Two-color Circularly Polarized Laser Fields Research Articles

Terahertz dependence on the laser phase and wavelength in two-color circularly polarized laser fields

Two-color circularly polarized laser fields with the same helicity (CP-S) are an appealing type of driving field that is essential for generating strong terahertz (THz) radiation. In this work, we theoretically investigate how the phase delay between two components in a CP-S field and their wavelength affect THz radiation yield with a photocurrent model. Simulations show that, as the laser wavelength increases, the THz yield becomes more and more phase dependent, which is maximized when the relative phase is 0 and minimized when the relative phase is π. Such a phase dependence is completely different from the commonly used two-color linearly polarized laser pulse with parallel polarizations (LP-P). In addition, in the CP-S field, the THz radiation energy may exhibit a wavelength scaling λ α (λ is the fundamental wavelength) with a bigger exponent than in the LP-P field at longer wavelengths. Our findings have important implications for the generation of powerful THz radiation via femtosecond laser interaction with gasses.

Nonsequential double ionization of Ar atoms in counter-rotating two-color elliptically polarized laser fields

Electron correlation behaviors and recollision dynamics in nonsequential double ionization (NSDI) of Ar atoms in counter-rotating two-color elliptically polarized (TCEP) laser fields are investigated by using the classical ensemble model. The combined electric field in counter-rotating TCEP laser pulses traces out a trefoil pattern, i.e. the waveform in a period shows three leaves in different directions, and each leaf is called a lobe. Unlike counter-rotating two-color circularly polarized laser field, the combined electric field has no spatial symmetry. The amplitudes of the three field lobes and the angles between them are different. Thus, the returning electron mainly returns to the parent ion from one direction, and the electron momentum distributions show strong asymmetry. Numerical results show that the NSDI yield gradually decreases as the ellipticity increases, and the correlated behavior of the correlated electron momentum along the long axis of the laser polarization plane gradually evolves from correlation behavior mainly located in the first quadrant and the third quadrant to anti-correlation behavior mainly located in the second quadrant and fourth quadrant. In order to further understand the correlation behaviors of electron pairs, different characteristic times in the NSDI processes are discussed, respectively. It is found that single ionization events and recollision events gradually decrease, but single ionization time and recollision time change slightly. This may be the main reason for the decrease in NSDI yield. And as the ellipticity increases, the traveling time and the recollision energy gradually decrease, while the delay time increases. Therefore, we can conclude that ellipticity may be responsible for the NSDI process. In addition, further analysis finds that the shape of the trajectory becomes more and more triangular as the ellipticity increases due to the counter-rotating TCEP laser fields of the specific dynamical symmetries of the total net electric field. And it is found that whether it is a “short trajectory” or a “long trajectory”, more populations move to the second quadrant and the fourth quadrant as the ellipticity increases. The results show that increasing the ellipticity will gradually change the two electrons from emitting in the same direction to emitting in the opposite direction. This well demonstrates that both ellipticity and travelling time are responsible for the formation of the electron momentum distribution at the recollision time, meaning that both of them affect the emitted directions of both electrons.

Modulation of High-Order Harmonic Generation from a Monolayer ZnO by Co-rotating Two-Color Circularly Polarized Laser Fields

By numerically solving the two-dimensional semiconductor Bloch equation, we study the high-order harmonic emission of a monolayer ZnO under the driving of co-rotating two-color circularly polarized laser pulses. By changing the relative phase between the fundamental frequency field and the second one, it is found that the harmonic intensity in the platform region can be significantly modulated. In the higher order, the harmonic intensity can be increased by about one order of magnitude. Through time-frequency analysis, it is demonstrated that the emission trajectory of monolayer ZnO can be controlled by the relative phase, and the harmonic enhancement is caused by the second quantum trajectory with the higher emission probability. In addition, near-circularly polarized harmonics can be generated in the co-rotating two-color circularly polarized fields. With the change of the relative phase, the harmonics in the platform region can be altered from left-handed near-circularly polarization to right-handed one. Our results can obtain high-intensity harmonic radiation with an adjustable ellipticity, which provides an opportunity for syntheses of circularly polarized attosecond pulses.

