Optimization of extreme ultraviolet vortex beam based on high harmonic generation

In high harmonic generation(HHG),Laguerre–Gaussian(LG) beams are used to generate extreme ultraviolet(XUV)vortices with well-defined orbital angular momentum(OAM),which have potential applications in fields such as microscopy and spectroscopy.An experimental study on the HHG driven by vortex and Gaussian beams is conducted in this work.It is found that the intensity of vortex harmonics is positively correlated with the laser energy and gas pressure.The structure and intensity distribution of the vortex harmonics exhibit significant dependence on the relative position between the gas jet and the laser focus.The ring-like structures observed in the vortex harmonics,and the interference of quantum paths provide an explanation for the distinct structural characteristics.Moreover,by adjusting the relative position between the jet and laser focus,it is possible to discern the contributions from different quantum paths.The optimization of the HH vortex field is applicable to the XUV,which opens up a new way for exploiting the potential in optical spin or manipulating electrons by using the photon with tunable orbital angular momentum.

Frequency dependence of quantum path interference in non-collinear high-order harmonic generation

High-order harmonic generation（HHG） driven by two non-collinear beams including a fundamental and its weak second harmonic is numerically studied. The interference of harmonics from adjacent electron quantum paths is found to be dependent on the relative delay of the driving pulse, and the dependences are different for different harmonic orders.This frequency dependence of the interference is attributed to the spatial frequency chirp in the HHG beam resulting from the harmonic dipole phase, which in turn provides a potential way to gain an insight into the generation of high-order harmonics. As an example, the intensity dependent dipole phase coefficient α is retrieved from the interference fringe.

High-order harmonics generation by few-cycle and multi-cycle femtosecond laser pulses

This paper investigates experimentally high-order harmonic generation （HHG） of neon gas with 5-fs and 25-fs driving laser pulses. It has been demonstrated that the cutoff energy of the harmonic extreme ultraviolet photons is extended to 131 eV and the HHC spectrum near the cutoff region becomes continuum as the driving laser pulse duration is 5 fs; whereas much lower cutoff photon energy and discrete harmonic spectrum near the cutoff region are presented as the laser pulse duration is 25 fs. The results can be explained by the fact that neutral atoms can be exposed to more intense laser field before they are depleted by ionization because of the extremely short rising time of the few-cycle pulse. The 5-fs driving laser pulse paves the way of generation of coherent x-ray in the water window and single attosecond pulse.

A tunable XUV monochromatic light source based on the time preserving grating selection of high-order harmonic generation

We accomplish a laboratory facility for producing a femtosecond XUV coherent monochromatic radiation with a broad tunable spectral range of 20 eV-75 eV. It is based on spectral selected single-order harmonics from intense laser driven high harmonic generation in gas phase. The time preserving for the selected harmonic radiation is achieved by a Czerny-Turner type monochromator designed with a conical diffraction grating mount for minimizing the time broadening caused by grating diffraction and keeping a relatively high diffraction efficiency. Our measurement shows that the photon flux of the 23-order harmonic（H23） centered at 35.7 eV is 1×10~9 photons/s approximately with a resolving power E/？E ≈ 36.This source provides an ultrashort tunable monochromatic XUV beam for ultrafast studies of electronic and structural dynamics in a large variety of matters.

High-order harmonic generations in tilted Weyl semimetals

We investigate high-order harmonic generations(HHGs)under comparison of Weyl cones in two types.Due to the hyperboloidal electron pocket structure,strong noncentrosymmetrical generations in high orders are observed around a single type-ⅡWeyl point,especially at zero frequency.Such a remarkable DC signal is proved to have attributions from the intraband transition after spectral decomposition.Under weak pulse electric field,the linear optical response of a nontilted Weyl cone is consistent with the Kubo theory.With extensive numerical simulations,we conclude that the non-zero chemical potential can enhance the even-order generations,from the slightly tilted system to the over-tilted systems.In consideration of dynamical symmetries,type-Ⅰand type-ⅡWeyl cones also show different selective responses under the circularly polarized light.Finally,using a more realistic model containing two pairs of Weyl points,we demonstrate that paired Weyl points with opposite chirality can suppress the overall even-order generations.

