Electron Rescattering Research Articles

Attosecond near-threshold photoionization in a strong laser field

A drastic modification of the conventional streaking patterns of double differential cross section for attosecond near-threshold ionization of atoms in a strong infrared (IR) field is theoretically investigated. Rescattering of slow electrons from the ionic core leads to appearance of the interference fringes and strong diffraction maxima in the spectra of photoelectrons at small energies. The computations based on solving the time-dependent Schr\odinger equation show that both these spectral features strongly depend on the IR intensity and frequency. Investigations of low-energy streaking can provide unique information on slow photoelectron dynamics in combined fields of ionic core and strong IR laser.

Quantum trajectories for high-order-harmonic generation from multiple rescattering events in the long-wavelength regime

We have performed the quantum trajectory analysis for high-order-harmonic generation (HHG) with different driving laser wavelengths. By defining the ratio of HHG yields of the $N$th and first rescattering events (${Y}_{N}/{Y}_{1}$), we quantitatively evaluate the HHG contributions from multiple rescatterings. The results show that the HHG yield ratio increases gradually with the increase of the laser wavelength, which demonstrates that high-order rescatterings provide ascendent contributions to HHG at longer wavelength. By calculating the classical electron trajectories, we find significant differences exist in the electron behaviors between the first and high-order rescatterings. Further investigations have demonstrated that the increasing HHG yield ratio is mainly attributed to the relatively smaller contributions from the short path of the first electron rescattering at longer laser wavelength.

Strong-field approximation for above-threshold ionization of polyatomic molecules. II. The role of electron rescattering off the molecular centers

We consider high-order above-threshold ionization of polyatomic molecules by a strong laser field. An improved molecular strong-field approximation which takes into account the electron rescattering off the molecular centers is developed. The presented theory is applied to calculate the photoelectron energy and angular distributions for the ozone molecule. The obtained spectra exhibit pronounced minima, and this is explained as a three-point destructive interference of the rescattered electron wave packets.

Coherent contribution of consecutive electron rescatterings in the extreme ultraviolet supercontinuum

In this article, coherent contributions of high-order quantum paths are proposed to generate a highly efficient and fine appearance attosecond pulse. We show how the electron dynamics of the high-order harmonics evolves so that harmonics are generated by a helium atom exposed to the two-color waveform composed of sub-one-cycle pulses. The leading and the trailing of the pulse is constructed by the near-infrared driving pulse and a midinfrared control pulse, respectively, thereby tunnel ionization and recombination are effectively manipulated. This waveform not only broadens the bandwidth but also leads to the contribution of high-order rescatterings in the generated supercontinuum and thereby enhances the harmonic yields. Whereas the effective duration of the waveform is lesser than the midinfrared pulse, with prolonging the pulse trailing, the long path of first-order rescattering is completely suppressed and high-order rescatterings of different electron trajectories appear. The most interesting feature is that under optimized conditions, the short paths of consecutive rescatterings coherently contribute in the high-order-harmonic generation process that leads to a fine appearance in the attosecond pulses.

Electron rescattering at metal nanotips induced by ultrashort laser pulses

We theoretically investigate the interaction of moderate intensity near-infrared few cycle laser pulses with nano-scale metal tips. Local field enhancement in a nanometric region around the tip apex triggers coherent electron emission on the nanometer length and femtosecond time scale. The quantum dynamics at the surface are simulated with time-dependent density functional theory (TDDFT) and interpreted based on the simple man's model. We investigate the dependence of the emitted electron spectra on the laser wavelength.

Rescattering and frustrated tunneling ionization of atoms in circularly polarized laser fields

We investigate strong-field ionization dynamics of atoms in circularly polarized laser fields by a three-dimensional electron ensemble method which is validated by comparison with ab initio results of solving the time-dependent Schr\"odinger equation. We show that the Coulomb potential and the electron recollision play very crucial roles for single ionization of atoms with a lower ionization potential in circularly polarized laser fields. We find that the critical laser field strength for recollision scales as ${F}_{0}\ensuremath{\sim}2ln10{\ensuremath{\omega}}^{2}/\sqrt{2{I}_{p}}$(${I}_{p}$, ionization potential; $\ensuremath{\omega},$ laser frequency), below which the rescattering is very crucial. As a consequence of recollision, a large amount of tunneled electrons will be ejected into the elliptical orbits of Rydberg states or strongly rescattered off the nucleus and eventually achieve large energy from laser fields. The characteristic feature is that both the relative frustrated tunneling rate and the hard rescattering rate decrease with increasing the laser intensity and the wavelength. This study sheds a light on those processes that are closely related with electron rescattering in circularly polarized laser fields, e.g., high-order harmonic generation and nonsequential double ionization.

