Extracting the phase distribution of the electron wave packet ionized by an elliptically polarized laser pulse

We use an interferometic scheme to extract the phase distribution of the electron wave packet from above-threshold ionization in elliptically polarized laser fields. In this scheme, an electron wave packet released from a circularly polarized laser pulse acts as a reference wave and interferes with the electron wave packet ionized by a time-delayed counter-rotating elliptically polarized laser field. The generated vortex-shaped interference pattern in the photoelectron momentum distribution enables us to extract the phase distribution of the electron wave packet in the elliptically polarized laser pulse with high precision. By artificially screening the ionic potential at different ranges when solving the time-dependent Schördinger equation, we find that the angle-dependent phase distribution of the electron wave packet in the elliptically polarized laser field shows an obvious angular shift as compared to the strong-field approximation, whose value is the same as the attoclock shift. We also show that the amplitude of the angle-dependent phase distribution is sensitive to the ellipticity of the laser pulse, providing an alternative way to precisely calibrate the laser ellipticity in the attoclock measurement.     

Investigation of vortex arms in electron vortices by counter-rotating elliptically polarized attosecond laser pulses

We theoretically investigate the vortex patterns in photoelectron momentum distributions of He⁺driven by counter-rotating elliptically polarized,time delayed attosecond laser pulses by numerically solving the two-dimensional time-dependent Schrodinger equation.It is found that the number of vortex arms is extremely sensitive to the ellipticity and wavelength of counterrotating elliptically polarized laser pulses,which is illustrated by the attosecond perturbation ionization models.In addition,the effect of different time delays between two pulses on the interference patterns is also investigated and the corresponding physical mechanism is demonstrated.Since the wavelength,ellipticity and time delay have a significant effect on the vortex interference patterns,this may be a new method for laser field detection.     

Nonsequential double ionization of diatomic molecules by elliptically polarized laser pulses

Using the classical ensemble method, we investigate nonsequential double ionization （NSDI） of diatomic molecules by elliptically polarized laser pulses. The results show that the ellipticity of the laser field has a strong suppression effect on NSDI probabilities both in parallel and perpendicular alignments. The double ionization （DI） channel is commonly dominated by NSDI, and the NSDI channel changes with ellipticity. As ellipticity increases, more and more NSDIs occur through recollision excitation with subsequent field ionization （RESI）. Moreover, like the case of linear polarization, the two electrons involved in NSDI for perpendicularly aligned molecules are more likely to emit into the opposite hemispheres as compared to the case of parallel alignment. Additionally, this alignment effect increases as ellipticity increases.     

Amplitude and rotation of the ellipticity of harmonicsfrom a linearly polarized laser field

We simulate the dynamic response of H₂⁺ in a linearly polarized laser field by numerically solving the time-dependent Schrödinger equation. The elliptically polarized high-order harmonics generated by H₂⁺ irradiated by the linearly polarized laser field are systematically investigated. The result shows that the amplitude and rotation of the ellipticity of harmonics are affected by the alignment angle and internuclear distance of the molecule. Analyzing the change in forces acted on the ionized electrons and the trajectories of the electrons, the phenomena are found to be due to the change in the direction of the total Coulomb forces from the two nuclei felt by the recollided ionized electrons in the direction perpendicular to the laser polarization direction. Based on the influence law, we can select the harmonics with a specific frequency band under different alignment angles and then synthesize the isolated attosecond pulses with different rotations, which can be continuously converted from right-handed circular polarization, linear polarization, and left-handed circular polarization by changing the alignment angle. This study provides a new possible approach to the real-time detection of molecular states by using attosecond pulses and obtaining more optimized harmonics with molecular properties.     

The Study of “Coulomb Asymmetry” in an Elliptically Polarized Laser Field

Due to the effect of Coulomb potential, the angular distribution of electron ionized in an elliptically polarized field presents an asymmetric structure, which is called "Coulomb asymmetry". In this paper, we study how to modulate the asymmetric degree of the electron angular distribution by using a semi-classical simplified tunneling model. It is found that the asymmetric structure is easily affected by three parameters:the ionization potential, the laser ellipticity, and the laser wavelength. However, the laser intensity has little effect on the asymmetric structure. To explain these phenomena we have derived an analytical formula, which clearly demonstrates the relationship between the asymmetric degree and these parameters. Moreover, we find that in elliptically polarized laser field only those electrons that are released in a certain narrow window of initial field phase are greatly effected by the Coulomb potential and play the key role in the formation of asymmetric structure. This study provides some reference values in the development of attoclock technique, which can be used to probe the tunneling process.     

