Angle-resolved Energy Spectra Research Articles

Plasmon Excitation in the Interaction of Slow Singly Charged Argon Ions with Magnesium

We report angle-resolved energy spectra of electron emitted in the interaction of slow singly charged heavy ions with Mg surface. The work is focused mainly on the excitation of plasmons of Mg under Argon impact. Potential excitation of plasmons occurs when incoming ions are neutralized at the expense of the potential energy carried by incoming ions. The process competes with the known mechanisms of neutralization via Auger transitions. Differently from Al samples, our results show that the neutralization of Ar+ ions at Mg is dominated by the excitation of surface plasmons by the potential energy released in the electron capture process that neutralizes incoming ions. Bulk plasmon excitation is observed at higher impact energy and is ascribed to fast electrons excited by the transfer of the kinetic energy of incoming particles. The data show that bulk plasmon excitation occur inside the bulk, while the theoretically predicted excitation by potential energy transfer of incoming projectiles is not observed.

Revealing the dissociation channels of mixed photons for in bicircularly polarized laser pulses

We theoretically study the dissociation of driven by the bicircularly polarized (BiCP) laser pulses. It is shown that there is a possibility for the molecule dissociating through the mixed-photon channels, in which the system simultaneously absorbs multiple photons of different frequencies from the BiCP pulses. Setting the frequency ratios of 1:2 and 1:3 for the BiCP pulses reveals the mixed-photon dissociation channels from the interference patterns in the angle-resolved kinetic energy spectra. In addition, by applying the wave packet interference approach, we show that one can further estimate the fragment yield ratios between different dissociation channels that lead to the same kinetic energy.

Electron-molecule scattering in a bichromatic elliptically polarised laser field: Plateau structures and two-centre interference minima

Scattering of electrons off diatomic molecules in a bichromatic elliptically polarised laser field is considered by applying the S-matrix theory within the second Born approximation. Two characteristic plateaus appear in the energy spectrum of scattered electrons. The higher plateau is observed in the low-energy part of the spectrum and describes the single scattering, while the lower plateau extends to the high-energy part of the spectrum and describes the double scattering. Scattering and rescattering of electrons off molecular targets may occur at any molecular centre and in any order. Interference of contributions results in increasing/decreasing the differential cross section in particular regions of the energy spectrum of scattered electrons. Two contributions for single scattering and four contributions for double scattering exist in the case of diatomic molecules. For some molecular orientations, a sequence of declining maxima may be observed instead of the plateaus in the electron energy spectrum. We have also observed parabolic structures in the angle-resolved energy spectra. Analytical formulas that explain these structures have been provided. We have also explored the impact of the laser-field ellipticity on the scattered-electron energy spectra. The bichromatic ω– and ω– laser fields have been considered.

Influence of polarization directions of the IR+XUV two-color laser fields on angle-resolved photoelectron energy spectrum.

By employing the frequency-domain theory, we investigate the influence of polarization directions on angle-resolved photoelectron energy spectrum in the above-threshold ionization (ATI) process of atoms exposed to the IR+XUV two-color laser fields, which shows the multiplateau structures. When the ionized electron is emitted along the IR laser's polarization direction, the width of each plateau keeps a certain energy range, and the jet structures and main lobes are determined by both the emission angle relative to the polarization direction of the XUV laser field and the number of the XUV photons absorbed by the electron. While when the ionized electron is emitted along the XUV laser's polarization direction, the width of each plateau depends on the polarization direction of the IR laser field, and the angular distribution of the ionized electron exhibits the isotropic characteristics. These results show that the ATI spectrum may be effectively controlled by changing the angle between the two laser fields' polarization directions.

Application of the time-dependent surface flux method to the time-dependent multiconfiguration self-consistent-field method

We present a numerical implementation of the time-dependent surface flux (tSURFF) method [New J. Phys. 14, 013021 (2012)], an efficient computational scheme to extract photoelectron energy spectra, to the time-dependent multiconfiguration self-consistent-field (TD-MCSCF) method. Extending the original tSURFF method developed for single particle systems, we formulate the equations of motion for the spectral amplitude of orbital functions constutiting the TD-MCSCF wave function, from which the angle-resolved photoelectron energy spectrum, and more generally, photoelectron reduced density matrices (RDMs) are readiliy obtained. The tSURFF method applied to the TD-MCSCF wave function, in combination with an efficient absorbing boundary offered by the infinite-range exterior complex scaling, enables accurate {\it ab initio} computations of photoelectron energy spectra from multielectron systems subject to an intense and ultrashort laser pulse with a computational cost significantly reduced compared to that required in projecting the total wave function onto scattering states. We apply the present implementation to the photoionization of Ne exposed to an attosecond extreme-ultraviolet (XUV) pulse and above-threshold ionization of Ar irradiated by an intense mid-infrared laser field, demonstrating both accuracy and efficiency of the present method.

