Electron vortices generation of photoelectron of H_(2)^(+) by counter-rotating circularly polarized attosecond pulses

Molecular-frame photoelectron momentum distributions(MF-PMDs) of an H_(2)^(+) molecule ion in the presence of a pair of counter-rotating circularly polarized attosecond extreme ultraviolet laser pulses is studied by numerically solving the two-dimensional time-dependent Schrodinger equation within the frozen-nuclei approximation. At small time delay, our simulations show that the electron vortex structure is sensitive to the time delay and relative phase between the counterrotating pulses when they are partially overlapped. By adjusting time delay and relative phase, we have the ability to manipulate the MF-PMDs and the appearance of spiral arms. We further show that the internuclear distance can affect the spiral vortices due to its different transition cross sections in the parallel and perpendicular geometries. The lowest-order perturbation theory is employed to interpret these phenomena qualitatively. It is concluded that the internuclear distancedependent transition cross sections and the confinement effect in diatomic molecules are responsible for the variation of vortex structures in the MF-PMDs.

Generating attosecond pulses with controllable polarization from cyclic H_(3)^(2+) molecules by bichromatic circular fields

We investigate the polarization properties of harmonics from the cyclic H_(3)^(2+) molecular ions in tailored bichromatic counter-rotating circularly polarized(BCCP)fields by solving the time-dependent Schrödinger equation.The allowed harmonics and their helicities are associated with the symmetry compatibility of the field-target systems,and large intensity difference between adjacent harmonics with opposite helicities appears in a wide spectral range when the BCCP field is at certain rotation angles.We try to explain the intensity difference by using a recombination model based on the quantum-orbit theory and by analyzing the ionization pathways.Moreover,to synthesize attosecond pulse trains with tunable polarization,the intensity difference is manipulated by introducing a seed XUV field,and by changing the relative amplitude ratio as well as the helicity of BCCP fields.

Generation of quasi-chirp-free isolated attosecond pulses from atoms under the action of orthogonal two-color combined pulse of fundamental frequency and higher intensity second harmonic fields

The intrinsic chirp of high-order harmonic generation is an important factor limiting the production of ultrashort attosecond pulses.Based on numerically solving the time-dependent Schrodinger equation,the generation process of highorder harmonic from the He atom under the action of orthogonal two-color combined pulse of fundamental frequency and higher intensity second harmonic fields is studied.In this paper,we propose to achieve quasi-chirp-free isolated attosecond pulses by superimposing a higher second-harmonic field on the orthogonal direction of the fundamental frequency field.It is found that the high-energy part of its harmonic emission exhibits small chirp characteristics,which can be used to synthesize isolated attosecond pulses.Through the analysis of the wave packets evolution and the classical motion trajectories of the electron,it is demonstrated that the quasi-chirp-free harmonic can be attributed to the simultaneous return of electrons ionized at different times to the parent particle.The influence of the relative phase of the two pulses on the harmonics is further analyzed,and it is observed that this phenomenon is sensitive to the relative phase,but it can still generate isolated attosecond pulses within a certain phase.

Generation of isolated attosecond pulses in bowtie-shaped nanostructure with three-color spatially inhomogeneous fields

We theoretically investigate high-order harmonic generation in a two-color multi-cycle inhomogeneous field combined with a 27th harmonic pulse. By considering a bowtie-shaped gold nanostructure, the spatiotemporal profiles of enhanced plasmonic fields are obtained by solving the Maxwell equation using finite-domain time-difference method. Based on quantum-mechanical and classical models, the effect of 27th harmonic pulse, temporal profile of enhanced plasmonic field and inhomogeneity on supercontinuum generation are analyzed and discussed. As a result, broadband supercontinuum can be generated from our approach with optimized gap size of nanostructure. Moreover, these results are not sensitively dependent on the relative phase in the two-color field.

Extension of high-order harmonics and generation of an isolated attosecond pulse in the chirped laser field

This paper theoretically investigates the high-order harmonic generation cutoff extension using intense few-cycle linearly chirped laser pulses. It shows that the cutoff of the harmonic can be extended remarkably by optimising the chirping parameters. The time-frequency characteristics of high-order harmonics with different chirping parameters are analysed by means of wavelet transform of the dipole acceleration. It also gives out the classical three-step model pictures of electron. By superposing a properly selected range of the harmonic spectrum, it obtains an isolated 65as pulse.

Ionization of atoms by chirped attosecond pulses

We investigate the ionization dynamics of atoms by chirped attosecond pulses using the strong field approximation method. The pulse parameters are carefully chosen in the regime where the strong field approximation method is valid. We analyse the effects of the chirp of attosecond pulses on the energy distributions and the corresponding left-right asymmetry of the ionized electrons. For a single chirped attosecond pulse, the ionized electrons can be redistributed and the left-right asymmetry shows oscillations because of the introduction of the chirp. For time-delayed double attosecond pulses at different intensities with the weaker one chirped, exchanging the order of the two pulses shows a relative shift of the energy spectra, which can be explained by the different effective time delays of different frequency components because of the chirp.

