Harmonic Generation Scheme Research Articles

Transverse echo effect induced multiple harmonic generation scheme in an electron storage ring

Multiple harmonic generation is a key issue for coherence radiation generated by an electron beam modulated by the seeding laser. A new multiple harmonic generation scheme by combining the angular dispersion-induced microbunching (ADM) with the transverse echo effect, which can be easily generated by using pulsed dipoles, a pulsed quadrupole and a pulsed multipole, is investigated in a multi-bend achromatic storage ring. Simulation results demonstrate a triple of harmonic number compared to the case of pure ADM, making it possible to generate coherent extreme ultraviolet radiation in storage rings.

Wavelength scaling and multicolor operation of a plasma-driven attosecond x-ray source via harmonic generation

The generation of high-power coherent soft x-ray pulses of sub-100 as duration and 10 nm wavelength using beams from a GeV energy plasma wakefield accelerator has been recently investigated in Emma []. As a future upgrade to this concept, this contribution investigates scaling to shorter x-ray wavelengths by cascading undulators tuned to higher harmonics of the fundamental. We present two simulation studies for plasma-driven attosecond harmonic generation schemes with final photon wavelengths of 2 and 0.40 nm. We demonstrate in these schemes that using undulators with retuned fundamental frequencies can produce GW-scale pulses of sub-nm radiation with tens of attosecond-scale pulse lengths, an order of magnitude shorter than current state-of-the-art attosecond x-ray free electron lasers (XFELs). This multipulse multicolor operation will be broadly applicable to attosecond pump-probe experiments. Published by the American Physical Society 2024

Numerical experiment of phase-matched ion-based high-order harmonic generation in the water-window x-ray spectral region via electromagnetic envelope equation.

We present a phase-matching scheme for efficient high-order harmonic generation in the water-window x-ray spectral region using a 405-nm driving pulse. A high-intensity pulse (∼1016 W/cm2) is used to produce He1+ ions as the target medium, increasing the cutoff photon energy to the water-window x-ray spectral region. By adjusting the driving pulse divergence, the positive dipole phase variation balances the negative plasma dispersion and geometrical phase shift, achieving phase matching. Using the electromagnetic envelope equation coupled with the Keldysh ionization model, numerical experiments identify the optimal conditions. Results show that the relative conversion efficiencies of the 95th harmonic (4.26 nm) and the 169th harmonic (2.4 nm) reach 66% and 79% of the perfect phase-matching conditions, respectively.

Generation of high-energy, sub-20 fs deep-UV pulses in a twin-crystal third harmonic generation scheme.

Ultrashort deep ultraviolet (DUV) pulses serve as indispensable tools for investigating molecular dynamics on the femtosecond scale. Nonlinear frequency upconversion of near-infrared (NIR) light sources in a sequence of nonlinear crystals is a common method for their generation. However, preserving the temporal duration of the starting source encounters challenges owing to phase-matching bandwidth limitations within the harmonic generation process. Here we propose an approach for circumventing this limitation and demonstrate it for the case of generation of the third harmonic of 800 nm pulses in a two-stage scheme (second harmonic generation succeeded by sum-frequency mixing of the fundamental and second harmonic pulses). Expanding the bandwidth of the DUV pulse involves the utilization for the last mixing process of two nonlinear crystals, detuned to convert opposite sides of the spectrum. The implementation of this approach yields 20 µJ, 263 nm DUV pulses as short as 19 fs after compression. The setup is very compact and extremely stable due to the common-path scheme, which makes it very interesting for a variety of advanced ultrafast spectroscopy applications.

High-efficiency fourth harmonic generation and polarization smoothing based on an orthogonal cascade of DKDP crystals.

