Efficient High-order Harmonic Generation Research Articles

Strain effect on the orientation-dependent harmonic spectrum of monolayer aluminum nitride

In this study, we theoretically investigate the strain effect on the orientation-dependent high-order harmonic generation (HHG) of monolayer aluminum nitride (AlN) by solving the multiband semiconductor Bloch equations in strong laser fields. Our simulations denote that the efficiency of the orientation-dependent HHG is considerably enhanced when a 15% biaxial tensile strain is applied to AlN, which is attributed to the downshifting energy level of the conduction band. Furthermore, the odd-even feature in the orientation-dependent high harmonic spectra owing to the strain is considerably different when compared with that in the case without strain. The enhanced quantum interference between different energy bands in strained AlN around the Γ-M direction is responsible for the observed odd-even distributions of the orientation-dependent HHG. This study helps to better understand the HHG in solids by tuning their electronic structures.

High-order harmonic generation using quasi-phase matching and two-color pump in the plasmas containing molecular and alloyed metal sulfide quantum dots

As high-order harmonic emitters, quantum dots are produced through laser-induced plasmas. Subsequently, we generate high-order harmonics with 800-nm and 30-fs pulses from laser-produced plasmas containing quantum dots of different metal sulfides (Ag2S, CdS, and Cd0.5Zn0.5S). The high-order harmonic generation is analyzed using different approaches, including two-color (800 nm + 400 nm) pump, application of alloyed quantum dots, and quasiphase matching of interacting waves. We discuss the self-phase modulation induced splitting of harmonics, the difference in the application of thick and thin crystals for second harmonic (400 nm) emission during two-color pumping of the quantum dot plasma, the spatial modulation of the quantum dot plasma for quasiphase matching, and the comparison of harmonic yields from monomer and quantum dot plasmas. This study allows us to determine the mechanisms of coherent extreme ultraviolet radiation generation using a few nanometer-sized emitters as well as optimal methods for further enhancing the high-order harmonic generation efficiency.

Aluminum nanoparticle plasma formation for high-order harmonic generation

We demonstrate the efficient high-order harmonic generation (HHG) of 35 fs pulses from the nanoparticle (NP)–containing plasmas produced during laser ablation of aluminum (Al) target using picosecond and nanosecond pulses. The role of NPs in the enhancement of harmonic yield is discussed. To achieve the maximal HHG yield, we use different experimental schemes, including two-color pump, HHG using extended and multi-jet laser-produced plasmas, ablation of rotating target and temporal variation between the heating and driving pulses. A fivefold increase of harmonic yield from Al NP-containing plasmas compared to the plasmas containing only Al atoms and ions is obtained. The harmonics up to the 35th order are generated from the Al NP-containing plasmas. HHG calculations show that this cutoff is attributed to Al neutral atoms rather than Al ions. To interpret the experimental results, we also study the fundamental mechanism of NP formation. The simulations are carried out for different Al NP-containing ablation plumes. Our calculations and plasma debris analysis show the presence of NPs in the plasmas exposed to the driving 35 fs pulses.

Wavelength scaling laws for high-order harmonic yield from atoms driven by mid- and long-wave infrared laser fields

