Coulomb-induced emission time shifts in high-order harmonic generation from H2.

Accurate emission times of high-order harmonic generation (HHG) are vital for high-precision ultrafast detection in attosecond science, but a quantitative analysis of Coulomb effects on this time is absent in the molecular HHG. Here, we investigate the Coulomb-induced emission-time shift in HHG of H2+ with two different internuclear distances R, where the times obtained via the Gabor transform of numerical data from solving the time-dependent Schrödinger equation are used as simulation experiment results. Based on the molecular strong-field approximation, we develop a trajectory-resolved classical model that takes into account the molecular two-center structure. By selecting appropriate electron trajectories and including Coulomb interactions, the classical trajectory method can reproduce Gabor emission times well. This consistence reveals that Coulomb tails cause an emission-time shift of ∼35 as at the R = 2.0 a.u. case and of ∼40-60 as at the R = 2.6 a.u. case under the present laser parameters when compared to the Coulomb-free quantum-orbit model. Our results are of significance to probe the attosecond dynamics via two-center interference.

A redshift mechanism of high-order harmonics: Change of ionization energy.

We theoretically study the high-order harmonic generation of H2+ and its isotopes beyond the Born-Oppenheimer dynamics. It is surprising that the spectral redshift can still be observed in high harmonic spectra of H2+ driven by a sinusoidal laser pulse in which the trailing (leading) edge of the laser pulse is nonexistent. The results confirm that this spectral redshift originates from the reduction in ionization energy between recombination time and ionization time, which is obviously different from the nonadiabatic spectral redshift induced by the falling edge of the laser pulse. Additionally, the improved instantaneous frequency of harmonics by considering the changeable ionization energy can deeply verify our results. Therefore, this new mechanism must be taken into account when one uses the nonadiabatic spectral redshift to retrieve the nuclear motion.

Enhancement of the second plateau in solid high-order harmonic spectra by the two-color fields.

We theoretically investigate high-order harmonic generation (HHG) from solids in two-color fields. It is found that under the premise of maintaining the same amplitude, the intensity of the second plateau can be enhanced by two to three orders in a proper two-color field compared with the result in the monochromatic field with the same frequency as the driving pulse of the two-color field. This can be attributed to the fact that most excited electrons can be driven to the top of the first conduction band due to the larger vector potential of the two-color fields, which leads to the higher electron population of upper conduction bands. Moreover, we also find that isolated attosecond pulses can be generated from solids by choosing a proper two-color field that allows the electrons to reach the top of the first conduction band only once. This work provides a promising method for extending the range of solid HHG spectra in experiments.

Reexamining the high-order harmonic generation of HD molecule in non-Born-Oppenheimer approximation.

The high-order harmonic generation of the HD molecule is studied in non-Born-Oppenheimer approximation. It is found that there are only the odd harmonics in the harmonic spectrum of the HD molecule though the generation of even harmonics is possible in principle. Theoretical analysis [T. Kreibich et al., Phys. Rev. Lett. 87, 103901 (2001)] reveals that the nuclear dipole moment can contribute to the generation of the even harmonics, but the acceleration of the nucleus is about three orders of magnitude less than that of the electron. Hence, the even harmonics cannot be observed in the harmonic spectrum of the HD molecule.

Theoretical scheme for simultaneously observing forward-backward photoelectron holography.

Photoelectron angular momentum distribution of He+ driven by a few-cycle laser is investigated numerically. We simultaneously observe two dominant interference patterns with one shot of lasers by solving the 3D time-dependent Schrodinger equation. Analysis of a semiclassical model identifies these two interference patterns as two types of photoelectron holography. The interference pattern with Pz>0 is a type of forward rescattering holography, which comes from the interference between direct (reference) and rescattered (signal) forward electrons ionized in the same quarter-cycle. The interference pattern with Pz<0 is a type of backward rescattering holography, which comes from the interference between a direct electron ionized in the third quarter-cycle and rescattered backward electron ionized in the first quarter-cycle. Moreover, we propose a method to distinguish this backward rescattering holography and intracycle interference patterns of direct electrons.

Intense supercontinuum generation exceeding 300eV using a two-color field in combination with a 400-nm few-cycle control pulse.

We propose a method to control the harmonic process by using a two-color field in combination with a 400-nm few-cycle control pulse for the generation of an ultra-broadband supercontinuum with high efficiency. The ionization and acceleration steps in the harmonic process can be simultaneously controlled by using a three-color field synthesized by a 2000-nm driving pulse and two weak 800-nm and 400-nm control pulses. Then an intense supercontinuum covered by the spectral range from 140 eV to 445 eV is produced. The 3D macroscopic propagation is also employed to select the short quantum path of the supercontinuum, then intense isolated sub-100-as pulses with tunable central wavelengths are directly obtained within water window region. In addition, the generation of isolated attosecond pulses in the far field is also investigated. An isolated 52-as pulse can be generated by using a filter centered on axis to select the harmonics in the far field.

Attosecond ionization control for broadband supercontinuum generation using a weak 400-nm few-cycle controlling pulse.

We theoretically demonstrate a method for generating the broadband supercontinuum. It is found that a weak 400-nm few-cycle pulse can be used to replace the ultraviolet attosecond pulse for controlling the ionization dynamics of the electron wave packets when a long-wavelength driving pulse is adopted. By adding a 400-nm few-cycle laser pulse to a 2000-nm driving pulse at proper time, only a quantum path can be selected to effectively contribute to the harmonics, leading to the efficient generation of a broadband supercontinuum. Moreover, our scheme is stable against nearly all the small parameter shift of the driving pulse and the controlling pulse. The macroscopic investigation reveals that the macroscopic supercontinuum with the bandwidth of about 165eV can be obtained. Then isolated sub-110-as pulses can be directly generated. Moreover, the generated attosecond pulse has a divergence angle of about 0.1mrad in the far field, which indicates its beam quality is good. Besides, it is also found that a near-field spatial filter can be used to select the different quantum paths (short or long) in the far field.

Isolated attosecond pulse generation from pre-excited medium with a chirped and chirped-free two-color field.

We theoretically investigate the isolated attosecond pulse generation from pre-excited medium with a chirped and chirped-free two-color field. It is found that the large initial population of the excited state can lead to the high density of the free electrons in the medium and the large distortion of the driving laser field after propagation, though it benefits large enhancement of harmonic intensity in single atom response. These effects can weaken the phase-match of the macroscopic supercontinuum. On the contrary, the small initial population of 4% can generate well phase-match intense supercontinuum. We also investigate an isolated attosecond pulse generation by using a filter centered on axis to select the harmonics in the far field. Our results reveal that the radius of the spatial filter should be chosen to be small enough to reduce the duration of the isolated attosecond pulse due to the curvature effect of spatiotemporal profiles of the generated attosecond pulses in the far field.

Broadband supercontinuum generation method combining mid-infrared chirped-pulse modulation and generalized polarization gating.

We present a method to control the harmonic process by a mid-infrared modulated generalized polarization gating for the generation of the broadband supercontinuum. Using a mid-IR generalized polarization gating modulated by a weaker mid-IR linearly polarized chirped field, the ionization, acceleration and recombination steps in the HHG process are simultaneously controlled, leading to the efficient generation of an ultra-broadband supercontinuum covered by the spectral range from ultraviolet to water window x-ray. Using this method we expect that isolated sub-100 attosecond pulses with tunable wavelength could be obtained straightforwardly.