High harmonic generation

-Q-switching operation mode → radiation at 220 nm (third harmonic of FEL at 660 nm) -Energy, temporal and spectral characterization -Comparison with theory CHG using an external seed -Time dependent and time independent simulations -Conclusions and Perspectives dispersive section radiator modulator e -beam energy modulation micro-bunching coherent emission The principle external seed coherent light cavity mirror cavity mirror FEL light coherent light e -beam CHG on a storage ring dispersive section radiator modulator e -beam energy modulation micro-bunching coherent emission The principle external seed coherent light coherent light external laser e -beam CHG on a storage ring

Topology-driven nonlinear light-matter effects open up new paradigms for both topological photonics and nonlinear optics. Here, we propose to achieve high-efficiency second-harmonic generation in a second-order photonic topological insulator. Such system hosts highly localized topological corner states with large quality factors for both fundamental and second harmonic waves, which could be matched perfectly in frequency by simply tuning the structural parameters. Through the nonlinear interaction of the doubly resonant topological corner states, unprecedented frequency conversion efficiency is predicted. In addition, the robustness of the nonlinear process against defects is also demonstrated. Our work opens up new avenues toward topologically protected nonlinear frequency conversion using high-order photonic topological modes.

A near-field effect has been discovered experimentally in thermal radio emission of an absorbing dielectric medium. It is related to a specific character of the distribution of a quasistationary field component near a radiating surface. The effect consists of the fact that the effective depth of the received emission formation appears to be less than the skin-layer depth and depends on the size of the receiver antenna and its height above the surface. It can be considered as a new source of information about depth temperature distribution. A theory has been developed that allows for determining the relative contribution of wave and quasistationary components to the Plank emission received near the surface.

The effect of fluctuations on the nonlinear response of an underdamped oscillator to an external periodic field at a subharmonic frequency has been investigated theoretically, numerically, and with an analog electronic circuit model. The system studied has often been analyzed in nonlinear optics in the context of twophoton absorption and second-harmonic generation. We consider its nonlinear spectroscopy. Its resonant nonlinear response is described over a broad range of the fluctuation intensities. It is shown that the fluctuation intensity can be used to ''tune'' the oscillator so as to maximize the nonlinear response. The dependence of the absorption cross section on the fluctuation intensity displays a clearly resolved maximum. If the eigenfrequency of the oscillator is a nonmonotonic function of its energy, the signal at the second harmonic displays a resonant peak at one of two different frequencies, depending on the noise intensity.

Coherent short-wavelength radiation from laser-plasma interactions is of increasing interest in disciplines including ultrafast biomolecular imaging and attosecond physics. Using solid targets instead of atomic gases could enable the generation of coherent extreme ultraviolet radiation with higher energy and more energetic photons. Here we present the generation of extreme ultraviolet radiation through coherent high-harmonic generation from self-induced oscillatory flying mirrors-a new-generation mechanism established in a long underdense plasma on a solid target. Using a 30-fs, 100-TW Ti:sapphire laser, we obtain wavelengths as short as 4.9 nm for an optimized level of amplified spontaneous emission. Particle-in-cell simulations show that oscillatory flying electron nanosheets form in a long underdense plasma, and suggest that the high-harmonic generation is caused by reflection of the laser pulse from electron nanosheets. We expect this extreme ultraviolet radiation to be valuable in realizing a compact X-ray instrument for research in biomolecular imaging and attosecond physics.

The interactions of large xenon clusters irradiated by intense, femtosecond extremeultraviolet pulses at a wavelength of 38 nm have been studied. Using high harmonic generation from a 35 fs near-infrared terawatt laser, clusters have been irradiated by XUV pulses of 10 11 W/cm 2 intensity. Charge states up to Xe 8+ are observed, states well above that produced by single atom illumination, indicating that plasma continuum lowering is important. Furthermore the kinetic energy distribution of the exploding ions is consistent with a quasineutral hydrodynamic expansion, rather than a Coulomb explosion.

