Classical Trajectory Monte Carlo Simulations Research Articles

Optical properties of InSb derived from reflection electron energy loss spectroscopy spectrum

The energy loss function (ELF) of the narrow bandgap semiconductor, InSb, was derived from the reflection electron energy loss spectroscopy (REELS) spectrum measured at 4 keV incident electron energy in an energy loss range of 1.6–200 eV using a high energy resolution electron spectrometer. The experimental spectrum was analyzed with the reverse Monte Carlo (RMC) method, which integrates the classical trajectory Monte Carlo simulation with the simulated annealing method for optimizing the trial ELF. Subsequently, the complex dielectric function ε(ω), refractive index and extinction coefficient were determined from the obtained ELF in the energy loss (i.e. photon energy) range of 1.6–200 eV. The validity of the obtained data was verified by the f-sum rule, ps-sum rule, inertial sum rule and dc-conductivity sum rule. We found that our calculated data of InSb fulfill the sum rules with very high accuracy; therefore, the use of these calculated optical data in material science and surface analysis is highly recommended for further applications.

Electron Impact Ionization Cross-Section Maxima of Atoms

Using measured cross-sections and polarizability data, an empirical scaling law is extracted for the electron collision single-ionization cross-section maxima of neutral atoms. We found that the cross sections scale linearly with the target’s static polarizability. We confirm this observation using our present three-body classical trajectory Monte Carlo simulations.

Fragmentation dynamics of electron-impact double ionization of helium

We study the double ionization dynamics of a helium atom impacted by electrons with full-dimensional classical trajectory Monte Carlo simulation. The excess energy is chosen to cover a wide range of values from 5 eV to 1 keV for comparative study. At the lowest excess energy, i.e., close to the double-ionization threshold, it is found that the projectile momentum is totally transferred to the recoil-ion while the residual energy is randomly partitioned among the three outgoing electrons, which are then most probably emitted with an equilateral triangle configuration. Our results agree well with experiments as compared with early quantum-mechanical calculation as well as classical simulation based on a two-dimensional Bohr’s model. Furthermore, by mapping the final momentum vectors event by event into a Dalitz plot, we unambiguously demonstrate that the ergodicity has been reached and thus confirm a long-term scenario conceived by Wannier. The time scale for such few-body thermalization, from the initial nonequilibrium state to the final microcanonical distribution, is only about 100 attoseconds. Finally, we predict that, with the increase of the excess energy, the dominant emission configuration undergoes a transition from equilateral triangle to T-shape and finally to a co-linear mode. The associated signatures of such configuration transition in the electron-ion joint momentum spectrum and triple-electron angular distribution are also demonstrated.

All-optical nanoscopic spatial control of molecular reaction yields on nanoparticles

Molecular adsorbate reactions on nanoparticles play a fundamental role in areas such as nano-photocatalysis, atmospheric, and astrochemistry. They can be induced, enhanced, and controlled by field localization and enhancement on the nanoparticle surface. In particular, the ability to perform highly controlled near-field-mediated reactions is key to deepening our understanding of surface photoactivity on nanosystems. Here, using reaction nanoscopy, we experimentally demonstrate all-optical nanoscopic control of surface reaction yields by tailoring the near fields on nanoparticles with waveform-controlled linear and bicircular two-color laser pulses, respectively. We observe site-selective proton emission from the dissociative ionization of adsorbate molecules on Si O 2 nanoparticles as a function of the polarization and relative phase of the two-color pulses. The angularly resolved close-to-uniform mapping between the surface reaction yields and the measured ion momentum enables the observation and spatial control of molecular reactions on the nanoparticle surface with nanoscopic resolution. The experimental results are modeled and reproduced qualitatively by classical trajectory Monte Carlo simulations. Our work paves the way toward reliable all-optical control of photocatalytic chemical reactions on nanoscale surfaces.

Magnetic-Field Effect as a Tool to Investigate Electron Correlation in Strong-Field Ionization

The influence of the magnetic component of the driving electromagnetic field is often neglected when investigating light-matter interaction. We show that the magnetic component of the light field plays an important role in nonsequential double ionization, which serves as a powerful tool to investigate electron correlation. We investigate the magnetic-field effects in double ionization of xenon atoms driven by near-infrared ultrashort femtosecond laser pulses and find that the mean forward shift of the electron momentum distribution in light-propagation direction agrees well with the classical prediction, where no under-barrier or recollisional nondipole enhancement is observed. By extending classical trajectory MonteCarlo simulations beyond the dipole approximation, we reveal that double ionization proceeds via recollision-induced doubly excited states, followed by subsequent sequential over-barrier field ionization of the two electrons. In agreement with this model, the binding energies do not lead to an additional nondipole forward shift of the electrons. Our findings provide a new method to study electron correlation by exploiting the effect of the magnetic component of the electromagnetic field.

