Ellipticity Of Harmonics Research Articles

Near-circularly polarized isolated attosecond pulse generation from a current-carrying state of Ar atom by two-color cross-linearly-polarized laser fields

Abstract We theoretically propose an efficient method to generate near-circularly polarized isolated attosecond (as) pulses (NCP-IAPs) from a current-carrying state of Ar atom driven by two-color cross-linearly-polarized laser fields. We find that the ellipticity of high harmonics can be controlled by adjusting the crossing angle of two linearly polarized lasers and the near-circularly polarized supercontinuum harmonics are obtained when the crossing angle is around 140°. Furthermore, we can produce the NCP-IAPs with the ellipticity up to 0.94 and the shortest one achieves 196 as. This work demonstrates the possibility for generating the NCP-IAPs using a current-carrying state of atoms driven by two-color cross-linearly-polarized laser fields.

Elliptically polarized high-order harmonic generation from N[formula omitted]-CO mixed gases

We theoretically study the elliptically polarized high-order harmonic generation from N2-CO mixed gases. Our simulations show that the polarization of HHG is highly sensitive to both the mixing ratio and molecular alignment angle. In particular, even a small addition of CO gas results in a significant enhancement of harmonic ellipticity compared to pure N2 gas. Under a proper mixing ratio and molecular alignment angle, a large ellipticity of HHG is observed, which is larger than that in reported N2-Ar mixture. Furthermore, when considering the molecular alignment effect, the dependence of ellipticity of HHG on mixing ratio exhibits slight variations. These findings pave the way for generating elliptically polarized extreme ultraviolet pulses.

Orientation Dependence of High-Order Harmonic Generation from HeH2+ in a Corotating Two-Color Circularly Polarized Laser Field

By numerically solving the time-dependent Schrödinger equation, we study high-order harmonic generation from the asymmetric diatomic molecule HeH2+ in a corotating two-color circularly polarized laser field. Our results reveal a strong correlation between the molecule orientation and the harmonic yield. The harmonics in the plateau region can achieve an intensity modulation of one to two orders of magnitude with the change in the orientation angle. Through the time-dependent evolution of ionized electron wave packets combined with the analysis of the transition dipole moment between the continuum and bound states, the modulation of the harmonic strength may be attributed to the difference in the recollision angle of ionized electron wave packets relative to the molecules. In addition, the harmonic ellipticity is also affected by the molecular orientation. Notably, we found that the harmonic with greater ellipticity and higher intensity can be obtained with an orientation angle of 147°. These findings open up new avenues for achieving enhanced efficiency, the near-circular polarization of harmonics, and precise control over harmonic polarization states.

Elliptical high-order harmonic generation from current-carrying orbitals of prealigned molecules

The polarization of high harmonics generated from current-carrying state of nitric oxide molecules irradiated by linear laser fields is investigated by numerically solving the three-dimensional time-dependent Schrödinger equation. It is found that the ellipticity of high harmonics is obviously dependent on the polar angle between the driving laser polarization and molecular axis which is interpreted by the strong field approximation model. Moreover, our results also show that the helicity of near-threshold harmonics is opposite to that of plateau harmonics when the molecule is at any polar angle. To analyze this phenomenon, we simulate the dipole matrix element numerically. Finally, the attosecond pulses with opposite helicities can be obtained by synthesizing near-threshold and plateau harmonics. The ellipticity can be tuned by the alignment angle of molecules. Our work may provide a theoretical guiding and detection tool for the electron dynamics of molecular current-carrying states.