Angle-resolved photoelectron energy spectrum from the high-order above-threshold ionization process in IR+XUV two-color laser fields

The angle-resolved photoelectron energy spectrum (PES) of high-order above-threshold ionization (HATI) spectrum in IR+XUV two-color laser fields has been investigated. We found that the quantum feature corresponding to the absorption of the XUV photon is well illustrated by a peculiar dip structure in the second plateau of the HATI spectrum. By the channel analysis, we show that the angle-resolved PES is attributed to the coherent summation over contributions of different channels, and the dip structure in the spectrum is directly related to the absorption of one XUV photon of the ionized electron during the laser-assisted collision (LAC) with its parent ion in the two-color laser fields. Moreover, by employing the saddle-point approximation, we obtain the classical energy orbit equation, and find that the dip structure comes from the fact that the LAC is limited at a certain direction by the momentum conservation law as the electron absorbs one XUV photon during the collision, where the probability of the HATI gets its minimum value. Finally, we find that the interference pattern in the whole spectrum is attributed to the interference of different orbits at collision moments t0 and in the LAC process.

Electron-molecule scattering in a strong laser field: Two-center interference effects

Laser-assisted scattering of electrons on diatomic molecules is considered using the $S$-matrix theory within the second Born approximation. The first term of the expansion in powers of the scattering potential corresponds to the direct or single laser-assisted scattering of electrons on molecular targets, while the second term of this expansion corresponds to the laser-assisted rescattering or double scattering. The rescattered electrons may have considerably higher energies in the final state than those that scattered only once. For multicenter polyatomic molecules scattering and rescattering may happen at any center and in any order. All these cases contribute to the scattering amplitude and the interference of different contributions leads to an increase or a decrease of the differential cross section in particular electron energy regions. For diatomic molecules there are two such contributions for single scattering and four contributions for double scattering. Analyzing the spectra of the scattered electrons, we find two interesting effects. For certain molecular orientations, the plateaus in the electron energy spectrum, characteristic of laser-assisted electron-atom scattering, are replaced by a sequence of gradually declining maxima, caused by the two-center interference effects. The second effect is the appearance of symmetric $\mathsf{U}$-shaped structures in the angle-resolved energy spectra, which are described very well by the analytical formulas we provide.

Temporal interferences driven by a single-cycle terahertz pulse in the photodetachment dynamics of negative ions

We present theory and calculations of a real-time-domain interferometry for the photodetachment dynamics of negative ions in the presence of a single-cycle terahertz pulse. The photoelectron can follow two or more classical trajectories to arrive at a detector simultaneously allowing the electron waves to interfere quantum mechanically. Both the in-phase and antiphase oscillations can be observed in the photoelectron interferences from negative hydrogen and fluorine ions depending on the pulse strength and the observing angle. Especially, a temporal-caustic bifurcation is observed when the detection angle is not in line with the pulse polarization direction. Similar interferences and bifurcations are also expected in the angle-resolved energy spectrum, as a result of its approximate equivalence with the time-dependent electron flux at large distances.

Strong Field Acceleration and Steering of Ultrafast Electron Pulses from a Sharp Metallic Nanotip

We report a strong, laser-field induced modification of the propagation direction of ultrashort electron pulses emitted from nanometer-sized gold tapers. Angle-resolved kinetic energy spectra of electrons emitted from such tips are recorded using ultrafast near-infrared light pulses of variable wavelength and intensity for excitation. For sufficiently long wavelengths, we observe a pronounced strong-field acceleration of electrons within the field gradient at the taper apex. We find a distinct narrowing of the emission cone angle of the fastest electrons. We ascribe this to the field-induced steering of subcycle electrons as opposed to the diverging emission of quiver electrons. Our findings are corroborated by simulations based on a modified Simpleman model incorporating the curved, vectorial field gradient in the vicinity of the tip. Our results indicate new pathways for designing highly directional nanometer-sized ultrafast electron sources.