Because of the high efficiency of frequency conversion and beam-target coupling, a fourth harmonic (4ω) laser has a splendid application prospect in a high-power laser facility. The polarization smoothing (PS) crystal is preferably after the frequency conversion crystal to flexibly obtain the best uniformity illumination of the target. However, as a high irradiance 4ω laser beam propagates through the PS crystal, the transverse stimulated Raman scattering (TSRS) effect of the PS crystal will be stronger, resulting in significant energy dissipation and crystal damage. This paper proposes a novel, to the best of our knowledge, fourth harmonic generation (FHG) scheme based on an orthogonal cascade of the DKDP crystals. This orthogonal cascaded FHG (OC-FHG) scheme employs two cascaded FHG crystals with orthogonal optical axes, and the PS crystal is in the middle. The PS crystal can rotate the polarization direction of the 2ω laser by 90°, while the polarization direction of the 4ω laser is maintained to a great extent. This OC-FHG scheme realizes the FHG by two steps, and the laser intensity at the PS crystal cuts down nearly 50%. The output intensity of the 4ω laser can be increased from 1.8G W/c m 2 to about 3.6G W/c m 2 under the condition of effectively inhibiting the TSRS effect. Meanwhile, the output 4ω laser contains two orthogonal polarized beams realizing in-beam polarization smoothing instantaneously. In addition, the novel FHG scheme can also have a high conversion efficiency and bandwidth tolerance.

A novel common-path scheme for fourth harmonic generation by ultrashort laser pulses

A new compact common-path scheme for Fourth-Harmonic Generation (FHG) of femtosecond laser pulses is proposed here. Guidelines for selection of non-linear crystals and birefringent crystals used for delay pre-compensation are derived based on approximation of non-saturated sum-frequency mixing of Gaussian pulses. We experimentally demonstrate the scheme and study its performance for a different combinations of BBO nonlinear crystals for the case of generation of sub-200 nm deep ultraviolet pulses by FHG of pulses delivered by a Ti:Sapphire ultrafast laser. Pulses with duration between 130 fs and 370 fs and pulse energy of 19 to 85 μJ were generated. It is shown, that in addition to its compactness and intrinsic stability, the scheme allows a superior spectrum and pulse quality.

Suspended-core fiber with embedded GaSe nanosheets for second harmonic generation.

We report an all-fiber scheme for the second harmonic generation (SHG) by embedding gallium selenide (GaSe) nanosheets into a suspended-core fiber (SCF). Based on modes analysis and theoretical calculations, the phase-matching modes from multiple optional modes in the SHG process and the optimal SCF length are determined by calculating the effective refractive index and balancing the SHG growth and transmission loss. Due to the long-distance interaction between pumped fundamental mode and GaSe nanosheets around the suspended core, an SHG signal is observed under a milliwatt-level pump light, and exhibits a quadratic growth with the increased pump power. The SHG process is also realized in a broad wavelength range by varying the pump in the range of 1420∼1700 nm. The SCF with the large air cladding and suspended core as an excellent platform can therefore be employed to integrate low-dimensional nonlinear materials, which holds great promise for the applications of all-fiber structures in new light source generating, signal processing and fiber sensing.

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.

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.

Efficient generation of third harmonics in Yb-doped femtosecond fiber laser via spatial and temporal walk-off compensation

On the basis of a home-made femtosecond Yb-doped fiber laser, we designed a compact and efficient third harmonic generation scheme by a simple compensation plate of β-BaB2O4 crystal. The compensation plate is optimized through its thickness and cutting angle to reverse both spatial and temporal walk-off. By optimizing the parameters of the compensation plate and incident light intensity, a maximum output of 2.23 W with a repetition rate of 1 MHz at 345 nm is obtained, which implies a conversion efficiency of 23% from the infrared to ultraviolet.

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.

