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In Anbetracht des steigenden Umweltbewusstseins vieler Unternehmen wird in diesem Vortrag vorgestellt, wie Machine Learning (ML) eingesetzt werden kann, um Produktionsanlagen ressourcenschonender zu betreiben. Es wird ein Verfahren vorgestellt, mit dem die Energieeffizienz von Anlagen mithilfe von unüberwachten ML-Methoden analysiert werden kann. Mit den dargestellten Verfahren kann nicht nur zwischen „Produktion ist aktiv“ und „Produktionspause“ unterschieden werden, sondern vielmehr können ineffiziente Anlagenzustände identifiziert werden. Bezogen auf den Strom- und Druckluftverbräuchen, welche als Eingabedaten für die Modelle dienen, wird ein zeitunabhängiger und ein zeitabhängiger Modellansatz vorgestellt und die unterschiedlichen Fähigkeiten dargestellt. Neben der Erläuterung der algorithmischen Umsetzung sowie der Datenerhebung liegt ein Augenmerk der Arbeit darin, die Vorgehensweise so generisch zu halten, dass sich die mit Festo Didactic Lernfabriken erzielten Ergebnissen mit vertretbarem Aufwand auch auf andere Produktionsanlagen übertragen lassen.

Nondipole effects occurring in the process of atomic ionization by an intense, mid-infrared, counter-rotating bicircular laser field are investigated using the strong-field approximation with leading-order nondipole corrections. The time integrals appearing in the expression for the differential ionization rate are computed in two ways: numerically, and by applying the saddle-point approximation. The nondipole corrections introduce an asymmetry in the photoelectron momentum distribution along the field propagation direction. The asymmetry is quantified by the partial average value of the propagation-direction momentum component of the photoelectrons and by the normalized difference of the differential ionization rates computed including and excluding the nondipole corrections. Using the saddle-point approximation, it is investigated how the nondipole corrections change the solutions for direct photoelectrons and how this affects the momentum spectra. The impact of nondipole corrections increases with increasing photoelectron energy. Analysis of the complete photoelectron spectra including both direct and rescattered photoelectrons shows that, in the low-energy region, a shift against the propagation direction occurs. The partial average of the propagation-direction momentum component in the rescattering region exhibits a plateau structure and also a local minimum structure that was recently observed in an experiment with a linearly polarized laser field (Lin et al., Phys Rev. Lett. 128, 023201 (2022)).

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

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 $$r\omega $$ and $$s\omega $$ . Here, r and s are integers and $$\omega $$ 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 $$\theta _L$$ and the harmonic order n. The corresponding curves in the ( $$\theta _L$$ , 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.

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.

Based on the strong-field approximation, we report results for high-order harmonic generation by bi-elliptical orthogonally polarized two-color (BEOTC) fields with frequency ratios of 2:1 and 3:1 and fundamental wavelengths of 800 and 1800 nm. A BEOTC field denotes the superposition of two copropagating counter-rotating elliptically polarized fields with different wavelengths and orthogonal semimajor axes. Its two limiting cases are the bicircular field and the linearly polarized orthogonal two-color field [D. B. Milo\ifmmode \check{s}\else \v{s}\fi{}evi\ifmmode \acute{c}\else \'{c}\fi{} and W. Becker, Phys. Rev. A 100, 031401(R) (2019)]. A detailed analysis of the high-order harmonic intensities and ellipticities as functions of the harmonic order, the ellipticity, and the relative phase between the two driving-field components is presented. Regions of the parameter space are identified where the harmonic ellipticities are very high. Surprisingly, this can be the case already for very small ellipticity (as small as $\ensuremath{\varepsilon}=0.01$) of the driving field. This can be important for practical applications. In the opposite limit where the BEOTC field is close to bicircular, the selection rules that govern the latter case can also be very quickly invalidated. For the 2:1 case, this can result in an apparent shift of the selection rules by one harmonic order.

