy, steering and dispersion and the application to observe undulator radiation.

Laser Plasma Accelerators (LPA) can sustain GeV/m accelerating fields offering outstanding new possibilities for compact applications. Despite the impressive recent developments, the LPA beam quality is still significantly lower than in the conventional radio-frequency accelerators, which is an issue in the cases of demanding applications such as Free Electron Lasers (FELs). If the electron beam duration is below few tens of femtosecond keeping pC charges, the mrad level divergence and few percent energy spread are particularly limiting. Several concepts of transfer line were proposed to mitigate those intrinsic properties targetting undulator radiation applications. We study here the robustness of the chromatic matching strategy for FEL amplification at 200~nm in a dedicated transport line, and analyze its sensitivity to several parameters. We consider not only the possible LPA source jitters, but also various realistic defaults of the equipment such as magnetic elements misalignements or focussing strength errors, unperfect undulator fields, etc...

The behavior of submicrometer-sized thin-film YBa 2 Cu 3 O 7-x (YBCO) detectors under illumination with picosecond terahertz (THz) pulses was investigated. Real-time measurements with a temporal resolution of 15 ps full width at half maximum were performed at ANKA, the synchrotron facility of Karlsruhe Institute of Technology, and the UVSOR-III facility at the Institute for Molecular Science in Okazaki, Japan. The capability of YBCO detectors to reproduce the shape of a several picosecond long THz pulse was demonstrated. Single-shot measurements adhering to a reversal of the direction of the electrical field of the THz radiation were carried out. They provided evidence for the electrical field sensitivity of the YBCO detector. Exploiting the electrical field sensitivity of the YBCO detector, the effect of microbunching was observed at UVSOR-III.

The photonic time-stretch technique allows electric field pulse shapes to be recorded with picosecond resolution, at megahertz acquisition rates. Using this strategy, we could directly record spatial patterns that spontaneously appear in relativistic electron bunches, and follow their dynamical evolution over time. We present recent results obtained using two strategies. At SOLEIL, we present the shapes of the THz pulses which are emitted by the structures, and detected far from the emission point, at the end of a beamline. At ANKA, we present how it has been possible to monitor directly the electron bunch near-field. These new types of single-shot recordings allow direct and stringent tests to be performed on electron bunch dynamical models in synchrotron radiation facilities.

International audience; This article reports on the generation of narrowband coherent synchrotron radiation from an electron storage ring. For the first time, this kind of radiation was now produced with continuously tunable frequencies in the so-called “THz gap” (between 1.2 and 5.6 THz), whereas previous experiments were limited to below 750 GHz. The experiment was performed at the DELTA storage ring in Dortmund, Germany, employing the interaction of external intensity-modulated laser pulses with an electron bunch, which causes a periodic longitudinal modulation of the charge density on a sub-millimeter scale. Furthermore, a strong influence of third-order dispersion in the laser pulses on the bandwidth and peak intensity of the THz radiation was observed. This effect is discussed in detail based on numerical simulations of the laser pulse generation and laser-electron interaction, and a modification of the laser system for compensating third-order dispersion is proposed.

International audience; In recent synchrotron radiation facilities, the use of short (picosecond) electron bunches is a powerful method for producing giant pulses of terahertz coherent synchrotron radiation. Here we report on the first direct observation of these pulse shapes with a few picoseconds resolution, and of their dynamics over a long time. We thus confirm in a very direct way the theories predicting an interplay between two physical processes. Below a critical bunch charge, we observe a train of identical THz pulses (a broadband Terahertz comb) stemming from the shortness of the electron bunches. Above this threshold, a large part of the emission is dominated by drifting structures, which appear through spontaneous self-organization. These challenging single-shot THz recordings are made possible by using a recently developed photonic time stretch detector with a high sensitivity. The experiment has been realized at the SOLEIL storage ring.

Photonic time-stretch enables to record electric field pulse shapes with picosecond resolution, at megahertz acquisition rates. Using this strategy, we could record the complex spatiotemporal evolution of relativistic electron bunches circulating in storage ring accelerators. We tested two complementary approaches. At SOLEIL, we monitored the THz pulses of coherent synchrotron that are emitted by the electrons. At ANKA, we monitored directly the electron bunch near-field.

