High-gain Harmonic Generation Research Articles

Enhanced harmonic generation for high-repetition-rate soft x-ray free-electron laser

Externally seeded free-electron lasers are promising for generating intense, stable, and fully coherent soft X-ray pulses. An earlier study demonstrates that high brightness and coherent soft X-ray radiation can be produced based on coherent harmonic generation and superradiant principles, termed high-brightness high-gain harmonic generation (HB-HGHG). However, the seed laser at the ultraviolet region cannot induce sufficient energy modulation at high repetition rates due to state-of-the-art laser system limitations. A recently suggested self-modulation scheme shows that the peak power requirement of a seed laser can be reduced by around one order of magnitude in an HGHG setup. In this paper, we present start-to-end simulation results to estimate the feasibility of the self-modulation-enhanced HB-HGHG scheme.

Wavelength control in high-gain harmonic generation seeded free-electron lasers

Wavelength control in high-gain harmonic generation seeded free-electron lasers

High-repetition-rate seeded free-electron laser enhanced by self-modulation

The spectroscopic methods for the ultrafast electronic and structural dynamics of materials require fully coherent extreme ultraviolet and soft X-ray radiation with high-average brightness. Seeded free-electron lasers (FELs) are ideal sources for delivering fully coherent soft X-ray pulses. However, due to state-of-the-art laser system limitations, it is challenging to meet the ultraviolet seed laser’s requirements of sufficient energy modulation and high repetition rates simultaneously. The self-modulation scheme has been proposed and recently demonstrated in a seeded FEL to relax the seed laser requirements. Using numerical simulations, we show that the required seed laser intensity in the self-modulation is ~3 orders of magnitude lower than that in the standard high-gain harmonic generation (HGHG). The harmonic self-modulation can launch a single-stage HGHG FEL lasing at the 30th harmonic of the seed laser. Moreover, the proof-of-principle experimental results confirm that the harmonic self-modulation can still amplify the laser-induced energy modulation. These achievements reveal that the self-modulation can not only remarkably reduce the requirements of the seed laser but also improve the harmonic upconversion efficiency, which paves the way for realizing high-repetition-rate and fully coherent soft X-ray FELs.

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.

Improved stabilization scheme for extreme ultraviolet quantum interference experiments

Interferometric pump–probe experiments in the extreme ultraviolet (XUV) domain are experimentally very challenging due to the high phase stability required between the XUV pulses. Recently, an efficient phase stabilization scheme was introduced for seeded XUV free electron lasers (FELs) combining shot-to-shot phase modulation with lock-in detection Wituschek et al (2020 Nat. Commun. 11 883). This method stabilized the seed laser beampath on the fundamental ultraviolet wavelength to a high degree. Here, we extend this scheme including the stabilization of the XUV beampath, incorporating phase fluctuations from the FEL high gain harmonic generation process. Our analysis reveals a clear signal improvement with the new method compared to the previous stabilization scheme.

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.

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.

High repetition rate seeded free electron laser with an optical klystron in high-gain harmonic generation

Many high-gain free electron lasers worldwide are planning to incorporate seeding setups into their day-to-day operation. These techniques provide both longitudinal and transverse coherence and extended control of the output free electron laser radiation spectral properties. However, the output wavelength and repetition rate strongly depend on the properties of the seed laser system. With the laser peak power required for successful seeded operation, it is currently not possible to increase their repetition rate to an extent that it matches the electron bunch repetition rate of superconducting accelerators. Here, we investigate the advantages of a modification of standard seeding setups, by combining the seeding with the so-called optical klystron. With this new seeding setup, it is possible to decrease the seed laser power requirements and therefore, seed laser systems can increase their repetition rate at the same wavelength. We show simulation results in a high-gain harmonic generation (HGHG) setup for a range of harmonics (8th to 15th) and we verify the reduction of seed laser power required with an Optical Klystron HGHG scheme. Finally, we comment on the stability of the proposed setup to jitter sources and to shot-to-shot fluctuations and compare to the standard HGHG scheme.

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.