Frequency-conversion of vector vortex beams with space-variant polarization in single-pass geometry

Nonlinear frequency conversion processes depend on the polarization state of the interacting beams. On the other hand, vector vortex beams have space-variant polarization in the transverse beam plane. In light of these two points, is it possible to do nonlinear frequency conversion of the vector vortex beam in single-pass geometry and retain the characteristics of the beam? To address this question, here, we report an experimental scheme for single-pass second harmonic generation (SHG) of vector vortex beams. Using an ultrafast Ti:Sapphire laser of pulse width ∼17 fs and a set of spiral phase plates in a polarization based Mach–Zehnder interferometer (MZI), we have generated vector vortex beams of order as high as lp = 12 at an average power of 860 mW. Using two contiguous bismuth borate crystals with the optic axis orthogonal to each other, we have frequency-doubled the near-IR vector vortex beam into visible vector vortex beam with order as high as lsh = 24. The maximum output power of the vector vortex beam of order, lsh = 2, is measured be as high as 20.5 mW at a single-pass SHG efficiency of 2.4%. Controlling the delay in MZI, we have preserved the vector vortex nature of both the pump and frequency-doubled beams. Measurement on the mode purity confirms the generation of high quality vector vortex beams at pump and SHG wavelengths. This generic scheme can be used to generate vector vortex beams across the electromagnetic spectrum in all time scales, continuous-wave to ultrafast.

Coherent extreme ultraviolet free-electron laser with echo-enabled harmonic generation

The echo-enabled harmonic generation (EEHG) scheme holds promising prospects for efficiently generating intense coherent radiation at very high harmonics of a conventional ultraviolet seed laser. We report the lasing of the EEHG free-electron laser (FEL) at an extreme ultraviolet (EUV) wavelength with a seeded FEL facility, the Shanghai soft x-ray FEL. For the first time, we have benchmarked the basic theory of EEHG by measuring the bunching factor distributions over one octave down to the EUV region. Our results demonstrated the key advantages of the EEHG FEL, i.e., generation of very high harmonics with a small laser-induced energy spread and insensitivity to beam imperfections, and marks a great step towards fully coherent x rays with the EEHG scheme.

Large aperture and non-critical phase-matched fourth harmonic generation of Nd:Glass lasers

A fourth harmonic generation (FHG) scheme in focusing beams is proposed and demonstrated for large aperture Nd:glass laser facilities. By placing the focusing lens before the FHG crystal, the problem of ultraviolet damage can be overcome, largely without affecting FHG conversion efficiency owing to the large angular acceptance of the non-critical phase matching technique. A numerical simulation of the FHG process indicates that angular acceptance can be appropriately increased by lowering the working temperature and jointing the two adjacent compensating angles, so that FHG in focusing beams with relatively small F numbers becomes feasible. With a 170 mm × 170 mm × 7 mm and 65% deuterated potassium dihydrogen phosphate crystal mounted in a high-precision, temperature-controlled system, high-efficiency FHG has been demonstrated in the focusing beam with a full beam convergence angle of 36 mrad. When driven with a 223 J, second harmonic radiation (2ω), 1 ns flat-top pulse with a beam area of 130 cm2, corresponding to 1.7 GW/cm2 2ω input intensity, 182 J of fourth harmonic radiation (4ω) were generated.

Second harmonic generation of q-Gaussian laser beam in plasma channel created by ignitor heater technique

AbstractThis paper presents a scheme for second harmonic generation (SHG) of q-Gaussian laser beam in plasma channel created by ignitor heater technique. The ignitor beam creates plasma by tunnel ionization of air. The heater beam heats the plasma electrons and establishes a parabolic density profile. The third beam (q-Gaussian beam) is guided in this plasma channel under the combined effects of density nonuniformity of the plasma channel and relativistic mass nonlinearity of the plasma electrons. The propagation of q-Gaussian laser beam through the plasma channel excites an electron plasma wave at pump frequency that interacts with the incident laser beam to produce its second harmonics. The formulation is based on finding the numerical solution of the nonlinear Schrodinger wave equation for the fields of the incident laser beams with the help of moment theory approach. Particular emphasis is put on dynamical variations of the spot size of the laser beams and conversion efficiency of the second harmonics with distance of propagation.