High-order harmonic generation (HHG) in gases is known to benefit from using mid-infrared driving laser fields, since, due to a favorable wavelength scaling of the electron ponderomotive energy, higher-energy photon production becomes feasible with longer-wavelength drivers. On the other hand, recent studies have revealed a number of physical effects whose importance for HHG increases with increasing laser wavelength. These effects, as a rule, result not only in a general decrease of the harmonic yield but also in a reshaping of the emission spectrum. Therefore, detailed study of the dependence of HHG yield on the laser wavelength has become an important issue for producing intense extremely short extreme ultraviolet (XUV) and x-ray pulses using HHG driven by long-wavelength laser fields. Here we address this issue by calculating the HHG spectra for laser wavelengths ranging from 2 to 20 µm. This study has been carried out in a frame of strong-field approximation modified properly to take into account the effect of the magnetic field of a laser pulse on the dynamics of the field-ionized electron and the atomic bound-state depletion. We show that different regions of the HHG spectrum behave differently with the laser wavelength and discuss the origins of this behavior. In particular, we show that in a weak ionization regime, the dipole-approximation scaling law for the harmonic yield, which is calculated as the integral over the spectral interval of fixed width and relative position with respect to the cutoff energy, obeys the power law, where the absolute value of the exponent is an integer equal to $\mu = {7}$μ=7 for the cutoff and $\mu = {8}$μ=8 for the plateau harmonics. Above a certain critical wavelength, due to the nondipole effects, the efficiency of HHG decreases more strongly than according to a power law, and this decrease is different for different regions of the spectrum. The analytical formulas are derived that match well the calculated wavelength scalings.

Dependence of solid-HHG on relative potential energy of occupied sites

The role of relative potential energy of occupied sites in high-order harmonic generation from solid states is investigated. It is found that the conversion efficiency of high-order harmonic spectrum can be enhanced by tuning the relative potential energy of neighboring occupied sites in one-dimensional model. This phenomenon can be attributed to the changing of energy bands. A two-dimensional Kronig–Penney potential is applied to model the salt–rock structure. Similar phenomenon as in the one-dimensional case is also found. Our results provide a potential method to enhance the efficiency of high-order harmonic generation from solids.

Intense X-ray isolated attosecond pulse generation by using low-intensity chirped pulse combined with a UV seeding pulse

We theoretically investigate intense isolated attosecond pulse (IAP) generation from high-order harmonic generation (HHG) driven by a low-intensity chirped pulse combined with a UV seeding pulse. The results show that, driven by a two-color chirped pulse, the harmonic cutoff can be remarkably extended and a spectral continuum in X-ray region can be obtained. Moreover, as the pulse duration increases or the delay time of the two pulses changes, a larger harmonic cutoff can be found. Further, with the introduction of a UV seeding pulse, the efficiency of HHG can be enhanced by three orders of magnitudes due to the UV resonance ionization. Moreover, as the UV pulse intensity increases, the enhanced ratio of HHG yield can be further improved. The enhancement of HHG yield is related to the pulse duration and delay time of the UV pulse. For instance, when adding a shorter duration UV pulse, the enhancement of HHG is dependent on the delay time of the UV pulse. However, when adding a longer duration UV pulse, the HHG enhancement is not very sensitive to the delay time of the UV pulse. Finally, the obtained spectral continuum supports the generation of intense IAP with the duration of 36 as.

Effect of plasma-core-induced self-guiding on phase matching of high-order harmonic generation in gases

In this work, we numerically study a self-guiding process in which ionization plays a dominant role and analyze its effect on high-order harmonic generation (HHG) in gases. Although this type of self-guiding—termed “plasma-core-induced self-guiding” in previous works—limits the achievable cutoff by regulating the intensity of the laser beam, it provides favorable conditions for phase matching, which is indispensable for high-flux-gas high-harmonic sources. To underline the role of self-guiding in efficient HHG, we investigate the time-dependent phase-matching conditions in the guided beam and show how the spatiotemporally constant fundamental intensity contributes to the constructive buildup of the harmonic field in a broad photon energy range up to the provided cutoff.

Experimental Evidence of Sensitivity of the High Harmonic Generation to Hydrogen Bonding.

The influence of hydrogen bonding and the associated attosecond hole delocalization on the high-order harmonic generation (HHG) process is investigated with the help of hydrogen-bonded binary mixture of acetonitrile and chloroform solvent vapors. We observe a strong enhancement of the HH yield compared to the results obtained with pure samples. We propose that the observed increase of HHG efficiency is due to the presence of hydrogen-bonded binary mixture. Numerical simulations show evidence of the attosecond hole delocalization in the hydrogen-bonded complex of acetonitrile and chloroform. This attosecond hole delocalization contributes to the enhancement of the harmonic yield in the hydrogen-bonded complex. To the best of our knowledge, this is the first report on the sensitivity of the high harmonic generation process to the hydrogen bonding.

