Echo-enabled Harmonic Generation Research Articles

Ultra-high harmonic conversion of a seeded free-electron laser via harmonic optical klystron

External seeded free-electron lasers (FELs) are compelling tools for generating fully coherent EUV and soft x-ray radiations. Echo-enabled harmonic generation (EEHG), the most typical representative of external seeded FELs, has witnessed a remarkable growth of fully coherent FELs in the last decade, continuously evolving towards higher harmonic conversions and shorter wavelengths. Ultra-high harmonic generation is imperative in the field of FELs. This paper presents a novel method for generating FEL radiation with ultra-high harmonic conversion, utilizing harmonic optical klystron in combination with EEHG. This method can effectively increase the harmonic conversion order to about 90. Theoretical analysis and numerical simulations show that intense and almost fully coherent FEL pulses can be generated with a wavelength of 3 nm. At the same time, the seed laser intensity required by this scheme is lower compared to nominal EEHG, thus facilitating the generation of high-repetition-rate seeded FELs.

Tailoring of the longitudinal phase space for improved Free-Electron Laser performance

Free-electron lasers are capable of producing high-quality radiation in a wide wavelength range and at very high power and brilliance. To reach improved performance especially regarding coherence, bandwidth and wavelength stability, different seeding techniques are often required. However, a successful implementation of seeding typically demands a very high-quality electron beam, in terms of energy distribution and emittance. Techniques like Echo-Enabled Harmonic Generation (EEHG) and High-Brightness SASE (HB-SASE) require, or are significantly enhanced, by a flat distribution of particles in the longitudinal phase space. In this paper we describe how the initially chirped longitudinal phase space in the proposed Soft X-ray Laser (SXL) at the MAX IV laboratory can be tailored by first overcompressing and then de-chirping the electron pulse. We also show that it is possible to retain the properties of the electron bunch and how such an enhanced distribution can drive HB-SASE “seeding”, resulting in a significantly reduced bandwidth and a better wavelength stability.

Chirped-Pulse Amplification in an Echo-Enabled Harmonic-Generation Free-Electron Laser

The field of ultrafast science has experienced significant growth over the last decade, largely attributed to advancements in optical and laser technologies such as chirped-pulse amplification and high-harmonic generation. The distinctive characteristics of intense ultrafast free-electron lasers (FELs) have introduced novel prospects for investigating molecular dynamics, as well as providing an opportunity to gain deeper insights into nonlinear processes in materials. Therefore, high-power ultrafast FELs can be widely used for both fundamental research and practical applications. This study presents a novel approach for producing high-power femtosecond FEL pulses, utilizing chirped-pulse amplification in echo-enabled harmonic generation. Chirped seed pulses are employed to induce frequency-chirped energy modulation in the electron beam. The generated FEL pulse, which inherits the chirped frequency, can be compressed through the gratings in the off-plane mount geometry to provide ultraintense ultrafast pulses. The numerical modeling results indicate that peak power exceeding 20 GW and a pulse duration in the order of several femtoseconds can be achieved.

Toward a fully coherent tender and hard X-ray free-electron laser via cascaded EEHG in fourth-generation synchrotron light sources.

Free-electron-laser-based beamlines utilize fully coherent laser pulses with extremely narrow bandwidth allowing direct use of X-rays without monochromators. This could be very beneficial for all users of current and future fourth-generation diffraction-limited synchrotron light sources (DL-SLSs) who need narrowband full-coherence high-brightness X-ray pulses. Based on our previous finding, i.e. that separating the two stages of echo-enabled harmonic generation (EEHG) with a few extra bending-magnet sections provides an effective way to increase the momentum compaction of chicane 1, one can simultaneously achieve adequate prebunching at extremely high harmonics as well as keep the energy modulation to the ideal minimum. This could open the door for cascaded EEHG, toward fully coherent tender and hard X-ray wavelengths. Built on our compact design of a twin-pulse seeding electron beam with an adjustable delay and timing jitter at the level of a few femtoseconds, a cascaded EEHG can be implemented, which includes two EEHG beamlines, where the radiation pulse generated by the first beamline with harmonic h1 could be used as the input seed laser pulse to the second beamline with harmonic h2. Hence, the second radiator could potentially reach very high harmonics [h = h1(20)h2(25-100)] from 500 to 2000, corresponding to tender and hard X-ray wavelengths. It is demonstrated that the cascaded EEHG scheme is compatible with almost any current or planned fourth-generation DL-SLS, with significant benefits for space-limited storage rings in particular. The main advantage is that this scheme requires almost no change of the storage-ring lattice and is fully compatible with other beamlines. Current proposals for rings with much longer straight sections would add self-amplified spontaneous emission as another viable option for storage-ring-based free-electron lasers.

