A macroscopic theory of high-order harmonic generation (HHG) is presented, which applies a focal-averaging method based on the integral solution of the wave equation. The macroscopic high-harmonic ...yield is the coherent superposition of the single-atom contributions of all atoms of the generating medium, which are positioned at different spatial points of the laser focus and exposed to the space-time-dependent laser pulse. The HHG spectrum obtained in our macroscopic simulations is qualitatively different from the one obtained using the microscopic or single-atom theory of HHG. Coherent intensity focal averaging, the simpler and more approximate of two methods we introduced, gives the spectrum which forms a declining plateau with the same cutoff position as that of the microscopic spectrum. The second, more precise method, which we call coherent spatio-temporal focal averaging, shows that it is possible, changing the macroscopic conditions, to obtain an observable peak in the harmonic spectrum at an energy much lower than the microscopic cutoff energy. Generally, the high-harmonic yield appears to be dominated by the contributions of laser-pulse spatio-temporal regions with lower intensities as well as by interference, so that the high-energy plateau and its sharp cutoff are quenched in the theoretical simulation and, presumably, in the experiment. The height and position of this peak strongly depend on the macroscopic conditions. We confirmed these findings by applying our macroscopic theory to simulate two recent experiments with mid-infrared laser fields, one with a linearly polarized field and the other one with a bicircular field.
The differential ionization rate for strong-field ionization by tailored laser fields of atomic systems averaged over the magnetic quantum number satisfies particular inversion and reflection ...symmetries. The symmetries of the elliptic-dichroism parameter, which is related to the change of sign of the ellipticity of the laser field, are considered in detail, with particular emphasis on high-order above-threshold ionization. The general results are illustrated by the examples of an elliptically polarized laser field and a bi-elliptical orthogonally polarized two-color (BEOTC) field. For the BEOTC field the differential ionization rate and the elliptic-dichroism parameter are investigated for the
ω
-2
ω
and
ω
-3
ω
field combinations and for various relative phases between the laser-field components. The inversion and reflection symmetries of the photoelectron momentum distribution in the polarization plane of the field depend on the parities of
r
and
s
in the
rω
--
sω
BEOTC field combination and on the relative phase between the field components. We suggest that, by analyzing the symmetry properties of the measured momentum distribution of the elliptic-dichroism parameter, one can identify the mechanism of strong-field ionization. If the rescattering mechanism is dominant one can use these distributions to obtain information about the atomic and molecular structure and dynamics.
Elliptic dichroism parameter (from −1 (blue) to +1 (yellow)) in strong-field ionization of argon by an
ω
-2
ω
BEOTC (
= 0.4 and 0.6) field.
Nondipole effects in processes assisted by a THz field having the strength of a few MV/cm can be significant due to its long wavelength. We illustrate this for strong-laser-field-induced ionization ...assisted by a THz field. To this end, we generalize our strong-field-approximation theory so that it includes the first-order term in a 1/
c
expansion of the vector potential. We show that in this case, in addition to a shift of the maximum of the photoelectron momentum distribution, the differential ionization probability as well as the cutoff energy can be significantly increased. For an explanation of these unexpected results we use the saddle-point method adjusted to include nondipole effects.
Above-threshold ionization of rare-gas atoms by a bicircular field with its two components counterrotating is theoretically investigated by means of the improved strong-field approximation. Both ...direct and rescattered electrons are considered and the quantum orbits that lead into a specific final state are calculated and depicted. The angle-dependent spectrum reflects the discrete rotational symmetry of the bicircular field. The backward-scattering contributions are very similar to those generated by a linearly polarized field; several such contributions are rotated one versus the other by the symmetry angle of the discrete rotational symmetry. The forward-scattering contributions dramatically affect the velocity map at comparatively low momenta. The direct-electron spectrum observes reflection symmetry about several symmetry axes determined by the field symmetry. This is broken by rescattering.
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.
We introduce the theory of high-order harmonic generation by homonuclear diatomic cations. The elliptically polarised harmonics can be produced using the orthogonal two-colour field and the cations whose molecular orbital does not have nodal planes.
We investigate above-threshold detachment induced by an ultrashort laser pulse with one or two carrier frequencies. Particular attention is devoted to the phase-dependent effects in the low- and ...medium-energy parts of the spectrum. In particular, we show that the photoelectron spectra can be controlled using the phases of the field components and the ellipticity as parameters. Also, using the saddle-point method, we show that the interference between various ionization pathways can also be controlled using these parameters. Depending on the value of the phases and the ellipticity, one or more saddle-point solutions can be significant in the examined part of the photoelectron spectra. If the contribution of only one saddle-point solution is dominant, the photoelectron yield is a smooth function of the photoelectron energy. On the other hand, when two or more contributions have to be taken into consideration, it is important whether the corresponding ionization times are within the same optical cycle or not. If they are, the interference pattern of these contributions is characterized by deep minima. On contrary, if the ionization times of the contributions which have to be taken into consideration are in different optical cycles, their interference would produce a rapidly oscillating spectrum. We propose a scheme for analyzing the asymmetry of the photoelectron spectra emitted in the directions characteristic for a particular driving field. We show that, by using a two-component driving pulse, it is possible to achieve a fine control on which contributions are significant and which can be neglected. This control is more advanced than the control by the linearly polarized field for which the electron dynamics is rather simple.
Graphic abstract
Quantum-orbit theory is a powerful tool in strong-field physics and attoscience which enables useful insights into the physics of atomic processes in strong fields. We first review this theory with ...an emphasis on more complex tailored fields for which exact calculations are difficult. This is followed by examples of high-order harmonic generation and high-order above-threshold ionization by a bicircular field. Relevant quantum orbits and the corresponding quasiclassical electron trajectories are identified and used to describe the photoelectron momentum distribution. We have also applied quantum-orbit theory to describe terahertz-pulse-assisted strong-field ionization. A novel result is the discovery that, by adjusting the time delay between the laser and terahertz pulses, the low-energy structures in the photoelectron spectra can be extended to much higher energies (in comparison with that in the absence of the THz pulse), which allows to analyze them with a much better resolution.
The contributions of two energetically highest molecular orbitals to the harmonic emission rate are analysed for a two-component laser field. For diatomic molecules exposed to the elliptically ...polarised field, the emission from the highest-occupied molecular orbital (HOMO) is dominant for various molecular orientations with respect to the laser field. However, the contribution of the lower molecular orbital (HOMO-1) can become significant or even dominant for some molecular orientations. We introduce the ratio of the coherent over the incoherent sum of the HOMO and HOMO-1 contributions as a quantitative measure of the significance of the particular molecular orbital. Also, the gaseous medium response is different for the left and right elliptically polarised light and the molecular characteristics are imprinted into this difference. Moreover, for the orthogonally polarised two-colour (OTC) laser field the relative contributions of HOMO and HOMO-1 depend to a great extent on the relative phase between the field components. The importance of the HOMO-1 can be assessed by the relative error which is made if the harmonic spectra are obtained only with the HOMO contribution. Finally, we investigate the interference of the contributions of two highest molecular orbitals. We show that, for the OTC field, the destructive interference depends linearly on the intensity of the field components. Also, the interference minima shift towards the higher energies with the increase of the component wavelength.
Atoms interacting with intense laser fields can emit electrons and photons of very high energies. An intuitive and quantitative explanation of these highly nonlinear processes can be found in terms ...of a generalization of classical Newtonian particle trajectories, the so-called quantum orbits. Very few quantum orbits are necessary to reproduce the experimental results. These orbits are clearly identified, thus opening the way for an efficient control as well as previously unknown applications of these processes.
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