Waveform control in generations of intense water window attosecond pulses via multi-color combined field

The waveform control in the improvements of high-order harmonic generation (HHG) spectra and attosecond pulse signals driven by the two-color and three-color combined fields has been theoretically investigated. (a) The results show that by properly controlling the [Formula: see text]–2[Formula: see text] two-color laser beam (including the modulations of chirps, carrier envelope phases and delay time), either the harmonic cutoff can be extended, showing a water window spectral continuum, or the selective enhancement of the single-order and two-order harmonics can be found. Further, with the introduction of a third controlling field, the efficiency of spectral continuum can be enhanced by two orders of magnitude compared with that from the two-color field. Moreover, the enhancement of HHG is not very sensitive to the frequency of the third field (i.e., the frequency of the third field is chosen to be 3[Formula: see text], 4[Formula: see text] and 6[Formula: see text]). Thus, some water window attosecond pulses with the durations of 60 as can be obtained. (b) Furthermore, the harmonic cutoff can be further extended when using a half-cycle controlling pulse or introducing the inhomogeneous effect of the laser field. Moreover, the efficiency of HHG can be further improved when the initial state is prepared as the superposition state of the ground state and some excited state of He atom. Consequently, a much broader spectral continuum with an intensity enhancement of another two orders of magnitude can be found. Finally, through the Fourier transformation of some spectral continuum, the intense water window attosecond pulses with the durations of 60 as can be produced.

Low- and high-order nonlinear optical properties of Ag2S quantum dot thin films

Abstract Thin films containing small-sized quantum dots (QDs) and nanoparticles have shown strong optical nonlinearities caused by the confinement effect. Here, we report the study of third-order optical nonlinearities of silver sulfide (Ag2S) QD thin films using 800 and 400 nm, 30 fs pulses. The absorption spectrometry and transmission electron microscopy are used to characterize the synthesized 80 and 500 nm Ag2S QD films. The giant enhancement of nonlinearities is observed up to three to six orders of magnitude larger compared to those for the bulk and liquid Ag2S samples. We also demonstrate the efficient high-order harmonic generation in the plasmas produced during ablation of the Ag2S QD thin films. The analysis of the dynamics of the QD-containing plasma spreading allowed optimization of the delay between the heating and the driving pulses for an enhancement of harmonics conversion efficiency.

Significantly enhanced conversion efficiency of high-order harmonic generation by introducing chirped laser pulses into scheme of spatially inhomogeneous field.

An effective scheme to enhance the yield of high-order harmonic generation originated from spatially inhomogeneous field through the interaction between few-cycle chirped laser pulses and a nano-tip structure is demonstrated. The conversion efficiency of harmonics from chirped laser pulses was significantly improved by nearly three more orders of magnitude than that of chirp-free pulses, and the cutoff energy of the corresponding harmonics was dramatically enhanced. By superimposing a series of properly selected orders of harmonics, isolated attosecond pulses of high intensity can be obtained. Furthermore, we compared the effects of different types of chirps on harmonics.

Generation of water window single attosecond pulse from multi-cycle mid-infrared laser field with chirp gating modulation

A potential scheme to produce the water window single attosecond pulses (SAPs) from the multi-cycle mid-infrared (MIR) laser field has been investigated with the help of the chirp gating modulation. It is found that with the introduction of the laser chirp (i.e. up-chirp or down-chirp modulation), the extension of the harmonic cutoff can be achieved and the single harmonic radiation peak (HRP) can be selected during the harmonic emission process. Moreover, the chirp gating modulation on the high-order harmonic generation (HHG) is sensitive to the few-cycle pulse duration, but it is not very sensitive to the multi-cycle pulse duration. Moreover, a larger extension of the harmonic cutoff covering the whole water window region can be found with the help of the multi-cycle down-chirp modulation. Further, by properly choosing the coherent superposition of the ground state and the high Rydberg state as the initial state, the efficiency of HHG can be enhanced by 5 orders of magnitude. Finally, a series of high-intensity sub-40as pulses covering the water window region can be obtained.