The Study of “Coulomb Asymmetry” in an Elliptically Polarized Laser Field

Due to the effect of Coulomb potential, the angular distribution of electron ionized in an elliptically polarized field presents an asymmetric structure, which is called "Coulomb asymmetry". In this paper, we study how to modulate the asymmetric degree of the electron angular distribution by using a semi-classical simplified tunneling model. It is found that the asymmetric structure is easily affected by three parameters: the ionization potential, the laser ellipticity,and the laser wavelength. However, the laser intensity has little effect on the asymmetric structure. To explain these phenomena we have derived an analytical formula, which clearly demonstrates the relationship between the asymmetric degree and these parameters. Moreover, we find that in elliptically polarized laser field only those electrons that are released in a certain narrow window of initial field phase are greatly effected by the Coulomb potential and play the key role in the formation of asymmetric structure. This study provides some reference values in the development of attoclock technique, which can be used to probe the tunneling process.     

Multiorbital tunneling ionization of the CO molecule

We coincidently measure the molecular-frame photoelectron angular distribution and the ion sum-momentum distribution of single and double ionization of CO molecules by using circularly and elliptically polarized femtosecond laser pulses, respectively. The orientation dependent ionization rates for various kinetic energy releases allow us to individually identify the ionizations of multiple orbitals, ranging from the highest occupied to the next two lower-lying molecular orbitals for various channels observed in our experiments. Not only the emission of a single electron, but also the sequential tunneling dynamics of two electrons from multiple orbitals are traced step by step. Our results confirm that the shape of the ionizing orbitals determine the strong laser field tunneling ionization in the CO molecule, whereas the linear Stark effect plays a minor role.     

Effect of elliptical polarizations on nonsequential double ionization in two-color elliptically polarized laser fields

Using the classical ensemble model, we investigate the nonsequential double ionization(NSDI) of Ar and Mg in the two-color elliptically polarized laser pulse for different elliptical polarizations. Numerical results show that for Ar atoms the NSDI yield increases as the ellipticity increases, which is different from the case of Mg atoms. Moreover, the correlated behavior in the correlated electron momentum along the x direction and ion momentum distributions of Ar atoms are influenced by the ellipticity. By statistical analysis of different times, we can conclude that the ellipticity may be responsible for the NSDI processes. The correlated momenta distributions along the x direction at the recollision time are demonstrated and the results show that the travelling time and ellipticity can affect the emitted directions of both electrons.     

High-order above-threshold ionization of heteronuclear diatomic molecules by a strong laser field with arbitrary polarization

The molecular strong-field approximation is applied to calculate angle-resolved photoelectron spectra in the process of high-order above-threshold ionization of carbon-monoxide molecules by an elliptically polarized laser field. The theory is formulated to include the Stark shift of the initial bound state of the valence electron. It is shown that the angle-resolved photoelectron spectra of aligned CO molecules exhibit pronounced minima which can be explained by destructive interference of two partial T-matrix contributions. The dependence of contributing partial amplitudes on the laser field ellipticity is analyzed in detail.     

Double ionization of helium interacting with elliptically polarized laser pulse by classical ensemble simulations

This paper uses the classical ensemble method to study the double ionization of a 2-dimensional (2D) model helium atom interacting with an elliptically polarized laser pulse. The classical ensemble calculation demonstrates that the ratio of double to single ionization decreases with the increasing ellipticity of the driving field. The classical scenario shows that there are hardly any e--e recollisions with the circularly polarized laser pulse. The double ionization probability is studied for linearly and circularly polarized laser pulses. The classical numerical results are consistent with the semiclassical rescattering mechanism and in agreement with the experimental results and the quantum calculations qualitatively.     

Bifurcation of ion momentum distributions in sequential double ionization by elliptically polarized laser pulses

Using a fully classical model, we have studied sequential double ionization (SDI) of argon driven by elliptically polarized laser pulses at intensities well in the over-barrier ionization region. The results show that the width of the ion momentum along the major elliptical axis increases with the ellipticity while that in the laser propagation direction decreases with the ellipticity. The ion momentum in the minor elliptical axis bifurcates from one peak structure to three-peak, then to four-peak, finally to six-peak structure. Analysis shows that this ellipticity dependence of the ion momentum distribution is a result of the subcycle nature of the ionization dynamics in SDI. By changing the ellipticity and wavelength of the driving pulses, this subcycle ionization dynamics is more observable. This provides a simple and efficient way to study the subcycle ionization dynamics in strong field processes.     