High-order above-threshold ionization with few-cycle laser pulses: Molecular improved strong-field approximation vs. molecular low-frequency approximation

We investigate high-order above-threshold ionization (HATI) of homonuclear diatomic molecules by a few-cycle laser pulse. In order to describe molecular HATI in ultrashort laser pulses we have modified our molecular improved strong-field approximation (MISFA), which was developed for long laser pulses and in which the rescattering of the ionized electron off the parent ion was described using the first-order Born approximation (1BA). Now, we introduce the so-called molecular low-frequency approximation (MLFA) in which the elastic rescattering amplitude is calculated exactly. The angle-resolved electron energy spectra for HATI of N2 and O2 obtained using the MLFA are compared with those obtained within the MISFA. The difference between these spectra becomes significant for larger (re)scattering angles. This is due to the fact that the exact scattering amplitude, used in the MLFA, has minima for some values of the rescattering angles that are absent in the 1BA. Also, the rescattering plateau is lower for the MLFA spectra. We investigate the influence of the carrier-envelope phase on the high-energy part of the molecular HATI spectra. As in the atomic case, the left-right (backward-forward) asymmetry is also observed in the molecular case.

Multiphoton detachment from a zero-range potential revisited

Direct detachment of an electron bound by a regularized zero-range potential is reinvestigated. For the definition of the S-matrix amplitude for detachment, the wave function of the electron after the laser pulse has passed through is projected on an exact scattering state of the zero-range potential rather than a plane-wave state, which is normally used. The exact scattering state generates an additional contribution to the amplitude, which leads to an isotropic term in the angle-resolved energy spectrum.

High-order above-threshold ionization beyond the first-order Born approximation

In the improved strong-field approximation, which describes high-order above-threshold ionization (HATI), the rescattering of the ionized electron on the parent ion is described within the first-order Born approximation. The low-frequency approximation for laser-assisted scattering goes beyond the first Born approximation. In the present paper, we derive the low-frequency approximation for HATI. The rescattering amplitude in the first Born approximation is replaced by the exact scattering amplitude calculated on the energy shell. Our numerical results for the angle-resolved HATI energy spectra show that the difference between the improved strong-field approximation and the low-frequency approximation is significant for scattering away from the laser polarization axis. In the context of quantum-orbit theory and the uniform approximation, we also show that on the back-rescattering ridge, the rescattering $T$-matrix element can be factorized into the product of the incoming flux and the elastic-scattering cross section so that the latter can be extracted from the angle- and energy-resolved HATI spectra.

Large solid-angle analyzer applied to angle-resolved ultraviolet photoelectron spectroscopy

We have applied a large acceptance solid-angle energy analyzer to measure angle-resolved energy spectra of photoelectrons excited by ultraviolet light. The observed photoemission patterns as a function of a binding energy provides the energy dispersion curves of highly oriented pyrolytic graphite. The measured dispersion curves of the σ and π bands agree with both the reported and theoretical ones based on ab initio calculations. The energy resolution of the analyzer estimated in this experiment agrees with the reported value measured by EELS experiment. The comparison of properties of three different analyzers clarifies that the simultaneous realization of the short measurement time and high energy resolution is the most advantageous feature of this analyzer.

Femtosecond electron pulse gating using surface plasmons

We present a theoretical investigation of a novel all-optical method for electron beam gating via ponderomotive surface plasmon (SP) interaction. Using femtosecond optical pulses, large electric field gradient SP waves are launched on the surface of a metal film and selectively gate an external electron beam. It is shown that this method can generate electron pulses having similar durations as the laser pulse. The ultrashort electron packets are highly directional and examination of their spatial distribution reveals a large degree of spatial microbunching. Angle-resolved energy spectra of the electrons reveal that their final velocities are highly correlated with exit angle. Furthermore, it is demonstrated that the SP gating technique can be utilized for temporal characterization of ultrashort electron pulses with durations <100 fs.

Surface-plasmon-based electron acceleration

In this paper, we describe a surface-plasmon-based electron acceleration model, the results of which were supported by our recent experimental observations [S. E. Irvine et al., Phys. Rev. Lett. 93, 184801 (2004)]. The model incorporates femtosecond electromagnetic field dynamics and nonlinear electron photoemission characteristics of metallic surfaces. To account for the electromagnetic field structure in space and time, we numerically solve Maxwell's equations in two dimensions. Photoelectron emission is treated quasiclassically in accordance with empirical multiphoton statistics, whereas electron dynamics and energy gain are governed by the Lorentz force. Various aspects of the acceleration mechanism are discussed including surface plasmon coupling and evanescent decay, kinetic energy spectra, angular distributions, angle-resolved energy spectra, and the dependence of maximum energy on the surface electric field.