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

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.

Non-sequential double ionization of Mg atoms in elliptically polarized laser fields

The non-sequential double ionization of the Mg atom in elliptically polarized laser fields is investigated. The numerical results indicate that the ‘knee’ structure is more obvious with increasing ellipticity in the laser intensity range (1013–1015 W cm−2) we considered, and recollision excitation with subsequent tunnelling ionization occurs much more easily at higher ellipticity, which can be well explained by the corresponding momentum distribution of electrons. Moreover, the ionized electron energy of Mg atoms at the end of the pulse also indicates that rescattering of electrons still occurs in elliptically polarized laser fields. In addition, the angular distribution of ionized electrons is also calculated and the result shows that angular distribution of electrons is no longer along the x-axis in elliptically polarized laser fields.

Controlling ionisation and fragmentation processes in CO2via inelastic electron recollisions

The angular dependence of nonsequential double ionisation and dissociation induced by laser driven inelastic electron rescattering was investigated experimentally in aligned CO2 . A clear dependence on the recollision angle was found demonstrating quantum control of ionisation and dissociation processes in the strong field regime.

Electron rescattering at metal nanotips induced by ultrashort laser pulses

We investigate plateau and cutoff structures in photoelectron spectra from nanoscale metal tips interacting with few-cycle near-infrared laser pulses. These hallmarks of electron rescattering, well-known from atom-laser interaction in the strong-field regime, appear at remarkably low laser intensities with nominal Keldysh parameters of the order of $\ensuremath{\gtrsim}\phantom{\rule{-0.16em}{0ex}}\phantom{\rule{-0.16em}{0ex}}10$. Quantum and quasiclassical simulations reveal that a large field enhancement near the tip and the increased backscattering probability at a solid-state target play a key role. Plateau electrons are by an order of magnitude more abundant than in comparable atomic spectra, reflecting the high density of target atoms at the surface. The position of the cutoff serves as an in situ probe for the locally enhanced electric field at the tip apex.

Electron Rescattering in Above-Threshold Photodetachment of Negative Ions

We present experimental and theoretical results on photodetachment of Br(-) and F(-) in a strong infrared laser field. The observed photoelectron spectra of Br(-) exhibit a high-energy plateau along the laser polarization direction, which is identified as being due to the rescattering effect. The shape and the extension of the plateau is found to be influenced by the depletion of negative ions during the interaction with the laser pulse. Our findings represent the first observation of electron rescattering in above-threshold photodetachment of an atomic system with a short-range potential.

Strong-field ionization of molecules by few-cycle pulses

Few-cycle pulses of 800 nm light cause ionization and dissociation of triatomic molecules like H2O and CS2 in the temporal regime where only electron rescattering dominates the laser-molecule interaction. In case of ionization of H2O, significantly higher amounts of kinetic energy are released upon dissociation into atomic fragments. However, the case of CS2 is somewhat special in that the wave packet of the rescattered electron destructively interferes with the antibonding π orbital of CS2+ such that rescattering is also essentially turned off. Under such circumstances the dissociation channel is absent and long-lived singly, doubly, and triply charged molecular ions dominate the mass spectrum in the few-cycle regime. This brings to the fore the importance of molecular symmetry in strong-field ionization. Ultrafast atomic rearrangements are also observed: H atoms in H2O are rearranged by strong optical fields generated by intense 9.3 fs laser pulses to form a new bond leading to H2+; experiments show that this bond formation occurs within a single laser pulse.

Ionization and Fragmentation of Alkylphenols by 0.8−1.5 μm Femtosecond Laser Pulses