High efficiency tapered free-electron lasers with a prebunched electron beam from echo-enabled harmonic generation

High efficiency tapered free-electron lasers with a prebunched electron beam from echo-enabled harmonic generation

Tunable frequency comb from echo-enabled harmonic generation free electron laser

We propose a novel scheme for the generation of a tunable soft x-ray frequency comb in a seeded free-electron laser (FEL) via the chirped pulse beating technology. Our research shows that harnessing the chirped pulse laser to imprint a submillimeter-scale energy modulation in the phase space of the relativistic electron beam together with the process of echo-enabled effect, multichromatic output soft x-ray radiation with a series of longitudinal modes can be amplified in an echo-enabled harmonic generation (EEHG) free electron laser, which finally forms a comb-liked shape in the frequency spectrum with the mode spacing frequency at terahertz (THz) band. Based on the theoretical and numerical analyses of the modulation process, the electron beam maintains a nanometer-scale microstructures due to the echo effect, while the beam obtains an energy modulation at submillimeter-scale from the chirped pulse beating laser. This leads to a series of longitudinal modes in the downstream radiator. Three-dimension time-dependent simulation results show that a frequency comb with a central wavelength of 8.9 nm can be generated directly with the help of chirped beating laser. The frequency spacing between the frequency lines on the radiation spectrum can be tuned easily by changing the parameters of chirped beating laser.

Status and future of the soft X-ray free-electron laser beamline at the SHINE

The Shanghai High repetition rate XFEL and Extreme light facility (SHINE) is under construction and aims at generating X-rays between 0.4 and 25 keV with three FEL beamlines at repetition rates of up to 1 MHz. The soft X-ray FEL beamline, FEL-II, will be ready for commissioning in 2025. It is designed to cover the photon energy from 0.4 to 3 keV, in which the baselines of the FEL operation modes are self-amplified spontaneous emission (SASE), self-seeding, echo-enabled harmonic generation (EEHG), and polarization control. Therefore, a high repetition-rate external seed laser, large period length modulator, soft X-ray monochromator, planar undulator, and elliptically polarized undulator have been adopted in the FEL-II beamline. Several potentials such as an ultra-short pulse mode and a multi-color mode are also foreseeable without significant equipment changes in the follow-up operation. A dual-period undulator design is suggested for the echo-enabled harmonic generation (EEHG) commissioning, and it has great potential to break through the unreachable energy of the fully coherent X-ray in the future. The FEL-II beamline will deliver SASE radiation and fully coherent radiation in all the wavelengths of interest.

Twin-pulse seeding enables pump-probe capabilities in the EUV to soft X-ray spectrum at synchrotron light sources

Having previously reported that separating the two stages of echo-enabled harmonic generation (EEHG) with one or more bending magnet (BM) sections allows the BMs to serve as the desired source of momentum compaction, here we demonstrate that this arrangement can greatly reduce the total energy modulation required by any 4th generation synchrotron light source, leading to higher repetition rates as well as stronger coherent radiation output power, with significant benefits. Since the EEHG beamline performance is mainly determined by the momentum compaction, beam emittances and beta functions of a storage ring lattice, allowing for different separations between the two stages is a straightforward way to increase the momentum compaction of chicane 1. This also enables pump-probe capabilities in a novel context, where twin-pulse seeding on the same electron bunch would allow two distinct radiation pulses with an adjustable delay in the range of 0.1 to 10 ps. In the twin-pulse seeding scheme, the same electron bunch could undergo modulation from two distinct laser pulses. Later stages would produce independent harmonics in subsequent straight sections. There are two variations of this twin-pulse seeding scheme, supporting different scientific applications. With a common modulation in stage 1, the first option allows simultaneously two independent radiation sources, with a full coverage of the EUV (2.5 to 50 nm) to soft X-ray (1.25 to 2.5 nm) spectrum; for the second option, the same stage 2 undulator could generate two coherent pulses both fitting within the FEL bandwidth, or at distinct harmonics. We present particle tracking simulation studies based on the APS-U lattice, including quantum excitation and radiation damping. These simulations indicate that there is no degradation of the modulated longitudinal phase space even when the two stages are separated by as many as 10 BM sections.