Analysis of a higher-energy structure in nanotip enhanced fields

We investigate strong field ionization of an atomic gas in a plasmonically enhanced field resulting from the illumination of a nanometer-sized structure with ultrafast laser pulse. We use perturbation theory to derive an approximate solution for electron’s motion following ionization. These analytical estimates are corroborated by the time-dependent Schrödinger equation and classical trajectory Monte Carlo simulations. Notably, our approach can be used to obtain electron energy spectra without having to rely on numerical simulations. This allows for a deeper study of the dependence of electron energy spectrum on the properties of the near-field, suggesting electric field sensor applications. We derive an analytical expression for the location of the peak of the higher-energy structure (HES) as a function of laser parameters and near-field decay length. We find a particularly strong dependence of the energy peak on laser frequency, with lower frequencies causing a significant upward shift in the final electron energies. Combined with control of the width of the HES, which can be done by changing the size of the nanostructure, this points to the possibility of using nanotips as sources of ultrashort electron beams of tunable energy.

Semiclassical study of nonsequential triple ionization of Ar in strong laser fields

We study nonsequential triple ionization of Ar in strong laser fields using a classical trajectory Monte Carlo simulation. By tracing electrons' trajectories, we reveal the mechanisms of triple ionization, including multiple recollision and sequential ionization. One electron tunnels out and rescatters with its parent ion, either kicking off two electrons together or kicking off one of them and exciting another one, which will be freed by the laser field. Besides the above-dominated channels, the cascade rescattering for triple ionization is explored, in which the first tunneling electron rescatters with the parent ion ${\mathrm{Ar}}^{+}$ and kicks off the second electron and then the second electron gains energy in the laser field and rescatters with ${\mathrm{Ar}}^{2+}$, kicking off the third electron or boosting it to excited states to be freed later. Such a cascade channel connects three electrons step by step, and ${\mathrm{Ar}}^{3+}$ may have larger ultimate momenta compared to the triple ionization mediated by only one rescattering. Our simulation shows it is possible to control the cascade channel and extract it through the ion momentum distribution.

Controlling polarization of attosecond pulses with plasmonic-enhanced bichromatic counter-rotating circularly polarized fields

The use of bichromatic counter-rotating laser field is known to generate high-order harmonics with nonzero ellipticity. By combining such laser field with a plasmonic-enhanced spatially inhomogeneous field, we propose a way to influence the subcycle dynamics of the high-harmonic generation process. Using the numerical solution of the time-dependent Schr\"odinger equation combined with classical trajectory Monte Carlo simulations, we show that the change of the direction and the strength of the plasmonic field selectively enhances or suppresses certain recombining electron trajectories. This in turn modifies the ellipticity of the emitted attosecond pulses.

Wavelength-Dependent Features of Photoelectron Spectra from Nanotip Photoemission

If a metal nanotip is irradiated with the light of a wavelength much larger than the nanotip’s radius of curvature, optical near-fields become excited. These fields are responsible for distinct strong-field electron dynamics, due to both the field enhancement and spatial localization. By classical trajectory, Monte Carlo (CTMC) simulation, and the integration of the time-dependent Schrödinger equation (TDSE), we find that the photoelectron spectra for nanotip strong-field photoemission, irradiated by mid-infrared laser pulses, present distinctive wavelength-dependent features, especially in the mid- to high-electron energy regions, which are different from the well known ones. By extracting the electron trajectories from the CTMC simulation, we investigate these particular wavelength-dependent features. Our theoretical results contribute to understanding the photoemission and electron dynamics at nanostructures, and pave new pathways for designing high-energy nanometer-sized ultrafast electron sources.

