Above-threshold ionization in the long-wavelength limit

Corkum, P. B.; Burnett, N. H.; Brunel, F.

doi:10.1103/physrevlett.62.1259

Cited by 793 publications

(458 citation statements)

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“…We base the quantitative description of the photoionisation process of atoms and molecules on statictunnelling theory 23 , with the following expression for the ionisation rate:…”

Section: Ionisation Model Employed In the Simulationsmentioning

confidence: 99%

“…The same argument concerning the transfer of the CE phase to the THz field can be readily generalised to the case of higherorder non-linear contributions. Whilst such a wave-mixing process illustrates the mechanism for CE phase-sensitive THz generation, we will give an alternative description based on static-tunnelling theory 23 , which explains the origin of non-linear polarisation on a microscopic level. For simplicity, we assume the air to consist only of N 2 .…”

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confidence: 99%

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Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy

et al. 2006

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PACS numbers: 62.65.Re, 72.30.+q The availability of few-cycle optical pulses opens a window to physical phenomena occurring on the attosecond time scale. In order to take full advantage of such pulses, it is crucial to measure 1,2,3,4 and stabilise 1,2 their carrierenvelope (CE) phase, i.e., the phase difference between the carrier wave and the envelope function. We introduce a novel approach to determine the CE phase by down-conversion of the laser light to the terahertz (THz) frequency range via plasma generation in ambient air, an isotropic medium where optical rectification (down-conversion) in the forward direction is only possible if the inversion symmetry is broken by electrical or optical means 5,6,7,8,9,10 . We show that few-cycle pulses directly produce a spatial charge asymmetry in the plasma. The asymmetry, associated with THz emission, depends on the CE phase, which allows for a determination of the phase by measurement of the amplitude and polarity of the THz pulse.The ability to measure 1,2,3,4 and stabilise 1,2 the CE phase, which is also often named absolute phase and defined by Eq. 4 (Methods), of few-cycle laser pulses, i.e., the ability to completely control ultrashort high-intensity electromagnetic fields, provides access to a whole series of novel physical phenomena, and creates options for their coherent control. An example is the manipulation of the electron recombination process during "recollision" 11 , with the aim to fully control the generation of both intense VUV higher-harmonic radiation 12,13 as well as of high-intensity single attosecond pulses. The progress has led to the establishment of a new field of research, "attosecond science", with highlights of recent work including the efficient tomography of molecular wave functions by coherent diffraction of rescattered electrons 14 as well as the preparation of high-intensity, monochromatic femtosecond electron beams evolving from "bubble generation" 15 . Many of the phenomena studied depend critically on the CE phase. Examples include the dynamics of above-threshold ionisation (ATI) 4 , light-induced non-sequential double ionisation 16 , Gouy phase observation 17 , and quantum interference in photocurrents 18 . An exciting prospect is the application of the CE phase as a coherent-control tool, e.g., to steer bound electrons in molecules 19 .The state-of-the-art method for CE phase determination of amplified laser pulses is stereo ATI 20,21 . In this letter, we present a new approach based on downconversion into the THz frequency range in a lasergenerated ambient air-plasma. The concept relies on the detection of the THz electromagnetic pulses emitted during photo-ionization of the air by the focussed few-cycle pulses. The method is easy to apply, because it does not require a vacuum chamber and relies on standard optoelectronic THz detection technology 5,8 .THz-pulse emission from laser-generated plasmas has been investigated in the past, but only with much longer laser pulses. There, the transient electric currents responsibl...

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“…We base the quantitative description of the photoionisation process of atoms and molecules on statictunnelling theory 23 , with the following expression for the ionisation rate:…”

Section: Ionisation Model Employed In the Simulationsmentioning

confidence: 99%

mentioning

confidence: 99%

Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy

et al. 2006

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“…Experiments with molecules display a much richer range of phenomena than with atoms, due to the additional molecular degrees of freedom [1,2,3]. These include above threshold ionization [4,5], multiple ionization [6,7], alignment effects [8], electron localization [9], non-sequential double ionization [10], direct excitation [11], stabilization [12], dissociative recombination [13], and separation effects [14]. However, molecules (even the simplest diatomic molecules) and their ionization are clearly more difficult to treat theoretically.…”