Over the past three decades numerous numerical methods for solving the time-dependent Schr\"odinger equation within the single-active electron approximation have been developed for studying ionization of atomic targets exposed to an intense laser field. In addition, various numerical techniques for extracting the photoelectron spectra from the time-dependent wave function have emerged. In this paper we compare photoelectron spectra obtained by either projecting the time-dependent wave function at the end of the laser pulse onto the continuum state having the proper incoming boundary condition or by using the window-operator method. Our results for three different atomic targets show that the boundary condition imposed onto the continuum states plays a crucial role for obtaining correct spectra accurate enough to resolve fine details of the interference structures of the photoelectron angular distribution.

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.

High-harmonic generation by aligned diatomic molecules in orthogonally po-larized two-color laser fields is considered using the molecular strong-field approximation. Regions of the parameter space with large harmonic ellipticity are identified.

Orthogonally polarized two-color fields, typically with a frequency ratio of 2:1, only rarely of 3:1, have been utilized for a variety of purposes. Driving high-order harmonic generation (HHG), the former yield linearly and the latter elliptically polarized harmonics. With emphasis on the 3:1 frequency ratio, we investigate the shape of the HHG spectrum for the fundamental frequency being in the midinfrared range (2200 nm). Depending on the relative phase between the two field components, a plethora of spectral shapes can be realized. For a suitable phase, the harmonic power can be concentrated within the highest 10% of the spectrum. The results are analyzed in terms of quantum orbits. For the 3:1 case, the scheme suggests an efficient table-top source of elliptically polarized soft x rays.

We introduce an approximation for strong-laser-field-induced ionization of atoms, which we call atom-Volkov strong-field approximation (aV SFA). For the final state, instead of a plane wave (used in the standard well-known SFA) or a Coulomb wave (used in the Coulomb-Volkov SFA), in the aV SFA we use the exact atom-specific scattering states. We first introduce the aV SFA as an ansatz and show that it yields results that are closer to the exact results than those obtained using the SFA. After that, we systematically derive an iterative theory whose zeroth order is equal to the introduced aV SFA. We analyze its first-order correction, which corresponds to electron rescattering off the parent ion and show that, in the case of forward scattering, this correction leads to the low-energy structures in the photoelectron spectra which are observed in the experiments.

Strong-field ionization and Rydberg-state excitation (RSE) near the continuum threshold exhibit two phenomena that have attracted a lot of recent attention: the low-energy structure (LES) just above and frustrated tunneling ionization just below the threshold. The former becomes apparent for longer laser wavelengths, while the latter has been especially investigated in the near infrared; both have been treated as separate phenomena so far. Here we present a unified perspective based on electron trajectories, which emphasizes the very important role of the electron-ion Coulomb interaction as expected in this energy region. Namely, those trajectories that generate the LES can also be recaptured into a Rydberg state. The coherent superposition of the contributions of such trajectories with different travel times (each generating one of the various LES peaks) causes an oscillation in the intensity dependence of the RSE yield, which is especially noticeable for longer wavelengths. The theory is illustrated by RSE experiments at 1800 nm, which agree very well with the theory with respect to position and period of the oscillation. The wavelength scaling of the RSE oscillation is also discussed. Our work establishes a solid relationship between processes below and above the threshold and sheds new light on atomic dynamics driven by intense laser fields in this critical energy region.

We investigate laser-assisted electron-ion recombination (LAR), high-order harmonic generation (HHG) and above-threshold ionization (ATI) of argon atoms by a bicircular laser field, which consists of two coplanar counter-rotating circularly polarized fields of frequencies r? and s?. The energy of soft x rays generated in the LAR process is analyzed as a function of the incident electron angle and numerical results of direct recombination of electrons with Ar+ ions are presented. We also present the results of HHG by a bicircular field and confirm the selection rules derived earlier for inert-gas atoms in a p ground state. We show that the photoelectron spectra in the ATI process, presented in the momentum plane, as well as the LAR spectra exhibit the same discrete rotational symmetry as the applied field.

