Competition between multiphoton/tunnel ionization and filamentation induced by powerful femtosecond laser pulses in air

In this work we present experiments by focusing 42 femtosecond laser pulses in air using three differentfocal length lenses: f=100, 30 and 5 cm. For the longest focal length, only the filament, which is aweak plasma column,is observed. When the shorter focal length lens is used, a high density plasma isgenerated near the geometrical focus and coexists with a weak plasma channel of the filamemt. Under thetightest focusing condition, filamentation is prevented and only a strong plasma volume appears at tehgeometrical focus.

Theoretical approach to the study of vibrational effects on strong field ionization of molecules with alignment-dependent tunneling ionization rates

The tunneling ionization rates of vibrationally excited N2 molecules at the ground electronic state are calculated using molecular orbital Ammosov–Delone–Krainov theory considering R-dependence. The results show that molecular alignment significantly affects the ionization rate, as the rate is mainly determined by the electron density distribution of the highest occupied molecular orbital. The present work indicates that the ratios of alignment-dependent rates of different vibrational levels to that of the vibrational ground level increase for the aligned N2 at the angle θ = 0？, and suggests that the alignment-dependent tunneling ionization rates can be used as a diagnostics for the influence of vibrational excitation on the strong field ionization of molecules.

Calculation of the Duration of the Atomic Tunneling Ionization in a Strong Electrostatic Field by Using Bohmian Trajectories Approach

The duration of a bound electron tunneling through the barrier formed by atomic potential and electrostatic field is calculated by the Bohmian trajectories scheme. The time of the tunneling ionization decreases with the increase of the amplitude of the electrostatic field. By using the information about the position, velocity and force of the Bohmian trajectories, the dynamical process of tunneling through the barrier is investigated.

Simple formula for the ionization rate of diatomic molecules in an intense laser field using the velocity gauge

We derive a general ionization rate formula for the system of diatomic molecules in the velocity gauge. A more concise expression of the photoionization rate in the tunnel region is obtained for the first time. Comparisons are made among the different versions of strong-field approximation. The numerical study shows that the ionization rate in the velocity gauge is underestimated by a few orders compared with that in the length gauge. Our simple formula of ionization rate may provide an insight into the ionization mechanism for the system of diatomic molecules.

Modulation of ionization on laser frequency in ultra-short pulse intense laser-gas-target

Based on the dispersion relation of intense laser pulse propagating in gradually ionized plasma, this paper discusses the frequency modulation induced by ionization of an ultra-short intense laser pulse interacting with a gas target. The relationship between the frequency modulation and the ionization rate, the plasmas frequency variation, and the polarization of atoms （ions） is analysed. The numerical results indicate that, at high frequency, the polarization of atoms （ions） plays a more important role than plasma frequency variation in modulating the laser frequency, and the laser frequency variation is different at different positions of the laser pulse.

Classical trajectory Monte Carlo investigation for Lorentz ionization of H (1s)

Lorentz ionization of H（1s） is investigated by classical trajectory Monte Carlo （CTMC） simulation. The effect of the transverse magnetic field on the considered process is analyzed in terms of the time evolution of interactions in the system, total electron energy, and electron trajectories. A classical mechanism for the ionization is found, where the variation of the kinetic energy of the nuclei is found to be important in the process. Compared with the results of tunneling ionization, the classical mechanism becomes more and more important with the increase of the velocity of the H-atom or the strength of the magnetic field.

Photoelectron angular distributions of H ionization in low energy regime:Comparison between different potentials

We theoretically investigate the low energy part of the photoelectron spectra in the tunneling ionization regime by numerically solving the time-dependent Schrdinger equation for different atomic potentials at various wavelengths.We find that the shift of the first above-threshold ionization（ATI） peak is closely related to the interferences between electron wave packets,which are controlled by the laser field and largely independent of the potential.By gradually changing the short-range potential to the long-range Coulomb potential,we show that the long-range potential＇s effect is mainly to focus the electrons along the laser＇s polarization and to generate the spider structure by enhancing the rescattering process with the parent ion.In addition,we find that the intermediate transitions and the Rydberg states have important influences on the number and the shape of the lobes near the threshold.

Dynamics simulation on the interaction of intense laser pulses with atomic clusters

Under classical particle dynamics, the interaction process between intense femtosecond laser pulses and icosahedral noble-gas atomic clusters was studied. Our calculated results show that ionization proceeds mainly through tunnel ionization in the combined field from ions, electrons and laser, rather than the electron-impact ionization. With increasing cluster size, the average and maximum kinetic energy of the product ion increases. According to our calculation, the expansion process of the clusters after laser irradiation is dominated by Coulomb explosion and the expansion scale increases with increasing cluster size. The dependence of average kinetic energy and average charge state of the product ions on laser wavelength is also presented and discussed. The dependence of average kinetic energy on the number of atoms inside the cluster was studied and compared with the experimental data. Our results agree with the experimental results reasonably well.

Resolving and weighing the quantum orbits in strong-field tunneling ionization

Tunneling ionization of atoms and molecules induced by intense laser pulses contains the contributions of numerous quantum orbits.Identifying the contributions of these orbits is crucial for exploring the application of tunneling and for understanding various tunneling-triggered strong-field phenomena.We perform a combined experimental and theoretical study to identify the relative contributions of the quantum orbits corresponding to the electrons tunneling ionized during the adjacent rising and falling quarter cycles of the electric field of the laser pulse.In our scheme,a perturbative second-harmonic field is added to the fundamental driving field.By analyzing the relative phase dependence of the signal in the photoelectron momentum distribution,the relative contributions of these two orbits are unambiguously determined.Our results show that their relative contributions sensitively depend on the longitudinal momentum and modulate with the transverse momentum of the photoelectron,which is attributed to the interference of the electron wave packets of the long orbit.The relative contributions of these orbits resolved here are important for the application of strong-field tunneling ionization as a photoelectron spectroscopy for attosecond time-resolved measurements.

