Modeling harmonic generation by a zero-range potential

Conservation laws for electron vortices in strong-field ionisation

ABSTRACT

We investigate twisted electrons with a well-defined orbital angular momentum, which have been ionised via a strong laser field. By formulating a new variant of the well-known strong field approximation, we are able to derive conservation laws for the angular momenta of twisted electrons in the cases of linear and circularly polarised fields. In the case of linear fields, we demonstrate that the orbital angular momentum of the twisted electron is determined by the magnetic quantum number of the initial bound state. The condition for the circular field can be related to the famous ATI peaks, and provides a new interpretation for this fundamental feature of photoelectron spectra. We find the length of the circular pulse to be a vital factor in this selection rule and, employing an effective frequency, we show that the photoelectron OAM emission spectra are sensitive to the parity of the number of laser cycles. This work provides the basic theoretical framework with which to understand the OAM of a photoelectron undergoing strong field ionisation.

Symphony on strong field approximation

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the 'simple man's models' which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron ionization (NSMI). 'Simple man's models' provide both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation and the motivation for the powerful analytic approximations generally known as the strong field approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions are described by including continuum-continuum interactions in a systematic perturbation-like theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom molecules. The main novel part of the presented theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between electron impact ionization and resonant excitation with subsequent ionization; (ii) time-dependent treatment in the single active electron approximation of 'large' molecules and targets which are themselves undergoing dynamics during the HHG or ATI processes. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields. We dedicate this work to the memory of Bertrand Carré, who passed away in March 2018 at the age of 60.

Control of quasi-phase-matching of high-harmonics in a spatially structured plasma

High-harmonic generation is widely used for providing extreme ultraviolet radiation in attosecond science. Such experiments include photoelectron spectroscopy, diffractive imaging, or the investigation of spin dynamics. Many applications are restricted by a low photon flux which originates from the low efficiency of the generation process. In this article an effective method based on the quasi-phase-matched generation of high harmonics in spatially structured, laser ablated plasma is demonstrated. Through a proper dimensioning of the plasma structure, the harmonic yield is optimized for a controllable range of harmonic orders. By using four coherent zones, the intensity of a single harmonic is increased to a maximal possible value of 16 compared to using a single zone. The Gouy phase shift of the fundamental field is identified as the primary effect responsible for constructive interference of the harmonic fields generated in the individual plasma jets of the plasma structure.

Under-the-Tunneling-Barrier Recollisions in Strong-Field Ionization

A new pathway of strong-laser-field-induced ionization of an atom is identified which is based on recollisions under the tunneling barrier. With an amended strong-field approximation, the interference of the direct and the under-the-barrier recolliding quantum orbits are shown to induce a measurable shift of the peak of the photoelectron momentum distribution. The scaling of the momentum shift is derived relating the momentum shift to the tunneling delay time according to the Wigner concept. This allows us to extend the Wigner concept for the quasistatic tunneling time delay into the nonadiabatic domain. The obtained corrections to photoelectron momentum distributions are also relevant for state-of-the-art accuracy of strong-field photoelectron spectrograms in general.

Spatiotemporal characterization of single-order high harmonic pulses from time-compensated toroidal-grating monochromator

Extreme ultraviolet (XUV) single-order high harmonic pulses with 10(6) photons/pulse were separated from multiple harmonic orders by a time-compensated toroidal-grating monochromator consisting of a pair of toroidal gratings. The first grating separates the harmonic order and the second one compensates for the pulse-front tilt. The center photon energies were tunable between 42 and 23 eV. The separated single harmonic pulses were spatially and temporally characterized as having a spot size of 58 +/- 3 microm at the focus, with a shortest pulse duration of 47 +/- 2 fs. The developed XUV light source is versatile for application to time- and space-resolved spectroscopy.

Analytic description of the high-energy plateau in harmonic generation by atoms: can the harmonic power increase with increasing laser wavelengths?

A closed-form analytic formula for high-order harmonic generation (HHG) rates for atoms (that generalizes an HHG formula for negative ions [M. V. Frolov, J. Phys. B 42, 035601 (2009)10.1088/0953-4075/42/3/035601]) is used to study laser wavelength scaling of the HHG yield for harmonic energies in the cutoff region of the HHG plateau. We predict increases of the harmonic power for HHG by Ar, Kr, and Xe with increasing wavelength lambda over atom-specific intervals of lambda in the infrared region, lambda approximately (0.8-2.0) microm.

Strong field double ionization: the phase space perspective

We identify the phase-space structures that regulate atomic double ionization in strong ultrashort laser pulses. The emerging dynamical picture complements the recollision scenario by clarifying the distinct roles played by the recolliding and core electrons, and leads to verifiable predictions on the characteristic features of the "knee", a hallmark of the nonsequential process.

Wavelength scaling of high-harmonic yield: threshold phenomena and bound state symmetry dependence

Describing harmonic generation (HG) in terms of a system's complex quasienergy, the harmonic power P_{DeltaE}(lambda) (over a fixed interval, DeltaE, of harmonic energies) is shown to reproduce the wavelength scaling predicted recently by two groups of authors based on solutions of the time-dependent Schrödinger equation: P_{DeltaE}(lambda) approximately lambda;{-x}, where x approximately 5-6. Oscillations of P_{DeltaE}(lambda) on a fine lambda scale are then shown to have a quantum origin, involving threshold phenomena within a system of interacting ionization and HG channels, and to be sensitive to the bound state wave function's symmetry.