We investigate high-order harmonic generation of non-planar ammonia molecules by a bicircular field, which consists of two coplanar counter-rotating circularly polarised fields of frequencies ω and 2ω. This field possesses dynamical symmetries, which can be used together with the symmetry of the molecular Hamiltonian to obtain the selection rules for harmonic emission. We show analytically and confirm by numerical calculations that circularly polarised harmonics of order n = 3q ± 1, with q integer, as well as linearly polarised harmonics of order n = 3q are emitted. The presence of well-separated both linearly and circularly polarised harmonics in the same spectrum is unique to non-planar molecules.

We consider the problem of the choice of gauge in nonrelativistic strong-laser-field physics. For this purpose, we use the phase-space path-integral formalism to obtain the momentum-space matrix element of the exact time-evolution operator. With the assumption that the physical transition amplitude corresponds to transitions between eigenstates of the physical energy operator rather than the unperturbed Hamiltonian H0=(&minus, i&part, /&part, r)2/2+V(r), we prove that the aforementioned momentum-space matrix elements obtained in velocity gauge and length gauge are equal. These results are applied to laser-assisted electron-ion radiative recombination (LAR). The transition amplitude comes out identical in length gauge and velocity gauge, and the expression agrees with the one conventionally obtained in length gauge. In addition to the strong-field approximation (SFA), which is the zeroth-order term of our expansion, we present explicit results for the first-order and the second-order terms, which correspond to LAR preceded by single and double scattering, respectively. Our general conclusion is that in applications to atomic processes in strong-field physics the length-gauge version of the SFA (and its higher-order corrections) should be used. Using the energy operator as the basis-defining Hamiltonian, we have shown that the resulting transition amplitude is gauge invariant and agrees with the form commonly derived in length gauge.

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.

Journal of physics / B Atomic, molecular and optical physics B 51(16), 162002 (2018). doi:10.1088/1361-6455/aad150, Published by IOP Publ.36472, Bristol

Intense-laser-induced above-threshold ionization of a bound electron into continuum states with low energy is investigated in the context of the strong-field approximation that allows for one act of rescattering of the revisiting electron. The quantum orbits for forward and backward scattering are evaluated and generalized to arbitrary scattering angles. The velocity map of the liberated electron exhibits the well-known low-energy structure as well as other features off the polarization axis.

In this Letter, we propose a novel laser-induced inelastic diffraction (LIID) scheme based on the intense-field-driven atomic nonsequential double ionization (NSDI) process and demonstrate that, with this LIID approach, the doubly differential cross sections (DDCSs) of the target ions, e.g., ${\mathrm{Ar}}^{+}$ and ${\mathrm{Xe}}^{+}$, can be accurately extracted from the two-dimensional photoelectron momentum distributions in the NSDI process of the corresponding atoms. The extracted DDCSs exhibit a strong dependence on both the target and the laser intensity, in good agreement with calculated DDCSs from the scattering of free electrons. The LIID scheme may be extended to molecular systems and provides a promising approach for imaging of the gas-phase molecular dynamics induced by a strong laser field with unprecedented spatial and temporal resolution.

Quantum interference plays an important role in various intense-laser-driven atomic phenomena, e.g., above-threshold ionization and high-order-harmonic generation, and provides a useful tool in ultrafast imaging of atomic and molecular structure and dynamics. However, it has eluded observation in nonsequential double ionization (NSDI), which serves as an ideal prototype to study electron-electron correlation. Thus far, NSDI usually could be well understood from a semiclassical perspective, where all quantum aspects have been ignored after the first electron has tunneled. Here we perform coincidence measurements for NSDI of xenon subject to laser pulses at 2400 nm. It is found that the intensity dependence of the asymmetry parameter between the yields in the second and fourth quadrants and those in the first and third quadrants of the electron-momentum-correlation distributions exhibits a peculiar fast oscillatory structure, which is beyond the scope of the semiclassical picture. Our theoretical analysis indicates that this oscillation can be attributed to interference between the contributions of different excited states in the recollision-excitation-with-subsequent-ionization channel. Our work demonstrates the significant role of quantum interference in NSDI and may create an additional pathway towards manipulation and imaging of the ultrafast atomic and molecular dynamics in intense laser fields.