Probing the launching position of the electron wave packet in molecule strong-field tunneling ionization

Strong-field tunneling ionization is the first step for a broad class of phenomena in intense laser-atom/molecule interactions. Accurate information about the electron wave packet from strong-field tunneling ionization of atoms and molecules is of essential importance for understanding various tunneling ionization triggered processes. Here, we survey the property of the electron wave packet in tunneling ionization of molecules with a method based on strong-field photoelectron holography. By solving the time-dependent Schr ¨odinger equation, it is shown that the holographic interference in the photoelectron momentum distribution exhibits the asymmetric behavior with respect to the laser polarization direction, when the molecule is aligned with a nonzero angle to the linearly polarized laser field. We demonstrate that this asymmetry is due to the nonzero initial transverse displacement of the electron wave packet at tunneling. By analyzing the holographic interference, this transverse displacement for the launching of electron wave packet tunneling from the molecules is accurately retrieved. This displacement is directly related to the electron density distribution in molecules, and thus our work developed a novel concept for probing electronic structure in molecules.

Investigation of Angular Dependence of Strong-Field Tunneling Ionization for Asymmetric Diatomic Molecule HeH^(2+)

We determine the structure parameters for the asymmetric heteronuclear diatomic molecule HeH2＋ at several internuclear distances with the molecular wavefunctions obtained by solving the time-independent Schr6dinger equation with B-spline basis. Then the angular dependence of strong-field ionization rates of HeH2＋ are investigated with the molecular tunneling ionization theory. We show that the shape of several lowly excited states （i.e. 2pσ, 2pπ, 3dσ） for HeH2＋ are reflected in the orientation dependent ionization rates very well, however, the angle-dependent ionization rate fails to follow the angular distribution of the asymptotic electron density for the ground state lsσ. We also show that the internuclear distance dependent ionization probabilities are in a good agreement with the more accurate result obtained from the numerical solution of the time-dependent Schr6dinger equation.

High-order harmonic generation of CO_2 with different vibrational modes in an intense laser field

We apply the strong-field Lewenstein model to demonstrate the high-order harmonic generation of CO2 with three vibrational modes（balance vibration,bending vibration,and stretching vibration） driven by an intense laser field.The results show that the intensity of harmonic spectra is sensitive to molecular vibrational modes,and the high harmonic efficiency with stretching vibrational mode is the strongest.The underlying physical mechanism of the harmonic emission can be well explained by the corresponding ionization yield and the time-frequency analysis.Finally,we demonstrate the attosecond pulse generation with different vibrational modes and an isolated attosecond pulse with a duration of about 112 as is generated.

Accurate electron beam phase-space theory for ionization-injection schemes driven by laser pulses

After the introduction of the ionization-injection scheme in laser wake field acceleration and of related high-quality electron beam generation methods,such as two-color and resonant multi-pulse ionization injection(Re MPI),the theory of thermal emittance has been used to predict the beam normalized emittance obtainable with those schemes.We recast and extend such a theory,including both higher order terms in the polynomial laser field expansion and non-polynomial corrections due to the onset of saturation effects on a single cycle.Also,a very accurate model for predicting the cycle-averaged distribution of the extracted electrons,including saturation and multi-process events,is proposed and tested.We show that our theory is very accurate for the selected processes of Kr^(8+→10+) and Ar^(8+→10+),resulting in a maximum error below 1%,even in a deep-saturation regime.The accurate prediction of the beam phase-space can be implemented,for example,in laser-envelope or hybrid particle-in-cell(PIC)/fiuid codes,to correctly mimic the cycle-averaged momentum distribution without the need for resolving the intra-cycle dynamics.We introduce further spatial averaging,obtaining expressions for the whole-beam emittance fitting with simulations in a saturated regime,too.Finally,a PIC simulation for a laser wakefield acceleration injector in the Re MPI configuration is discussed.

Rydberg state excitation in molecules manipulated by bicircular two-color laser pulses

Multiphoton resonant excitation and frustrated tunneling ionization,manifesting the photonic and optical nature of the driving light via direct excitation and electron recapture,respectively,are complementary mechanisms to access Rydberg state excitation(RSE)of atoms and molecules in an intense laser field.However,clear identification and manipulation of their individual contributions in the light-induced RSE process remain experimentally challenging.Here,we bridge this gap by exploring the dissociative and nondissociative RSE of H2 molecules using bicircular two-color laser pulses.Depending on the relative field strength and polarization helicity of the two colors,the RSE probability can be boosted by more than one order of magnitude by exploiting the laser waveform-dependent field effect.The role of the photon effect is readily strengthened with increasing relative strength of the second-harmonic field of the two colors regardless of the polarization helicity.As compared to the nondissociative RSE forming H2
,the field effect in producing the dissociative RSE channel of eHt;H
T is moderately suppressed,which is primarily accessed via a three-step sequential process separated by molecular bond stretching.Our work paves the way toward a comprehensive understanding of the interplay of the underlying field and photon effects in the strong-field RSE process,as well as facilitating the generation of Rydberg states optimized with tailored characteristics.