Sensitivity of EEHG simulations to dynamic beam parameters

Currently, the Free electron laser user facility FLASH at DESY is undergoing a significant upgrade involving the complete transformation of one of its beamlines to allow external seeding. With the Echo-Enabled Harmonic Generation (EEHG) seeding method, we aim for the generation of fully coherent XUV and soft X-ray pulses at wavelengths down to 4 nm. The generated FEL radiation is sensitive to various electron beam properties, e.g., its energy profile imprinted either deliberately or by collective effects such as Coherent Synchrotron Radiation (CSR). In dedicated particle tracking simulations, one usually makes certain assumptions concerning the beam properties and the collective effects to simplify implementation and analysis. Here, we estimate the influence of some of the common assumptions made in EEHG simulations on the properties of the output FEL radiation, using the example of FLASH and its proposed seeding beamline. We conclude that the inherent properties of the FLASH1 beam, namely the negatively chirped energy profile, has dominant effect on the spectral intensity profile of the radiators output compare to that of the CSR induced chirp.

Mitigation of CSR induced spectral broadening in EEHG FEL

Externally seeded schemes have offered a major leap in improving the longitudinal coherence of FELs in the EUV and soft X-ray range. The Echo Enabled Harmonic Generation (EEHG) technique creates bunching at wavelengths of a few nanometers in two stages of longitudinal phase space manipulation, each consisting of an energy modulator and a chicane. Compared to other seeding techniques, EEHG is less sensitive to electron beam phase space distortions occurring during acceleration and compression. However the strong chicane needed in the first stage makes the system vulnerable to Coherent Synchrotron Radiation (CSR), which imprints a long-wavelength energy modulation on the electron bunch after the EEHG process has been initiated. Coupled with the second dispersive section, this modulation creates a position dependent change in the final bunching wavelength. In this work we show that tailoring the second seed laser wavelength can successfully compensate for the varying energy profile induced by CSR.

Toward fully coherent soft x-ray free-electron laser via echo-enabled harmonic generation in fourth generation synchrotron light sources.

Having previously reported on bunching via echo-enabled harmonic generation (EEHG) as an effective way to improve the longitudinal coherence in the NSLS-II storage ring [X. Yang et al., Sci. Rep. 12, 9437 (2022)], we demonstrate that this EEHG scheme can be easily adopted to any fourth generation diffraction-limited synchrotron light source with significant benefits. The advantage of the scheme is that it requires no change of the lattice and is fully compatible with other beamlines. Since the EEHG performance is mainly determined by the momentum compaction, beam emittances, and beta functions of a SR lattice, we have identified these crucial parameters and successfully built a generalized model, which can predict the performance of nearly any SLS. Regarding the fourth generation SLSs, momentum compactions are often significantly smaller; thus, to cover the x rays with a photon energy of up to 1keV, we utilize a specific design, including a 250nm seed-laser wavelength. Our model predicts that for most of the current and future fourth generation SLSs, the EEHG scheme can produce significant prebunching up to harmonic 200 and, thus, generate a few MW scale peak power at 1.25nm wavelength.

First commissioning results of the coherent scattering and imaging endstation at the Shanghai soft X-ray free-electron laser facility

The Shanghai soft X-ray free-electron laser (SXFEL) user facility project started in 2016 and is expected to be open to users by 2022. It aims to deliver ultra-intense coherent femtosecond X-ray pulses to five endstations covering a range of 100–620 eV for ultrafast X-ray science. Two undulator lines are designed and constructed, based on different lasing modes: self-amplified spontaneous emission and echo-enabled harmonic generation. The coherent scattering and imaging (CSI) endstation is the first of five endstations to be commissioned online. It focuses on high-resolution single-shot imaging and the study of ultrafast dynamic processes using coherent forward scattering techniques. Both the single-shot holograms and coherent diffraction patterns were recorded and reconstructed for nanoscale imaging, indicating the excellent coherence and high peak power of the SXFEL and the possibility of “diffraction before destruction” experiments at the CSI endstation. In this study, we report the first commissioning results of the CSI endstation.