Elliptically polarized high-order harmonics from mixed gases by a combined laser field

We theoretically investigate the elliptically polarized (EP) high-order harmonic generation (HHG) from the mixed gases driven by the combined laser field, which is combined with an EP laser field and a linearly polarized (LP) laser field. The numerical results show that the harmonic intensity is enhanced, and the cutoff is extended compared with that in the EP laser field. Benefiting from the interference between the harmonics generated from the two single gases, we obtain the bright broadband EP HHG with large ellipticity from the mixed gases. The origin of the harmonic ellipticity is illustrated by the trajectories of the electrons. The result indicates that the harmonic ellipticity is large if the angle between the velocity directions at the initial time and the final time is close to 90°. In addition, the analysis shows that the left-handed components of the harmonics from two single gases produce destructive interference, and the right-handed components of that produce constructive interference, which results in the enhancement of the intensity difference of the left- and right-handed harmonics from the mixed gases. Thus, the harmonic ellipticity is large from the mixed gases. Our results are conducive to obtaining near circularly polarized (CP) XUV and attosecond pulse radiation from mixed gases in a broad spectral range.

Interference effects in harmonic ellipticity from H molecules in an orthogonally polarized two-color laser field

We theoretically investigate the elliptically polarized harmonics from aligned molecular ion H in orthogonally polarized two-color laser pulses. Our results show that a striking peak appears in the ellipticity curve of odd-order harmonics, and this peak shows obvious alignment dependence and shifts toward higher energy as the amplitude ratio of the two colors increases. The location of the peak is close to that of the interference minimum predicted by using a modified dipole model, indicating strong two-center interference effects in ellipticity. Through adjusting the frequency ratio of the two colors, large ellipticity is obtained for both odd and even harmonics in a wide energy region. As a result, we synthesize a bright, elliptically polarized, isolated attosecond pulse with an ellipticity up to 0.63.

Generation of elliptically polarized isolated attosecond pulses from [formula omitted] and [formula omitted] molecules in orthogonal few-cycle two-color fields

We theoretically study the generation of high-order harmonics and ultrashort isolated attosecond (as) pulses (IAPs) with large ellipticity from the perfectly aligned N2 and O2 molecules driven by the few-cycle orthogonally polarized two-color (OTC) field by numerically solving the reduced two-dimensional time-dependent Schrödinger equation (2D-TDSE). We show that the ellipticity of high-order harmonics strongly depends on the alignment angle and the amplitude ratio of the few-cycle OTC fields. Furthermore, high-order harmonics with large ellipticity are generated at proper alignment angles where ionization events mainly happens at larger laser ellipticities, namely when electrons distribute along the crossing lines in Lissajous diagram of the OTC fields. By superposing the supercontinuum harmonics from N2 and O2 molecules at proper alignment angles, we can directly produce the elliptically polarized IAPs with ellipticity up to 0.76 and the shortest one achieves 141 as. This work demonstrates the possibility for generating the elliptically polarized IAPs with large ellipticity using high-order harmonics from the aligned N2 and O2 molecules exposed to the few-cycle OTC fields.

High-order harmonic generation by aligned homonuclear diatomic cations.

We introduce the theory of high-order harmonic generation by aligned homonuclear diatomic cations using a strong-field approximation. The target cation is represented as a system which consists of two atomic (ionic) centres and one active electron, while the driving field is either a monochromatic or bichromatic field. For a linearly polarised driving field, we investigate the differences between the harmonic spectra obtained with a neutral molecule and the corresponding molecular cation. Due to the larger ionisation potential, the molecular cations can withstand much higher laser-field intensity than the corresponding neutral molecule before the saturation effects become significant. This allows one to produce high-order harmonics with energy in the water-window interval or beyond. Also, the harmonic spectrum provides information about the structure of the highest-occupied molecular orbital. In order to obtain elliptically polarised harmonics, we suggest that an orthogonally polarised two-colour field is employed as a driving field. In this case, we analyse the harmonic ellipticity as a function of the relative orientation of the cation in the laser field. We show that the regions with large harmonic ellipticity in the harmonic energy-orientation angle plane are the broadest for cations whose molecular orbital does not have a nodal plane. Finally, we show that the molecular cations exposed to an orthogonally polarised two-colour field represent an excellent setup for the production of elliptically polarised attosecond pulses with a duration shorter than 100 as.

