We theoretically study atomic laser-assisted photoelectric emission (LAPE) beyond the electric dipole approximation. We present a theoretical description based on the strong-field approximation (SFA) for first-order nondipole corrections [O(c-1), where c is the speed of light] to the nonrelativistic description of the laser-atom interaction for a strong circularly polarized IR laser field combined with a train of extreme-ultraviolet pulses. We investigate the photoelectron momentum distribution (PMD) as the product of two main contributions: the intra- and interpulse factors. Whereas the interpulse factor gives rise to a sideband pattern with a shift opposite to the IR beam propagation direction, the intrapulse factor forms an angular streaking pattern following the IR time-dependent polarization direction. We explore the transition of the PMD from the dipole to the nondipole framework, showing the gradual break of the forward-backward symmetry as the laser parameters are varied. Furthermore, we find nonzero contributions in dipole forbidden directions independent of the IR polarization state, wherein Cooper-like minima are observed. Our work lays a theoretical foundation for understanding time-resolved nondipole LAPE in cutting-edge ultrafast experiments.

We present a method for accurately computing transition probabilities in one-dimensional photoionization problems. Our approach involves solving the time-dependent Schrödinger equation and projecting its solution onto scattering states that satisfy the correct incoming or outgoing boundary conditions. Conventionally, the photoelectron emission spectrum is obtained by projecting the time-evolved wave function onto the stationary continuum eigenstates of the unperturbed, time-independent Hamiltonian. However, when the spatial potential is symmetric, both the initial bound state and the final continuum states exhibit well-defined parity. The propagated wave function retains structural features of the initial bound state, including its parity. As a result, changes in the parity of the continuum states can introduce substantial variations in the projections, leading to spurious oscillations in the computed electron emission spectrum. Our method circumvents this issue by employing scattering states without defined parity. Furthermore, it enables the calculation of directional emission, making it possible to study emission asymmetries. To illustrate the capabilities of our scattering projection method, we analyze the partial differential photoionization probabilities of Al(111) metallic surfaces under short laser pulses at grazing incidence. Photoelectron spectrum of an aluminum surface. The conventional projection method (thin brown solid line) produces a highly oscillatory spectrum. Smoothing via the standard convolution method (window operator, thick green solid line) results in over-smoothing, eliminating genuine physical oscillations that our method correctly preserves (thick red line).

Phase and time delays of atomic above-threshold ionization are usually experimentally explored by the reconstruction of attosecond harmonic beating by interference of two-photon transitions (RABBIT) technique. Theoretical studies of RABBIT rely on the perturbative treatment of the probe (NIR or visible) laser pulse with respect to the atomic electric field and the pump composed of a train of attosecond pulses made of several harmonics with frequencies multiple of the probe fundamental frequency. In this work we present a semiclassical non-perturbative description of the phase delays for the emission of electrons from hydrogen atoms based on the strong-field approximation as the relative phase between pump and probe pulses is varied, where more than two photons are involved. Ionization times are calculated within the saddle-point approximations and serve to individualize the different electron wave packets that produce the RABBIT interferometric scheme. We observe different behaviors of the phase delays at different intensities of the probe. For example, for moderate and intense probe fields, the harmonics and sidebands happen to be in phase ($ \gtrsim 4 \times 10^{11}$ W/cm$^2$). In turn, when the probe field is sufficiently weak, we recover the well-known rule of thumb for the phase delays developed within the perturbative RABBIT theory [see D. Guenot et al. Phys. Rev. A 85, 053424 (2012)]. We show that the intracycle interference of the different paths contributing to the final energy (sideband or high harmonic) is responsible for the different behaviors of the interference pattern. Comparisons with the numerical solution of the strong-field approximation and time-dependent Schr\"odinger equation confirm the reliability of our semiclassical non-perturbative theory.

We present a theoretical study of atomic laser-assisted photoionization emission (LAPE) beyond the dipole approximation. By considering the non-relativistic non-dipole strong-field approximation (non-dipole Gordon-Volkov wave function), we analyze the different contributions to the photoelectron spectrum (PES), which can be written in terms of intra- and intercycle factors. We find that not only does our non-dipole approach exhibit asymmetric emission in the direction of light propagation, but also allows emission in dipole-forbidden directions. The former feature can be rooted both in intra- and intercycle interference processes, whilst the latter stems from a dependence of the sideband energy on the emission angle with respect to the propagation direction. Our theoretical scheme, presented here for He atoms in the 1s quantum state, is general enough to be applied to other atomic species and field configurations.

Phase delays for a typical ω-2ω configuration for hydrogen ionization are characterized. A splitting of the maximum of the forward ionization as a function of the relative phase exhibits the preclusion of the perturbative regime.

The ionization phases from argon atoms subject to a linearly polarized laser field ( – ω2ω) setting are calculated. We find excellent agreement between our results and measured phase delays [L. J. Zipp et al, Optica 1 , 361].