Nonsequential double ionization of atoms driven by few-cycle counter-rotating two-color circularly polarized laser fields

Using a classical ensemble model, we investigated the dependence of nonsequential double ionization (NSDI) on the relative phase driven by few-cycle counter-rotating two-color circularly polarized (TCCP) laser fields, which consist of 1600-nm laser pulse and 800-nm laser pulse. The numerical results reveal that NSDI probability is strongly dependent on the relative phase of counter-rotating TCCP fields, which shows a sin-like behavior of period 2π. The inversion analysis shows that the returning probability of the first electron is very sensitive to the relative phase of counter-rotating TCCP fields, resulting in dependence of NSDI probability on the relative phase. Furthermore, the dynamic behavior of two electrons can be regulated by adjusting the relative phase, leading to the sensitive dependence of momentum distribution of Ar2+ ions on the relative phase of counter-rotating TCCP fields. In addition, our results show that the traveling electron can be controlled to return to the parent ion core from a relatively single direction, which leave an imprint on the momentum distribution of Ar2+ ions.

Enhancement of terahertz radiation from a filament by using circularly polarized two-color laser fields

We investigate the terahertz radiation from a filament in two-color laser fields with various polarizations. It has been experimentally demonstrated that the efficiency of terahertz emission in co-rotating two-color circularly polarized laser fields is eight times as strong as that in linearly polarized two-color laser fields with parallel polarization. This enhancement is explained based on the polarization-dependent clamping intensity inside a filament and the dynamics of electrons ionizing from a single atom or molecule. Our finding provides a simple method to improve the THz intensity from an air filament in two-color fields.

Nonsequential Double Ionization of Molecules in Counter-Rotating Two-Color Circularly Polarized Laser Fields

Nonsequential Double Ionization of Molecules in Counter-Rotating Two-Color Circularly Polarized Laser Fields

Helicity-dependent time delays in multiphoton ionization by two-color circularly polarized laser fields

Helicity-dependent time delays in multiphoton ionization by two-color circularly polarized laser fields

Influence of relative phase on the nonsequential double ionization process of CO2 molecules by counter-rotating two-color circularly polarized laser fields

We investigate the nonsequential double ionization (NSDI) of linear triatomic molecules by the counter-rotating two-color circularly polarized (CRTC) laser fields with a classical ensemble method. The results of the simulation reveal that NSDI yield strongly connected with the relative phase. The trajectory tracking method shows that the return time of the electron is controlled by the relative phase. In addition, when we change the CRTC laser wavelengths, the relative phase of the maximum and minimum yield of NSDI also changes. This shows that the influence of the Coulomb potential in the triatomic molecules on the electron return process cannot be ignored. This work will effectively promote the electronic dynamics study of NSDI for the triatomic molecule.

Frequency-ratio-dependent ultrafast dynamics in nonsequential double ionization by co-rotating two-color circularly polarized laser fields

Using a three-dimensional classical ensemble model, we investigate ultrafast dynamics in nonsequential double-ionization (NSDI) of Ar atom by co-rotating two-color circularly polarized laser fields with the frequency ratio varying between 2 and 5. Numerical results indicate that the NSDI probability gradually increases with the frequency ratio between the two components increasing. The probability for the frequency ratio 5 is one order of magnitude higher than for the frequency ratio 2. Back analysis of NSDI trajectories shows that recollision occurs mainly via a short looping trajectory. With the frequency ratio increasing, the traveling time of the free electron shortens. Furthermore, the relative contribution of recollision-induced excitation with subsequent field ionization mechanism in NSDI gradually increases as the frequency ratio increases. It is attributed to smaller recollision energy and larger recollision distance for larger frequency ratio.