High-order harmonic generation by two linearly polarized laser fields with an arbitrary angle between their polarization axes

High-order harmonic generation by two linearly polarized fields that enclose an arbitrary crossing angle $\ensuremath{\theta}$ is investigated using the strong-field approximation. We investigate the combinations with frequency ratios $s/r=2$ and 3 with integer $r$ and $s$. In the former case, the emitted harmonics are elliptically polarized unless $\ensuremath{\theta}={0}^{\ensuremath{\circ}}$ or ${90}^{\ensuremath{\circ}}$, while in the latter they are always elliptically polarized except for $\ensuremath{\theta}={0}^{\ensuremath{\circ}}$. The possibility to control the intensity and ellipticity of the emitted harmonics by variation of the relative phase $\ensuremath{\varphi}$ between the field components and the crossing angle $\ensuremath{\theta}$ is explored. There are regions with large harmonic ellipticity and appreciable intensity in the relative-phase--harmonic-order plane and they are more extended for values of the crossing angle closer to ${90}^{\ensuremath{\circ}}$. The overall shape of the spectra (smooth, oscillatory, or erratic) for different values of $\ensuremath{\theta}$ and $\ensuremath{\varphi}$ is explained using the saddle-point method and quantum-orbit theory. The simple-man model is utilized to assess the regions with large harmonic intensity and to predict the position of the cutoff. For the frequency ratio $s/r=2$, the harmonic ellipticity is significant even for extremely small deviations of the crossing angle $\ensuremath{\theta}$ from ${90}^{\ensuremath{\circ}}$.

Amplitude and rotation of the ellipticity of harmonics from a linearly polarized laser field

We simulate the dynamic response of in a linearly polarized laser field by numerically solving the time-dependent Schrödinger equation. The elliptically polarized high-order harmonics generated by 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.

Anomalous resonance-enhanced harmonic ellipticity in an elliptically polarized laser field

We investigate theoretically resonant harmonic generation in $\text{H}{\text{e}}^{+}$ from an elliptically polarized laser field. The results show that there are two anomalous resonance-enhanced harmonics and the intensities of the anomalous resonance-enhanced harmonics remain unchanged for different laser ellipticities which are approximately two orders of magnitude stronger than those of nonresonant harmonics. We illustrate that the first resonance-enhanced harmonic is due to the transition between the ground state and the first excited state and the second one is due to the transition between the ground state and the second excited state. Our results also show that the enhancements of the harmonic intensities are related to the continuous collisions of the electron with the parent ion due to multiphoton resonance. The two resonance-enhanced harmonic intensities decrease gradually and orders do not change with an increase of the laser intensity, which can be illustrated through the Stark effect. The ellipticities of the two resonance-enhanced harmonics are approximately equal to the selected driving laser ellipticities regardless of the $\ifmmode\pm\else\textpm\fi{}$ sign under different driving laser ellipticities, which might provide an accessible route toward characterizing the polarization properties of the laser. Our results offer a way for the generation of quasimonochromatic circularly polarized EUV radiation with high intensity.

Dynamical symmetry and valley-selective circularly polarized high-harmonic generation in monolayer molybdenum disulfide

Circularly polarized high harmonics (CHHs) have been observed in several solid targets under single-color circularly polarized excitation. However, experimental observations show that CHHs cannot be efficiently generated in monolayer molybdenum disulphide (${\text{MoS}}_{2}$) driving by a single-color circularly polarized laser, thus letting its unique valley-selective circular dichroism (VSCD) to remain unexploited in the high harmonic generation process. Here we demonstrate that the efficient generation of CHHs in monolayer ${\text{MoS}}_{2}$ driven by counterrotating bicircular (CRB) fields and the broken inversion symmetry of monolayer ${\text{MoS}}_{2}$ leads to the generation of forbidden $3n$ ($n\ensuremath{\in}\mathbb{N}$) harmonic orders. Interestingly, we find that the VSCD lead to a distinctive valley selection of harmonic orders, while the valley selection caused by the trefoil orientation relative to the lattice is also observed. Dynamical symmetry analyses show that the rotational symmetry of the crystals can be decoded by the combination of a linearly polarized excitation scheme and CRB excitation scheme via the lowest common multiple rule. Additionally, VSCD leaves unique fingerprints in the ellipticity of harmonics.