Experimental and theoretical investigations of the wavelength dependence of the nonsequential double ionization (NSDI) process of the xenon atom in intense laser fields are reported. The observed wavelength dependence of the ratio Xe2+/Xe+ deviates significantly from the prediction of the three-step model of ionization (sometimes called the "simple-man" model), both in the slope of the overall decrease with increasing wavelength and in the existence of some pronounced humps. A semiclassical model calculation reproduces the changing slope of the overall decrease, which is due to the interplay of wave-packet diffusion, Coulomb focusing, and a closely related Coulomb defocusing effect of the liberated electron. The hump is beyond the scope of the semiclassical model.

We investigate strong-field ionization of linear molecules by a two-color laser field of frequencies rω and sω having coplanar counterrotating or corotating elliptically polarized components (ω is the fundamental laser field frequency and r and s are integers). Using the improved molecular strong-field approximation we analyze direct above-threshold ionization (ATI) and high-order ATI (HATI) spectra. More precisely, reflection and rotational symmetries of these spectra for linear molecules aligned in the laser-field polarization plane are considered. The reflection symmetries for particular molecular orientations, known to be valid for a bicircular field (this is the field with circularly polarized counterrotating components), are valid also for arbitrary component ellipticities. However, specific rotational symmetries that are satisfied for HATI by a bicircular field, are violated for an arbitrary elliptically polarized field with counterrotating components. For the corotating case and the N2 molecule we analyze molecular-orientation-dependent interferences and plateau structures for various ellipticities.

The nonlinear scattering of a laser pulse off spherical nanoclusters with free electrons and with a diffuse surface is examined in the collisionless hydrodynamics approximation in the framework of perturbation theory with respect to the laser pulse intensity, as well as of the steady-state approximation. In a previous publication [S.V. Fomichev and W. Becker, Phys. Rev. A 81, 063201 (2010)] we reported the full nonlinear hydrodynamic model of forced collective electron motion confined to a cluster with diffuse surface and introduced two different perturbation theories corresponding to different laser intensity regimes. In the current paper, in the framework of this hydrodynamic model we focus on the properties of plasmon resonance-enhanced third-harmonic generation in a spherical cluster and its dependence on the shape of its diffuse surface whose role increases for nonlinear processes. At the same time, the quadrupole second-harmonic generation in a spherical cluster is also inspected as a necessary intermediate step. Both cold metal clusters in vacuum or in a dielectric surrounding and hot laser-heated and laser-ionized clusters are considered within the same approach for a wide range of the fundamental laser frequency. Nonlinear laser excitation of the dipole plasmon Mie resonance in spherical clusters, as well as of other respective multipole plasmon resonances is investigated analytically and numerically in detail (position, width, and strength) versus the cluster-surface diffuseness, the outer ionization degree in charged clusters, the electron-density diffuseness, and their interplay. Under certain conditions, depending on the various cluster parameters, different secondary nonlinear resonances are found. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

An atlas for drug interactions Kinase inhibitors are an important class of drugs that block certain enzymes involved in diseases such as cancer and inflammatory disorders. There are hundreds of kinases within the human body, so knowing the kinase “target” of each drug is essential for developing successful treatment strategies. Sometimes clinical trials can fail because drugs bind more than one target. Yet sometimes off-target effects can be beneficial, and drugs can be repurposed for treatment of additional diseases. Klaeger et al. performed a comprehensive analysis of 243 kinase inhibitors that are either approved for use or in clinical trials. They provide an open-access resource of target summaries that could help researchers develop better drugs, understand how existing drugs work, and design more effective clinical trials. Science , this issue p. eaan4368

