High-order above-threshold ionization in a laser field: Influence of the ionization potential on the high-energy cutoff

Busuladžić, M.; Gazibegović-Busuladžić, A.; Milošević, D. B.

doi:10.1134/s1054660x06020149

Cited by 54 publications

(41 citation statements)

References 30 publications

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“…Eq. (35)]. These amplitudes describe electrons ionized from a few neighboring optical cycles in the vicinity of the peak of the laser pulse intensity envelope.…”

Section: Discussionmentioning

confidence: 99%

“…where the explicit forms for E f } for the left and right hemispheres and introducing the unified notations {σ, ν} → j , we obtain the result (35) for the amplitude A (R) (p n ).…”

Section: Appendix: Quasiclassical Derivation Of Eq (35) For the Rescmentioning

confidence: 99%

“…Substituting the ATD amplitude (35) into Eq. (30), it is convenient to present the ATD rate Γ (p n ) as follows:…”

Section: E Detachment Rate For a Periodic Fieldmentioning

confidence: 99%

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Analytic model for the description of above-threshold ionization by an intense short laser pulse

et al. 2014

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We present an analytic model for the description of above-threshold ionization (ATI) of an atom by an intense, linearly polarized short laser pulse. Our treatment is based upon a description of ATI by an infinitely long train of short laser pulses whereupon we take the limit that the time interval between pulses becomes infinite. In the quasiclassical approximation, we provide detailed quantum-mechanical derivations, within the time-dependent effective range (TDER) model, of the closed-form formulas for the differential probability P(p) of ATI by an intense, short laser pulse that were presented briefly by Frolov et al. [Phys. Rev. Lett. 108, 213002 (2012)] and that were used to describe key features of the high-energy part of ATI spectra for H and He atoms in an intense, few-cycle laser pulse, using a phenomenological generalization of the physically transparent TDER results to the case of real atoms. Moreover, we extend these results here to the case of an electron bound initially in a p state; we also take into account multiple-return electron trajectories. The ATI amplitude in our approach is given by a coherent sum of partial amplitudes describing ionization by neighboring optical cycles near the peak of the intensity envelope of a short laser pulse. These results provide an analytical explanation of key features in short-pulse ATI spectra, such as the left-right asymmetry in the ionized electron angular distribution, the multiplateau structures, and both large-scale and fine-scale oscillation patterns resulting from quantum interferences of electron trajectories. Our results show that the shape of the ATI spectrum in the middle part of the ATI plateau is sensitive to the spatial symmetry of the initial bound state of the active electron. This sensitivity originates from the contributions of multiple-return electron trajectories. Our analytic results are shown to be in good agreement with results of numerical solutions of the time-dependent Schrödinger equation for He and Ar atoms. Comparison of our results with those of quantitative rescattering theory is also discussed.

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“…Eq. (35)]. These amplitudes describe electrons ionized from a few neighboring optical cycles in the vicinity of the peak of the laser pulse intensity envelope.…”

Section: Discussionmentioning

confidence: 99%

“…where the explicit forms for E f } for the left and right hemispheres and introducing the unified notations {σ, ν} → j , we obtain the result (35) for the amplitude A (R) (p n ).…”

Section: Appendix: Quasiclassical Derivation Of Eq (35) For the Rescmentioning

confidence: 99%

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Analytic model for the description of above-threshold ionization by an intense short laser pulse

et al. 2014

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“…In this case, quantum effects are only noticeable if M ≤ Q, because the rescattered electron would not be sensitive to the reduced field strength otherwise. The parameters in our experiments are M ≈ 1 nm (including a non-zero tunneling distance [37,38,49]) and L ≥ 8 nm, so quantum effects should only be visible if Q becomes larger than 0.5 nm for larger nanostructures. The agreement between experimental results and classical theory seems to suggest that M > Q.…”

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confidence: 99%

“…The cut-off kinetic energy (see Fig. 1(c)) after rescattering is given by T cutoff = 10.007 U p + 0.538 Φ, where Φ denotes the tip's work function [38]. Measuring T cutoff hence yields U p [39].…”