Generation of elliptically polarized high-order harmonic radiation with bi-elliptical two-color laser beams

High-harmonic generation (HHG) from an atomic gas target provides a valuable tool to generate high-energy radiation on the tabletop. The polarization properties of this radiation can be manipulated if the HHG process is driven by a bi-elliptical orthogonal two-color laser beam (BEOTC beam). Here we theoretically consider this setup within the so-called strong-field approximation and a quantum-orbit approach. We demonstrate that this approach allows the complete description of the geometry of the outgoing elliptically polarized harmonic radiation. In particular, we identify and classify the relevant quantum orbits that contribute to the process and analyze the harmonic spectrum, ellipticities, and offset angles in detail for $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ BEOTC beams with a fundamental wavelength of $\ensuremath{\lambda}=800\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$. For these specific beam parameters, we find that the ellipticity as well as the offset angle of the polarization ellipse with respect to the BEOTC driving beam changes rapidly for consecutive harmonic orders. We show that this oscillatory behavior of the harmonic ellipticity can be explained via the superposition of the dipole radiation emitted from the target atom during different time intervals within one optical cycle of the BEOTC beam. This understanding of the HHG process driven by BEOTC beams will facilitate the generation of highly energetic radiation with complex polarization properties on the tabletop.

Generation of elliptical isolated attosecond pulse from oriented in a linearly polarized laser field

We investigate the ellipticity of the high-order harmonic generation from the oriented exposed to a linearly polarized laser field by numerically solving the two-dimensional time-dependent Schrödinger equation (2D 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 angle θ = 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.

Attosecond pulse trains with elliptical polarization from an orthogonally polarized two-color field

Generation of an elliptically polarized attosecond pulse train by an orthogonally polarized two-color (OTC) laser field is investigated theoretically and simulated numerically. The OTC field consists of two linearly polarized fields with orthogonal polarizations and frequencies that are integer multiples of the fundamental frequency ω . For the ω − 3 ω OTC field, the emitted harmonics are elliptically polarized so that they may form an elliptically polarized attosecond pulse train provided that a group of harmonics is phase-locked. This is the case if only one quantum orbit generates the corresponding part of the harmonic spectrum. If so, then two attosecond pulses are emitted per optical cycle due to the dynamical symmetry of the ω − 3 ω OTC field. Atomic targets with an s ground state only generate attosecond pulses with almost linear polarization. Using, however, targets with a p ground state, attosecond pulses with substantial ellipticity can be produced because ground states with opposite magnetic quantum numbers m = + 1 and m = − 1 produce harmonics with opposite helicities at different rates. In this case, the harmonic intensity and harmonic ellipticity are different for the ground states with the magnetic quantum number m = ± 1 . These differences are the source of the attosecond pulse ellipticity and can be controlled using the relative phase as a control parameter. In addition, by choosing a particular group of harmonics, one can select the desired ellipticity of the attosecond pulse train.

Ellipticity of the harmonic emission from graphene irradiated by a linearly polarized laser

We investigate the high-order harmonic generation in graphene irradiated by a linearly polarized intense laser, addressing the ellipticity or polarization properties of the harmonics. We exploit time-dependent density functional theory to calculate the harmonic spectra for a laser wavelength of 4770 nm and an intensity of 1.7 $\mathrm{TW}/{\mathrm{cm}}^{2}$, and our numerical results can qualitatively reproduce recent experimental data. Our simulations also reveal that the harmonic ellipticity depends on both the harmonic order and the orientation angle between the graphene symmetric axis and the laser polarization direction. It can reach 0.68 for the ninth-order harmonic at the orientation angle of ${20}^{\ensuremath{\circ}}$. To understand the mechanism of the high ellipticity, we develop a two-band model based on the tight-binding approximation. We may explain the ellipticity of high-order harmonic generation by investigating the transition dipole moments in the two-band model. Our theory further predicts a sensitive dependence of the harmonic ellipticity on the laser intensity for various laser wavelengths.