High-order harmonic generation spectrum of an excited one-dimensional Coulomb atom in an intense laser field

Response of the wave packet of a one-dimensional Coulomb atom to an intense laser field is calculated using the symmetrized split operator fast Fourier method. The high-order harmonic generation （HHG） of the initial state separately being the ground and excited states is presented. When the hardness parameter a in the soft Coulomb potential V（x） =-1√x^2＋α is chosen to be small enough, the so-called hard Coulomb potential V（x）=1/｜x｜ can be obtained. It is well known that the hard one-dimensional Coulomb atom has an unstable ground state with an energy eigenvalue of - 0.5 and it has no states corresponding to physical states in the true atoms, and has the first and second excited states being degenerate. The parity effects on the HHG can be seen from the first and second excited states of the hard one-dimensional Coulomb atom. The HHG spectra of the excited states from both the soft and hard Coulomb atom models are shown to have more complex structures and to be much stronger than the corresponding HHG spectrum of the ground state of the soft Coulomb model with a = 2 in the same laser field. Laser-induced non-resonant one-photon emission is also observed.

Influence of intraband motion on the interband excitation and high harmonic generation

Tunnelling, acceleration, and collision of electrons are the basic events in the process of high harmonic generation(HHG) in strong-field interaction with atoms.However, the periodic array of atoms in semiconductor structure makes three steps become interatomic coherent process which leads to complicated carrier dynamics and two sources of high harmonic emission: interband polarization and intraband current.The difference of features of high harmonic generation between semiconductors and atoms is strongly linked to the unique presence of intraband motion which manifests itself a nontrivial role in intertwined two dynamics.Here, we review recent experimental and theoretical advances of understanding coupled interband and intraband mechanisms of HHG in semiconductors.Particularly we focus on the influence of intraband motion on the interband excitation, and on the subsequent HHG emission and attosecond pulse generation.

Porous organic cages as a novel platform for second harmonic generation

Second harmonic generation(SHG) is one of the most extensively applied nonlinear optical phenomena. Compared to traditional inorganic SHG materials, organic SHG materials, including non-centrosymmetric small molecular crystals and organic polymers, have been extensively explored for SHG optics due to their advantageous properties, including high light-induced damage threshold, ultrafast response speed, high polarization ratio, wide transparency range, and elevated dielectric constant. However,in organic SHG materials, most small molecular crystals often show poor thermal stability(<200 ℃) due to their low molecular weight, which is an important obstacle for practical application under high temperatures. On the other hand, the difficulty in the growth of large-size crystals as well as the disorderly array of chromospheres on polymer chains associated with organic polymers have hindered their widespread application in SHG due to the requirements of processability and homogeneity.Therefore, it is significantly necessary to develop novel organic SHG material with high thermal stability, large-size crystals,excellent processability, high homogeneity, and a well SHG effect. In the contribution, we developed herein porous organic cages(POCs) as a novel platform for SHG optics. Thanks to its inherent macromolecular composition and zero-dimensional discrete structures, POCs can not only solve the instability problem of small molecule crystals but also overcome the drawbacks in growing large-size crystals for organic polymer. The obtained two POCs with chiral asymmetric centers(CPOC-R-5 and CPOCS-7) display advantageous features for SHG optics including well SHG performance, large-size crystal(5 mm×3 mm×1 mm),high thermal stability(≥250 ℃), wide transparency window(750–2,000 nm) and high polarization ratio(up to 94.5%). This work thus develops POCs as a new platform toward the construction of organic NLO materials with the potential application in sorts of SHG optics.

