Elliptically polarized high-order harmonic generation of Ar atom in an intense laser field

High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(ε) in the lower-order harmonics is observed,specifically in the 13rd-order,which displays a maximal harmonic intensity at ε ≈ 0.1,rather than at ε = 0 as expected.This contradicts the general trend of harmonic yield,which typically decreases with the increase of laser ellipticity.In this study,we attribute this phenomenon to the disruption of the symmetry of the wave function by the Coulomb effect,leading to the generation of a harmonic with high ellipticity.This finding provides valuable insights into the behavior of elliptically polarized harmonics and opens up a potential way for exploring new applications in ultrafast spectroscopy and light–matter interactions.

Steering the energy sharing of electrons in nonsequential double ionization with orthogonally polarized two-color field

Using the semiclassical ensemble model,the dependence of relative amplitude for the recollision dynamics in nonsequential double ionization(NSDI)of neon atom driven by the orthogonally polarized two-color field(OTC)laser field is theoretically studied.And the dynamics in two typical collision pathways,recollision-impact-ionization(RII)and recollisionexcitation with subsequent ionization(RESI),is systematically explored.Our results reveal that the V-shaped structure in the correlated momentum distribution is mainly caused by the RII mechanism when the relative amplitude of the OTC laser field is zero,and the first ionized electrons will quickly skim through the nucleus and share few energy with the second electron.As the relative amplitude increases,the V-shaped structure gradually disappears and electrons are concentrated on the diagonal in the electron correlation spectrum,indicating that the energy sharing after electrons collision is symmetric for OTC laser fields with large relative amplitudes.Our studies show that changing the relative amplitude of the OTC laser field can efficiently control the electron–electron collisions and energy exchange efficiency in the NSDI process.

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.

Asymmetric structure of atomic above-threshold ionization spectrum in two-color elliptically polarized laser fields

According to the frequency-domain theory, we investigate the asymmetric structure of above-threshold ionization(ATI) spectrum of an atom in two-color elliptically polarized(EP) laser fields. When both laser fields are linearly polarized(LP), the spectrum shows that the multi-plateau structure is symmetric about the emitted angle of electron at π/2, while the spectrum becomes asymmetric and shifts rightwards with the increase of the EP degree of the IR laser field. Since the total ATI process is regarded as including direct ATI and the rescattering ATI, we analyze the spectrum structure of direct ATI and rescattering ATI separately. Using the saddle-point approximation, we find that for direct ATI, the fringes on the spectrum are mainly attributed to the fact that the ionization probability becomes very small when the direction of emitted electrons is perpendicular to the direction of the XUV laser polarization;while for the rescattering ATI, the interference fringes on the spectrum mainly come from the superposition of the waist structures on the spectra of all sub-channels.

Relative phase effect of nonsequential double ionization in Ar by two-color elliptically polarized laser field

We investigated the nonsequential double ionization(NSDI)in Ar by two-color elliptically polarized laser field with a three-dimensional(3D)classical ensemble method.We study the relative phase effect of NSDI and distinguish two particular recollision channels in NSDI,which are recollision–impact ionization(RII)and recollision-induced excitation with subsequent ionization(RESI),according to the delay-time between the recollision and the final double ionization.The numerical results indicate that the ion momentum distribution is changed and the triangle structure is more obvious with the decrease of the relative phase.We also demonstrate that the RESI process always dominates in the whole double ionization process and the ratio of RESI and RII channels can be influenced by the relative phase.

Semiclassical investigation of Coulomb focusing effects in atomic above-threshold ionization with elliptically polarized laser fields

We investigate atomic above-threshold ionization in elliptically polarized strong laser fields with a semiclassical approach.With increasing laser intensity,the Coulomb focusing（CF） effects are found to become stronger in both parallel and perpendicular directions with respect to the polarization plane.The dependence of CF effects on tunnel exit,initial transverse momentum distribution and laser electric field is analyzed.It was revealed that the effects of tunnel exit are most prominent with variation of the laser intensity,and the other two factors both play non-negligible roles.Our results provide a deeper insight to the recent experiments of Coulomb asymmetry[Shafir D,et al.,2013 Phys.Rev.Lett.111 023005 and Li M,et al,2013 Phys.Rev.Lett.111 023006].

Decoding the electron dynamics in high-order harmonic generation from asymmetric molecular ions in elliptically polarized laser fields

The high-order harmonic generation from an asymmetric molecular ion is theoretically investigated based on the Born-Oppenheimer model with two-dimensional electron dynamics.It is shown that the harmonic intensity changes periodically in elliptically polarized laser fields.The periodical character is ellipticity-dependent.By establishing the physical image,the periodicity of the harmonic intensity can be ascribed to the contributions of the ground state and the excited state.Furthermore,the electron dynamics from different electronic states can be selected via combining the elliptically polarized laser field with a static electric field.The harmonics dominated either by ground state or excited state are emitted once in an optical cycle in the combined laser field.