Section: Introductionmentioning

confidence: 99%

Simple soluble molecular ionization model

Dunne

Gauthier

2004

Phys. Rev. A

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We present a simple exact analytical solution, using the Weyl-Titchmarsh-Kodaira spectral theorem, for the spectral function of the one-dimensional diatomic molecule model consisting of two attractive delta function wells in the presence of a static external electric field. For sufficiently deep and far apart wells, this molecule supports both an even and an odd state, and the introduction of a static electric field turns these bound states into quasi-bound states which are Stark shifted and broadened. The continuum spectrum also inherits an intricate pattern of resonances which reflect the competition between resonant scattering between the two atomic wells and between the linear potential and one or both atomic well(s). All results are analytic and can be easily plotted. The relation between the large orders of the divergent perturbative Stark shift series and the non-perturbative widths of quasi-bound levels is studied.

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“…Frequently, a semiclassical two-step model is invoked, which assumes that ionization leads to the birth of an unbound electron at the outer exit of the laser-induced tunneling barrier. After appearing in the classically allowed region, the electron motion is modeled by a Newtonian trajectory [6]. This has been used for many purposes, e.g., to derive cutoff laws in ATI [7,8], to describe Coulomb focusing [9], to correct the strong-field approximation for elliptically polarized fields [10], and to model the momentum distribution in angular streaking [11].…”

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confidence: 99%

Adiabaticity in the lateral electron-momentum distribution after strong-field ionization

Henkel

Lein

Engel³

et al. 2012

Phys. Rev. A

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By solving the time-dependent Schrödinger equation for atoms in short laser pulses of different polarizations, it is shown that in strong-field ionization without rescattering, the lateral width of the electron-momentum distribution corresponds adiabatically to the instantaneous laser field on a sub-laser-cycle time scale, as expected in pure tunneling ionization. In contrast to the distributions along the polarization direction, the width is affected little by depletion or Coulomb effects. Over the past three decades, rapid progress has been made in the development of lasers capable of producing strong pulses in the femtosecond regime. This had led to progress in many areas ranging from above-threshold ionization (ATI) [1] over highorder harmonic generation [2] and attosecond pulse generation [3] to laser-induced fragmentation of molecules [4,5], to name just a few. Many of the phenomena induced by strong fields have been explained on the basis of tunneling ionization. Tunneling is a purely quantum mechanical process, which is considered as one of the main differences from classical mechanics. Frequently, a semiclassical two-step model is invoked, which assumes that ionization leads to the birth of an unbound electron at the outer exit of the laser-induced tunneling barrier. After appearing in the classically allowed region, the electron motion is modeled by a Newtonian trajectory [6]. This has been used for many purposes, e.g., to derive cutoff laws in ATI [7,8], to describe Coulomb focusing [9], to correct the strong-field approximation for elliptically polarized fields [10], and to model the momentum distribution in angular streaking [11]. The semiclassical model is also the basis for the three-step model of high-order harmonic generation [12].For an understanding of strong-field processes it is essential to verify the validity of the tunneling and semiclassical pictures. Along these lines, attosecond angular streaking [13][14][15], originally proposed to measure the carrier-envelope phase of few-cycle pulses [16], has been utilized to put a small upper limit on the tunneling delay time between the maximum of the electric field and the appearance of the escaping electron [17], thus giving insight into strong-field ionization on extremely short time scales. The interpretation of the momentum spectra in angular streaking, however, is complicated by Coulomb effects on the electron trajectories after tunneling and furthermore it is restricted to the intensity range below saturation [11]. It is desirable to overcome these limitations of angular streaking.Recently, the importance of the lateral momentum distribution, i.e., the distribution in the direction perpendicular to the laser field, has been recognized [18][19][20]. If not modified by electron recollision, the lateral distribution carries direct information about the ionization step since there is no laserinduced force in this direction. The tunneling ionization rate decreases with increasing lateral momentum approximately as a Gaussian. The width of the Ga...

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Above-threshold ionization in the long-wavelength limit

Cited by 793 publications

References 9 publications

Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy

Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy

Simple soluble molecular ionization model

Adiabaticity in the lateral electron-momentum distribution after strong-field ionization

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