Attosecond twisted beams from high-order harmonicgeneration driven by optical vortices

Optical vortices are structures of the electromagnetic field with a spiral phase ramp about a point-phase singularity,carrying orbital angular momentum(OAM). Recently, OAM has been imprinted to short-wavelength radiation through high-order harmonic generation(HHG), leading to the emission of attosecond twisted beams in the extreme-ultraviolet(XUV) regime. We explore the details of the mapping of the driving vortex to its harmonic spectrum. In particular, we show that the geometry of the harmonic vortices is convoluted, arising from the superposition of the contribution from the short and long quantum paths responsible of HHG. Finally, we show how to take advantage of transverse phase-matching to select twisted attosecond beams with different spatiotemporal properties.

Generation of 15 W femtosecond laser pulse from a Kerr-lens mode-locked Yb:YAG thin-disk oscillator

We demonstrated a robust power-scalable Kerr-lens mode-locked（KLM） operation based on a Yb：YAG thin-disk oscillator.15-W,272-fs pulses were realized at a repetition rate of 86.7 MHz with an additional Kerr medium and a 2.5 mm hard aperture in the cavity.247-fs pulses with an average power of 11 W could also be obtained by using a 2.4 mm hard aperture.Based on this shorter pulse,high efficient second-harmonic generation（SHG） was performed with a 1.7-mm-long Li B3O5（LBO） crystal.The SHG laser power was up to 5 W with the power fluctuation RMS of 1% measured over one hour.

Generation of elliptical isolated attosecond pulse from oriented H_(2)^(+)in a linearly polarized laser field

We investigate the ellipticity of the high-order harmonic generation from the oriented H_(2)^(+)exposed to a linearly polarized laser field by numerically solving the two-dimensional time-dependent Schrodinger equation(2 D TDSE).Numerical simulations show that the harmonic ellipticity is remarkably sensitive to the alignment angle.The harmonic spectrum is highly elliptically polarized at a specific alignment angleθ=30°,which is insensitive to the variation of the laser parameters.The position of the harmonic intensity minima indicates the high ellipticity,which can be attributed to the two-center interference effect.The high ellipticity can be explained by the phase difference of the harmonics.This result facilitates the synthesis of a highly elliptical isolated attosecond pulse with duration down to 65 as,which can be served as a powerful tool to explore the ultrafast dynamics of molecules and study chiral light-matter interaction.

Attosecond pulse trains driven by IR pulses spectrally broadened via supercontinuum generation in solid thin plates

We utilized a set of fused silica thin plates to broaden the spectrum of 1kHz,30 fs Ti:sapphire amplified laser pulses to an octave.Following the compression by chirped mirror pairs,the generated few-cycle pulses were focused onto an argon filled gas cell.We detected high order harmonics corresponding to a train of 209 as pulses,characterized by the reconstruction of attosecond beating by interference of two-photon transition(RABITT)technique.Compared with the conventional attosecond pulse trains,the broad harmonics in such pulse trains cover more energy range,so it is more efficient in studying some typical cases,such as resonances,with frequency resolved RABITT.As the solid thin plates can support high power supercontinuum generation,it is feasible to tailor the spectrum to have different central wavelength and spectral width,which will make the RABITT source work in different applications.

The dependence of high-order harmonic generation on the laser frequency and inter-nuclear distance from multi-atom molecular ions

High-order harmonic generation from one-dimensional （1D） multi-atom molecular ions ill an ultra-short laser field is theoretically- investigated, The dynamics of the electron in a linearly polarized intense laser field is analyzed in terms of 1D Schroedinger equation with the Crank-Nicolson algorithm, The dependence of high-order harmonics on the laser frequeney and the biter-nuclear distance is discussed, It is found that the optimum range of inter-nuclear distance should be changed to get extended harmonic generation for different laser frequency, and the lower frequency laser pulse is favorable to higher order harmonic generation as the inter-nuclear distance increases.