Sub-cycle dynamics of nonsequential double ionization of Ar atom by few-cycle counter-rotating two-color circularly polarized laser fields

We have investigated the sub-cycle correlated electron dynamics of nonsequential double-ionization (NSDI) of Ar atom by few-cycle counter-rotating two-color circularly polarized (TCCP) laser fields using a three-dimensional classical ensemble model. Numerical results indicate that NSDI probability sensitively depends on the relative phase of the two components and achieves its maximum at the relative phase 0.7[Formula: see text]. Back analysis of NSDI trajectories shows that the return angle of the electron is closely related to the relative phase of the two components and can continuously be controlled by changing the relative phase. Furthermore, the relative phase also influences the relative contribution of recollision-induced direct ionization (RII) and recollision-induced excitation with subsequent field ionization (RESI) to NSDI and the final emitted direction of the electrons.

Relative phase-dependent two-electron emission dynamics with two-color circularly polarized laser fields**Project supported by the China Postdoctoral Science Foundation (Grant No. 2019M661108) and the Fundamental Research Funds for the Central Universities, China (Grant No. N2005023).

With the semiclassical ensemble model, we explore the relative phase-dependent nonsequential double ionization (NSDI) of Mg by counter-rotating two-color circularly polarized (TCCP) laser pulses. The yield of Mg2+ sensitively depends on the relative phase Δφ and the intensity of TCCP laser fields. At Δφ = 1.5π, the yield of Mg2+ exhibits a pronounced peak in the 0.05 PW/cm2 laser field. This behavior results from the increase of the initial transverse velocity compensating for the drift velocity with the decreasing angle by analyzing the angular distributions of the electron pairs in four relative phases. By changing the relative phases, we find that the recollision excitation with subsequent ionization and the recollision-impact ionization mechanisms can be controlled with TCCP laser fields.

Dynamics of strong-field double ionization of H2 in co-rotating two-color circularly polarized laser fields

Double ionization of H2 in a co-rotating two-color circularly polarized (TCCP) laser field is theoretically investigated. By changing the ratio of electric field peak amplitudes of the TCCP laser pulses, the double ionization probability as a function of the laser intensity shows a clear knee structure, which is suppressed significantly in the case of the atom. Due to the large spatial range of the electronic initial distribution, with the analysis of classical trajectories of ionized electrons, it is found that the ionization of the electron in the farther distance increases the probability of recollision. Furthermore, the yield of nonsequential double ionization created by the recollision can be enhanced by controlling the amplitude ratio of the TCCP laser field.

Influence of intensity ratio of the two driving laser fields on the cutoff of the high-order harmonics

We investigate the high-order harmonic generation (HHG) of the helium atom at the various intensity ratios of the counter-rotating two-color circularly polarized laser fields. The results show that the cutoff energy of the harmonic spectra can be affected by changing the intensity ratios. By comparing the results from different intensity ratios, we find that the distances the electrons travel are short when the intensity ratio is increased. The dependence of the cutoff position in the HHG on the intensity ratios usually results from the classical trajectories of the electrons. As the intensity ratio increases, the electrons cannot be accelerated and it will gain less energy. As a result, the harmonic spectra are cut off at the lower energy. We compare the quantum and classical trajectories results to illustrate the reasons of the cut off dependence.

Evidence of ac-Stark-shifted resonances in intense two-color circularly polarized laser fields

We report on the appearance of a structure at low energies in the photo-electron momentum distribution of the hydrogen atom exposed to two-color counter-rotating bi-circular laser fields. These structures, which arise due to AC-Stark shifted resonances, break the three-fold symmetry, typical for the $\omega-2\omega$ bi-circular fields. We discuss the physical origin of this structure in terms of partial-wave interference between direct ionization channels and a resonant pathway, that passes through the AC-Stark shifted state and show how the underlying Rydberg state population depend on the field strength and pulse duration.

Scaling law in nonsequential double ionization by counter-rotating two-color circularly polarized laser fields

Nonsequential double ionization (NSDI) of noble gas atoms in counter-rotating two-color circularly polarized (CRTC) laser fields is investigated. A scaling law is concluded by qualitatively and quantitatively comparing the momentum distributions of two electrons from NSDI in CRTC laser fields for different atoms with different parameters. The scaling law indicates that the momentum distributions from an atom driven by CRTC laser frequency ω1, ω2, and laser intensity I are the same as that from another atom irradiated by CRTC laser frequency kω1, kω2, and laser intensity k3I. This study can provide an avenue in the research of two-color laser field ionization.