High-order harmonic generation of N2molecule in two-color circularly polarized laser fields

The generation of high-order harmonics and the attosecond pulse of the N2 molecule in two-color circularly polarized laser fields are investigated by the strong-field Lewenstein model. We show that the plateau of spectra is dramatically extended and a continuous harmonic spectrum with the bandwidth of 113 eV is obtained. When a static field is added to the x direction, the quantum path control is realized and a supercontinuum spectrum can be obtained, which is beneficial to obtain a shorter attosecond pulse. The underlying physical mechanism is well explained by the time-frequency analysis and the semi-classical three-step model with a finite initial transverse velocity. By superposing several orders of harmonics in the combination of two-color circularly polarized laser fields and a static field, an isolated attosecond pulse with a duration of 30 as can be generated.

Controlling Three-Dimensional Electron-Electron Correlation via Elliptically Polarized Intense Laser Field

The three-dimensional electron-electron correlation in an elliptically polarized laser field is investigated based on a semiclassical model. Asymmetry parameter α of the correlated electron momentum distribution is used to quantitatively describe the electron-electron correlation. The dependence of α on elliptieity e is totally different in three directions. For the z direction （maJor polarization direction）, α first increases and reaches a maximum at ε = 0.275, then it decreases quickly. For the y direction in which the laser field is always absent, the ellipticity has a minor effect, and the asymmetry parameter fluctuates around α = -0.15. However, for the x direction （minor polarization direction）, α increases monotonously with ellipticity though starts from the same value as in the y direction when ε = 0. The behavior of α in the x direction actually indicates a transformation from the Coulomb interaction dominated correlation to the laser field dominated correlation. Therefore, our work provides an efficient way to control the three-dimensional electron electron correlation via an elliptically polarized intense laser field.

Controlling the contributions to high-order harmonic generation from different nuclei of N_2 with an orthogonally polarized two-color laser field

The generation of high-order harmonic and the attosecond pulse of the N2 molecule with an orthogonally polarized two-color laser field are investigated by the strong-field Lewenstein model.We show that the control of contributions to high-order harmonic generation（HHG） from different nuclei is realized by properly selecting the relative phase.When the relative phase is chosen to be φ= 0.4π,the contribution to HHG from one nucleus is much more than that from another.Interference between two nuclei can be suppressed greatly; a supercontinuum spectrum of HHG appears from 40 e V to125 e V.The underlying physical mechanism is well explained by the time–frequency analysis and the semi-classical threestep model with a finite initial transverse velocity.By superposing several orders of harmonics,an isolated attosecond pulse with a duration of 80 as can be generated.

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.

Exploration of High-Harmonic Generation from the CS2 Molecule by the Lewenstein Method in Two-Color Circularly Polarized Laser Field

The high harmonic generation (HHG) from the CS2 molecule in intense laser fields is investigated using the extended Lewenstein method. The initial state is the highest-occupied molecular orbital of the CS2 molecule, which can be well described by Gaussian wave packet using GAMESS-UK package. Compared with the case of the elliptical laser, the HHG can be extended in two-color circularly polarized laser field. The time-frequency analysis and classical electron trajectory as well as the ionization yield curve are also presented to further explain the underlying mechanism. After adding a static electric field on the z-direction, the single quantum path control is realized and the supercontinuum spectra are obtained. Moreover, an isolated 110 as pulse can be obtained by superposing the harmonics from 130th to 180th order.

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.

Manipulation of Spontaneous Emission via Quantum Interference in an Elliptically Polarized Laser Field

Manipulation of spontaneous emission from an atom confined in three kinds of modified reservoirs has been investigated by means of an elliptically polarized laser field. Some interesting phenomena such as the multi-peak structure, extreme spectral narrowing, and cancellation of spontaneous emission can be observed by adjusting controllable system parameters. Moreover, these phenomena depend on the constructive or destructive quantum interference between multiple decay channels and which can be changed appreciably by varying the phase difference between the two circularly polarized components of the probe field. These results demonstrate the importance of an elliptially polarized laser field in controlling the spontaneous emission and its potential applications in high-precision spectroscopy.

反旋双色椭圆偏振激光场中Ar原子的非序列双电离

利用经典系综方法研究了不同椭偏率的反旋双色椭圆偏振(two-color elliptically polarized,TCEP)激光场中Ar原子非序列双电离(nonsequential double ionization,NSDI)的电子关联特性和再碰撞动力学.不同于反旋双色圆偏振激光场,反旋TCEP激光场不再具有空间对称性,返回电子主要从一个方向返回母离子,从而导致电子动量分布表现出很强的不对称性.数值结果显示随着椭偏率的增大,Ar原子NSDI的产量逐渐减小,并且电子对在椭圆偏振激光场长轴方向上的关联电子动量分布,从主要位于第一和第三象限的正相关逐渐演变为主要位于第二和第四象限的反相关.通过对不同特征时间的统计分析表明,随着椭偏率的增大,旅行时间和返回电子的重碰撞能量逐渐减小,而延迟时间却增大,这是电子对关联特性发生变化的主要原因.此外,进一步分析发现,无论是“短轨迹”还是“长轨迹”,椭偏率的增大都会使两个电子由同向出射逐渐转变为反向出射,这表明椭偏率和旅行时间都影响着电子的出射方向.

