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A general method for solving numerically the time-dependent Schr\"odinger equation, that is based on the Suzuki-Trotter scheme with the split-step Fourier approach, is introduced. The method relies on a Hamiltonian decomposition, where except of the components depending exclusively on the momentum or on the position operators, there are also terms depending on both momentum and position operators in particular configurations. We demonstrate that, for as long as the latter does not depend on noncommuting coordinates of the momentum and position operators, nondipole effects in laser-matter interactions can be studied without applying extra unitary operations. Specifically, we analyze the effect of nondipole corrections in ionization of a two-dimensional hydrogen atom for low- and high-frequency pulses. In the former case, the electron wave packet dynamics is dominated by rescattering processes within the laser pulse, leading to the high-order harmonic generation. We illustrate that harmonics of even orders are generated in the direction of the laser field polarization. On the contrary, for high-frequency pulses, such rescattering processes can be neglected. We demonstrate that a significant portion of the low-energy photoelectrons is detected opposite to the laser pulse propagation direction as a consequence of their post-pulse wave packet spreading and interaction with the parent ion., Comment: 9 figures

The concept of the electron mass dressing by a powerful laser pulse is discussed. It is shown, by considering the coherent frequency combs generated out of the Compton radiation, how the electron dressed mass can be determined experimentally. This also opens a possibility to measure properties of extremely intense pulses for which the previously developed methods, working at moderate intensities, are not applicable. Namely, one can determine these properties from the properties of coherent Compton radiation., Comment: 7 pages, 4 figures; lecture delivered during the 24th International Laser Physics Workshop, Shanghai, August 21-25, 2015

The generalized Klein-Nishina formula for Compton scattering of charged particles by a finite train of pulses is derived in the framework of quantum electrodynamics. The formula also applies to classical Thomson scattering provided that frequencies of generated radiation are smaller that the cut-off frequency. The validity of the formula for incident pulses of different durations is illustrated by numerical examples. The positions of the well-resolved Compton peaks, with the clear labeling by integer orders, opens up the possibility of the precise diagnostics of properties of relativistically intense, short laser pulses. This includes their peak intensity, the carrier-envelope phase, and their polarization properties., Comment: 9 pages, 6 figures

Electron-positron pair creation in collisions of a modulated laser pulse with a high-energy photon (nonlinear Breit-Wheeler process) is studied by means of strong-field quantum electrodynamics. It is shown that the driving pulse modulations lead to appearance of comb structures in the energy spectra of produced positrons (electrons). It is demonstrated that these combs result from a coherent enhancement of probability amplitudes of pair creation from different modulations of the laser pulse. Thus, resembling the Young-double slit experiment for anti-matter (matter) waves., Comment: 9 pages, 5 figures

The Compton and Thomson radiation spectra, generated in collisions of an electron beam with a powerful laser beam, are studied in the framework of quantum and classical electrodynamics, respectively. We show that there are frequency regimes where both radiation spectra are nearly identical, which for Compton scattering relates to the process which preserves the electron spin. Although the radiation spectra are nearly identical, the corresponding probability amplitudes exhibit different global phases. This has pronounced consequences, which we demonstrate by investigating temporal power distributions in both cases. We show that, contrary to Thomson scattering, it is not always possible to synthesize short laser pulses from Compton radiation. This happens when the global phase of the Compton amplitude varies in a nonlinear way with the frequency of emitted photons. We also demonstrate that while the Compton process driven by a non-chirped laser pulse can generate chirped bursts of radiation, this is not the case for the Thomson process. In principle, both processes can lead to a generation of coherent frequency combs when single or multiple driving laser pulses collide with electrons. Once we synthesize these combs into short bursts of radiation, we can control them, for instance, by changing the time delay between the driving pulses., Comment: 18 pages, 15 figures

Spectra of Thomson and Compton radiation, emitted during electron scattering off an intense laser beam, are calculated using the frameworks of classical and strong-field quantum electrodynamics, respectively. Both approaches use a plane-wave-fronted pulse approximation regarding the driving laser beam. Within this approximation, a very good agreement between Thomson and Compton frequency distributions is observed provided that frequencies of the emitted radiation is relatively low. The dependence of frequency spectra on the laser pulse envelope is analyzed. This becomes important in the context of ultra-short pulse generation, as illustrated by numerical examples., Comment: 13 pages, 4 figures; lecture delivered during the 22nd International Laser Physics Workshop, Prague, July 15-19, 2013

Nonlinear Thomson and Compton processes, in which energetic electrons collide with an intense optical pulse, are investigated in the framework of classical and quantum electrodynamics. Spectral modulations of the emitted radiation, appearing as either oscillatory or pulsating structures, are observed and explained. It is shown that both processes generate a bandwidth radiation spanning the range of few MeV, which occurs in a small cone along the propagation direction of the colliding electrons. Most importantly, these broad bandwidth structures are temporarily coherent which proves that Thomson and Compton processes lead to generation of a supercontinuum. It is demonstrated that the radiation from the supercontinuum can be synthesized into zeptosecond (possibly even yoctosecond) pulses. Thus, confirming that Thomson and Compton scattering can be used as novel sources of an ultra-short radiation, opening routes to new physical domains for strong laser physics., Comment: 10 pages, 11 figures

Nonlinear Bethe-Heitler process in a bichromatic laser field is investigated using strong-field QED formalism. Symmetry properties of angular distributions of created $e^-e^+$ pairs are analyzed. These properties are showed to be governed by a behavior of the vector potential characterizing the laser field, rather than by the respective electric field component., Comment: 4 pages, 4 figures

The spectra of Compton radiation emitted during electron scattering off an intense laser beam are calculated using the framework of strong-field quantum electrodynamics. We model these intense laser beams as finite length plane-wave-fronted pulses, similar to Neville and Rohrlich [Phys. Rev. D {\bf 3}, 1692 (1971)], or as trains of such pulses. Expressions for energy and angular distributions of Compton photons are derived such that a comparison of both situations becomes meaningful. Comparing frequency distributions for both an isolated laser pulse and a laser pulse train, we find a very good agreement between the results for long pulse durations which breaks down however for ultrashort laser pulses. The dependence of angular distributions of emitted radiation on a pulse duration is also investigated. Pronounced asymmetries of angular distributions are found for very short laser pulses, which gradually disappear with increasing the number of laser field oscillations. Those asymmetries are attributed to asymmetries of the vector potential describing an incident laser beam., Comment: 12 pages, 7 figures