Scaling of wave-packet dynamics in an intense midinfrared field

A theoretical investigation is presented that examines the wavelength scaling from near-visible (0.8 micro m) to midinfrared (2 micro m) of the photoelectron distribution and high harmonics generated by a "single" atom in an intense electromagnetic field. The calculations use a numerical solution of the time-dependent Schrödinger equation (TDSE) in argon and the strong-field approximation in helium. The scaling of electron energies (lambda2), harmonic cutoff (lambda2), and attochirp (lambda -1) agree with classical mechanics, but it is found that, surprisingly, the harmonic yield follows a lambda -(5-6) scaling at constant intensity. In addition, the TDSE results reveal an unexpected contribution from higher-order returns of the rescattering electron wave packet.

Frequency-resolved optical gating of isolated attosecond pulses in the extreme ultraviolet

The pulse shape and phase of isolated attosecond extreme ultraviolet (XUV) pulses with a duration of 860 asec have been determined simultaneously by using frequency-resolved optical gating based on two-photon above-threshold ionization with 28-eV photons in He. From the detailed characterization, we succeeded in shaping isolated XUV pulses on an attosecond time scale by precise dispersion control with Ar gas density or by changing the driving pulse width. These results offer a novel way to excite and observe an electron motion in atoms and molecules.

Role of many-electron dynamics in high harmonic generation

High harmonic generation (HHG) in many-electron atoms is studied theoretically. The breakdown of the frozen-core single active electron approximation is demonstrated, as it predicts roughly the same radiation amplitude in all noble gases. This is in contradiction with experiments, where heavier noble gases are known to emit much stronger HHG radiation than lighter ones. This experimental behavior of the noble gases can be qualitatively reproduced when many-electron dynamics, within a simple approximation, is taken into account.

Nonlinear optics in the extreme ultraviolet

Nonlinear responses to an optical field are universal in nature but have been difficult to observe in the extreme ultraviolet (XUV) and soft X-ray regions owing to a lack of coherent intense light sources. High harmonic generation is a well-known nonlinear optical phenomenon and is now drawing much attention in attosecond pulse generation. For the application of high harmonics to nonlinear optics in the XUV and soft X-ray regime, optical pulses should have both large pulse energy and short pulse duration to achieve a high optical electric field. Here we show the generation of intense isolated pulses from a single harmonic (photon energy 27.9 eV) by using a sub-10-femtosecond blue laser pulse, producing a large dipole moment at the relatively low (ninth) harmonic order nonadiabatically. The XUV pulses with pulse durations of 950 attoseconds and 1.3 femtoseconds were characterized by an autocorrelation technique, based on two-photon above-threshold ionization of helium atoms. Because of the small cross-section for above-threshold ionization, such an autocorrelation measurement of XUV pulses with photon energy larger than the ionization energy of helium has not hitherto been demonstrated. The technique can be extended to the characterization of higher harmonics at shorter wavelengths.

Frequency-resolved optical gating of femtosecond pulses in the extreme ultraviolet

Femtosecond extreme ultraviolet (XUV) pulses were fully characterized for the first time by using a newly developed cross-correlation frequency-resolved optical gating (FROG) technique in the XUV region. This method utilizes laser-assisted two-photon ionization as a nonlinear optical process. Near-infrared pulses characterized by FROG were used as a reference. The amplitude and phase of XUV pulses with a pulse duration of 10 fs were found to be in good agreement with a model analysis, taking into account phase modulation by ionization, self-phase modulation, and the atomic dipole phase.

Model-independent quantum approach for intense laser detachment of a weakly bound electron

We present a model-independent theory for laser detachment of a weakly bound electron having a nonzero angular momentum. Our treatment reduces to the well-known Keldysh result for tunnel ionization upon neglecting rescattering effects. Numerical results for the above-threshold detachment spectrum of a negative ion having an outer p electron show significant modification of the rescattering plateau as compared to that for an ion having an outer s electron.

Measurement of the intensity-dependent atomic dipole phase of a high harmonic by frequency-resolved optical gating

The temporal profile and phase of the fifth harmonic of a Ti:sapphire laser were fully characterized by two-photon ionization frequency-resolved optical gating technique for the first time. The fifth harmonic was found to have negative chirp and the pulse compression was demonstrated. The negative chirp is well explained by using a zero-range potential model. This technique is scalable to extreme ultraviolet (XUV) and soft x-ray regions by using currently available light sources, making it possible to measure the pulse duration and phase of vacuum ultraviolet, XUV, and soft x-ray pulses.

High harmonic generation beyond the electric dipole approximation

A generalization of the analytical theory of high harmonic generation in the long wavelength limit and in the single active electron approximation is developed taking into account the magnetic dipole and electric quadrupole interaction. Quantum mechanical and classical theories are found to be in excellent agreement, which allows one to explain the influence of multipole effects in terms of an intuitive picture. For Ti:S lasers ( 0.8 &mgr;m) multipole contributions are found to be small below an intensity of about 10(17) W/cm(2), at which harmonic radiation with photon energies of several keV is generated. This promises the extension of high harmonic generation well into the sub-nm wavelength regime.

Static-electric-field-induced polarization effects in harmonic generation

Two static-electric-field-induced effects on harmonic generation are demonstrated analytically and numerically: elliptic dichroism (in which the harmonic yield is different for right and left elliptically polarized laser fields) and elliptical polarization of harmonics produced by linearly polarized driving laser fields. Both effects stem from interference of real and imaginary parts of the nonlinear atomic susceptibilities. Possibilities for experimentally measuring these effects are discussed.