Intense laser-induced recombination: The inverse above-threshold ionization process

Hu, S. X.; Collins, L. A.

doi:10.1103/physreva.70.013407

Cited by 29 publications

(19 citation statements)

References 47 publications

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“…However, the difficulty with this approach to studying recombination via particle detection lies in the fact that if the field is sufficiently intense to ionize an electron from a ground state atom in the first place, then recombination to any bound atomic state will usually be rapidly followed by reionization. Such a scenario has recently been described by Hu and Collins [14].…”

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confidence: 81%

Excited Ions in Intense Femtosecond Laser Pulses: Laser-Induced Recombination

et al. 2007

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Electron-ion recombination in a laser-induced electron recollision is of fundamental importance as the underlying mechanism responsible for the generation of high-harmonic radiation and hence for the production of attosecond pulse trains in the extreme ultraviolet and soft x-ray spectral regions. By using an ion beam target, remotely prepared to be partially in long-lived excited states, the recombination process has for the first time been directly observed and studied. DOI: 10.1103/PhysRevLett.99.173002 PACS numbers: 32.80.Rm, 32.80.Wr Intense ultrashort laser pulses are an important tool for probing the nonlinear physics of atoms, molecules and clusters in the inherent strong fields. Such studies have been used to elucidate fundamental quantum processes in the regime where electric (E) field strengths are of a similar order of magnitude to that binding electrons and where pulse time scales approaching a femtosecond constrain the quantum dynamics. In addition some of the resulting processes are being harnessed, for example, high-harmonic generation to produce attosecond x-ray pulses [1] in order to further probe atomic systems [2] and for practical nanotechnological applications [3,4].Arguably the single most important aspect of intense field studies is the ''rescattering'' of an ionized electron from its ionic core in a linearly polarized pulse. Proposed in a seminal paper by Corkum [5], the process relies on the ejected electron periodically revisiting the core as it is driven to and from it by the oscillating E-field of the laser. Acceleration in the external field, coupled with Coulombic acceleration and focussing may lead to recollision with the ion core. The narrow momentum distribution of the wave packet results in a significant probability of electron-ion interaction. This opens up the fascinating prospect of studying electron-ion scattering phenomena, notoriously difficult to investigate in a conventional beam-beam approach [6], with the added bonus that the electron ''pulse'' is on a femtosecond time scale [7].The possible electron collision mechanisms, i.e., elastic scattering, inelastic scattering, and recombination, have all been observed by various means. Elastic scattering leads to momentum transfer, such that the scattered electron is unlikely to further recollide with the core and will be observable at the high energy extreme of the detected electron spectrum, contributing to the above-threshold ionization process [8]. Inelastic scattering contributes to the nonsequential ionization process, either directly by electron impact ionization [9] or indirectly by excitation followed by tunnelling ionization in the field [10]. Recombination, which may be regarded as the inverse of above-threshold ionization, has been observed by detection of the stabilizing photon, the source of high-harmonic generation [11]. However, the underlying effect of laserinduced recombination has not been independently experimentally studied in the femtosecond pulse regime, and indeed recombination has never been detect...

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confidence: 81%

Excited Ions in Intense Femtosecond Laser Pulses: Laser-Induced Recombination

et al. 2007

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“…On the other hand, if a Coulomb-core of strength γ is present at the grid point z R = 0 and m = 0 then, according to (12), equation (34) will be overridden at i = R by…”

Section: The Finite Difference Schemementioning

confidence: 99%

“…For the m = 0 configuration, the equations forced by the Neumann and Robin boundary conditions for all i ∈ [0, N z ] from (32), (34), (35) are…”

Section: The Finite Difference Schemementioning

confidence: 99%

“…The most basic method is just to use a staggered grid which avoids the singularity of the Coulomb potential [32]: then the scheme will be easily solvable, although with low accuracy. A somewhat refined version of this is using a smoothed version of the potential, for example the so called soft Coulomb-form of 1/ α 2 + |r| 2 , where the value of α can be fitted by matching the ground state energy with that of the true hydrogen atom [32][33][34][35]. These approximations are rather crude, but can reproduce important features of the quantum system [23].…”

Section: Introductionmentioning

confidence: 99%

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Fourth order real space solver for the time-dependent Schrödinger equation with singular Coulomb potential

Majorosi

Czirják

2016

Computer Physics Communications

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We present a novel numerical method and algorithm for the solution of the 3D axially symmetric timedependent Schrödinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent potential. We use fourth order finite difference real space discretization, with special formulae for the arising Neumann and Robin boundary conditions along the symmetry axis. Our propagation algorithm is based on merging the method of the split-operator approximation of the exponential operator with the implicit equations of second order cylindrical 2D Crank-Nicolson scheme. We call this method hybrid splitting scheme because it inherits both the speed of the split step finite difference schemes and the robustness of the full Crank-Nicolson scheme. Based on a thorough error analysis, we verified both the fourth order accuracy of the spatial discretization in the optimal spatial step size range, and the fourth order scaling with the time step in the case of proper high order expressions of the split-operator. We demonstrate the performance and high accuracy of our hybrid splitting scheme by simulating optical tunneling from a hydrogen atom due to a few-cycle laser pulse with linear polarization.

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“…Numerical solutions of the TDSE are discussed in many articles, e.g. [1][2][3][4][5][6]. In most cases, the Cayley form of the time translation operator b UðDtÞ ¼ 1 À 1 2 i b HDt…”

Section: Introductionmentioning

confidence: 99%