Coherent and ultrashort soft x-ray pulses from echo-enabled harmonic cascade free-electron lasers

It is a long-standing challenge for laser technologies to generate intense fully coherent pulses in the x-ray regime. Here, we demonstrate an external seeding mechanism, termed echo-enabled harmonic cascade (EEHC) for generating coherent and ultrashort soft x-ray pulses. The mechanism uses echo-enabled harmonic generation as the first stage, producing intense extreme ultraviolet pulses that seed the second stage x-ray free-electron laser (FEL) with the high-gain harmonic generation setup. Benefiting from the low sensitivity to electron-beam imperfections of EEHC, we generated high-power nearly transform-limited soft x-ray pulses. We have also demonstrated a unique feature of EEHC in generating isolated few-femtosecond-long x-ray pulses. The supreme up-frequency conversion efficiency and flexible pulse length control of this EEHC mechanism allow us to exceed the current limitations of seeded FELs while preserving the coherence of the seed. Our results are a step towards fully coherent and ultrashort x-ray lasers and could enable the extension of nonlinear optical techniques to shorter wavelengths.

Optimization and stability analysis of the cascaded EEHG-HGHG free-electron laser

X-ray free-electron lasers (XFELs) are powerful tools to explore and study nature for achieving remarkable advances. Generally, seeded FELs are ideal sources for supplying fully coherent soft x-ray pulses. Benefiting from the high-frequency up-conversion efficiency, the cascading configuration with echo-enabled harmonic generation (EEHG) and high-gain harmonic generation (HGHG) holds promising prospects for generating fully coherent radiation at 1 nm wavelength. In this paper, we design and optimize EEHG-HGHG configuration using parameters of Shanghai High-Repetition-Rate XFEL and Extreme Light Facility. In addition, we systematically analyze the effect of relative timing jitter on the output FEL performance based on various start-to-end electron beams. The intensive numerical simulations show that the cascaded EEHG-HGHG scheme can achieve 1 nm FEL pulses with peak power up to 15 GW. Further sensitivity analysis indicates that the relative timing jitter between the electron beam and seed laser has a significant impact on the FEL performance. The RMS timing jitter of 3 fs can lead to the final output pulse energy fluctuations of 29%.

Seeding with a harmonic optical klystron resonator configuration in a high repetition rate free electron laser

The generation of highly coherent radiation in a high repetition rate free electron laser driven by a superconducting linear accelerator has become a topic of growing interest. External seeding schemes like high-gain harmonic generation (HGHG) and echo-enabled harmonic generation are proven to be able to generate coherent radiation in the extreme ultraviolet and x-ray range. However, the repetition rate of current laser systems with sufficient power to modulate the electron beam is limited to the kilohertz range. Recently, to achieve seeding at a high repetition rate, an optical resonator scheme has been introduced to recirculate the radiation in the modulator to seed the electron bunches. In this paper, two harmonic optical klystron resonator configurations either starting with a seed laser or starting from shot noise are studied. With the harmonic optical klystron as the seeding source, the efficiency of harmonic radiation generation at a comparatively high harmonic can be significantly enhanced when compared with a standard single-stage HGHG. Simulation results show that highly coherent, stable, and high repetition rate pulses in the water window range could be generated by the proposed seeding schemes. Some practical considerations including beam energy chirp effects and the power density effects on mirrors are discussed.

Optimization of echo-enabled harmonic generation toward coherent EUV and soft X-ray free-electron laser at NSLS-II.

Prebunching via echo-enabled harmonic generation (EEHG) is an efficient way to reduce the radiator length and improve the longitudinal coherence as well as output stability in storage-ring-based free-electron lasers. We propose a conceptual design, which uses two straight sections to seed coherent extreme-ultraviolet (EUV) and soft X-ray emission with nearly MHz repetition rate. To take the large energy spread (10−3) of a storage ring into account and utilize the existing bending magnets between the two straight sections as the first chicane, we implement a special modeling tool, named EEHG optimizer. This tool has been successfully applied to maximize the prebunching with a reasonably low energy modulation, thereby generating intense coherent X-ray pulses within a short undulator length (a few meters) limited by the available space of a storage ring. Numerical simulations confirm that the optimized EEHG parameters can be directly applied to generate a 10 MW scale peak power with fully coherent ultrafast EUV to soft X-ray pulses based on the NSLS-II parameters. This method can be easily extended to other types of diffraction-limited storage rings.