A pump-probe scheme for preparing and monitoring electron-nuclear motion in a dissociative coherent electron-nuclear wave packet is explored from numerical solutions of a non-Born-Oppenheimer time-dependent Schrödinger equation. A mid-ir intense few-cycle probe pulse is used to generate molecular high-order-harmonic generation (MHOHG) from a coherent superposition of two or more dissociative coherent electronic-nuclear wave packets, prepared by a femtosecond uv pump pulse. Varying the time delay between the intense ir probe pulse and the uv pump pulse by a few hundreds of attoseconds, the MHOHG signal intensity is shown to vary by orders of magnitude, thus showing the high sensitivity to electron-nuclear dynamics in coherent electron-nuclear wave packets. We relate this high sensitivity of MHOHG spectra to opposing electron velocities (fluxes) in the electron wave packets of the recombining (recolliding) ionized electron and of the bound electron in the initial coherent superposition of two electronic states.

The Accelerator Test Facility (ATF) at Brookhaven National Laboratory (BNL) is an accelerator and beam physics user facility capable of producing a highbrightness, 70-MeV electron beam. Currently, a highgain harmonic generation (HGHG) free-electron laser (FEL) experiment is underway at the ATF. This is a collaborative effort between BNL and the Advanced Photon Source (APS). The experiment consists of two phases: 1) self-amplified spontaneous emission (SASE) and 2) HGHG. Here, a brief introduction to the HGHG theory, measurements in the SASE phase, the recent modifications in preparation for the HGHG phase, and future plans will be discussed.

We report results from characterization of the output of a high-gain harmonic-generation (HGHG) free-electron laser (FEL). A CO 2 seed laser at a wavelength of 10.6 µm is amplified and frequencydoubled in the FEL to produce 5.3-µm output. The wavelength spectrum, pulse duration, and correlation length of the output verify that the light is longitudinally coherent. Comparisons of the measured electron energy distribution and the nonlinear harmonics of the 5.3-µm radiation with values obtained from numerical models are consistent with saturated HGHG FEL operation. In addition, a brief discussion of the extension of this technique to ever-shorter wavelengths as well as wavelength tailoring for specific experiments will be discussed.

Ultrafast adiabatic frequency conversion is a powerful method, capable of efficiently and coherently transfering ultrashort pulses between different spectral ranges, e.g. from near-infrared to mid-infrared, visible or ultra-violet. This is highly desirable in research fields that are currently limited by available ultrafast laser sources, e.g. attosecond science, strong-field physics, high-harmonic generation spectroscopy and multidimensional mid-infrared spectroscopy. Over the past decade, adiabatic frequency conversion has substantially evolved. Initially applied to quasi-monochromatic, undepleted pump interactions, it has been generalized to include ultrashort, broadband, fully-nonlinear dynamics. Through significant theoretical development and experimental demonstrations, it has delivered new capabilities and superior performance in terms of bandwidth, efficiency and robustness, as compared to other frequency conversion techniques. This article introduces the concept of adiabatic nonlinear frequency conversion, reviews its theoretical foundations, presents significant milestones and highlights contemporary ultrafast applications that may, or already do, benefit from utilizing this method.

We report experimental results on correlated double ionization of magnesium (Mg) by near-infrared (0.8and 1.03-μm) circularly polarized laser fields. With 0.8 μm, we confirm the recollision interpretation of the observed "knee" structure of Mg [Gillen et al., Phys. Rev. A 64, 043413 (2001)], even though the experiments are performed in the multiphoton regime. Our experiments show that, even in the multiphoton regime, which is normally thought to be a purely quantum-mechanical territory, some ionization phenomena can still be understood classically.

Synopsis Increasing the wavelength of the fundamental driving laser at constant intensity in high harmonic generation allows one to significantly increase the upper bound of the harmonic energies produced [1, 2]. This feature of harmonic generation is employed in an effort to improve the spatial resolution achieved in the method of tomographic reconstruction of molecular orbitals from high harmonics . Current experimental measurements and comparison with theoretical work [4] will be presented.

We report on low-order harmonic generation utilising the plasmonic field enhancement in arrays of rodtype gold optical antennae. Furthermore, we examine their suitability to support high-order harmonic generation (HHG). The low-order harmonics are used as a tool to investigate the nonlinear properties of the antennae. Particular attention is paid to the thermal properties, which become significant at the peak intensities necessary for HHG. A theoretical model explains the experimental findings and enables future improvements. In experiments we observe up to the fifth harmonic order and measure a field enhancement sufficient to support high-order harmonic generation. Moreover, we find a damage threshold for the antennae.