Ionization and fragmentation were studied on alkylphenols with long alkyl chains (p-(C6H4)(OH)(C(n)H(2n+1)), n = 1,3,5,8,9) and, for reference, on alkylbenzenes ((C6H5)(C(n)H(2n+1)), n = 1,3,5,7,9) by intense femtosecond laser pulses, typically with 43 fs duration at 0.8 microm and 140 fs at 1.3 microm in an intensity range of 10(14) W cm(-2). The major products were the corresponding molecular and C7 fragment ions from the alkylphenols and alkylbenzenes. The molecular ion yields decreased from nearly 1 (n = 1) to 0.3-0.5 (n = 9) when the carbon number in the alkyl chain increased for both excitation wavelengths. Higher yields of the molecular ions were observed at a longer wavelength of 1.3 microm. The long wavelengths in the range of 1.3-1.5 microm were used to determine whether or not -OH absorption had any increase in fragment ions. No effect was observed by vibrational overtone excitation of the -OH group in this wavelength range. Direct dissociation by cation absorption is the most plausible explanation of the present fragmentation results. Other possible mechanisms were discussed, including a statistical model, an effect of electron rescattering, a multiactive electron model, and dissociation from the superexcited state. In the case of cyclohexane, nonresonant wavelength excitation with a pulse of 1.3 microm (150 fs) effectively suppressed fragmentation more than excitation by a resonant but short-duration pulse (0.8 microm, 15 fs).

Electron re-scattering from aligned linear molecules using the R-matrix method

Electron re-scattering in a strong laser field provides an important probe of molecular structure and processes. The laser field drives the ionization of the molecule, followed by acceleration and subsequent recollision of the electron with the parent molecular ion, the scattered electrons carry information about the nuclear geometry and electronic states of the molecular ion. It is advantageous in strong field experiments to work with aligned molecules, which introduces extra physics compared to the standard gas-phase, electron–molecule scattering problem. The formalism for scattering from oriented linear molecules is presented and applied to H2 and CO2. Differential cross sections are presented for (re-)scattering by these systems concentrating on the most common, linear alignment. In H2 these cross sections show significant angular structure which, particularly for a scattering angle of 90°, are predicted to vary significantly between re-collisions stimulated by an even or an odd number of photons. In CO2 these cross sections are zero indicating the necessity of using non-parallel alignment with this molecule.

Electron emission from laser-irradiated atomic clusters

The mechanism of fast-electron emission from laser-irradiated clusters is studied by model calculations. Rescattering of electrons at the charged cluster is shown to be an important process. In contrast to rescattering at atoms, the structure, that is the size and strength, of the scattering potential determines final kinetic energies of the electrons. This becomes evident in a strong cluster-size dependence of the electron spectra.

Research on cluster-assistant multiple ionization of acetonitrile by intense nanosecond laser

To further investigate the relation between cluster and multi-charged ions, the photo-ionization of acetonitrile molecular beam carried by helium was studied by time-of-flight mass spectrometry using 25 ns, 532 nm and 1 064 nm Nd-YAG laser with an intensity of 10(10) W x cm(-2). When the effused beam of CH3CN at a pressure of about 11 kPa was irradiated by a 532 nm laser, only a few mono-charged ions appeared in the mass spectrum and were clearly resolved, While the pulsed molecular beam seeded in 0.15 MPa He, multi-charged species appeared between H+ and C+, and parent ions containing one or more acetonitrile molecules were also discovered. The intrinsical difference between effused beam and pulsed one was that for the latter it was easier to generate molecule clusters. Adjusting delay time between laser and pulsed valve to shine the laser on different potions of pulsed beam, the change tendency of integral intensity of different multi-charged ions was found to remain similar to that of acetonitrile cluster, and the highest intensity of different ion species appeared at the same 0.75 ms delay time. When the wavelength of laser was changed from 532 nm to 1064 nm, the type of ions and their proportion from effused beam were alike except intensity, but the result of pulsed beam altered obviously. Multi-charged ions showed peak splitting, which characters CE (Coulomb explode). As a powerful tool to understand some chemical physics processes involved, correlation analysis of the time of flight mass spectrum was used. The spectrum of 532 nm was selected owing to its multi-charged ions distinguished easily. The correlations among N(n+) (n = 2-5) and C(n+) (n = 2-4) were all above 0.25, with some even above 0.7, indicating that these ions are highly correlated and probably come from the CE events simultaneously. An electron re-scattering and re-colliding ionization model was proposed to explain the appearances of those multiple charged ions under such low laser intensity. From the theory, the longer wavelength facilitates the energy absorption rate during inverse bremsstrahlung, which leads to the resulting wavelength dependence of the multi-charged atomic ions.