线偏振激光场中分子高次谐波椭偏率的调控

高次谐波椭偏率的调控为人们研究磁性材料和手性介质中的超快动力学过程提供了有效途径.本文理论研究了线偏振激光脉冲驱动下,H₂~+和H₃²⁺分子高次谐波的偏振特性及阿秒脉冲产生.结果表明当取向角为0~o时,H₂~+分子谐波的椭偏率几乎为0,而H₃²⁺分子谐波具有较大椭偏率,这是由于分子轨道对称性决定的.通过改变取向角的大小,可以调控高次谐波强度以及谐波椭偏率大小,为产生椭偏XUV脉冲提供了手段.同时,发现椭偏率较大的谐波阶次对应的谐波强度较小,分析表明分子的双中心干涉效应对椭偏率有很大的影响.对于H₂~+和H₃²⁺分子,分别合成了椭偏率为0.75和0.55的椭圆偏振阿秒脉冲.这种大椭偏XUV脉冲的产生为高次谐波在材料与生物科学领域提供了重要应用.     

Quantum interference of multi-orbital effects in high-harmonic spectra from aligned carbon dioxide and nitrous oxide

We investigate experimentally multi-orbital effects in high-order harmonic generation(HHG) from aligned CO_2 and N_2O molecules by intense femtosecond laser fields with linear and elliptical polarizations.For either of the aligned molecules, a minimum in the harmonic spectrum is observed, the position of which shifts to lower-order harmonics when decreasing the intensity or increasing the ellipticity of the driving laser.This indicates that the minimum originates from the dynamic interference of different channels, of which the tunneling ionization and recombination are contributed via different molecular orbitals.The results show that both the highest occupied molecular orbital(HOMO) and low-lying HOMO-2 in CO_2(or HOMO-1 in N_2O) contribute to the molecular HHG in both linearly and elliptically polarized strong laser fields.Our study would pave a way for understanding multi-electron dynamics from polyatomic molecules irradiated by strong laser fields.     

Magnetic field effects on the optical properties of an azo-dye doped liquid crystal

Homeotropically aligned nematic liquid crystals doped with azo-dye were subjected both to a linear polarized light of a He–Ne laser and to a magnetic field perpendicular to the incident light beam. We found that the emerging light was elliptically polarized when using magnetic field strengths higher than the threshold value for the magnetic Freedericksz transition. The light transmission, the rotatory power (induced by azo-dye) and the ellipticity varied quasiperiodically when increasing magnetic field strength. The number and positions of maxima and minima depend on the cell thicknesses. Changes in the phase difference between the emergent ordinary and extraordinary rays were computed from the experimental data and the magnetic field dependence of the birefringence was determined.     

Electron correlations in nonsequential double ionization of argon atoms by elliptically polarized laser pulses

Using a classical ensemble model, we investigate the correlation behaviour of electrons originating from nonsequential double ionization (NSDI) of argon atoms by the elliptically polarized laser pulses. Because of the ellipticity, not only the first electron to return but also the later return of tunneled electrons contribute significantly to NSDI. We mainly discuss two kinds of events of NSDI originating from the first and the second return separately. For the NSDI resulting from the recollision of the first return, the correlated electron momentum spectrum along the long axis of the laser polarization plane reveals an obvious V-like shape, located at the first and third quadrant. However, for the NSDI resulting from the recollision of the second return, the momenta of two electrons are distributed in the four quadrants uniformly. By analysing the trajectories of these two kinds, we find that the recollision energy and the laser phase at recollision are different for the first and second returning trajectories, which are responsible for the difference in the correlated behavior of the final electron momentum.     

Coulomb exploded directional double ionization of N_2O molecules in multicycle femtosecond laser pulses

We experimentally investigate Coulomb exploded directional double ionization of N_2O molecules in elliptically polarized femtosecond laser pulses.The denitrogenation and deoxygenation channels are accessed via various pathways.It leads to distinct asymmetries in directional breaking of the doubly ionized N_2O molecules versus the instantaneous laser field vector, which is revealed by tracing the sum-momentum spectra of the ionic fragments as a recoil of the ejected electrons.Our results demonstrate that the accessibility of the Coulomb exploded double ionization channels of N_2O molecules are ruled by the detailed potential energy curves, and the directional emission of the fragments are governed by the joint effects of the electron localization-assisted enhanced ionization of the stretched molecules and the profiles of the molecular orbitals.     