Resolving the polarization of high-order harmonic generation by temporal multislit interferometry

We propose a temporal multislit interference model of high-order harmonic generation (HHG). By using the interference picture, we investigate the polarization features of harmonics generated by atoms and the two-dimensional synthesized driving laser fields. The result shows that the selection rules and ellipticity of harmonics can be understood by intracycle interference. Based on quantum path analysis, we show the harmonic polarization can be controlled by modifying the structure of the temporal interferometer. We perform a quantitative analysis of the harmonic polarization spectrum in terms of electron dynamics and provide an intuitive picture and a general tool for HHG investigation.

Elliptical high-order harmonic generation from H2+ driven by orthogonally polarized two-color laser fields

We theoretically investigate the elliptical high-order harmonic generation from the H${}_{2}^{+}$ molecule driven by the orthogonally polarized two-color laser field by numerically solving the two-dimensional time-dependent $\mathrm{Schr}\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\text{o}}\mathrm{dinger}$ equation. The results show that the odd-order harmonics in the $x$ component and the even-order harmonics in the $y$ component can be generated with the specific alignment angle $\ensuremath{\theta}={0}^{\ensuremath{\circ}}$ for the different intensity ratios of the laser fields. The harmonic intensity distribution and ellipticity distribution at the different intensity ratios of the laser fields and the alignment angles differ significantly from each other. The result also shows that the ellipticity-tunable high-order harmonics can be generated through adjusting the intensity ratio of the laser fields and the alignment angles. Further analyses show that the amplitude ratio and the phase difference of the $x$ and $y$ components of the harmonics are the origin of the ellipticity of the harmonics in general. The two-center interference effect can also affect the ellipticity of the harmonics. The results show that the ellipticity of the harmonics can be used as a potential tool to probe the position of the minimum. The results we obtained can be useful for the optimization of elliptically polarized XUV radiation generation.

High ellipticity of harmonics from molecules in strong laser fields of small ellipticity

We study high-order harmonic generation (HHG) from aligned molecules in strong elliptically polarized laser fields numerically and analytically. Our simulations show that the spectra and polarization of HHG depend strongly on the molecular alignment and the laser ellipticity. In particular, for small laser ellipticity, large ellipticity of harmonics with high intensity is observed for parallel alignment, with forming a striking ellipticity hump around the threshold. We show that the interplay of the molecular structure and two-dimensional electron motion plays an important role here. This phenomenon can be used to generate bright elliptically-polarized EUV pulses.

Model-potential method for high-order harmonic generation in monolayer graphene

We develop a model potential to simulate the effective potential of a single active electron in monolayer graphene by taking the electron energy band structure calculated by the density functional theory (DFT) as a reference. Based on the single-electron Schr\"odinger equation, the model potential is used to calculate not only the energy band structure but also the transition dipole moment, charge density, and other physical quantities of graphene. These quantities are compared with results from DFT and a good consistency is achieved. The simulation of laser-graphene interaction with the same laser parameters as Yoshikawa et al. [Science 356, 736 (2017)] is performed with the time-dependent Schr\"odinger equation. The obtained driving laser ellipticity scaling, the harmonic ellipticity, and the harmonic major-axis angle can well reproduce the experimental results. It is found that the carrier-envelope phase and chirp effects are capable of regulating high-order harmonic generation in monolayer graphene. The model potential method can be extended to field-free calculations and dynamic simulations in other materials as long as the corresponding model potential is constructed.