Analytical Study of Pair Production Rate from Vacuum in an Elliptic Polarized Field by a Two-Level Transition Technique

Electron-positron pair production rate created from vacuum in the presence of an elliptically polarized laser field is investigated.By applying the technique of two level transition amplitude,a routine for obtaining pair production rate is presented,and approximate analytical expressions are given both for the low frequency strong field regime and the high frequency weak field regime.We found that for an elliptically polarized field,the electron-positron pair production rate decrease when the elliptic eccentricity increase in the high frequency weak field regime,however,in the low frequency strong field regime,there is almost the same electron-positron pair production rate as in the constant electric field case.

Laser Polarization Effect on Molecular Harmonic and Elliptically Polarized Attosecond Pulse Generation

Molecular harmonic spectra of H+2driven by the linearly polarized laser pulses with different polarized angles have been theoretically investigated through solving the two-dimensional time-dependent Schr¨odinger equation.(i) Below-threshold harmonic spectra show a visible enhanced peak around the 7th harmonic(H7), which produces a red-shift phenomenon as the internuclear distance increased. Theoretical analyses show the red-shift enhanced peak is caused by the laser-induced electron transfer between the ground state and the 1st excited state of H+2.(ii) Due to the two-centre interference phenomenon, the above-threshold harmonic spectra exhibit many maxima and minima.(iii)With the introduction of the polarized angle, the anomalous elliptically polarized harmonics can be found. But, with the introduction of the spatial inhomogeneous effect, not only the ellipticities of the harmonics are equal to a stable value of ε～ 0.1–0.3, but also the harmonic cutoffs are extended. As a result, four super-bandwidths of 407 e V, 310 e V,389 e V, and 581 e V can be obtained. Time profiles of the harmonic generations have been shown to explain the harmonic characteristics. Finally, a series of elliptically polarized(ε～ 0.1–0.3) attosecond X-ray pulses with durations from 18 as to 25 as can be directly produced through Fourier transformation of the spectral continuum.

Control of Spontaneous Emission via a Single Elliptically Polarized Light in a Five-Level Atomic System

We investigate the features of the spontaneous emission spectra in a cold five-level atomic system coupled by a single elliptically polarized control field. We use wave function approach to derive the explicit and analytical expressions of atomic spontaneous emission spectra. It is shown that some interesting phenomena such as spectralline enhancement, spectral-line suppression, spectral-line narrowing, spectral-line splitting and dark fluorescence can be observed in the spectra by appropriately modulating the phase difference between the right-hand circularly (LHC) and left-hand circularly (RHC) polarized components of the elliptically polarized control field and the intensity of external magnetic field. The number of emission peaks, the positions of fluorescence-quenching points can be also controlled. Furthermore, we propose an ultracold 87Rb atomic system for experimental observation. These investigations may find applications in high-precision spectroscopy.

反旋双色椭圆偏振激光脉冲驱动的氩原子非次序双电离对椭偏率的依赖

利用三维经典系综模型系统地研究了反向旋转双色椭偏场中Ar原子非次序双电离对椭偏率的依赖。数值结果显示双电离发生的概率随800 nm激光场椭偏率增大而增大,随1600 nm激光场椭偏率增大而减小。这是因为当固定1600 nm激光场椭偏率时,电子的返回概率和碰撞能量随800 nm激光场椭偏率增大而增大。而当固定800 nm激光场椭偏率时,电子的返回概率和碰撞能量随1600 nm激光场椭偏率增大而减小。在两椭圆激光场的长轴沿x方向条件下,当1600 nm激光场椭偏率为0.3时,离子动量分布由x负半轴向x正半轴移动。随着1600 nm激光场和800 nm激光场椭偏率的增大,离子动量分布逐渐在y方向扩展最终形成一个分布于x轴两侧的两层结构。

椭偏激光场中原子次序双电离的离子动量分布

利用海森伯势经典系综模型,研究了椭偏激光场中氩原子的次序双电离.结果发现,激光相位随机时,随着激光波长的增加,离子动量分布从800 nm时的六带结构逐渐转变成1600 nm时的八带结构.激光相位固定时,1600 nm激光场产生的离子动量分布呈现出十带结构.这些多带结构直接反映了椭偏场中电子的亚光周期电离动力学.随着激光相位的变化,离子动量谱的外部三带出现显著的移动.正是由于外部三带位置的相位依赖导致相位随机时离子动量谱的外部区域只能观测到一条带状分布.两电子电离时序分析发现,相位随机时,离子动量谱中的内带源于时间差为0.5个光周期的电离脉冲组合,而外带来源于时间差为1,2和3个光周期的电离脉冲的组合.对于800 nm中间的一个带,源于时间差为1.5和2.5个光周期的电离脉冲组合;对于1600 nm中间的两个带,一个源于时间差为1.5个光周期的电离脉冲组合,另一个源于时间差为2.5和3.5个光周期的电离脉冲组合.这些结果表明长波长和相位稳定的激光更容易观测到原子次序双电离的亚光周期动力学.