High-repetition-rate seeded free-electron laser with direct-amplification of an external coherent laser

Various scientific and industrial researches such as spectroscopy and advanced nano-technologies have been demanding high flux and fully coherent extreme ultraviolet (EUV) and x-ray radiation. These demands can be commendably satisfied with a MHz-level repetition-rate seeded free-electron laser (FEL). Dictated by the seed laser system, seeded FELs have faced obstacles for the realization of MHz repetition rate. Reducing the required peak power of an external coherent seed laser can effectively increase the repetition rate of a seeded FEL. This paper presents a novel technique that employs a long modulator as a carrier for laser amplification and electron modulation, which is quite different from nominal seeded FELs. Applications of the proposed technique into high-gain harmonic generation (HGHG) and echo-enabled harmonic generation (EEHG) are investigated. Simulation results demonstrate that seed laser power is reduced by about three orders of magnitude and the FEL radiation possesses consistently high coherence and power stability with respect to the nominal HGHG or EEHG. The proposed technique paves the way for the realization of fully coherent EUV and soft x-ray FELs with a repetition rate of MHz and an average power of about 100 W.

Generating Isolated Attosecond X-Ray Pulses by Wavefront Control in a Seeded Free-Electron Laser

We proposed a simple method based on the seeded free-electron laser (FEL) to generate fully coherent X-ray pulses with durations at dozens of attosecond level. The echo-enabled harmonic generation technique is utilized to generate the fully coherent laser pulse covering the water-window range. A wavefront rotation laser is adopted as the seed to tailor the longitudinal contour of the radiation pulse. Due to the sensitivity of seeded FEL to external lasers, this method can effectively inhibit the bunching of the adjacent regions while preserving an isolated bunching in the middle. Sending such an electron beam into a short undulator, simulation results show that ultrashort X-ray pulses with peak power of GW level and pulse duration as short as 86 attoseconds can be generated. The proposed scheme can make it possible to study the electronic dynamic of the valence electrons of which the time scale is about 100 attoseconds and may open up a new frontier of ultrafast science.

Hybrid echo-enabled harmonic generation scheme for seeding coherent soft x-ray free-electron lasers

A two-stage echo-enabled harmonic generation (EEHG) scheme is proposed to produce sub-nanometer coherent x-ray radiation. The proposed scheme is not a simple two-stage cascaded EEHG but consists of an EEHG as the first stage and a high-gain harmonic generation as the second stage. By using double seed laser pulses with independently tunable powers in the first stage, the second stage can also work in the EEHG principle. To study various effects on the energy bands when the electron beam is traveling through the first stage radiator, theoretical analysis and 3D simulations have been performed and the results show that the fine structure of EEHG can be well maintained. Simulations also indicate the possibility of generating fully coherent x-ray radiation around 1 nm directly from a conventional UV seed laser.

Inhibition of current-spike formation based on longitudinal phase space manipulation for high-repetition-rate X-ray FEL

The formation of a double-horn current profile is a challenging issue in the achievement of electron bunch with high peak current, especially for high-repetition-rate X-ray free-electron lasers (XFELs) where more nonlinear and intricate beam dynamics propagation is involved. Here, we propose to correct the nonlinear beam longitudinal phase space distortion in the photoinjector section with a dual-mode buncher. In combination with the evolutionary many-objective beam dynamics optimization, this method is shown to be effective in manipulating the longitudinal phase space at the injector exit. Furthermore, the formation of the current spike is avoided after the multi-stage charge density modulation and electron bunch with a peak current of 1.6 kA is achieved for 100-pC bunch charge. Start-to-end simulations based on the Shanghai high-repetition-rate XFEL and extreme light facility demonstrate that the proposed scheme can increase the FEL pulse energy by more than 3 times in a cascading operation of echo-enabled harmonic generation and high-gain harmonic generation. Moreover, this method can also be used for longitudinal phase space shaping of electron beams operating at a high repetition rate to meet the specific demands of different researches.