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confidence: 99%

Probing of Optical Near-Fields by Electron Rescattering on the 1 nm Scale

et al. 2013

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We present a new method of measuring optical near-fields within ∼1 nm of a metal surface, based on rescattering of photoemitted electrons. With this method, we precisely measure the field enhancement factor for tungsten and gold nanotips as a function of tip radius. The agreement with Maxwell simulations is very good. Further simulations yield a field enhancement map for all materials, which shows that optical near-fields at nanotips are governed by a geometric effect under most conditions, while plasmon resonances play only a minor role. Last, we consider the implications of our results on quantum mechanical effects near the surface of nanostructures and discuss features of quantum plasmonics.The excitation of enhanced optical near-fields at nanostructures allows the localization of electromagnetic energy on the nanoscale [1,2]. At nanotips, this effect has enabled a variety of applications, most prominent amongst them are scanning near-field optical microscopy (SNOM) [3][4][5][6][7], which has reached a resolving power of 8 nm [8], and tip-enhanced Raman spectroscopy (TERS) [3,9]. Because of the intrinsic nanometric length scale, measuring and simulating the tips' near-field has proven hard and led to considerably diverging results (see Refs. [1,7] for overviews). Here we demonstrate a nanometric field sensor based on electron rescattering, a phenomenon well known from attosecond science [10]. It allows measurement of optical near-fields, integrating over only 1 nm right at the structure surface, close to the length scale where quantum mechanical effects become relevant [11][12][13][14][15]. Hence, this method measures near-fields on a scale that is currently inaccessible to other techniques (such as SNOM or plasmonic methods in electron microscopy [16][17][18]), and reaches down to the minimum length scale where one can meaningfully speak about a classical field enhancement factor. In the future, the method will allow tomographic reconstruction of the optical near-field and potentially the sensing of fields in more complex geometries such as bow-tie or split-ring antennas.In general, three effects contribute to the enhancement of optical electric fields at structures that are smaller than the driving wavelength [7,[20][21][22]. The first effect is geometric in nature, similar to the electrostatic lightning rod effect: the discontinuity of the electric field at the material boundary and the corresponding accumulation of surface charges lead to an enhanced near-field at any sharp protrusion or edge. This effect causes singularities in the electric field at ideal edges of perfect conductors. For real materials at optical frequencies, the electric field is not as strongly enhanced and remains finite [23]. The second effect occurs at structures whose size is an odd multiple of half the driving wavelength: optical antenna resonances can be observed there. The third effect concerns only plasmonic materials like gold and silver, where an enhanced electric field can arise due to a localized surface plasmon resonance. ...

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From Attosecond Control of Electrons at Nano‐Objects to Laser‐Driven Electron Accelerators

Süßmann

Kling

Hommelhoff

2014

Attosecond Nanophysics

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Electron emission from nano-objects, in particular from sharp tips, is not a new field at all. It is well known since the end of the 19th century that electrons can be extracted from a pointy wire if a voltage is applied to it [1]. Because of the lightning rod effect, this voltage translates into a large electric field right at the end of the wire, or better, at a tip-shaped wire. With a moderate voltage of a couple of hundred volts electric field strengths of more than a few gigavolt per meters can be reached at the tip's apex -if it is sharp and pointy. For typical metals, from these field strengths on an appreciable field emission current sets in. Fowler and Nordheim in 1928 were able to explain this effect with the newly established quantum mechanical tunneling, representing one of the first applications of the Wentzel-Kramers-Brillouin (WKB) approximation [2][3][4]. Nowadays, field emission electron sources are employed in any high-resolution electron microscope because of their superb electron beam emission characteristics [5].Similar to the lightning rod effect with DC fields, an optical field is also enhanced at the tip's apex, as introduced in Chapter 3. Here we discuss what happens if this effect generates light intensities exceeding 10 11 W cm −2 right at the tip's apex. It is convenient from the experimenter's point of view that a simple laser oscillator suffices to do so, just because of the optical field enhancement effect. Numerical tools such as the finite-difference-time-domain method allow calculating typical field enhancement factors to around 3 … 10 for a light field with a wavelength of 800 nm polarized along the tip axis. Similar to the observations using DC fields, one can generally state that the sharper the tip the higher the field enhancement.The light field at the tip apex triggers electron emission and subsequent processes that are well known in atomic physics for decades already. These include above-threshold photoemission, strong-field effects, but also effects such as electron recollision and electronic matter wave interference in the time-energy domain.The setup for the tip-based experiments is shown in Figure 6.1. A sharp metal tip -most initial experiments were done with a tip made of tungsten or gold

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High-order above-threshold ionization in a laser field: Influence of the ionization potential on the high-energy cutoff

Cited by 54 publications

References 30 publications

Analytic model for the description of above-threshold ionization by an intense short laser pulse

Analytic model for the description of above-threshold ionization by an intense short laser pulse

Probing of Optical Near-Fields by Electron Rescattering on the 1 nm Scale

From Attosecond Control of Electrons at Nano‐Objects to Laser‐Driven Electron Accelerators

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