Phase and time delays of atomic above-threshold ionization were recently experimentally explored in an $\omega -2\omega$ setting [Zipp et al, Optica 1, 361 (2014)]. The phases of wavepackets ejected from argon by a strong $2\omega$ pulse were probed as a function of the relative phase of a weaker $\omega$ probe pulse. Numerical simulations solving the time-dependent Schrödinger equation (TDSE) displayed a sensitive dependence of the doubly differential momentum distribution on the relative phase between the $\omega$ and $2\omega$ fields. Moreover, a surprisingly strong variation of the extracted phase delays on the intensity of the probe pulse was found. We present a semiclassical strong-field description of the phase delays in the emission of electrons in an $\omega -2\omega$ setting and apply it to atomic hydrogen. Non-perturbative effects in both the $2\omega$ pump and the $\omega$ probe field are included. The semiclassical description allows tracing phase delays to path interferences between emission during different points in time of emission within the temporal unit cell of the two-color laser field. We find good agreement between the semiclassical saddle-point approximation, the full strong field approximation (SFA), and previous results applicable in the perturbative limit of probe fields. We show that the RABBIT-like perturbative description of phase delays breaks down for stronger fields and higher-energy electron emission. In this regime, characterization of the ionization signal requires an entire ensemble of phase delays {$\delta_i(E)$} with $i=1,2,\ldots$ the difference in photon numbers of the strong $2\omega$ field involved in the interfering paths. Comparison between SFA and TDSE calculations reveals the influence of the Coulomb field even in this strong-field scenario.

We analyze interference processes in atomic ionization induced by a two-color laser with fundamental frequency $\omega $ and its second harmonic $2\omega $. The interplay between inter- and intracycle interference processes give rise to multiphoton peaks which can be named as main or ATI peaks and sidebands, in analogy to the well-known RABBIT (reconstruction of attosecond harmonic beating by interference of two-photon transitions). We use the saddle point approximation (SPA) to extract the complex ionization times of the interfering electron trajectories. Changing the relative phase between the two colors, the doubly differential momentum distribution of emitted electrons can be controlled. We study the dependence of the electron emission as a function of the relative phase between the $\omega $ and $% 2\omega $ fields within the strong field approximation (SFA) but beyond the perturbative regime. We focus on the extraction of the phase delays accounting the electron forward emission in the direction of the polarized electric fields. We characterize the time delays in the emission of electrons for visible frequency of the pump and its first harmonic as a probe [Ti:Sapphire laser ($800$ nm) together with the first harmonic ($400$ nm)] for a typical $\omega -2\omega $ configuration for argon ionization. We find excellent agreement between our SPA results and the corresponding SFA (without any further approximation) and also with previous perturbative theories.

Relative phases of atomic above-threshold ionization wavepackets have been investigated in a recent experiment [L. J. Zipp, A. Natan, and P. H. Bucksbaum, Optica 1, 361-364 (2014)] exploiting interferences between different pathways in a weak probe field at half the frequency of the strong ionization pulse. In this work we theoretically explore the extraction of phase delays and time delays of attosecond wavepackets formed in strong-field ionization. We perform simulations solving the time-dependent Schrödinger equation and compare these results with the strong-field and Coulomb-Volkov approximations. In order to disentangle shortfrom longranged effects of the atomic potential we also perform simulations for atomic model potentials featuring a Yukawa-type short-range potential. We find significant deviations of the ab-initio phase delays between different photoelectron pathways from the predictions by the strong-field approximation even at energies well above the ionization threshold. We identify similarities but also profound differences to the well-known interferometric extraction of phaseand time delays in one-photon ionization. PACS numbers: 32.80.Rm,32.80.Fb,03.65.Sq

Synopsis We consider the ionization of argon atoms induced by a femtosecond laser pulse composed by overlapping extreme ultraviolet and infrared fields. We study several geometrical arrangements within the polarization vectors and emission direction that determinate only odd or even sideband peaks are present in the photoelectron spectrum.

We present a theoretical study of atomic ionization due to an XUV pulse in the presence of an infrared laser. Within the strong field approximation and considering the periodicity and symmetry of the transition matrix we show that the photoelectron spectrum can be described from the contribution during only one (or half) infrared cycle. These symmetry and periodicity properties impress selection rules which destructively cancel certain sideband orders favoring others. In particular, we analyze the photoionization of Argon in four geometrical arrangements of the polarization vector and the photoelectron momentum direction.

Synopsis We theoretically investigate on the origin of lateral ring structures in the doubly differential momen-tum distribution for atomic ionization by laser pulses in the midinfrared spectral region. We demonstrate that such structures stems from the interplay between intra- and intercycle interference patterns which work as two separate grids in the two-dimensional momentum domain. When the periods of the two grids (intra- and intercycle) are similar, moiré patterns arise as concentric rings at high electron kinetic energy.