Improvement of High-Order Harmonic Generation Via Controlling Multiple Acceleration–Recombination Process

Abstract The multiple acceleration–recombination process in high-order harmonic generation (HHG) has been investigated and discussed. Generally, the HHG can be explained through the ionization–acceleration–recombination process in each half-cycle waveform of the laser field. In this article, through the waveform control via the two-colour frequency-chirping laser field, the multiple acceleration–recombination process of the free electron in a specific “W” waveform structure can be found, which will lead to the larger emitted photon energies. Moreover, with the optimization of this “W” waveform by changing the frequency chirps, the carrier envelope phases, and the delay time, not only the efficiency of HHG can be enhanced compared with that from the original chirp-free pulse, but also the larger harmonic cutoff can be obtained. Further, with the assistance of the unipolar pulses, the cutoff and the efficiency of HHG can be further improved, showing a water window spectral continuum with the intensity enhancement of 66 times. As a result, by properly superposing some selected harmonics on the spectral continuum, three intense 38-as pulses in the water window region can be obtained.

Generation of high-intensity single attosecond x-ray pulses with multi-laser beam superposition

The generation of high-intensity single attosecond x-ray pulses from high-order harmonic generation (HHG) has been investigated via superposition of multi-laser beams. The results can be separated into three parts: (i) single-color chirp modulation; (ii) ultraviolet (UV)-chirp two-color modulation; and (iii) multi-laser beam modulation. Firstly, for the single chirp modulation, with the introduction of the up-chirp, although the harmonic cutoff can be slightly extended, the efficiency of the HHG is reduced. With the introduction of the down-chirp, both the cutoff and the efficiency of the HHG can be improved compared with the up-chirp. Moreover, as the pulse duration increases, a larger harmonic cutoff can be found. Secondly, by appropriate addition of a UV pump pulse, the efficiency of HHG can be further enhanced due to UV-resonance-enhancement-ionization. Thirdly, with the assistance of the third controlling pulse or the inhomogeneous effect of the laser field, the harmonic cutoff can be further extended and keV-HHG can be produced. Finally, through Fourier transformation of some selected harmonics on the spectral continuum, high-intensity x-ray pulses (including the keV region) with durations of sub-90 as can be obtained.

Enhanced high-order harmonic generation in donor-doped band-gap materials

We find that a donor-doped band-gap material can enhance the overall high-order harmonic generation (HHG) efficiency by several orders of magnitude, compared with undoped and acceptor-doped materials. This significant enhancement, predicted by time-dependent density functional theory simulations, originates from the highest-occupied impurity state which has an isolated energy located within the band gap. The impurity-state HHG is rationalized by a three-step model, taking into account that the impurity-state electron tunnels into the conduction band and then moves according to its band structure until recombination. In addition to the improvement of the HHG efficiency, the donor-type doping results in a harmonic cutoff different from that in the undoped and acceptor-doped cases, explained by semiclassical analysis for the impurity-state HHG.

Application of optimized waveforms for enhancing high-harmonic yields in a three-color laser-field synthesizer.

We apply the optimization method suggested by Jin et al. [Nat. Commun.5, 4003 (2014)24873949] to a three-color laser-field synthesizer in a recent experiment by Burger et al. [Opt. Express25(25), 31130 (2017)29245790] for efficient high-order harmonic generation (HHG). With the experimental laser parameters being precisely tuned according to those returned by the genetic optimization, the three-color waveform composed by a 790-nm laser with its second and third harmonic fields, can enhance the macroscopic HHG yields by one to two orders with only 80% pulse energy compared to the fundamental single-color field. We check that this enhancement can be realized for He or Ne gas at both low and high gas pressures. The optimized waveform enables the short-trajectory emissions dominant to facilitate the buildup of the harmonic field, which is revealed by analyzing the behaviors of electron trajectories and the time-frequency pictures of the single-atom and macroscopic HHG. We also optimize the two-color waveform consisting of the fundamental laser and its third harmonic field for the flexible choice in the experiment. This study provides with a practical route to implement the optimization technique in the experiment for the high-flux harmonic generation from the extreme ultraviolet to the X-rays.