Magnetic confinement of effectively unmagnetized plasma particles

A purely magnetic applied field may provide plasma confinement under conditions where the bulk of the plasma is effectively free of the applied magnetic field. The applied magnetic field surrounds the bulk of the plasma, and plasma particles that are incident on the applied magnetic field can be reflected back into the effectively unmagnetized region of plasma. The concept belongs to a class of magnetic plasma confinement approaches studied long ago, for which some experimental results indicated that classical (collision-based) cross-magnetic-field transport may occur. However, multiple magnetic coils are required to be immersed within the confined plasma, and rapid plasma loss may occur if material structures are present, which pass through the plasma (e.g., to hold the immersed coils in place). In the work reported, the concept is studied in combination with magnetic plasma expulsion [R. E. Phillips and C. A. Ordonez, Phys. Plasmas 25, 012508 (2018)], which would be employed to keep plasma away from material structures that pass through the plasma. A planar model is used for the study. A classical trajectory Monte Carlo simulation is carried out on particles that are independently incident on the applied magnetic field. With monoenergetic incident particles, the results indicate that the applied magnetic field can reflect all independently incident particles in certain regions of parameter space. Prospects for achieving three-dimensional magnetic confinement of an effectively unmagnetized plasma with a Maxwellian velocity distribution are discussed.

Ellipticity-dependent sequential over-barrier ionization of cold rubidium

We perform high-resolution measurements of momentum distribution on Rb$^{n+}$ recoil ions up to charge state $n=4$, where laser-cooled rubidium atoms are ionized by femtosecond elliptically polarized lasers with the pulse duration of 35 fs and the intensity of 3.3$\times$10$^{15}$ W/cm$^2$ in the over-barrier ionization (OBI) regime. The momentum distributions of the recoil ions are found to exhibit multi-band structures as the ellipticity varies from the linear to circular polarizations. The origin of these band structures can be explained quantitatively by the classical OBI model and dedicated classical trajectory Monte Carlo simulations with Heisenberg potential. Specifically, with back analysis of the classical trajectories, we reveal the ionization time and the OBI geometry of the sequentially released electrons, disentangling the mechanisms behind the tilted angle of the band structures. These results indicate that the classical treatment can describe the strong-field multiple ionization processes of alkali atoms.

Dynamics of Rydberg states and terahertz waves generated in strong few-cycle laser pulses

Physical processes near threshold in strong-field ionization are complex owing to the important role of many intermediate states. Two typical near-threshold processes in few-cycle laser pulses, the generations of Rydberg electrons and terahertz waves, are investigated using classical trajectory Monte Carlo simulations. Mapping final energies of electrons to the tunneling coordinates, the two processes are distinguished based on the contributions from different kinds of electron trajectories, which highlights the complex interplay between the Coulomb potential and the laser field on the electron dynamics. We clarify the dependence of momentum and energy spectra on the carrier-envelope phase. We find that the optimal phases for terahertz wave generation and creation of the Rydberg state in few-cycle laser pulses are opposite. This finding can be applied to further experiments on attosecond electron dynamics.

L-changing through very-long-range interactions in high-n, n∼300, Rydberg-Rydberg collisions

SynopsisState-changing in thermal-energy collisions between strontium atoms in high-n, n∼300, n1F3 Rydberg states is studied in an atomic beam and analyzed using classical trajectory Monte Carlo simulations. The L-changing cross section is large, ∼10-4 cm2, much greater than the corresponding “hard-sphere” cross section.

Classical trajectory Monte Carlo simulation of plasma fueling using magnetic plasma expulsion

The possibility of fueling a magnetically confined plasma using particle sources located inside of the plasma is studied by computer simulation. Magnetic plasma expulsion [R. E. Phillips and C. A. Ordonez, Phys. Plasmas 25, 012508 (2018)] would serve to keep the magnetically confined plasma away from the particle sources without adversely affecting plasma confinement. The simulations show how charged particles can be injected into a plasma by using particle sources located directly between two current-carrying wires that create a magnetic expulsion field. Plasma fueling with the average energy of injected particles greater than the average energy of plasma particles may serve for heating the plasma. Also, plasma fueling with positive and negative particles injected at different rates may serve for changing the neutrality of the plasma. Conditions for plasma fueling are investigated using a classical trajectory Monte Carlo simulation. Two types of particle sources are considered, and the fraction of emitted particles that reach (and fuel) the magnetically confined plasma is evaluated for each.

Comparison between quantum and classical calculations for above threshold ionization of argon

We present comparisons between quantum and classical calculations for above threshold ionization of an Argon atom interacting with a strong laser pulse. The time-dependent complete-active-space self-consistent field (TD-CASSCF) method and the classical trajectory Monte Carlo (CTMC) method are used for the cases of quantum and classical calculations, respectively. We find and discuss differences between the results obtained by the TD-CASSCF and the CTMC simulations.