Single-shot recording of terahertz electric signals has recently become possible at high repetition rates, by using the photonic time-stretch electro-optic sampling (EOS) technique. However the moderate sensitivity of time-stretch EOS is still a strong limit for a range of applications. Here we present a variant enabling to increase the sensitivity of photonic time-stretch for free-propagating THz signals. A key point is to integrate the idea presented in Ref. [Ahmed et al., Rev. Sci. Instrum. 85, 013114 (2014)], for upgrading classical time-stretch systems. The method is tested using the high repetition rate terahertz coherent synchrotron radiation source (CSR) of the SOLEIL synchrotron radiation facility. The signal-to-noise ratio of our terahertz digitizer could thus be straightforwardly improved by a factor $\approx 6.5$, leading to a noise-equivalent input electric field below $1.25$~V/cm inside the electro-optic crystal, over the 0-300~GHz band (i.e, 2.3~$\mu$V/cm/$\sqrt{\text{Hz}}$). The sensitivity is scalable with respect to the available laser power, potentially enabling further sensitivity improvements when needed., Comment: 9 pages, 7 figures

The original version of this Article contained an error in the last sentence of the first paragraph of the Introduction and incorrectly read ‘A proper electron beam control is one of the main challenges towards the Graal of developing a compact alternative of X-ray free-electron lasers by coupling LWFA gigaelectron-volts per centimetre acceleration gradient with undulators in the amplification regime in equation 11, nx(n-β) x β: n the two times and beta the two times should be bold since they are vectorsin Eq. 12, β should be bold as well.’ The correct version is ‘A proper electron beam control is one of the main challenges towards the Graal of developing a compact alternative of X-ray free-electron lasers by coupling LWFA gigaelectron-volts per centimetre acceleration gradient with undulators in the amplification regime.’This has been corrected in both the PDF and HTML versions of the Article.

A tunable source of coherent narrowband terahertz radiation is realized by using a laser to modulate the emission characteristics of a relativistic electron beam. In the quest for sources of optical radiation in the terahertz domain, promising candidates are nonlinear optical processes occurring when an intense laser beam interacts with a material medium1,2,3,4,5. Besides conventional media (such as crystals), relativistic electrons also show striking nonlinear collective behaviours, which can lead to powerful laser-induced coherent emission6,7, revealing huge potentials of these devices as terahertz sources8. However, up to now only broadband emissions were reported, and experimental control of their radiation properties, such as their spectra9,10, remained an important challenge. Here, we demonstrate the possibility of mastering the coherent emission experimentally by producing tunable narrowband terahertz radiation. The interaction is made to occur between an electron beam and laser pulses possessing a longitudinal quasi-sinusoidal modulation, and the narrowband emission occurs in a region of quasi-uniform magnetic field. The process therefore strongly differs from classical synchrotron radiation experiments, where narrowband emission occurs inside a periodic magnetic field.

We consider the problem of shot-by-shot acquisition of pulse shapes at high repetition rate in accelerator-basedsystems. More speci cally, we examine the two-step strategy consisting in (i) encoding the pulse information ontoa laser pulse, and (ii) use the so-called time-stretch strategy to \slow-down" the information before recording.We thus show that the repetition rate of already existing electro-optic sampling setups can be straightforwardlyincreased up to the 100 10 6 pulses/s range, and make a demonstration for the detection of coherent THz pulses.The strategy is however not limited to electro-optic sampling of THz pulses or electron bunches. It can be appliedto other types of wavelengths, provided the desired information (as e.g., FEL pulses or electron bunches shapes)can be imprinted onto a laser pulse.Keywords: Coherent Synchrotron Radiation, Electro-optic sampling, Photonic time-stretch, Terahertz optics 1. INTRODUCTION In accelerator-based coherent sources, there is a growing need for pulse shape characterization at high repetitionrates. High repetition rates is encountered in existing Free-Electron Lasers (FEL), when the emission is composedof bursts of pulses at multi-MHz repetition rates.

International audience; Free-electron lasers (FELs) are a unique source of light, particularly in the x-ray domain. After the success of FELs based on conventional acceleration using radio-frequency cavities, an important challenge is the development of FELs based on electron bunching accelerated by a laser wakefield accelerator (LWFA). However, the present LWFA electron bunch properties do not permit use directly for a significant FEL amplification. It is known that longitudinal decompression of electron beams delivered by state-of-the-art LWFA eases the FEL process. We propose here a second order transverse beam manipulation turning the large inherent transverse chromatic emittances of LWFA beams into direct FEL gain advantage. Numerical simulations are presented showing that this beam manipulation can further enhance by orders of magnitude the peak power of the radiation.

In storage rings, when the number of electrons in a bunch exceeds a threshold value, microstructures appear spontaneously in the bunch. Experimental observations of these microstructures and their evolution are indirect to obtain. In practice, most information is obtained from the terahertz coherent synchrotron radiation (THz CSR), since microstructures in the millimeter range radiate THz CSR. Here we show, thanks to a simple analytical formula associated to numerical simulations, that a frequency component in the THz CSR signal permits one to obtain information about the structure of the electron bunch longitudinal phase space during the microbunching instability. The proposed formula permits one also to link experimental information together, in particular the bunch length and the THz CSR spectrum.

We study the efficiency limitation affecting laser-induced coherent synchrotron radiation (CSR) at high laser power. Experiments are made on the UVSOR-II storage ring in conditions of narrowband terahertz CSR emission. While, at moderate power, CSR power increases quadratically with laser power, a noticeable decrease in efficiency and eventually a decrease in CSR power is observed experimentally at high power. Details of the underlying process are analyzed numerically. As the saturation effect depends almost instantaneously on the laser intensity, the saturation occurs locally in longitudinal space. This has important consequences on the modulation pattern induced on the electron bunch.