强激光场下原子超快动力学过程中的能量交换

利用三维经典系综模型,研究了整个系综两电子(Ar原子为例)从激光场吸收的能量对激光参数(波长、激光强度和椭偏率)的依赖关系.结果显示,当激光强度固定,波长增加时,整个系综两电子从激光场吸收的能量整体呈上升趋势,但不同强度下趋势略有差异.在较低强度时整个系综两电子从激光场吸收的能量对波长的依赖关系呈现持续平稳增加的趋势,在较高强度时呈现先缓慢减小再快速增大的趋势.对强度的依赖关系在不同波长时呈现两个有趣的交叉点.对椭偏率的依赖关系在较低强度时呈现先逐渐减小再缓慢增大的趋势;在中等强度时呈现一个“阶梯型”即先缓慢增大再逐渐减小最后缓慢增大;在更高强度时呈现先逐渐增大再逐渐减小的趋势.为了解释整个系综两电子从激光场吸收的能量对激光参数的依赖关系,把整个系综的动力学过程分为双电离、单电离、受挫单电离和受挫双电离4种通道.然后分析各个通道的特征及其如何主导整个系综两电子从激光场吸收的能量的变化趋势.分析结果表明,整个系综两电子从激光场吸收的能量对波长、激光强度和椭偏率的依赖均是由于某种通道主导整个系综两电子从激光场吸收的能量的结果.     

Characterization of elliptically polarized femtosecond pulses by molecular-alignment-based frequency resolved optical gating

We demonstrated that molecular-alignment-based cross-correlation frequency resolved optical gating (M-XFROG) could be used for complete characterization of elliptically polarized femtosecond pulses by measuring the orthogonal linear polarization components and the additional polarization projection at 45 degree of the target pulse. The electric field orientation, polarization ellipticity angles, and phase information of the target pulse were also obtained. The transiently aligned air molecules functioned as a linear optical gating function in the measurement processes. The validity and robustness of M-XFROG were confirmed by the comparison between the retrieved optical gating function and measured molecular alignment signal in air.     

正交偏振双色激光场作用下高次谐波的椭偏特性研究

通过数值求解二维含时薛定谔方程,理论研究了正交偏振双色激光场作用下H2+分子高次谐波发射和孤立阿秒脉冲的产生. 数值结果显示,改变激光场的强度比,可以调控高次谐波强度以及谐波椭偏率. 结果表明随着场强比的增加,y方向的谐波强度不断提高. 当场强比为1:2.5时,x方向和y方向分别仅有奇次谐波和偶次谐波产生,并且偶次谐波的强度比奇次谐波强度高2-3个数量级. 此时,奇次谐波的椭偏率最大可以达到0.3,偶次谐波的椭偏率接近于0. 此外,通过改变分子的准直角可以控制谐波的椭偏率,基于这一现象,利用椭圆偏振高次谐波的平台区合成了椭偏率为0.05的椭圆偏振阿秒脉冲链.     

Elliptic dichroism, ellipticity and the offset angle of high harmonics generated by arbitrary homonuclear diatomic molecules

The nth harmonic emission rate has contributions of the components of the T-matrix element in the direction of the laser-field polarization and in the direction perpendicular to it. Using both components of the T-matrix element we present a theoretical approach for calculation of the ellipticity and the offset angle of high harmonics. The molecular bound state is represented by HOMO or by HOMO-1. We show that high harmonics, generated by molecules oriented by an angle ??_L with respect to the major semiaxis of the laserfield polarization ellipse, are elliptically polarized even if the applied field is linearly polarized. Using examples of N₂ and O₂ molecules we show the existence of extrema and sudden changes of the harmonic ellipticity and the offset angle for particular molecular alignment. The interference between different contributions to the T-matrix element depends on the molecular symmetry. Presenting partial or total parameters of elliptic dichroism in the (??_L, n) plane clear interference minima are observed. Therefore, the measurement of the elliptic dichroism may reveal information about the molecular structure and symmetry.