We present a theoretical study of atomic laser-assisted photoionization emission (LAPE). We consider an atom driven by a linearly polarized XUV laser in two different scenarios: i) a single attosecond pulse (in both the streaking and sideband regimes) and ii) an attosecond pulse train. The process takes place assisted by a linearly polarized infrared (IR) laser field. In all these cases the energy and angle-resolved photoelectron spectrum (PES) is determined by a leading contribution, related to the intracycle factor [Gramajo et al., J. Phys. B 51, 055603 (2018)], complemented by other ones, derived from the periodicity and symmetry properties of the dipole transition matrix with respect to the IR field. Each of these terms imprint particular features in the PES that can be straightforwardly understood in terms of generalized energy conservation laws. We investigate in detail these PES structures, in particular, for the case of argon initially in the 3s quantum state. Our theoretical scheme, based on the strong-field approximation (SFA), can be applied, however, to other atomic species and field configurations as well.

Synopsis We theoretically investigate on the holographic structure in doubly differential momentum distribution for atomic photoionization. We use the ab initio solution of the time dependent Schrödinger equantion and the two-step semiclassical model. We see how the holographic structures are formed due to the interference of the direct trajectories of electrons and the rescattered trajectories of electrons. We get rid of intra- and intercycle interferences by removing ionization in the second half of a one-cycle pulse.

We report on a combined experimental and theoretical study of XUV ionization of atomic argon in the presence of a near-infrared (NIR) laser field.Using a table-top source of wavelength-selected femtosecond XUV pulses in combination with a velocity map imaging spectrometer we record angleand energy-resolved photoelectron distributions and simulate the experimental data by solving the time-dependent Schrödinger equation ab initio.In order to compare with the experimental data we average the calculated energy-angle probability distributions over the experimental focal volume for different values of the magnetic quantum number of the photoelectron.This averaging procedure washes out the intracycle interference pattern, which would otherwise be observed in the form of angular modulations of the photoelectron spectra.We recover these modulations experimentally and in the simulations by evaluating the difference between two averaged distributions that are obtained for slightly different NIR laser field intensities.

We present a theoretical study of atomic laser-assisted photoionization emission (LAPE). We consider an atom driven by a linearly polarized XUV laser in two different scenarios: i) a single attosecond pulse (in both the streaking and sideband regimes) and ii) an attosecond pulse train. The process takes place assisted by a linearly polarized infrared (IR) laser field. In all these cases the energy and angle-resolved photoelectron spectrum (PES) is determined by a leading contribution, related to the intracycle factor [Gramajo et al., J. Phys. B 51, 055603 (2018)], complemented by other ones, derived from the periodicity and symmetry properties of the dipole transition matrix with respect to the IR field. Each of these terms imprint particular features in the PES that can be straightforwardly understood in terms of generalized energy conservation laws. We investigate in detail these PES structures, in particular, for the case of argon initially in the 3s quantum state. Our theoretical scheme, based on the strong-field approximation (SFA), can be applied, however, to other atomic species and field configurations as well.

We study the vicinage effects in the interaction of H-2(+) projectiles with C, Al, Si, Al2O3 and SiO2 targets considering the excitation of inner shells. On one side we extend the use of the semiclassical impactparameter model for the excitation of atomic shells, considering quantum corrections and the role of target screening in the vicinage effects. On the other hand, we adapt our extended wave packet model (EWPM) [3] to the calculation of stopping ratios and ionization cross sections for correlated ions. Lindhard model is used to evaluate valence electrons contributions.

A theoretical study of the interference pattern imprinted on the doubly differential momentum distribution of the photoelectron due to atomic ionization induced by a short laser pulse is developed from a semiclassical standpoint. We use the semiclassical two-step model of Shvetsov-Shilovski et al. [Phys. Rev. A 94, 013415 (2016)] to elucidate the nature of the holographic structure. Three different types of trajectories are characterized during the ionization process by a single-cycle pulse with three different types of interferences. We show that the holographic interference arises from the ionization yield only during the first half cycle of the pulse, whereas the coherent superposition of electron trajectories during the first half cycle and the second half cycle gives rise to two other kinds of intracycle interference. Although the picture of interference of a reference beam and a signal beam is adequate, we show that our results for the formation of the holographic pattern agree with the glory rescattering theory of Xia et al. [Phys. Rev. Lett. 121, 143201 (2018)]. We probe the two-step semiclassical model by comparing it to the numerical results of the time-dependent Schrodinger equation.

We perform a theoretical study of the holographic structures in photoelectron spectra for ionization of hydrogen atoms induced by short laser pulses. To elucidate the nature of the holographic structures present in the momentum distributions of photoelectrons, we use several quantum approximations, such as the strong field and Coulomb–Volkov approximations up to second order, as well as semiclassical Monte Carlo simulations. In a single-cycle pulse, we eliminate the intracycle interference from the spectra isolating the holographic structure formed in the photoionization process. We probe the different approaches and analyze the role of electron–core interaction numerically by solving the time dependent Schrödinger equation. We show that the two-step semiclassical model of Shvetsov-Shilovski et al. [Phys. Rev. A 94, 013415 (2016)] fully considers the effect of the Coulomb potential on the electron dynamics and semiclassical phase reproducing the holographic structure in full quantum calculations. Contrarily, perturbative quantum (strong field and Coulomb–Volkov) and semiclassical (quantum trajectory Monte Carlo) methods account only partially for some of the characteristics of the holographic interference pattern.