In this paper we discuss the harmonic undulator optical klystron free electron laser to enhance intensity and gain of free electron laser. Inclusion of betatron oscillation of electron while entering the undulator magnets gives extra perturbation which reduces its intensity and gain in free electron laser at several harmonics. In this we have enhanced our intensity and gain with the help of a harmonic undulator optical klystron scheme and compare the results with that of a standard optical klystron free electron laser.

In this work, the nonlinear electromagnetic response of a few-layer graphene sheet is experimentally analyzed. The few-layer graphene sheet is obtained through mechanical exfoliation from highly ordered pyrolytic graphite and embedded in a rectangular waveguide structure which is used to guide the exciting and the output signals. The nonlinear electromagnetic response of the graphene sheet is exploited to implement a frequency multiplier in which the output signal, in the 330-500 GHz frequency band, will be obtained as a high-order harmonic component of the input signal, in the 26-40 GHz frequency band. Due to the particular selection of the input and output frequency ranges, the behavior of several harmonic components, from order 9 to 17, can be characterized. The analysis will be focused on the frequency response of the graphene sheet, the influence of the input power on the output signal and the differences between the even-and odd-order harmonic components. Finally, it will be shown that the developed assembly can be used as THz signal source based on high-order frequency multiplication.

The development of attosecond pulses across different photon energies is an essential precursor to performing pump-probe attosecond experiments in complex systems, where the potential of attosecond science 1 can be further developed . We report the generation and characterization of synchronised XUV (90 eV) and VUV (20 eV) pulses generated simultaneously via high harmonic generation. The VUV pulses are well suited for pump-probe experiments that exploit the high photoionisation cross-section of many molecules in this spectral region 4 , and the higher photon flux due to the higher conversion efficiency of the high harmonics generation process at these energies 5 . We temporally characterised all pulses using the attosecond streaking technique 6 and the FROG-CRAB retrieval method 7 . We report 57616 as pulses at 20 eV and 25721 as pulses at 90 eV. Our demonstration of synchronised attosecond pulses at different photon energies, and inherently jitter-free due to the common-path geometry implemented, offers unprecedented possibilities for pump-probe studies. The production of isolated attosecond pulses (IAP) in the extreme ultraviolet (XUV) region (30-150 eV) with an intense near-infrared (NIR) femtosecond laser is nowadays a robust process. The generation of IAP via high harmonic generation 1 (HHG) requires temporally gating the high harmonics emission to a single burst by using one of several techniques. Most common are polarization gating 8 , double optical gating 9 , ionization gating 10 and amplitude gating 11 . However, the

The development of attosecond pulses across different photon energies is an essential precursor to performing pump-probe attosecond experiments in complex systems, where the potential of attosecond science 1 can be further developed . We report the generation and characterization of synchronised XUV (90 eV) and VUV (20 eV) pulses generated simultaneously via high harmonic generation. The VUV pulses are well suited for pump-probe experiments that exploit the high photoionisation cross-section of many molecules in this spectral region 4 , and the higher photon flux due to the higher conversion efficiency of the high harmonics generation process at these energies 5 . We temporally characterised all pulses using the attosecond streaking technique 6 and the FROG-CRAB retrieval method 7 . We report 57616 as pulses at 20 eV and 25721 as pulses at 90 eV. Our demonstration of synchronised attosecond pulses at different photon energies, and inherently jitter-free due to the common-path geometry implemented, offers unprecedented possibilities for pump-probe studies. The production of isolated attosecond pulses (IAP) in the extreme ultraviolet (XUV) region (30-150 eV) with an intense near-infrared (NIR) femtosecond laser is nowadays a robust process. The generation of IAP via high harmonic generation 1 (HHG) requires temporally gating the high harmonics emission to a single burst by using one of several techniques. Most common are polarization gating 8 , double optical gating 9 , ionization gating 10 and amplitude gating 11 . However, the

Attosecond light pulses within the vacuum ultraviolet (VUV) energy range are predicted by solving the time-dependent Schrödinger equation (TDSE) for a model neon atom in short laser pulses of different field polarization states. We compare high-order harmonic generation in linearly polarized laser pulses to the method of polarization gating and find attosecond pulses that approach the Fourier limit of 700 as given by an indium filter, spectrally centered at 15 eV. At such low energies, harmonic generation has low sensitivity to ellipticity, which enables the generation of elliptically polarized attosecond pulses. We also show that emission at the atomic transition energies is strongly damped by including intensity averaging.