Generation of two-color polarization-adjustable radiation pulses for storage ring light source

To date, two-color pulses are widely used in pump–probe experiments. For a ring-based light source, the power of the spontaneous radiation fluctuates randomly in the longitudinal direction. It is difficult to produce two-color double pulses by optical methods. In this paper, we introduce a method based on the echo-enabled harmonic generation scheme that generates two-color pulses in a storage ring light source. By adopting crossed undulators and a phase shifter, the polarization of the two-color pulses can be easily switched. A numerical simulation based on a diffraction-limited storage ring, the Hefei Advanced Light Source, suggests that the time delay and spectral separation of the two pulses can be adjusted linearly by changing the pulse duration and chirp parameters of the seed laser. A circular polarization degree above 80% could be achieved.

上海软X射线自由电子激光装置

Shanghai soft X-ray free-electron laser facility (SXFEL) is the first coherent X-ray light source in China with the shortest wavelength down to 2 nm. SXFEL is based on a 1.5 GeV C-band linac, including one seeded FEL line, one self-amplified spontaneous emission FEL line and five experimental stations. The development of SXFEL is in two stages, the test facility SXFEL-TF and the user facility SXFEL-UF. SXFEL-TF is based on a 0.84 GeV linac, aiming to master the key technologies of a cascaded FEL with high gain harmonic generation (HGHG) and echo-enabled harmonic generation (EEHG) scheme. Meanwhile, the object of SXFEL-UF is to start user operation at the end of 2019. This paper presents the design, construction and commissioning status of SXFEL. © 2019, Chinese Lasers Press. All right reserved.

Generating femtosecond coherent X-ray pulses in a diffraction-limited storage ring with the echo-enabled harmonic generation scheme

To study ultrafast processes at the sub-picosecond level, novel methods based on coherent harmonic generation technologies have been proposed to generate ultrashort radiation pulses in existing ring-based light sources. Using the High Energy Photon Source as an example, we numerically test the feasibility of implementing one coherent harmonic generation technology, i.e., the echo-enabled harmonic generation (EEHG) scheme, in a diffraction-limited storage ring (DLSR). Two different EEHG element layouts are considered, and the effect of the EEHG process on the electron beam quality is also analyzed. Studies suggest that soft X-ray pulses, with pulse lengths of a few femtoseconds and peak powers of up to 1 MW, can be generated by using the EEHG scheme, while causing little perturbation to the regular operation of a DLSR.

Time-resolved high harmonic spectroscopy of dynamical symmetry breaking in bi-circular laser fields: the role of Rydberg states.

The bi-circular scheme for high harmonic generation, which combines two counter-rotating circular fields with frequency ratio 2:1, has recently permitted to generate high harmonics with essentially circular polarization, opening the way for ultrafast chiral studies. This scheme produces harmonic lines at 3N + 1 and 3N + 2 multiples of the fundamental driving frequency, while the 3N lines are forbidden owing to the three-fold symmetry of the field. It is generally established that the routinely observed signals at these forbidden harmonic lines come from a slight ellipticity in the driving fields, which breaks the three-fold symmetry. We find that this is neither the only nor it is the dominant mechanism responsible. The forbidden lines can be observed even for perfectly circular, long driving pulses. We show that they encode rich information on the sub-cycle electronic dynamics that occur during the generation process. By varying the time delay and relative intensity between the two drivers, we demonstrate that when the second harmonic either precedes or is more intense than the fundamental field, the weak effects of dynamical symmetry breaking caused by finite pulse duration are amplified by electrons trapped in Rydberg orbits (i.e., Freeman resonances), and that the forbidden harmonic lines are a witness of this.

Two-stage EEHG for coherent hard X-ray generation based on a superconducting linac

A two-stage echo-enabled harmonic generation (EEHG) scheme is proposed for a superconducting linac-driven FEL to produce coherent hard X-rays. Electron beams of quite different bunch lengths are separately used in each stage of EEHG, and a monochromator is designed to purify the radiation from the first stage for seeding the second stage. Theoretical analysis and 3D simulations indicate that the proposed scheme can generate high-repetition-rate coherent hard X-ray pulses directly from a conventional UV seed laser.