Harmonic-enhanced high-gain harmonic generation for a high repetition rate free-electron laser

Abstract High-gain harmonic generation (HGHG) is effective to produce fully coherent free-electron laser (FEL) pulses for various scientific applications. Due to the limitation of seed lasers, HGHG typically operates at a low repetition rate. In this paper, a harmonic-enhanced HGHG scheme is proposed to relax the peak power requirement for the seed laser, which can therefore operate at megahertz and a higher repetition rate. Moreover, the setup of the scheme is compact and can be adopted in an existing single-stage HGHG facility to extend the shortest achievable wavelength. Simulations show that FEL emission at 13.5 nm (20th harmonic) can be obtained with a 270 nm, 1 MW (peak power) seed laser.

First observation of laser-beam interaction in a dipole magnet

As a new-generation light source, free-electron lasers (FELs) provide high-brightness X-ray pulses at the angstrom-femtosecond space and time scales. The fundamental physics behind the FEL is the interaction between an electromagnetic wave and a relativistic electron beam in an undulator, which consists of hundreds or thousands of dipole magnets with an alternating magnetic field. Here, we report the first observation of the laser-beam interaction in a pure dipole magnet, in which the electron beam energy modulation with 40-keV amplitude and 266-nm period is measured. We demonstrate that such an energy modulation can be used to launch a seeded FEL, that is, lasing at the sixth harmonic of the seed laser in a high-gain harmonic generation scheme. The results reveal the most basic process of the FEL lasing and open up a new direction for the study and exploitation of laser-beam interactions.

Generation and measurement of intense few-femtosecond superradiant extreme-ultraviolet free-electron laser pulses

Free-electron lasers producing ultrashort pulses with high peak power promise to extend ultrafast non-linear spectroscopic techniques into the extreme-ultraviolet–X-ray regime. Key aspects are the synchronization between pump and probe, and the control of the pulse properties (duration, intensity and coherence). Externally seeded free-electron lasers produce coherent pulses that can be synchronized with femtosecond accuracy. An important goal is to shorten the pulse duration, but the simple approach of shortening the seed is not sufficient because of the finite-gain bandwidth of the conversion process. An alternative is the amplification of a soliton in a multistage, superradiant cascade: here, we demonstrate the generation of few-femtosecond extreme-ultraviolet pulses, whose duration we measure by autocorrelation. We achieve pulses four times shorter, and with a higher peak power, than in the standard high-gain harmonic generation mode and we prove that the pulse duration matches the Fourier transform limit of the spectral intensity distribution. By amplifying a soliton in a multistage cascade, few-femtosecond extreme-ultraviolet free-electron laser pulses are achieved.

Optimization and stability of a high-gain harmonic generation seeded oscillator amplifier

The free-electron laser (FEL) community is interested in taking full advantage of the high-repetition-rates of FELs run by superconducting machines while maintaining the spectral properties achieved with external seeding techniques. Since the feasibility of seed lasers operating at a repetition-rate of MHz and with sufficient energy in a useful wavelength range, such as the ultraviolet (UV) range is challenging, a seeded oscillator-amplifier scheme is proposed instead for generation of fully coherent and high-repetition-rate radiation. The process is triggered by an external seed laser while an optical feedback system feeds the radiation back to the entrance of the modulator where it overlaps with the next electron bunch. Downstream from the feedback system, the electron bunches are then used for harmonic generation. We discuss the optimization of dedicated simulations and we investigate the stability of this scheme with numerical simulations. As a result, we address the control of the reflectivity of the resonator as a key parameter to achieve a stable HGHG seeded radiation. Finally, we show the impact of the power fluctuations in the oscillator on the bunching amplitude with analytical and simulated results. The output FEL radiation wavelengths considered are 4.167 nm and 60 nm.

Self-Amplification of Coherent Energy Modulation in Seeded Free-Electron Lasers.