A theory of above-threshold ionization of atoms by a strong laser field is formulated. Two versions of the strong-field approximation (SFA) are considered, the direct SFA and the improved SFA, which do not and do, respectively, take into account rescattering of the freed electron off the parent ion. The atomic bound state is included in two different ways: as an expansion in terms of Slater-type orbitals or as an asymptotic wave function. Even though we are using the single-active-electron approximation, multielectron effects are taken into account in two ways: by a proper choice of the ground state and by an adequate definition of the ionization rate. For the case of the asymptotic bound-state wave functions, using the saddle-point method, a simple expression for the $T$-matrix element is derived for both the direct and the improved SFA. The theory is applied to ionization by a bicircular field, which consists of two coplanar counterrotating circularly polarized components with frequencies that are integer multiples of a fundamental frequency $\ensuremath{\omega}$. Special emphasis is on the $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ case. In this case, the threefold rotational symmetry of the field carries over to the velocity map of the liberated electrons, for both the direct and the improved SFA. The results obtained are analyzed in detail using the quantum-orbit formalism, which gives good physical insight into the above-threshold ionization process. For this purpose, a specific classification of the saddle-point solutions is introduced for both the backward-scattered and the forward-scattered electrons. The high-energy backward-scattering quantum orbits are similar to those discovered for high-order harmonic generation. The short forward-scattering quantum orbits for a bicircular field are similar to those of a linearly polarized field. The conclusion is that these orbits are universal, i.e., they do not depend much on the shape of the laser field.

Strong-field ionization in two-color circularly polarized fields is studied, where both experimental measurements and theoretical analyses suggest that the production of high-energy electrons from electron-ion rescattering is optimized in counterrotating fields, and when the ponderomotive energies of the two laser fields are equal.

We investigate high-order above-threshold ionization (HATI) of homonuclear diatomic molecules by a few-cycle laser pulse. In order to describe molecular HATI in ultrashort laser pulses we have modified our molecular improved strong-field approximation (MISFA), which was developed for long laser pulses and in which the rescattering of the ionized electron off the parent ion was described using the first-order Born approximation (1BA). Now, we introduce the so-called molecular low-frequency approximation (MLFA) in which the elastic rescattering amplitude is calculated exactly. The angle-resolved electron energy spectra for HATI of N2 and O2 obtained using the MLFA are compared with those obtained within the MISFA. The difference between these spectra becomes significant for larger (re)scattering angles. This is due to the fact that the exact scattering amplitude, used in the MLFA, has minima for some values of the rescattering angles that are absent in the 1BA. Also, the rescattering plateau is lower for the MLFA spectra. We investigate the influence of the carrier-envelope phase on the high-energy part of the molecular HATI spectra. As in the atomic case, the left-right (backward-forward) asymmetry is also observed in the molecular case.

The molecular strong-field approximation is applied to calculate angle-resolved photoelectron spectra in the process of high-order above-threshold ionization of carbon-monoxide molecules by an elliptically polarized laser field. The theory is formulated to include the Stark shift of the initial bound state of the valence electron. It is shown that the angle-resolved photoelectron spectra of aligned CO molecules exhibit pronounced minima which can be explained by destructive interference of two partial T-matrix contributions. The dependence of contributing partial amplitudes on the laser field ellipticity is analyzed in detail.

Experimental advances with laser intensities above1 TW/cm(2), with pulse durations between roughly 50 and 5 fs, have led to the discovery of new atomic effects that include examples of startlingly high electron correlation. These phenomena have presented an unexpected theoretical challenge as they lie outside the domains of both of the nominally applicable theories, namely, straightforward perturbative radiation theory and quasistatic tunneling theory. The two liberated electrons present a new few-body collective effect. When they are not released independently, one by one, the term nonsequential double ionization has been adopted. Theoretical avenues of attack have emerged in two categories, which are strikingly different. They can be labeled as "all-at-once" and "step-by-step" approaches. Although different, even conceptually opposite in some ways, both approaches have been successful in confronting substantial parts of the experimental data. These approaches are examined and compared with their results in addressing key experimental data obtained over the past decade.