Quasi-phase matching of harmonics generating in laser plasmas: experiment and theory

We compare the results of experimental and theoretical studies of the quasi-phase matching (QPM) of high-order harmonic generation (HHG) during propagation of two-color femtosecond pulses through the indium multi-jet plasmas. The role of number of coherent zones and size of plasma jets on the HHG efficiency at QPM conditions is analysed. We demonstrate the enhancement of the HHG efficiency due to QPM during laser-plasma interaction.

Effective high-order harmonic generation from metal sulfide quantum dots.

In the past, common media for high-order harmonic generation (HHG) has been atoms and molecules. More recently, clusters, and nanoparticles have been introduced as HHG emitting media. Multi-particle media can enhance HHG yields but have more stringent requirements in determining the optimal parameters. Here, we demonstrate, for the first time, the effective application of 1-3 nm metal sulfide quantum dots (QDs) for harmonic generation in the 20 - 115 nm extreme ultraviolet range. We report on the syntheses, ablation of Ag2S, CdS, and ZnS QDs, and HHG from laser-produced plasmas by using single- and two-color pumps. We compare HHG efficiency from the ablated QDs to that of bulk metal sulfides and show a seven-fold increase in harmonic yields. Further, the study also allows us to understand the effects of QD-contained plasma spreading dynamics on HHG yield.

Towards GW-Scale Isolated Attosecond Pulse Far beyond Carbon K-Edge Driven by Mid-Infrared Waveform Synthesizer

We discuss the efficient generation of intense “water window” (0.28–0.54 keV) isolated attosecond pulses (IAPs) using a mid-infrared (MIR) waveform synthesizer. Our numerical simulations clearly indicate that not only a longer-wavelength driving laser but also a weak control pulse in the waveform synthesizer helps extend the continuum cutoff region and reduce the temporal chirp of IAPs in high-order harmonic generation (HHG). This insight indicates that a single-cycle laser field is not an optimum waveform for generating the shortest IAP from the veiwpoints of reducing the attochirp and increasing the efficiency of HHG. By combining a waveform synthesizer technology and a 100 mJ MIR femtosecond pulse based on a dual-chirped optical parametric amplification (DC-OPA) method, a gigawatt-scale IAP (55 as with 10 nJ order) in the water window region can be generated even without attochirp compensation. The MIR waveform synthesizer is highly beneficial for generating a shorter IAP duration in the soft X-ray region because there are no suitable transparent dispersive materials that can be used for compressing the attochirp.

Efficiency control of high-order harmonic generation in gases using driving pulse spectral features

The low conversion efficiency of high-order harmonic generation (HHG) in gases is an insurmountable limitation for many applications, where a considerable photon flux is an instrumental prerequisite. We present a study of the HHG conversion efficiency dependence on the driving laser intensity and analyze the conditions for optimal phase-matching in a loose focusing configuration and long generation medium using a Ti:Sapphire laser. Moreover, by determination of the influence of plasma effects on the driving laser pulse, we observe a correlation between the HHG conversion efficiency and the blueshift of the fundamental pulse. The maximal HHG conversion efficiency is achieved just before the driving laser spectrum is considerably affected by the plasma. Similar behavior is observed in HHG for different noble gases. In this respect, the appearance of a plasma-induced spectral shift in the driving laser might serve as an indication of a substantial loss of HHG conversion efficiency. Consequently, our findings can be exploited to obtain essential information about the laser-plasma interaction process during HHG and can pave the way for a more convenient control of optimal HHG conditions.