The spectroscopic techniques for time-resolved fine analysis of matter require coherent x-ray radiation with femtosecond duration and high average brightness. Seeded free-electron lasers (FELs), which use the frequency up-conversion of an external seed laser to improve temporal coherence, are ideal for providing fully coherent soft x-ray pulses. However, it is difficult to operate seeded FELs at a high repetition rate due to the limitations of present state-of-the-art laser systems. Here, we report a novel self-modulation method for enhancing laser-induced energy modulation, thereby significantly reducing the requirement of an external laser system. Driven by this scheme, we experimentally realize high harmonic generation in a seeded FEL using an unprecedentedly small external laser-induced energy modulation. An electron beam with a laser-induced energy modulation as small as 1.8 times the slice energy spread is used for lasing at the seventh harmonic of a 266-nm seed laser in a single-stage high-gain harmonic generation (HGHG) setup and the 30th harmonic of the seed laser in a two-stage HGHG setup. The results mark a major step toward a high-repetition-rate, fully coherent x-ray FEL.

The seed laser system of the FERMI free-electron laser: design, performance and near future upgrades

AbstractAn important trend in extreme ultraviolet and soft X-ray free-electron laser (FEL) development in recent years has been the use of seeding by an external laser, aimed to improve the coherence and stability of the generated pulses. The high-gain harmonic generation seeding technique was first implemented at FERMI and provided FEL radiation with high coherence as well as intensity and wavelength stability comparable to table-top ultrafast lasers. At FERMI, the seed laser has another very important function: it is the source of external laser pulses used in pump–probe experiments allowing one to achieve a record-low timing jitter. This paper describes the design, performance and operational modes of the FERMI seed laser in both single- and double-cascade schemes. In addition, the planned upgrade of the system to meet the challenges of the upgrade to echo-enabled harmonic generation mode is presented.

Enhanced seeded free electron laser performance with a “cold” electron beam

FERMI is a seeded free electron laser (FEL) based on the high gain harmonic generation (HGHG) scheme and has been generating intense and fully coherent extreme ultra-violet and soft x-ray pulses for several years. The high-degree performance of the FEL leans on a high brightness electron beam, with small transverse emittance ($\ensuremath{\sim}1\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$) and a peak current of about 700-800 A. The main constraint on lasing at high harmonics of the seed is low electron time-slice energy spread. The optimization of the photoinjector and of some linac parameters has allowed a reduction of the relative slice energy spread to the level of few times of ${10}^{\ensuremath{-}5}$. With these new conditions, the FEL can be operated without the need of a laser heater to suppress micro bunching instabilities and this ``cold'' beam has allowed generation of extreme UV pulses with pulse energy exceeding a mJ, and with peak power of about 10 GW. We describe the electron beam characterization and the FEL performance improvement, including the extension of the range of harmonics of the seed which can be amplified, up to the twenty-fifth harmonic, i.e., 10 nm.

Free Electron Laser High Gain Equation and Harmonic Generation

The FEL integral equation is reviewed here and is studied under different contexts, accounting for diverse physical regimes. We include higher order harmonics and saturation effects, and explain the origin of scaling relations, widely exploited to describe either FEL dynamics or nonnlinear harmonic generation.

High-gain harmonic generation with temporally overlapping seed pulses and application to ultrafast spectroscopy.

Collinear double-pulse seeding of the High-Gain Harmonic Generation (HGHG) process in a free-electron laser (FEL) is a promising approach to facilitate various coherent nonlinear spectroscopy schemes in the extreme ultraviolet (XUV) spectral range. However, in collinear arrangements using a single nonlinear medium, temporally overlapping seed pulses may introduce nonlinear mixing signals that compromise the experiment at short time delays. Here, we investigate these effects in detail by extending the analysis described in a recent publication (Wituschek et al., Nat. Commun., 11, 883, 2020). High-order fringe-resolved autocorrelation and wave packet interferometry experiments at photon energies > 23 eV are performed, accompanied by numerical simulations. It turns out that both the autocorrelation and the wave-packet interferometry data are very sensitive to saturation effects and can thus be used to characterize saturation in the HGHG process. Our results further imply that time-resolved spectroscopy experiments are feasible even for time delays smaller than the seed pulse duration.