We report the first experimental results on a high-gain harmonic-generation (HGHG) free-electron laser (FEL) operating in the ultraviolet. An 800 nm seed from a Ti-Sapphire laser has been used to produce saturated amplified output at the 266 nm third-harmonic. The results confirm the advantages of the HGHG FEL: stable central wavelength, narrow bandwidth and small pulse energy fluctuation. The harmonic output at 88 nm, which accompanies the 266 nm radiation, has been used in an ion pair imaging experiment in chemistry.

High-energy phase-stable sub-cycle mid-infrared pulses can provide unique opportunities to explore phase-sensitive strong-field light-matter interactions in atoms, molecules and solids. At the mid-infrared wavelength, the Keldysh parameter could be much smaller than unity even at relatively modest laser intensities, enabling the study of the strong-field sub-cycle electron dynamics in solids without damage. Here we report a high-energy sub-cycle pulse synthesiser based on a mid-infrared optical parametric amplifier and its application to high-harmonic generation in solids. The signal and idler combined spectrum spans from 2.5 to 9.0 µm. We coherently synthesise the passively carrier-envelope phase-stable signal and idler pulses to generate 33 μJ, 0.88-cycle, multi-gigawatt pulses centred at ~4.2 μm, which is further energy scalable. The mid-infrared sub-cycle pulse is used for driving high-harmonic generation in thin silicon samples, producing harmonics up to ~19th order with a cont...

Unraveling and controlling chemical dynamics requires techniques to image structural changes of molecules with femtosecond temporal and picometer spatial resolution. Ultrashort-pulse x-ray free-electron lasers have significantly advanced the field by enabling advanced pump-probe schemes. There is an increasing interest in using table-top photon sources enabled by high-harmonic generation of ultrashort-pulse lasers for such studies. We present a novel high-harmonic source driven by a 100 kHz fiber laser system, which delivers 10<sup>11</sup> photons/s in a single 1.3 eV bandwidth harmonic at 68.6 eV. The combination of record-high photon flux and high repetition rate paves the way for time-resolved studies of the dissociation dynamics of inner-shell ionized molecules in a coincidence detection scheme. First coincidence measurements on CH<sub>3</sub>I are shown and it is outlined how the anticipated advancement of fiber laser technology and improved sample deli...

The relativistic Doppler effect is one of the most famous implications of the principles of special relativity and is intrinsic to moving radiation sources, relativistic optics and many astrophysical phenomena. It occurs in the case of a plasma sail accelerated to relativistic velocities by an external driver, such as an ultra-intense laser pulse. Here we show that the relativistic Doppler effect on the high energy synchrotron photon emission (~10 MeV), strongly depends on two intrinsic properties of the plasma (charge state and ion mass) and the transverse extent of the driver. When the moving plasma becomes relativistically transparent to the driver, we show that the γ-ray emission is Doppler-boosted and the angular emission decreases; optimal for the highest charge-to-mass ratio ion species (i.e. a hydrogen plasma). This provides new fundamental insight into the generation of γ-rays in extreme conditions and informs related experiments using multi-petawatt laser facilities.

sFLASH is a seeded FEL experiment at DESY, which uses a 38nm high harmonic gain (HHG)-based XUV-beam laser in tandem with FLASH electron bunches at the entrance of a 10m variable-gap undulator. The temporal overlap between the electron and HHG beams is critical to the seeding process. Use of a 3rd harmonic accelerating module provides a high current electron beam (at the kA level) with ~ 600fs FWHM bunch duration. The length of the HHG laser pulse will be ~30fs FWHM. The desired overlap is achieved in steps. First is the synchronization of the HHG drive laser (Ti: Sapphire, 800nm) and the incoherent spontaneous radiation from an upstream undulator. Next, the IFEL-modulated electron bunch will pass through a dispersive section, producing a density modulation in the beam. This in turn yields emission of coherent radiation from a downstream undulator or transition radiation screen when the longitudinal overlap of the two beams is achieved. The coherently enhanced light emitted will be ...