Generation of an isolated sub-30 attosecond pulse in a two-color laser field and a static electric field

We theoretically investigate high-order harmonic generation（HHG） from a helium ion model in a two-color laser field,which is synthesized by a fundamental pulse and its second harmonic pulse.It is shown that a supercontinuum spectrum can be generated in the two-color field.However,the spectral intensity is very low,limiting the application of the generated attosecond（as） pulse.By adding a static electric field to the synthesized two-color field,not only is the ionization yield of electrons contributing to the harmonic emission remarkably increased,but also the quantum paths of the HHG can be significantly modulated.As a result,the extension and enhancement of the supercontinuum spectrum are achieved,producing an intense isolated 26-as pulse with a bandwidth of about 170.5 eV.In particular,we also analyse the influence of the laser parameters on the ultrabroad supercontinuum spectrum and isolated sub-30-as pulse generation.

Isolated sub-30-attosecond pulse generation using a multicycle two-color chirped laser and a static electric field

We present a theoretical investigation of high-order harmonic generation in a chirped two-color laser field, which is synthesized by a 10-fs/800-nm fundamental chirped pulse and a 10-fs/1760-nm subharmonic pulse. It is shown that a supercontinuum can be produced using the multicycle two-color chirped field. However, the supercontinuum reveals a strong modulation structure, which is not good for the generation of an isolated attosecond pulse. By adding a static electric field to the multicycle two-color chirped field, not only the harmonic cutoff is extended remarkably, but also the quantum paths of the high-order harmonic generation （HHG） are modified significantly. As a result, both the extension of the supercontinuum and the selection of a single quantum path are achieved, producing an isolated 23-as pulse with a bandwidth of about 170.6 eV. Furthermore, the influences of the laser intensities on the supercontinuum and isolated attosecond pulse generation are investigated.

Effects of pressure and gas-jet thickness on the generation of attosecond pulse

We investigate how the intensity and duration of an attosecond pulse generated from high-order harmonic generation are affected by the pressure and thickness of the gas jet by taking into account the macroscopic propagation of both fun- damental and harmonic fields. Our simulations show that, limited by the propagation effects, especially the absorption of harmonics, the intensity of an attosecond pulse cannot be improved by just independently increasing the gas pressure or the medium length. On the other hand, due to good phase-matching conditions, the duration of a generated attosecond pulse can be improved by changing the gas pressure.

Harmonic and attosecond pulse enhancement in the presence of noise

In this paper, we theoretically investigate the effect of noise on the photoionization, the generation of the high-order harmonic and the attosecond pulse irradiated from a model He＋ ion. It shows that by properly adding noise fields, such as Gaussian white noise, random light or colored noise, both the ionization probabilities （IPs） and the harmonic yields can be enhanced by several orders of magnitude. Further, by tuning the noise intensity, a stochastic resonance-like curve is observed, showing the existence of an optimal noise in the ionization enhancement process. Finally, by superposing a properly selected harmonic, an intense attosecond pulse with a duration of 67 as is directly generated.

Isolated attosecond pulse generation with few-cycle two-color counter-rotating circularly polarized laser pulses

Most of the schemes for generating isolated attosecond pulses（IAP） are sensitive to the carrier-envelope phase（CEP）of the driving lasers. We propose a scheme for generating IAP using two-color counter-rotating circularly polarized（TCCRCP） laser pulses. The results demonstrate that the dependence of the IAP generation on CEP stability is largely reduced in this scheme. IAP can be generated at most of CEPs. Therefore, the experiment requirements become lower.

Generation of Isolated Attosecond Pulse from Asymmetric Molecular Ions by Introducing Half-Cycle-Like Laser Fields

We propose an efficient method for the generation of an isolated attosecond pulse from the asymmetric molecular ions HeH^2＋ by adding a half-cycle-like field （HCLF） to the fundamental driving laser field. The high-order harmonic generation （HHG） is investigated by numerically sowing the time-dependent Schrodinger equation. By performing the time-frequency distributions and the electronic wave packet probability densities, we find that the optimizing combined field is not only useful for extending the HHG cutoff, but also for simplifying the recombination channels through controlling the electron localization. In addition, by adjusting the intensity of the HCLF, a dominant short quantum path is selected to contribute the HHG spectrum. As a result, a 75-as isolated attosecond pulse is obtained by superposing a proper range of the harmonics.

