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.

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.

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.

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 harmonic generation and application for photoemission spectroscopy in condensed matter

High harmonic generation(HHG)delivering attosecond pulse duration with photon energy in the extreme ultraviolet spectral range has been demonstrated as a robust table-top coherent light source,allowing for the observation and manipulation of ultrafast process within the shortest time window ever made by humans.The past decade has witnessed the rapid progress of HHG from a variety of solid targets and its application for photoemission spectroscopy in condensed matter.In this article,we review the HHG in solids and the understanding of the underlying physics of HHG,which allows all-optical band structure reconstruction.We also introduce combinations of HHG source and photoemission spectroscopy,such as angular-resolved photoemission spectroscopy and photoemission electron microscopy.With the capacity of exploring a wide momentum space and high temporal resolution,the extension of attosecond science to the field of condensed matter physics will lead to new insights into the fundamental ultrafast dynamics in novel quantum materials.

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.

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.

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.

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.

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.

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.

Table-top optical parametric chirped pulse amplifiers: past and present

The generation of power-and wavelength-scalable few optical cycle pulses remains one of the major challenges in modern laser physics.Over the past decade,the development of table-top optical parametric chirped pulse amplificationbased systems was progressing at amazing speed,demonstrating excellent performance characteristics in terms of pulse duration,energy,peak power and repetition rate,which place them at the front line of modern ultrafast laser technology.At present,table-top optical parametric chirped pulse amplifiers comprise a unique class of ultrafast light sources,which currently amplify octave-spanning spectra and produce carrier-envelope phase-stable,few optical cycle pulses with multi-gigawatt to multi-terawatt peak powers and multi-watt average powers,with carrier wavelengths spanning a considerable range of the optical spectrum.This article gives an overview on the state of the art of table-top optical parametric chirped pulse amplifiers,addressing their relevant scientific and technological aspects,and provides a short outlook of practical applications in the growing field of ultrafast science.

Time-dependent variational approach to solve multi-dimensional time-dependent Schr?dinger equation

We present an efficient approach to solve multi-dimensional time-dependent Schr?dinger equation(TDSE)in an intense laser field.In this approach,each spatial degree of freedom is treated as a distinguishable quasi-particle.The non-separable Coulomb potential is regarded as a two-body operator between different quasi-particles.The time-dependent variational principle is used to derive the equations of motion.Then the high-order multi-dimensional problem is broken down into several lower-order coupled equations,which can be efficiently solved.As a demonstration,we apply this method to solve the two-dimensional TDSE.The accuracy is tested by comparing the direct solutions of TDSE using several examples such as the strong-field ionization and the high harmonic generation.The results show that the present method is much more computationally efficient than the conventional one without sacrificing accuracy.The present method can be straightforwardly extended to three-dimensional problems.Our study provides a flexible method to investigate the laser-atom interaction in the nonperturbative regime.

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.

Nonlinear optics with structured light

The interest in tailoring light in all its degrees of freedom is steadily gaining traction,driven by the tremendous developments in the toolkit for the creation,control and detection of what is now called structured light.Because the complexity of these optical fields is generally understood in terms of interference,the tools have historically been linear optical elements that create the desired superpositions.For this reason,despite the long and impressive history of nonlinear optics,only recently has the spatial structure of light in nonlinear processes come to the fore.In this review we provide a concise theoretical framework for understanding nonlinear optics in the context of structured light,offering an overview and perspective on the progress made,and the challenges that remain.

Attosecond spectroscopy for filming the ultrafast movies of atoms,molecules and solids

Three decades ago,a highly nonlinear nonpertubative phenomenon,now well-known as the high harmonic generation(HHG),was discovered when intense laser irradiates gaseous atoms.As the HHG produces broadband coherent radiation,it becomes the most promising source to obtain attosecond pulses.The door to the attosecond science was opened ever since.In this review,we will revisit the incredible adventure to the attoworld.Firstly,the progress of attosecond pulse generation is outlined.Then,we introduce the efforts on imaging the structures or filming the ultrafast dynamics of nuclei and electrons with unprecedented attosecond temporal and Angstrom spatial resolutions,utilizing the obtained attosecond pulses as well as the high harmonic spectrum itself.

All optical method for measuring the carrier envelope phase from half-cycle cutoffs

An all optical method is demonstrated for measuring the carrier-envelope phase （CEP） of few-cycle laser pulses. It is found that, in the few-cycle regime, the high harmonic spectrum generated from asymmetric molecules shows several half-cycle cutoffs that change their positions as the CEP varies. Such half-cycle cutoffs represent the fingerprint of different quantum trajectories and the waveform of the driving pulse. In this case, the CEP can be accurately measured from the half-cycle cutoffs.

On the cutoff law of laser induced high harmonic spectra

The currently well accepted cutoff law for laser induced high harmonic spectra predicts the cutoff energy as a linear combination of two interaction energies, the ponderomotive energy Up and the atomic biding energy Ip, with coefficients 3.17 and 1.32, respectively. Even though, this law has been there for twenty years or so, the background information for these two constants, such as how they relate to fundamental physics and mathematics constants, is still unknown. This simple fact, keeps this cutoff law remaining as an empirical one. Based on the cutoff property of Bessel functions and the Einstein photoelectric law in the multiphoton case, we show these two coefficients are algebraic constants, 9 - 4√2 ≈ 3.34 and 2√2-1≈1.83, respectively. A recent spectra calculation and an experimental measurement support the new cutoff law.

Time-energy properties of an attosecond extreme ultra-violet pulse

The time-energy properties of high-order harmonic generation （HHG） are calculated for a linearly polarized 7- fs laser pulse with different carrier-envelope phases （CEPs）. The quantum trajectory paths that contribute to an as （1 as=10^-18 s） pulse in HHG are identified. The laser-duration dependence and the CEP dependence of HHG energy property are investigated. The study shows that an as extreme ultra-violet （XUV） pulse can be selected from HHG spectrum near cut-off energy with a bandpass optical filter. The theoretical prediction of the pulse duration is proportional to bandwidth. Analysis suggests that a measured narrowband as XUV pulse may consist of instantaneous shorter pulses each dependent on laser pulse duration, intensity, and CEP. These information can be used as references for producing, selecting, improving and manipulating （timing） as pulses.

Exploring new avenues in high repetition rate table-top coherent extreme ultraviolet sources

The process of high harmonic generation(HHG)enables the development of table-top sources of coherent extreme ultraviolet(XUV)light.Although these are now matured sources,they still mostly rely on bulk laser technology that limits the attainable repetition rate to the low kilohertz regime.Moreover,many of the emerging applications of such light sources(e.g.,photoelectron spectroscopy and microscopy,coherent diffractive imaging,or frequency metrology in the XUV spectral region)require an increase in the repetition rate.Ideally,these sources are operated with a multi-MHz repetition rate and deliver a high photon flux simultaneously.So far,this regime has been solely addressed using passive enhancement cavities together with low energy and high repetition rate lasers.Here,a novel route with significantly reduced complexity(omitting the requirement of an external actively stabilized resonator)is demonstrated that achieves the previously mentioned demanding parameters.A krypton-filled Kagome photonic crystal fiber is used for efficient nonlinear compression of 9 μJ,250 fs pulses leading to,7 μJ,31 fs pulses at 10.7 MHz repetition rate.The compressed pulses are used for HHG in a gas jet.Particular attention is devoted to achieving phase-matched(transiently)generation yielding.10^(13) photons s^(-1)(.50 μW)at 27.7 eV.This new spatially coherent XUV source improved the photon flux by four orders of magnitude for direct multi-MHZ experiments,thus demonstrating the considerable potential of this source.