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.
Using the strong-field approximation we systematically investigate the selection rules for high-order harmonic generation and the symmetry properties of the angle-resolved photoelectron spectra for ...various atomic and molecular targets exposed to one-component and two-component laser fields. These include bicircular fields and orthogonally polarized two-color fields. The selection rules are derived directly from the dynamical symmetries of the driving field. Alternatively, we demonstrate that they can be obtained using the conservation of the projection of the total angular momentum on the quantization axis. We discuss how the harmonic spectra of atomic targets depend on the type of the ground state or, for molecular targets, on the pertinent molecular orbital. In addition, we briefly discuss some properties of the high-order harmonic spectra generated by a few-cycle laser field. The symmetry properties of the angle-resolved photoelectron momentum distribution are also determined by the dynamical symmetry of the driving field. We consider the first two terms in a Born series expansion of the T matrix, which describe the direct and the rescattered electrons. Dynamical symmetries involving time translation generate rotational symmetries obeyed by both terms. However, those that involve time reversal generate reflection symmetries that are only observed by the direct electrons. Finally, we explain how the symmetry properties, imposed by the dynamical symmetry of the driving field, are altered for molecular targets.
Abstract
When exposed to strong laser fields, atoms or molecules can absorb more photons from the laser field than is necessary for ionization. This process is called above-threshold ionization ...(ATI). In analyzing this process, the strong-field approximation (SFA) turns out to be a very useful theoretical tool. In the SFA the differential ionization rate, which is an observable quantity, can be expressed as an integral over the ionization time and can be calculated by numerical integration (NI) or using the saddle-point method (SPM). When we use the Slater orbitals to describe the ground-state wave function of the valence electron, the results obtained using the SPM and NI do not agree. We find the reasons for this disagreement and introduce a modified SPM that leads to excellent agreement between the SPM and NI results for various strong laser fields.
Improved molecular strong-field approximation theory is used to calculate the ionisation probability for the high-order above-threshold ionisation process induced by a few-cycle pulse with two ...carrier frequencies and one envelope. The asymmetry in the photoelectron momentum distribution is due to the ultrashort nature of the driving pulse and due to the relative orientation of the molecule with respect to the laser field. We introduce the generalised asymmetry parameter, which can be used to quantitatively measure the asymmetry between the photoelectron spectra along arbitrarily many selected directions. We investigate the difference between the asymmetry parameters calculated for atomic and molecular targets and show that the contributions to the asymmetry strongly depend on the type of the employed driving pulse. For the driving pulse with components that are linearly polarised with mutually orthogonal polarisations, we find that the main source of the asymmetry, especially in the high-energy part of the spectrum, is the ultrashort nature of the pulse. The relative orientation of the molecule with respect to the laser pulse only affects the low- and medium-energy parts of the spectrum. On the other hand, for the driving pulse with circularly polarised counterrotating components, the asymmetry introduced by molecular orientation is more pronounced. We also analyse the influence of the characteristics of molecular orbitals on the asymmetries using the examples of N
2
and O
2
molecules.
Improved molecular strong-field approximation theory is used to calculate the ionisation probability for the high-order above-threshold ionisation process induced by a few-cycle pulse with two carrier frequencies and one envelope.
Using the molecular strong-field approximation, we investigate high-order harmonic generation by heteronuclear diatomic molecules exposed to an orthogonally polarized two-color laser field, which ...consists of two mutually orthogonal linearly polarized fields with frequencies
r
ω
and
s
ω
. Here,
r
and
s
are integers and
ω
is the fundamental frequency. The harmonic emission rate and the harmonic ellipticity can be controlled using the laser-field parameters, in particular the relative phase and the intensity ratio of the laser-field components. The value of the relative phase, for which the emission rate is optimal, and the position of the cutoff can be estimated using a classical model. Also, we analyze the harmonic emission rate and the harmonic ellipticity as functions of the molecular orientation, which can also be used as a control parameter. Two types of minima are present in the spectra, depending on
r
and
s
. For
r
+
s
even, interference minima are present in the spectra of the
T
-matrix component either parallel or perpendicular to the internuclear axis. Using quantum-orbit theory and the saddle-point method, we derive a condition for the interference minima, which relates the molecular orientation angle
θ
L
and the harmonic order
n
. The corresponding curves in the (
θ
L
,
n
) plane well reproduce the minima of the numerically calculated spectra. For
r
+
s
odd, minima are present in the spectra for a particular molecular orientation angle. These minima are explained using the explicit form of the
T
-matrix element. A heteronuclear as opposed to a homonuclear molecule affords a larger region in the parameter space where both the harmonic ellipticity and the harmonic intensity vary smoothly and both are large.