Generation of Linear Isolated Sub-60 Attosecond Pulses by Combining a Circularly Polarized Pulse with an Elliptically Polarized Pulse

The two-color circularly polarized pulses scheme was proposed to generate isolated attosecond pulses in our previous work [Phys. Rev. A 87 （2013） 043406], while the polarization of the attosecond pulse was not investigated. We show a supplementary explanation of this scheme and present another scheme to generate linear isolated attosecond pulses by combining a circularly polarized pulse with an elliptically polarized pulse. High-order harmonic generation and quantum path control are investigated to compare these two schemes. Both schemes can obtain supercontinuum spectra plateau from about 200eV to 550eV, which belong to the water window region. It is found that the latter scheme can clearly eliminate the short quantum path and extend the harmonic plateau. A linear isolated attosecond pulse with a duration of sub-6Oas can be generated by superposing a bandwidth of 70eV.

Effect of pulse duration on generation of attosecond pulse with coherent wake emission

High-order harmonics and attosecond pulse generation with coherent wake emission are theoretically investigated for the effect of pulse duration and carrier envelope phase(CEP)of few-cycle laser pulse.We find that short pulse duration will cause the negative chirp for the high harmonics.When the laser pulse is shortened to a few cycles,the influence of the laser CEP on the chirp of the harmonics will also become more prominent.

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.

Plasma Approach for Generating Ultra-Intense Single Attosecond Pulse

In our previous work, a plasma approach for single attosecond pulse （AP） generation was proposed. A few-cycle relativistic circularly polarized laser pulse will induce a single drastic oscillation of plasma boundary, from which high-order harmonics and furthermore an ultra-intense single AP can be generated naturally after it is reflected. Analytical model and simulations both demonstrate that the process is mostly efficient as the pulse duration is close to the plasma responding time. The effects of plasma density ramp are analyzed here, suggesting that the proposal is still quite efficient with appropriate density gradient in the ramp. At last, a combined approach is employed to obtain single AP with 30 fs incident laser. The relatively large-duration pulse is firstly shortened by a density dropping thin foil, and then reflected from an overdense plasma target. One-dimensional simulation shows that a 600 as single light pulse is generated with peak intensity of 3×10^20 W/cm^2.

Role of quantum paths in generation of attosecond pulses

We investigate the role of core potential in high ionization potential systems on high harmonic generation (HHG) spectra and obtain attosecond pulses. In our scheme, we use a standard soft core potential to model high ionization potential systems and irradiated these systems with fixed laser parameters. We observe the role of these systems on all the three steps involved in HHG process including ionization, propagation and recombination. In our study, the results illustrate that for high ionization potential systems, the HHG process is more sensitive to the ionization probability compared to the recombination amplitude. We also observe that due to the stronger core potential, small oscillations of the electrons during the propagation do not contribute to the HHG spectrum, which implies the dominance of only long quantum paths in the HHG spectrum. Our results, for attosecond pulse generation, show that long quantum path electrons are responsible for the supercontinuum region near the cutoff, which is suitable for the extraction of a single attosecond pulse in this region.

Effects of initial electronic state on vortex patterns in counter-rotating circularly polarized attosecond pulses

We theoretically investigate the effects of different electronic states as the initial state on the vortex patterns in photoelectron momentum distributions(PMDs)from numerical solutions of the two-dimensional(2D)time-dependent Schrodinger equation(TDSE)of He^(+)with a pair of counter-rotating circularly polarized attosecond pulses.It is found that the number of spiral arms in vortex patterns is equal to the number of the absorbed photons when the initial state is the ground state.However,the number of spiral arms in vortex patterns is always two more than the number of the absorbed photons when the initial state is the excited state.This sensitivity is attributed to the initial electron density distribution.In addition,we have demonstrated the PMDs for different initial electronic states with the same wavelengths and analyzed their corresponding physical mechanisms.It is illustrated that the method presented can be employed to effectively control the distribution of the electron vortices.

Single-pinhole diffraction of few-cycle isolated attosecond pulses with a two-color field

The spatio-temporal characterization of an isolated attosecond pulse is investigated theoretically in a two-color field. Our results show that a few-cycle isolated attosecond pulse With the center wavelength of 16 nm can be generated effectively by adding a weak controlling field. Using the split and delay units, the isolated attosecond pulse can be split to the two same ones, and then single-pinhole diffractive patterns of the two pulses with different delays can be achieved. The diffractive patterns depend severely on the periods of the attosecond pulses, which can be helpful to obtain temporal information of the coherent sources.

Generation of a single attosecond pulse from an overdense plasma surface driven by a laser pulse with time-dependent polarization

The influence of time-dependent polarization on attosecond pulse generation from an overdense plasma surface driven by laser pulse is discussed analytically and numerically. The results show that the frequency of controlling pulse controls the number and interval of the generated attosecond pulse, that the generation moment of the attosecond pulse is dominated by the phase difference between the controlling and driving pulses, and that the amplitude of the controlling pulse affects the intensity of the attosecond pulse. Using the method of time-dependent polarization, a ＂single＂ ultra-strong attosecond pulse with duration T ≈ 8.6 as and intensity I≈ 3.08 × 10^20 W.cm-2 can be generated.