Recently, the free-electron laser in Hamburg (FLASH) at DESY has been upgraded considerably. Besides increasing the maximum energy to about 1.2 GeV and installation of a third harmonic rf cavity linearizing the longitudinal phase space distribution of the electron bunch, an FEL seeding experiment at wavelengths of about 35 nm has been installed. The goal is to establish direct FEL seeding employing coherent VUV pulses produced from a powerful drive laser by high-harmonic generation (HHG) in a gas cell. The project, called sFLASH, includes generation of the required HHG pulses, transporting it to the undulator entrance of a newly installed FEL-amplifier, controlling spatial, temporal and energy overlap with the electron bunches and setting up a pump-probe pilot experiment. Sophisticated diagnostics is installed to characterize both HHG and seeded FEL pulses, both in time and frequency domain. Compared to SASE-FEL pulses, almost perfect longitudinal coherence and improved synchronizat...

We report results on the performance of a free electron laser operating at a wavelength of 13.7 nm where unprecedented peak and average powers for a coherent EUV radiation source have been measured. In the saturation regime the peak energy approached 170 μJ for individual pulses while the average energy per pulse reached 70 μJ. The pulse duration was in the region of 10 femtoseconds

We investigate the possibility of applying the iterative method,suggested in our previous work, for HCN molecule and its HNCisomer. We found that the high-order harmonic generation (HHG)spectra are quite insensitive to the change of H-C (or H-N) bondlength so that only the inter-nuclear C-N distance can beretrieved from the high-order harmonic spectra using ultrashortintense lasers. Furthermore, by analyzing the HHG spectra emittedby HCN during the chemical reaction path of isomerization weidentify the intensity peaks nearby the stable, meta-stable andtransition states. This finding can be useful for tracking theHNC/HCN isomerization process.

An angle-resolved photoemission spectroscopy (ARPES) study is reported on a Mott insulator NiGa 2 S 4 in which Ni 2þ (S ¼ 1) ions form a triangular lattice and the Ni spins do not order even in its ground state. The first ARPES study on the two-dimensional spin-disordered system shows that low-energy hole dynamics at high temperatures is characterized by wave vectors Q E which are different from wave vectors Q M dominating low-energy spin excitations at low temperatures. The unexpected difference between Q E and Q M is deeply related to charge fluctuation across the Mott gap in the frustrated lattice and is a key issue to understand the spin-disordered ground states in Mott insulators.

Exploring the dynamics of matter driven to extreme non-equilibrium states by an intense ultrashort X-ray pulse is becoming reality, thanks to the advent of free-electron laser technology that allows development of different schemes for probing the response at variable time delay with a second pulse. Here we report the generation of two-colour extreme ultraviolet pulses of controlled wavelengths, intensity and timing by seeding of high-gain harmonic generation free-electron laser with multiple independent laser pulses. The potential of this new scheme is demonstrated by the time evolution of a titanium-grating diffraction pattern, tuning the two coherent pulses to the titanium M-resonance and varying their intensities. This reveals that an intense pulse induces abrupt pattern changes on a time scale shorter than hydrodynamic expansion and ablation. This result exemplifies the essential capabilities of the jitter-free multiple-colour free-electron laser pulse sequences to study evolving states of matter with element sensitivity.

The shortest light pulses produced to date are of the order of a few tens of attoseconds, with central frequencies in the extreme ultraviolet range and bandwidths exceeding tens of eV. They are often produced as a train of pulses separated by half the driving laser period, leading in the frequency domain to a spectrum of high, odd-order harmonics. As light pulses become shorter and more spectrally wide, the widely-used approximation consisting in writing the optical waveform as a product of temporal and spatial amplitudes does not apply anymore. Here, we investigate the interplay of temporal and spatial properties of attosecond pulses. We show that the divergence and focus position of the generated harmonics often strongly depend on their frequency, leading to strong chromatic aberrations of the broadband attosecond pulses. Our argumentation uses a simple analytical model based on Gaussian optics, numerical propagation calculations and experimental harmonic divergence measurements. This effect needs to be considered for future applications requiring high quality focusing while retaining the broadband/ultrashort characteristics of the radiation.

Coherent sources of attosecond extreme ultraviolet (XUV) radiation present many challenges if their full potential is to be realized. While many applications benefit from the broadband nature of these sources, it is also desirable to produce narrow band XUV pulses, or to study autoionizing resonances in a manner that is free of the broad ionization background that accompanies above-threshold XUV excitation. Here we demonstrate a method for controlling the coherent XUV free induction decay that results from using attosecond pulses to excite a gas, yielding a fully functional modulator for XUV wavelengths. We use an infrared (IR) control pulse to manipulate both the spatial and spectral phase of the XUV emission, sending the light in a direction of our choosing at a time of our choosing. This allows us to tailor the light using opto-optical modulation, similar to devices available in the IR and visible wavelength regions.