In the present paper, some well-known tests based on empirical distribution functions (EDF) with estimated parameters for testing composite normality hypothesis are revisited, and some new results on ...asymptotic properties are provided. In particular, the approximate Bahadur slopes are obtained in the case of close alternatives for the EDF-based tests as well as the likelihood ratio test. The local approximate efficiencies are calculated for several close alternatives. The obtained results could serve as a benchmark for evaluation of the quality of recent and future normality tests.
Scientometrics and academia Zerem, Enver; Vranić, Semir; Hanjalić, Kemal ...
Biomolecules & Biomedicine,
03/2024, Letnik:
24, Številka:
2
Journal Article
Recenzirano
Odprti dostop
The social significance and quality of every human activity are proportional to its usefulness to the social community. Science belongs to the very top of the processes and events in the history of ...humankind that strongly influenced the development of society, which over time transformed it and contributed to the common good. Science produced new knowledge that made it possible for billions of people to rise out of poverty, develop industrialization and mass communication, eradicate many dangerous diseases for humankind, and enable humans to leave their footprints on the moon. Science is a human activity that produces new knowledge presented through innovations, patents, and publications, aimed at solving the problems facing humanity. Read more in the PDF.
A theory of high-order above-threshold ionization (HATI) of atoms is presented and applied to the ionization of inert gases by an orthogonal two-color (OTC) field. The transition matrix element is ...derived within the strong-field approximation and calculated by numerical integration and the saddle-point method. The atomic bound state is expressed as an expansion in terms of the Slater-type orbitals as well as an asymptotic wave function. The energy and momentum distributions of the HATI electrons are calculated for the
ω
–
2
ω
and
ω
–
3
ω
OTC fields. A detailed analysis of the saddle-point solutions and their contribution to the overall differential ionization rate for these two cases is presented. Optimal values of the OTC field parameters for which the ionization rate is maximal in the high-energy region of the photoelectron spectra are found. Special attention is devoted to the symmetry consideration of the photoelectron momentum distributions. All these results are analyzed in detail using the quantum-orbit formalism, which gives a better physical insight into the HATI process.
Graphic abstract
We investigate emission rate and ellipticity of high-order harmonics generated exposing a homonuclear diatomic molecule, aligned in the laser-field polarization plane, to a strong orthogonally ...polarized two-color (OTC) laser field. The linearly polarized OTC-field components have frequencies rω and sω, where r and s are integers. Using the molecular strong-field approximation with dressed initial state and undressed final state, we calculate the harmonic emission rate and harmonic ellipticity for frequency ratios 1:2 and 1:3. The obtained quantities depend strongly on the relative phase between the laser-field components. We show that with the OTC field it is possible to generate elliptically polarized high-energy harmonics with high emission rate. To estimate the relative phase for which the emission rate is maximal we use the simple man’s model. In the harmonic spectra as a function of the molecular orientation there are two types of minima, one connected with the symmetry of the molecular orbital and the other one due to destructive interference between different contributions to the recombination matrix element, where we take into account that the electron can be ionized and recombine at the same or different atomic centers. We derive a condition for the interference minima. These minima are blurred in the OTC field except in the cases where the highest occupied molecular orbital is modeled using only s or only p orbitals in the linear combination of the atomic orbitals. This allows us to use the interference minima to assess which atomic orbitals are dominant in a particular molecular orbital. Finally, we show that the harmonic ellipticity, presented in false colors in the molecular-orientation angle vs. harmonic-order plane, can be large in particular regions of this plane. These regions are bounded by the curves determined by the condition that the harmonic ellipticity is approximately zero, which is determined by the minima of the T-matrix contributions parallel and perpendicular to the fundamental component of the OTC field.
High-order harmonic generation by orthogonally polarized two-color (OTC) laser fields is analysed using strong-field approximation and quantum-orbit theory. Results for the field components frequency ...ratio of 2:1 and 3:1 are presented and compared. We have shown that, depending on the relative phase between the field components, the shape of the high-harmonic spectrum can be very different from that obtained by a monochromatic linearly polarized laser field. It is also shown that it is possible to generate elliptically polarized high-order harmonics with very high photon energies using OTC laser field with the frequency ratio of 3:1 and a long fundamental wavelength. An effective relative phase control of the harmonic emission is demonstrated. The obtained results are explained using the quantum-orbit theory.
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