A systematic investigation of high harmonic generation using mid-infrared driving laser pulses

We report on a systematic investigation of the influences of gas pressure,focal position and focusing geometry on high harmonic generation by use of mid-infrared femtosecond laser pulses. We also discuss the spatial characteristics of harmonics under different focusing conditions. By optimizing the parameters,we experimentally observed the generation of 1 kHz,low divergence coherent X-ray beams in the water-window region.

A nonperturbative quantum electrodynamic approach to the theory of laser induced high harmonic generation

Using nonperturbative quantum electrodynamics, we develop a scattering theory for high harmonic generation （HHG）. A transition rate formula for HHG is obtained. Applying this formula, we cal- culate the spectra of high harmonics generated from different noble gases shined by strong laser light. We study the cutoff property of the spectra. The data show that the cutoff orders of high harmonics are greater than that predicted by the ＂3.17＂ cutoff law. As a numerical experiment, the data obtained from our repeated calculations support the newly derived theoretical expression of the cutoff law. The cutoff energy of high harmonics described by the new cutoff law, in terms of the ponderomotive energy Up and the ionization potential energy Ip, is 3.34Up 1.83Ip. The higher cutoff orders predicted by this theory are due to the absorption of the extra photons, which participate only the photon-mode up-conversion and do nothing in the photoionization process.

2D semiclassical model for high harmonic generation from gas

The electron behavior in laser field is described in detail. Based on the ID semiclassical model, a2D semiclassical model is proposed analytically using 3D DC-tunneling ionization theory. Lots of harmonic features are explained by this model, including the analytical demonstration of the maximum electron energy 3.17U p Finally, some experimental phenomena such as the increase of the cutoff harmonic energy with the decrease of pulse duration and the “anomalous” fluctuations in the cutoff region are explained by this model.

High harmonic generation and ionization effects in cluster targets

High harmonic generation in gas jets was investigated in different gases up to more than 14 bar backing pressure. The observation of increase of harmonic intensity with increasing pressure and laser intensity shows evidence of the presence of clusters in Xe with an increased efficiency compared with He, whereas Ar is an intermediate case for which clusters will start to dominate above a certain backing pressure. Spectral investigations give evidence for tunable harmonic generation in a broad spectral range. A spectral shift of opposite signature caused by the free electrons in the focal volume and the nanoplasmas inside the cluster was observed.

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

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.

Efficient high harmonics generation by enhancement cavity driven with a post-compressed FCPA laser at 10 MHz

Efficient high harmonics generation(HHG) was demonstrated at 10 MHz repetition rate with an external femtosecond enhancement cavity, seeded by a ～70 fs post-compressed 10 MHz fiber chirped pulse amplifier(FCPA) laser. Operation lasting over 30 min with 0.1 m W outcoupled power at 149 nm was demonstrated. It was found that shorter pulse was beneficial for alleviating the nonlinear plasma effect and improving the efficiency of HHG. Low finesse cavity can relax the plasma nonlinearity clamped intra-cavity power and improve the cavity-locking stability. The pulse duration is expected to be below 100 fs for both 1040 nm and 149 nm outputs, making it ideal for applications such as time-resolved photoemission spectroscopy.

High efficiency second harmonic generation of nanojoule-level femtosecond pulses in the visible based on BiBO

We demonstrate high efficiency second harmonic generation(SHG) of near infrared femtosecond pulses using a BiB3 O6 crystal in a single-pass tight focusing geometry setup. A frequency doubling efficiency of 63% is achieved, which is,to the best of our knowledge, the highest value ever reported in the femtosecond regime for such low energy(nJ-level)pumping pulses. Theoretical analyses of the pumping scheme focusing waist and the SHG efficiency are performed, by numerically solving the three wave mixing coupled equations in the plane-wave scenario and by running simulations with a commercial full 3 D code. Simulations show a good agreement with the experimental data regarding both the efficiency and the pulse spectral profile. The simulated SHG pulse temporal profile presents the characteristic features of the group velocity mismatch broadening in a ‘thick' crystal.