Nonsequential Double Ionization Of Ar Atoms By Counter-rotating Two-color Elliptically Polarized Laser Fields

Nonsequential double ionization(NSDI)is a basic physical process of the interactions of strong laser field with matter.The two electrons involved in NSDI are highly correlated,which provides a simple and effective method for understanding the electron correlation.In the past three decades,the ionization mechanism of NSDI has been studied extensively.Based on the two-hump structure of ion momentum distributions and the disappearance of the "knee" structure in the circularly polarized laser fields,the recollision model has become a very suitable ionization mechanism.The mechanism is divided into three steps.Step 1: An electron in the atom or molecule is ionized in the laser field;Step 2: The ionized electron is accelerated in the laser field.When the direction of the laser field changes,the ionized electron may be pulled back and recollide with the parent ion;Step 3: After recollision,the returning electron can transfer a part of energy to the bound electron,and finally both electrons ionize immediately or with a time delay.In linearly polarized pulses,electrons are driven by electric field force only in one direction.The returning probability is relatively high and thus results in a high double ionization yield.Therefore,early studies mainly focus on linear polarization.In this case the control of electron dynamics is confined to one dimension.In order to manipulate electrons in two-dimensional space,recently much attention has been focused on the combined electric field composed of two pulses,such as the counter-rotating two-color circularly polarized(CTCP)laser fields.By changing laser parameters,the CTCP fields can control double ionization yield,electron returning direction and returning energy.However,the waveform of the combined electric field formed by the two-color circularly polarized pulses has multiple-fold symmetry,and the ionized electrons can return from multiple directions.If two elliptically polarized pulses are used to form a combined electric field,the multiple-fold symmetry of the electric field waveform can be broken,and the electron dynamics of the single-direction return event can be studied.In this paper,we study NSDI of argon atoms in the counter-rotating twocolor elliptically polarized(CTEP)laser fields by using the full classical ensemble model.The effects of the relative phase,intensities and ellipticities of two pulses on the electron dynamics and nonsequential double ionization are systematically studied.Firstly,we fixed the intensity and ellipticity of two pluses to study the dependence of NSDI on the relative phase of the two pulses.The results show that NSDI probability oscillates periodically with the increase of relative phase,and the oscillation period is0.5π.The two electrons show correlation behavior at 0.125π and 0.25π,and anticorrelation at 0.375π and 0.5π.Tracking the trajectories of two electrons,it is found that recollision time and electron returning angle can be well controlled by changing relative phase.The electron returning angle decreases with the increase of the relative phase of two pulses.Subsequently,we study the effect of the laser intensity on NSDI in CTEP fields.The intensity-dependent NSDI probability curve shows a knee structure,which is consistent with the linear polarization case.With the laser intensity increasing,the dominant correlation behavior evolves from correlation to anti-correlation and finally reverts back to correlation.The back analysis of NSDI trajectories shows that the single ionization in NSDI events mainly occurs in lobe 1 and lobe 3.the NSDI events triggered off by single ionization from different lobes are separately discussed.With the increase of laser intensity,the correlation behavior of NSDI events triggered off by single ionization from field lobe 1 evolves from anti-correlation behavior to correlation behavior,but the correlation behavior of NSDI events induced by single ionization from field lobe3 evolves from correlation behavior to anti-correlation behavior.With the laser intensity increasing,the NSDI events induced by single ionization from field lobe 1 increase gradually,but those from field lobe 3 decrease.This results in that the total dominant correlation behavior evolves from correlation to anti-correlation and finally reverts back to correlation as the laser intensity increases.Finally,the effect of the ellipticity on NSDI is studied.It is found that NSDI probability increases with the ellipticity of 800-nm pulse and decreases with the ellipticity of 1600-nm pulse.It is because that the electron returning probability and recollision energy increase with the increase of the ellipticity of the 800-nm pulse,and decrease with the increase of the ellipticity of 1600-nm pulse.Moreover,when the ellipticity of the 1600-nm pulse is 0.3,with the ellipticity of the 1600-nm pulse increasing the ion momentum distribution moves from the left to the right.As the ellipticities of 1600-nm and 800-nm pulses increase,the ion momentum distribution gradually expands in y direction and finally forms a two-layer structure distributed on both sides of the x axis.These results provide a deeper insight into electron correlations and electron ultrafast dynamics in strong-field NSDI.It is also very valuable for highorder harmonic generation,molecular orbital imaging and high-order above-threshold ionization,which are also dependent on rellision process.