Free-electron lasers (FELs) can produce radiation in the short wavelength range extending from the extreme ultraviolet (XUV) to the X-rays with a few to a few tens of femtoseconds pulse duration. These facilities have enabled significant breakthroughs in the field of atomic, molecular, and optical physics, implementing different schemes based on two-color photoionization mechanisms. In this article, we present the generation of attosecond pulse trains (APTs) at the seeded FEL FERMI using the beating of multiple phase-locked harmonics. We demonstrate the complex attosecond waveform shaping of the generated APTs, exploiting the ability to manipulate independently the amplitudes and the phases of the harmonics. The described generalized attosecond waveform synthesis technique with an arbitrary number of phase-locked harmonics will allow the generation of sub-100 as pulses with programmable electric fields.

Attosecond pulses are fundamental for the investigation of valence and core-electron dynamics on their natural timescale. [3] At present the reproducible generation and characterisation of attosecond waveforms has been demonstrated only through the process of high-order harmonic generation. [4][5][6][7] Several methods for the shaping of attosecond waveforms have been proposed, including metallic filters, 8, 9 multilayer mirrors 10 and manipulation of the driving field. 11 However, none of these approaches allow for the flexible manipulation of the temporal characteristics of the attosecond waveforms, and they suffer from the low conversion efficiency of the high-order harmonic generation process. Free Electron Lasers, on the contrary, deliver femtosecond, extreme ultraviolet and X-ray pulses with energies ranging from tens of µJ to a few mJ. 12, 13 Recent experiments have shown that they can generate sub-fs spikes, but with temporal characteristics that change shot-to-shot. [14][15][16] Here we show the first demonstration of reproducible generation of high energy (µJ level) attosec-

The attosecond streak camera method is usually implemented to characterize the temporal phase and amplitude of isolated attosecond pulses produced by high-order harmonic generation. This approach, however, does not provide any information about the carrier-envelope phase of the attosecond pulses. We demonstrate that the photoelectron spectra generated by an attosecond waveform and an intense synchronized infrared field are sensitive to the electric field of the attosecond pulse. The dependence on the carrier-envelope phase of the attosecond pulse is understood in terms of the coherent superposition of two photoelectron wave packets. This effect suggests an experimentally feasible method for complete reconstruction of attosecond waveforms.

Berry phase and topology of the Bloch wavefunction, originating from the interplay of internal quantum attributes of crystal electrons1, holds great significance in classifying novel quantum phases2,3 and endowing emergent functions4. In quantum materials with broken time-reversal or spatial-inversion symmetry, Bloch electrons in motion necessarily carry a geometric phase, and define the topological states2,3,5 and various quantum and nonlinear Hall effects6,7. Recent advances in light-wave-driven optical harmonic emission enable the observation of the rapid evolution of Bloch electrons on a subcycle time scale 8-13 and empower the harnessing of electron dynamics associated with Berry phase effects14,15. However, the correlation between subcycle electron motion and the accumulation of the quantum phase in geometric aspects of the evolving Bloch waves has not been observed. Here, we demonstrate that the Berry phase can be measured and manipulated in topological surface states using t...

Theoretical calculations of high-harmonic generation (HHG) from commensurate twisted bilayer graphene (tBLG) under intense laser fields are performed. The nonlinear electron dynamics in tBLG is considered by solving the Liouville-von Neumann equation for a single-particle density matrix, which combines the full energy bands and momentum matrix elements within the framework of tight-binding approximation. We show that the pump intensity determines the relative magnitude of two components of the harmonic spectrum parallel and perpendicular to driving polarization. The important dependence of HHG on twisted angles and crystal orientations is also presented. Especially in the absence of the relaxation process, the harmonic emission for twisted angles around 10 °exhibits an evident decrease in efficiency per layer compared to monolayer graphene (MLG), which can be interpreted according to Fermi velocity modification. Our calculation also shows that the relative emission efficiency of different harmonic orders between tBLG and MLG contains redundant information on both the dephasing time and an empirical parameter characterizing the decay of the interlayer electron hopping, thus suggesting an all-optical method for the reconstruction of the two parameters. The reconstruction feasibility is successfully demonstrated by a simple optimization algorithm even if considering the possible experimental uncertainty of both driving pulse parameters and high-harmonic signals. Our results show that HHG spectroscopic characteristics in tBLG might serve as a fingerprint to identify the geometric stacking angle and the electronic interaction between adjacent layers, as well as the strong-field laser induced ultrafast dephasing process.