The modeling of atom \u2013 neutral collisions for beam emission spectroscopy applications

The collisional radiative models used in the modeling of beam emission spectroscopy diagnostics neglect atom–atom collisions because of a lack of sufficiently detailed atomic data. Filling this scantiness we performed a classical trajectory Monte Carlo simulations to calculate the cross sections for various channels in collisions between H + H2 and Li + H2 for a wide range of projectile energies. Based on the calculated cross sections, a simplified version of the collisional radiative model has been derived. We show that the model is suitable to obtain the beam attenuation in neutral gases outside of the confined plasma region. A strong density dependence has been found for each beam species.Graphical abstract

Quantum effect of laser-induced rescattering from the tunneling barrier

Rescattering mediated by intense laser fields is one of the dominant processes in strong-field physics. It was usually described classically or semiclassically. Recently, laser-induced recollisions with the tunneling barriers have attracted great theoretical interest. However, fully distinguishing the ``quantum'' effect of rescattering with the tunneling barrier on photoelectron energy and momentum distributions is very difficult if using the linearly polarized light field. Here we perform the measurement of photoelectron momentum distributions by strong-field ionization of Ar atoms in orthogonally polarized two-color laser fields with comparable intensities. We observe the strong ionization enhancement due to rescattering on two-dimensional momentum distribution, which is in striking disagreement with the predictions by the plain strong-field approximation and the classical-trajectory Monte Carlo simulation. With the help of the analysis on the electron complex trajectories in both sub-barrier and quasicontinuum regions, the enhancement is illustrated to originate from the quantum effect of forward scattering between the tunneling electron and its parent ion. The study shows that the electron probability will be significantly modified when the rescattered electrons excurse in the continuum and the ``classical'' rescattering process needs the quantum description.

Dependence of Rydberg-state creation by strong-field ionization on laser intensity

We investigate numerically and analytically the intensity dependence of the fraction of electrons that end up in a Rydberg state after strong-field ionization with linearly polarized light. We find that including the intensity dependent distribution of ionization times and non-adiabatic effects leads to a better understanding of experimental results. Furthermore, we observe using Classical Trajectory Monte Carlo simulations that the intensity dependence of the Rydberg yield changes with wavelength and that the previously observed power-law dependence breaks down at longer wavelengths. Our work suggests that Rydberg yield measurements can be used as an independent test for non-adiabaticity in strong field ionization.

Interplay between Coulomb-focusing and non-dipole effects in strong-field ionization with elliptical polarization

We study strong-field ionization and rescattering beyond the long-wavelength limit of the dipole approximation with elliptically polarized mid-IR laser pulses. Full three-dimensional photoelectron momentum distributions (PMDs) measured with velocity map imaging and tomographic reconstruction revealed an unexpected sharp ridge structure in the polarization plane (2018 Phys. Rev. A 97 013404). This thin line-shaped ridge structure for low-energy photoelectrons is correlated with the ellipticity-dependent asymmetry of the PMD along the beam propagation direction. The peak of the projection of the PMD onto the beam propagation axis is shifted from negative to positive values when the sharp ridge fades away with increasing ellipticity. With classical trajectory Monte Carlo simulations and analytical analysis, we study the underlying physics of this feature. The underlying physics is based on the interplay between the lateral drift of the ionized electron, the laser magnetic field induced drift in the laser propagation direction, and Coulomb focusing. To apply our observations to emerging techniques relying on strong-field ionization processes, including time-resolved holography and molecular imaging, we present a detailed classical trajectory-based analysis of our observations. The analysis leads to the explanation of the fine structure of the ridge and its non-dipole behavior upon rescattering while introducing restrictions on the ellipticity. These restrictions as well as the ionization and recollision phases provide additional observables to gain information on the timing of the ionization and recollision process and non-dipole properties of the ionization process.

Disentangling Long Trajectory Contributions in Two-Colour High Harmonic Generation

This work investigates High Harmonic Generation (HHG) in gas targets, induced by intense two-colour driving fields. We compared classical trajectory Monte Carlo simulations based on a semiclassical model of strong field tunnel ionisation of helium to experimental HHG spectra, and investigated the relative contribution of long trajectories to low harmonic orders. This phenomenon can be found even when the experimental setup is chosen to suppress long trajectories and favour phase matching for short trajectories.