Selection of right-circular-polarized harmonics from p orbital of neon atom by two-color bicircular laser fields**Project supported by the National Natural Science Foundation of China (Grant Nos. 11974229, 11504221, and 11404204), the Scientific and Technological Innovation Program of Higher Education Institutions in Shanxi Province, China (Grant No. 2019L0452), the Natural Science Foundation for Young Scientists of Shanxi Province, China (Grant No.

The polarization properties of high-order harmonic generation (HHG) in the two-color circularly polarized laser fields are investigated by numerically solving the two-dimensional time-dependent Schrödinger equation. By adding a wavelength of 1600-nm right-circular-polarized field to an 800-nm left-circular-polarized field, HHG is simulated from a real model of neon atom with p orbital, but not from a hydrogen-like atom model with s orbital. The orders of 3n+1 can be selected while the orders of 3n+2 are suppressed by adjusting the intensities of the two pulses. The physical mechanism is analyzed by time–frequency analysis and semiclassical model.

Nonsequential double ionization by co-rotating two-color circularly polarized laser fields.

Nonsequential double ionization (NSDI) of Ar in co-rotating two-color circularly polarized (TCCP) laser fields is investigated with a three-dimensional classical ensemble model. Our numerical results indicate that co-rotating TCCP fields can induce NSDI by recollision process, while the yield is an order of magnitude lower than counter-rotating case. NSDI yield in co-rotating TCCP fields strongly depends on field ratio of the two colors and achieves its maximum at a ratio of 2.4. In co-rotating TCCP fields, the short recollision trajectory with traveling time smaller than one cycle is dominant. Moreover, the recollision time in co-rotating TCCP laser fields depends on the field ratio, which is mapped to the electron momentum distribution. This provides anavenue to obtain information about recollision time and access the subcycle dynamics of the recollision process.

Intensity-dependent two-electron emission dynamics in nonsequential double ionization by counter-rotating two-color circularly polarized laser fields.

Nonsequential double ionization of helium in counter-rotating two-color circularly polarized laser fields is investigated with a three-dimensional classical ensemble model. At moderate intensity, the momentum distribution of the two electrons shows a maximum in the middle of each side of the triangle of the negative vector potential. At high intensity, the momentum distribution exhibits a double-triangle structure, which is attributed to the different values of the laser intensity where the two electrons are released after recollision. At low intensity, the momentum distribution shows a shift deviating from the middle of the side of the triangle of the negative vector potential. This is because the first electrons are emitted within a narrow time window after the field maximum. In addition, at low intensity, double-recollision events and NSDI originating from doubly excited states induced by recollision are prevalent.

Enhancement of nonsequential double ionization in counter-rotating two-color circularly polarized laser fields

Nonsequential double ionization is theoretically investigated in the counter-rotating two-color [frequencies (ω1,ω2)] circularly polarized laser fields with classical ensemble approach. It is found that remarkable ionization enhancement is obtained by adjusting the relative electric field amplitude ratios (γE). The result indicates that there is a broader steerable range of γE to obtain higher ionization enhancement for ω2=3ω1 than that for ω2=2ω1. Through the analysis of trajectories, the recollision picture for ω2=3ω1 is complicated leading to slow change of double ionization, which is benefit to gentle control mechanism. However, the recollision ionization channel is easily distinguishable and sensitive to control double ionization in ω2=2ω1 laser fields and the travel time can be controlled in the order of magnitude of 100 attoseconds.

Multiple recollisions in nonsequential double ionization by counter-rotating two-color circularly polarized laser fields.

With the three-dimensional (3D) classical ensemble method, we theoretically investigate the recollision dynamics in strong-field nonsequential double ionization (NSDI) of Ar by counter-rotating two-color circularly polarized laser fields. With the analysis of the NSDI trajectories, we find that not only multiple-recollision but also single-recollision processes occur in the double ionization events. Furthermore, the multiple-recollision and single-recollision processes both undergo the recollision-induced excitation with subsequent ionization (RESI) and recollision-induced ionization (RII). The angle between the momentum and the force of the laser field at the recollision moment can affect the times of the recollision.