High-order harmonic generation in solid state materials is viewed as a means of studying strong field nonperturbative physics. Researching ellipticity dependence can help understand the dynamics of electron-hole pairs in the presence of strong laser field. In this work, ellipticity dependence of high harmonic generation in few layer MoS 2 is experimentally investigated with a midinfrared laser centered at 3.9 um. We irradiate monolayer, bilayer and trilayer MoS 2 with intense mid-infrared light to generate non-perturbative harmonics up to 11th order. We find that the normalized yield of each harmonic descends in a form of Gaussian-like profile as increasing the ellipticity of driving pulse. It is astonishing to see that ellipticity dependence of monolayer, bilayer and trilayer MoS 2 follows the same rules. We ascribe this similarity to the same deviation distance of electron-hole pairs in three sets of samples. Meanwhile, the higher the harmonic order is, the more sensitive it is to ellipticity, which shows agreement with gas-phase harmonics. To explain the phenomena, we explore the role of intraband and interband dynamics with multiband semiconductor Bloch equations, which helps to delve deeper into ultrafast and strong-field features of MoS 2 .

The physical origin of the recently reported wavelength scaling law of high harmonics generation (HHG) yield [Tate et al., Phys. Rev. Lett. 98, 013901 (2007); Shiner et al., Phys. Rev. Lett. 103, 073902 (2009)] is not fully understood. We re-investigate theoretically the wavelength (from 800 nm to 2000 nm) scaling of HHG yield in atoms with different soft-core Coulomb potentials. It is found that the power x of the wavelength scaling lambda(x) surprisingly oscillates in the region -3.63 similar to 6.32. A similar oscillation is found in the wavelength scaling of ionization ratio upon the ionization potential, indicating that the wavelength scaling of HHG yield is closely relevant to the ionization. The origin of this oscillation in ionization is also identified.

By optimizing the phase matching condition of high harmonic generation (HHG) from a supersonic neon gas jet, the enhanced HHG in the region of 60-70 eV has been selected. Three-dimensional numerical calculation shows that plasma plays a significant role in the phase matching process of HHG in a supersonic gas jet with short medium length. Due to plasma formation, the harmonic emission decays as the laser intensity reaches over 3.5 × 10 14 W/cm 2 . The plasma induces the broadening and blue shift of the HHG spectra, which provides a method for fine-tuning the harmonic wavelength.

We experimentally investigate the high-order harmonic generation in argon gas cell driven by a multi-cycle broadband infrared laser pulse from a tunable optical-parametric-amplifier (OPA) source. The generation of high-order harmonic continuum with the cut-off photon energy up to 110 eV is observed by tuning the chirp of the 800-nm laser pulse which pumps OPA source. The generation of harmonic continuum is understood in terms of the two-hump structure of the OPA output spectrum and the optimal relative phase of the two humps. The demonstrated scheme is of importance for the generation of extreme ultraviolet (XUV) continuum at higher photon energy region.

We propose a scheme to generate broadband high harmonic supercontinuum and single attosec ond pulse emission in time domain by employing a chirped polarization gating laser field. It is shown that this scheme can significantly extend the high harmonic cutoff to higher energy region, and the produced isolated attosecond pulse is shorter than 100 attoseconds after proper dispersion compensation, when a 7 fs driving laser pulse is used.

We experimentally investigate the high harmonic generation (HHG) from CH 4 molecules and Xe atoms in a two-color field (using the 800nm laser and the tunable laser with the longer wavelength from 1500nm to 1900nm), and observe that the longer wavelength component can destructively suppress the HHG from CH 4 molecules. By controlling the time delay between the two color laser pulses or tuning the laser intensity of the longer wavelength component, the suppressions of the HHG from CH 4 molecules and the enhancements of the HHG from Xe atoms at the same laser condition are observed. The results indicate that the longer wavelength component around the molecular infrared absorption can suppress the molecular HHG process.