We show that the macropulse instability affecting storage ring free-electron laser (FEL) oscillators can be suppressed using a delayed optical feedback. The principle, known as coherent photon seeding, consists in reinjecting a very small part of the laser output in the laser cavity in order to create a new deterministic solution. The feedback is shown to be efficient over a large range of the detuning parameter of the FEL cavity, even with very small fractions of reinjected power (

We analyze the narrowband terahertz emission process occurring from electron bunches passing in a bending magnet, after a laser-induced sinusoidal modulation has been performed. In particular, we focus on experimental tunability curves, and power scalings with current and laser power. Theoretically, we simplify the problem formulation using the slowly varying envelope approximation. At low powers, the scaling with laser power appears to be quadratic, and analytical expressions for the tuning curves are obtained. Emission at first passage in the bending magnet, and after one full turn in the storage ring, are considered both experimentally and theoretically. The experiments are performed on the UVSOR-II storage ring.

In spatiotemporal systems with advection, suppression of noise-sustained structures involves questions that are outside of the framework of deterministic dynamical systems control (such as Ott-Grebogi-Yorke-type methods). Here we propose and test an alternate strategy where a nonlocal additive feedback is applied, with the objective to create a new deterministic solution that becomes robust to noise. As a remarkable fact - though the needed parameter perturbations required have essentially a finite size - they turn out to be extraordinarily small in principle: 10{sup -8} in the free-electron laser experiment presented here.

We consider the suppression of the so-called "turbulent regimes" in optical systems with advection. It is well known that spatiotemporal systems submitted to advection can undergo a convective instability above a critical value of the drift parameter. The result is a hypersensivity to noise leading to spatiotemporal erratic regimes called noise sustained structures or "optical turbulence" (Morgner and Mitscke, 1999). This phenomenon appears with slight difference either in system with local saturation (e.g. liquid crystal with optical feedback) or with global saturation (e.g., actively mode-locked lasers). We demonstrate that it is possible to suppress those kind of instability with a rather simple method. To do this, we revisit the "coherent photon seeding" method applied empirically in the nineties to stabilized actively mode-locked laser (Beaud et al., 1990). We study numerically and experimentally the process of stabilization on a elementary advection-diffusion equation (Ginzburg-Landau equation with advection). In addition to determine the adequate parameters, this study allows to interpret the stabilization process: the feedback creates a new deterministic solution toward which the system evolves, the convective threshold has been shifted. This new solution is no more sensitive to noise. Although this process is very different from "Ott-Grebogy-Yorke" method, it requires extremely small perturbation to be achieved (just above noise level). Finally, we check experimentally this method on a free electron laser (UVSORTI FEL, Japan). We suppress the "turbulent" regimes occurring in this laser with a simple optical feedback. The ratio of the re-injected power is in the order of 10-8. This control scheme should be applicable in other systems (optical or not).

Many spatio-temporal systems can undergo instabilities, leading to the spontaneous formation of spatial structures (patterns). However, a range of cases exist for which the pattern itself is not directly visible because of technical or fundamental reasons. This is the case for the spontaneous formation of millimeter-scale patterns appearing inside relativistic electron bunches of accelerators. We demonstrate in this case how the study of responses to sine external perturbations can be used as a ‘probe’ to deduce the characteristic wavenumber of the pattern formation process. Experiments are performed in the UVSOR-II electron storage ring when the electron bunch is subjected to so-called microbunching instability, and the sine perturbations are provided by an external laser. The response is constituted of pulses of coherent synchrotron radiation, whose amplitude depends on the perturbation wavenumber. Experimental results on the dynamics are compared to numerical calculations obtained using a Vlasov–Fokker–Planck model.

We propose to produce femtosecond pulses of soft x-ray coherent undulator radiation in a storage ring for user pump–probe experiments using two energy exchanges between a picosecond relativistic electron bunch and two external ultra-short laser pulses. The coherent emission is generated thanks to the two laser–electron interactions that modulate the longitudinal charge distribution of the electron bunch at a harmonic of the laser wavelength, such as in the echo-enabled harmonic generation in free-electron lasers. Application to the SOLEIL storage ring in the soft x-ray range leads to coherent radiation and improvement of the flux of the photons by several orders in magnitude compared to the conventional slicing scheme. This is also accompanied by a significant enhancement of the signal-to-noise ratio.

Summary form only given. In this paper, a coherent narrowband tunable terahertz emission from an electron bunch is reported, transposing a technique well-known in nonlinear optics: interaction with laser pulses containing an internal modulation. The modulated pulses are produced from a titanium-sapphire laser using chirped pulse beating, and are focused on the electron beam, inside an undulator. The interaction leads to a modification of the energy distribution, which transforms into a charge density modulation when the electron bunch is deviated by the next bending magnet, and terahertz emission occurs.