The so-called low-frequency approximation (LFA) is an improved version of the strong-field approximation. The LFA describes the rescattering step of high-order above-threshold ionisation by utilising the exact field-free scattering amplitude, which has to be calculated separately. We apply the LFA to high-order above-threshold detachment of the fluorine negative ion. By comparing the so-obtained angle- and energy-resolved spectra with the exact results obtained as solutions of the time-dependent Schrodinger equation we show that the LFA is a more adequate approximation than the so-called improved strong-field approximation used previously. The LFA is also superior to the recently introduced quantitative rescattering (QRS) model. We show this by applying the LFA to the analysis of the intensity-dependent enhancements in above-threshold ionisation spectra of argon atoms. These enhancements can be explained as channel-closing-induced effects. In particular, we have observed and explained the behaviour of the...

Ionization of atoms by an intense bicircular laser field is considered, which consists of two coplanar corotating or counterrotating circularly polarized field components with frequencies that are integer multiples of a fundamental frequency. Emphasis is on the effect of a reversal of the helicities of the two field components on the photoelectron spectra. The velocity maps of the liberated electrons are calculated using the direct strong-field approximation (SFA) and its improved version (ISFA), which takes into account rescattering off the parent ion. Under the SFA all symmetries of the driving field are preserved in the velocity map while the ISFA violates certain reflection symmetries. This allows one to assess the significance of rescattering in actual data obtained from an experiment or a numerical simulation.

The nonequilibrium nanoplasma created by irradiation of a cluster, or other nanosystems such as large molecules, with an intense infrared-laser field may be used as an amplifying medium for a high-frequency probe field. We employ a simple description where the nanosystem is modeled by particles bound by a self-consitent potential. An incident probe field suffers gain or loss depending on the respective parameters by a mechanism that is usually referred to as collisionless damping. The model is simple enough to allow for an essentially analytical solution.

Direct detachment of an electron bound by a regularized zero-range potential is reinvestigated. For the definition of the S-matrix amplitude for detachment, the wave function of the electron after the laser pulse has passed through is projected on an exact scattering state of the zero-range potential rather than a plane-wave state, which is normally used. The exact scattering state generates an additional contribution to the amplitude, which leads to an isotropic term in the angle-resolved energy spectrum.

The low-frequency approximation (LFA) for high-order above-threshold ionization is presented. A factorization formula for the differential ionization rate is derived and its range of validity is analyzed. The theory developed is illustrated using the example of Ar atoms. Details of the modeling of the ground state and the rescattering potential for Ar are given. In particular, it is shown, by solving the stationary Schrodinger equation, that our rescattering potential reproduces the Hartree—Fock-type ground-state wave function that we used for the LFA. Electron momentum distributions for ionization of the Ar atom by a linearly polarized laser field having intensity 2.3 × 1014 W/cm2 and wavelength 800 nm are shown. The results obtained using the improved strong-field approximation on the one hand and the LFA on the other are compared.

High-order above-threshold ionization of diatomic molecules by a strong linearly polarized field is considered using the molecular strong-field approximation. Tunneling–rescattering as the mechanism of this ionization gives rise to a novel two-source double-slit interference, which involves the four geometrical paths that are available to an electron, which can be ionized from and rescattered off either of the two centers of the diatomic molecule. For a comparison of this theory with experiments in the absence of molecular alignment, it is necessary to average the theoretical results over the molecular orientation. This paper presents technical details of this averaging procedure. It is shown that, depending on the molecular symmetry, the destructive two-source double-slit interference minima can survive the orientation averaging and can be observed in the angle-resolved electron spectra. This is illustrated on the examples of N 2 and O 2 molecules. It is also shown that two- and three-dimensional versions of orientation averaging lead to qualitatively similar results.