We investigate theoretically the high-order harmonic generation in the argon gas cell driven with a 7-fs 800-nm intense laser pulse, by taking into account the phase-matching effect during the propagation process in the gas cell. We demonstrate a successful selection of single quantum path of the returning electrons and therefore the generation of an isolated xuv attosecond pulse in the plateau region of high-order harmonic spectrum, instead of the emission in the form of pulse trains if without optimizing the phase-matching process.

Single-photon ionization of a hydrogen atom irradiated by two time-delayed isolated attosecond pulses is theoretically investigated by numerically solving the fully three-dimensional time-dependent Schrödinger equation. It is demonstrated that the analysis of the angular-resolved electron energy spectrum, showing a complex interference pattern, allows one to completely retrieve the difference between the energy-dependent phases of the electron wave packets generated by the two delayed attosecond pulses. Moreover, it is shown that in the case of a pair of excitation pulses with the same chirp rate, the proposed interferometric technique can be used to measure the difference between the carrier envelope phase values of two attosecond pulses.

The electron-nuclear dynamics of one-dimensional H 2 + molecular high harmonic generation is investigated by numerical integration of the non-Born-Oppenheimer time-dependent Schrödinger equation. It is found that the nuclear motion and electron ionization are more significant for the longer wavelength and the stronger intensity of the driving laser pulse. When the ground-state H 2 + molecule is driven by a short laser pulse (ten optical cycles in the calculations), a strong signature of nuclear motion is seen in the wavelength scaling (800-2000 nm) of harmonic yield, following a λ -(7-8) scaling law at a constant laser intensity. It is attributed to the fast ground-state depletion induced by the strong nuclear motion, when using the long wavelength. Consequently, the wavelength scaling gives an insight into the nuclear dynamics.

We experimentally investigate the wavelength effect on highorder harmonic generation (HHG) in CH 4 molecules and Xe atoms driven by a tunable infrared parametric source, and observe that the molecular HHG around the vibrational resonance is more sensitive to the driver wavelength than HHG from an atomic gas with comparable ionization potential. The results can be attributed to the light nuclear motion induced by the driving laser field, and it becomes possible to control the proton vibration in the molecular HHG by tuning the infrared wavelength of the driving laser.

We theoretically investigate the quantum-path interference during the high harmonic generation in argon and observe the multiquantum-path-interference (MQPI) effect related to the chirp of driving laser pulse. We successfully identify the interference originated from four significantly contributing quantum paths in the interaction of "isolated" atom with the driving laser field. Moreover, the MQPI effect is further demonstrated beyond the single atom response by spatial filtering which is used for angle-selective detection of transmitted light when threedimensional propagation is considered. It implies that the role of high-order electron returning trajectories during high harmonic generation can be observed in the experiment.

The attosecond streak camera method is usually implemented to characterize the temporal phase and amplitude of isolated attosecond pulses produced by high-order harmonic generation. This approach, however, does not provide any information about the carrier-envelope phase of the attosecond pulses. We demonstrate that the photoelectron spectra generated by an attosecond waveform and an intense synchronized infrared field are sensitive to the electric field of the attosecond pulse. The dependence on the carrier-envelope phase of the attosecond pulse is understood in terms of the coherent superposition of two photoelectron wave packets. This effect suggests an experimentally feasible method for complete reconstruction of attosecond waveforms.

The electronic structure of benzene in the presence of a high-intensity high-frequency circularly polarized laser supports a middle-of-the-ring electron localization. Here, the laser polarization coincides with the ring plane of benzene. The high-frequency oscillating electric field creates circular currents centered at each atom with a circle radius equal to the maximum field amplitude of the laser. All six carbons have six such rings. For a maximum field amplitude of 1.42 Å, which is the carbon-carbon bond distance, all six dynamic current circles intersect to create a deep vortex in the middle, which supports a bound state of a pair of electrons. Such states for benzene can be realized in experiments using a circularly polarized XUV-laser in a range of intensities 10 16 -10 17 W/cm 2 and frequencies 16 eV to 22 eV. Electronic dynamics calculations predict a minimal ionization of benzene when the rise-time of the laser pulse is sudden, indicating a possible experimental realization of these states characterized by a large cut-off in the harmonic generation spectra. This stable electronic structure of the light-dressed benzene is doubly-aromatic due to an extra aromaticity from a D 6h symmetric circular distortion of the σ-framework while the π-electrons, with low density in the ring-plane, are least affected.