Vicinage effects in energy loss and electron emission during grazing scattering of heavy molecular ions from a solid surface

Vicinage effects in the energy loss and the electron emission spectra are studied in the presence of Coulomb explosion of swift, heavy molecular ions, during their grazing scattering from a solid surface. The dynamic response of the surface is treated by means of the dielectric theory within the specular reflection model using the plasmon pole approximation for the bulk dielectric function, whereas the angle-resolved energy spectra of the electrons emitted from the surface are obtained on the basis of the first-order, time-dependent perturbation theory. The evolution of the charge states of the constituent ions in the molecule during scattering is described by a nonequilibrium extension of the Brandt-Kitagawa model. The molecule scattering trajectories and the corresponding Coulomb explosion dynamics are evaluated for the cases of the internuclear axis being either aligned in the beam direction or randomly oriented in the directions parallel to the surface. Our calculations show that the vicinage effect in the energy loss is generally weaker for heavy molecules than for light molecules. In addition, there is clear evidence of the negative vicinage effect in both the energy loss and the energy spectra of the emitted electrons for molecular ions at lower speeds and with the axismore » aligned in the direction of motion.« less

Attosecond Double-Slit Experiment

A new scheme for a double-slit experiment in the time domain is presented. Phase-stabilized few-cycle laser pulses open one to two windows (slits) of attosecond duration for photoionization. Fringes in the angle-resolved energy spectrum of varying visibility depending on the degree of which-way information are measured. A situation in which one and the same electron encounters a single and a double slit at the same time is observed. The investigation of the fringes makes possible interferometry on the attosecond time scale. From the number of visible fringes, for example, one derives that the slits are extended over about 500 as.

Use of Electron Correlation to Make Attosecond Measurements without Attosecond Pulses

We describe how correlations between electrons can be used to trace the dynamics of correlated two-electron ionization with attosecond precision, without using attosecond pulses. The approach is illustrated using the example of Auger or Coster-Kronig decay triggered by photoionization with an extreme ultraviolet pulse. It requires correlated measurements of angle-resolved energy spectra of both the photo- and Auger electrons in the presence of a laser pulse. To reconstruct the dynamics, we use not only classical time and energy correlation, but also entanglement between the two electrons.

High-energy above-threshold detachment from negative ions

Above-threshold detachment of electrons from negative ions by an elliptically polarized laser field is analyzed within the strong-field approximation. The low-energy part of the spectrum, that is, its structure and its apparent cutoff, strongly depends on the orbital quantum number $l$ of the initial ground state. The high-energy part is characterized by the usual extended plateau caused by rescattering, which is essentially independent of the ground state. The potential that the returning electron experiences during rescattering is modeled by the sum of a polarization potential and a static potential. This rescattering potential does not have much effect on the shape of the plateau, but it does on its height. For ${\mathrm{H}}^{\ensuremath{-}}\phantom{\rule{0.2em}{0ex}}(l=0)$, the yield of rescattered electrons is five orders of magnitude below the direct electrons, while for ${\mathrm{I}}^{\ensuremath{-}}\phantom{\rule{0.2em}{0ex}}(l=1)$ the yields only differ by a factor of 40. We also analyze the dependence of the angle-resolved energy spectrum on the ellipticity of the laser field and confirm general symmetry properties. An angle-integrated elliptic dichroism parameter is introduced and analyzed.

大立体角電子エネルギー分析器の試作（ＩＩ）

By limiting the entrance solid angle of the display-type analyzer, new wide solid-angle electron analyzer with the simple configuration was realized. This analyzer provides “angle-resolved” and “energy-resolved” electron pattern. By using CCD camera with MCP, we measured angle-resolved energy spectra. We show typical EELS spectra of ZrB2 (0001) surface. The energy resolution and angle resolution were evaluated from the data. From LEED pattern of Si (111) - 7 × 7 surface, an angular resolution of 0.5° at the diffraction (00) spot was achieved (0.065 Å-1 at 209 eV). Ratio of the energy width to the pass energy ΔE/E0 of the analyzer were 0.017-0.022 depending on the incidence angle.