Strong-field approximation for ionization of a diatomic molecule by a strong laser field. II. The role of electron rescattering off the molecular centers

The strong-field approximation for ionization of diatomic molecules by a strong laser field [D. B. Milo\ifmmode \check{s}\else \v{s}\fi{}evi\ifmmode \acute{c}\else \'{c}\fi{}, Phys. Rev. A 74, 063404 (2006)] is generalized to include rescattering of the ionized electron wave packet off the molecular centers (the electron's parent ion or the second atom). There are four rescattering contributions to the ionization rate, which are responsible for the high-energy plateau in the electron spectra and which interfere in a complicated manner. The spectra are even more complicated due to the different symmetry properties of the atomic orbitals of which a particular molecular orbital consists. Nevertheless, a comparatively simple condition emerges for the destructive interference of all these contributions, which yields a curve in the $({E}_{{\mathbf{p}}_{f}},\ensuremath{\theta})$ plane. Here $\ensuremath{\theta}$ is the electron emission angle and ${E}_{{\mathbf{p}}_{f}}$ is the electron kinetic energy. The resulting suppression of the rescattering plateau can be strong and affect a large area of the $({E}_{{\mathbf{p}}_{f}},\ensuremath{\theta})$ plane, depending on the orientation of the molecule. We illustrate this using the examples of the $3{\ensuremath{\sigma}}_{g}$ molecular orbital of ${\mathrm{N}}_{2}$ and the $1{\ensuremath{\pi}}_{g}$ molecular orbital of ${\mathrm{O}}_{2}$ for various orientations of these molecules with respect to the laser polarization axis. For ${\mathrm{N}}_{2}$, for perpendicular orientation and the equilibrium internuclear distance ${R}_{0}$, we find that the minima of the ionization rate form the curve ${E}_{{\mathbf{p}}_{f}}\phantom{\rule{0.2em}{0ex}}{\mathrm{cos}}^{2}\phantom{\rule{0.2em}{0ex}}\ensuremath{\theta}={\ensuremath{\pi}}^{2}∕(2{R}_{0}^{2})$ in the $({E}_{{\mathbf{p}}_{f}},\ensuremath{\theta})$ plane. For ${\mathrm{O}}_{2}$ the rescattering plateau is absent for perpendicular orientation.

Quantum-mechanical models for photo-ionization: Uni-directional electron re-scattering by a laser pulse

The interaction of a hydrogen atom with a linearly (z-) polarized laser pulse is described by numerical solution of the three-dimensional Schrödinger equation. Photo-ionization of the ground state, with pulses having three or more optical cycles at photon energies well above the ionization potential and maximum intensity 1015Wcm−2, yields symmetric opposite fluxes of electrons preferentially in the +z and −z directions. One-cycle laser pulses can lead to modest symmetry breaking, e.g., more intense electron fluxes in the +z direction than in the −z direction, depending on the carrier-envelope phase (CEP) of the pulse. Production of uni-directional electron fluxes, similar to those observed in Coulomb scattering, calls for laser pulses with stronger intensity, or lower carrier frequency, or shorter duration with appropriate CEP, e.g., half-cycle pulses in the attosecond time domain. Here, uni-directionality is achieved by a four-step mechanism: (i) photo-ionization, (ii) turn-around of the electron, (iii) scattering from the atom's core and (iv) drift in the forward direction.

Retrieval of electron-atom scattering cross sections from laser-induced electron rescattering of atomic negative ions in intense laser fields

We investigated the two-dimensional electron momentum distributions of atomic negative ions in an intense laser field by solving the time-dependent Schr\odinger equation (TDSE) and using the first- and second-order strong-field approximations (SFAs). We showed that photoelectron energy spectra and low-energy photoelectron momentum distributions predicted from SFAs are in reasonable agreement with the solutions from the TDSE. More importantly, we showed that accurate electron-atom elastic scattering cross sections can be retrieved directly from high-energy electron momentum spectra of atomic negative ions in the laser field. This opens up the possibility of measuring electron-atom and electron-molecule scattering cross sections from the photodetachment of atomic and molecular negative ions by intense short lasers, respectively, with temporal resolutions in the order of femtoseconds.

Rescattering for Extended Atomic Systems

Laser-driven rescattering of electrons is the basis of many strong-field phenomena in atoms and molecules. Here, we will show how this mechanism operates in extended atomic systems, giving rise to effective energy absorption. Rescattering from extended systems can also lead to energy loss, which in its extreme form results in nonlinear light-induced trapping. Intense-laser interaction with atomic clusters is discussed as an example. We explain fast electron emission, seen in experimental and numerically obtained spectra, by rescattering of electrons at the highly charged cluster.