Ponderomotive Energy Research Articles

Above-threshold ionization with X-ray free-electron lasers

This study delves into the relatively uncharted territory of Above Threshold Ionization in atoms, triggered by intense X-ray radiation fields. At these frequencies, the energy of a single photon far exceeds the ionization potential of valence electrons in atoms and molecules. The conditions we examine are similar to those achievable with current or future free-electron laser facilities. Under such high-energy scenarios, the onset of strong field ionization requires a shift away from the traditional quasi-classical approach. Here, we present an analytical model to characterize how the field-free ionization potential, ponderomotive energy, and photon energy govern the transition to this regime, all accounted for by means of the Keldysh and Reiss parameters. We show that both of these parameters are needed to capture the onset of strong-field behavior due to both bound state and continuum state properties. At higher X-ray intensities, we find that ionization rates deviate from the linear intensity scaling expected from lowest order perturbative processes, corresponding to channel closure and higher-order photon absorption processes.

The influence of laser focusing conditions on the direct laser acceleration of electrons

Direct laser acceleration of electrons during a high-energy, picosecond laser interaction with an underdense plasma has been demonstrated to be substantially enhanced by controlling the laser focusing geometry. Experiments using the OMEGA EP facility measured electrons accelerated to maximum energies exceeding 120 times the ponderomotive energy under certain laser focusing, pulse energy, and plasma density conditions. Two-dimensional particle-in-cell simulations show that the laser focusing conditions alter the laser field evolution, channel fields generation, and electron oscillation, all of which contribute to the final electron energies. The optimal laser focusing condition occurs when the transverse oscillation amplitude of the accelerated electron in the channel fields matches the laser beam width, resulting in efficient energy gain. Through this observation, a simple model was developed to calculate the optimal laser focal spot size in more general conditions and is validated by experimental data.

Motion of charged particles in bright squeezed vacuum

The motion of laser-driven electrons quivers with an average energy termed pondermotive energy. We explore electron dynamics driven by bright squeezed vacuum (BSV), finding that BSV induces width oscillations, akin to electron quivering in laser light, with an equivalent ponderomotive energy. We identify closed and open trajectories of the electronic width that are associated with high harmonic generation and above-threshold ionization, respectively, similarly to trajectories of the electron position when its motion is driven by coherent light. In the case of bound electrons, the width oscillations may lead to ionization with noisy sub-cycle structure. Our results are foundational for strong-field and free-electron quantum optics, as they shed light on ionization, high harmonic generation, and nonlinear Compton scattering in BSV.

Identifying photoelectron releasing order in strong-field dissociative ionization of H2.

Driven by intense laser fields, the outgoing photoelectrons in molecules possess a quiver motion, resulting in the rise of the effective ionization potential. The coupling of the field-dressed ionization potential with abundant molecular dynamics complicates the laser-molecule interactions. Here, we demonstrate an approach to resolve photoelectron releasing order in the dissociative and non-dissociative channels of multiphoton ionization driven by an orthogonally polarized two-color femtosecond laser pulse. The photoelectron kinetic energy releases and the regular nodes in the photoelectron angular distributions due to the participation of different continuum partial waves allow us to deduce the field-dressed ionization potential of various channels. It returns the ponderomotive energy experienced by the outgoing electron and reveals the corresponding photoionization instants within the laser pulse. Our results provide a route to explore the complex strong-field ionization dynamics of molecules using two-dimensional photoelectron momentum spectroscopy.

Floquet-Bloch resonances in near-petahertz electroabsorption spectroscopy of SiO2

Complex nonadiabatic dynamics are observed when the quiver energy of an electron-hole pair in a strong laser field becomes comparable to the photon energy. Here, the authors extend quasistatic electromodulation spectroscopy based on the Franz-Keldysh effect to this regime and show that in this limit it is governed by resonant transitions between Floquet-Bloch states. This regime opens opportunities to probe the effective mass as well as the ponderomotive and binding energies of the electron-hole pair on the attosecond timescale.

Ionization Dynamics for Atomic and Molecular Ions in Relativistic, Ultrastrong Laser Fields

The discovery of laser-driven rescattering and high harmonic radiation out to a maximum photon energy of 3.17 times the ponderomotive energy (Up ) laid the groundwork for attosecond pulse generation and coherent X-rays. As the laser field drives the interaction to higher energies, relativity and the Lorentz force from the laser magnetic field enter into the dynamics. We present the results of recent studies of laser rescattering, including these effects, to give a quantitative description of rescattering dynamics in the high-energy limit, ie, recollision energies of order 1,000 hartree (27 keV). The processes investigated include inner K- and L-shell excitation and the ultimate limit of high harmonic generation via rescattering bremsstrahlung. The results indicate the path to the frontier area of x-ray strong field processes.

Probability of ionization of the noble gas atoms and ions for high harmonic generation

Radiation produced in high-order harmonic generation (HHG) process can be utilized to generate attosecond pulses. According to the semi-classical theory of HHG, the maximum emitted photon energy is [Formula: see text]. The ionization potential ([Formula: see text] and ponderomotive energy ([Formula: see text], play important roles in the generated photon energy; therefore, choosing the material and field for HHG is important. Here, investigating the probability of ionization of material in laser and plasmonic field for HHG is important. The ionization probability of noble gases atoms and ions was investigated. Using Ammosov–Delone–Krainov (ADK) model formulas, the parameters for ions and atoms were determined. The results show that helium is the most suitable noble gas atom for HHG in both fields. After ionizing the atoms, the ionization potential increases significantly, and the ionization probability also decreases. Then, ions are better than their corresponding atoms for HHG. Among noble gas atoms and ions, the helium ion is the most suitable for HHG. In addition, the plasmonic field increases the ponderomotive energy and decreases the probability of ionization for all atoms, as shown by the simulation. Then, extreme ultraviolet (XUV) high-energy photon can be efficiently generated using noble gas ions.

Enhanced cutoff energies for direct and rescattered strong-field photoelectron emission of plasmonic nanoparticles

Abstract The efficient generation, accurate detection, and detailed physical tracking of energetic electrons are of applied interest for high harmonics generation, electron-impact spectroscopy, and femtosecond time-resolved scanning tunneling microscopy. We here investigate the generation of photoelectrons (PEs) by exposing plasmonic nanostructures to intense laser pulses in the infrared (IR) spectral regime and analyze the sensitivity of PE spectra to competing elementary interactions for direct and rescattered photoemission pathways. Specifically, we measured and numerically simulated emitted PE momentum distributions from prototypical spherical gold nanoparticles (NPs) with diameters between 5 and 70 nm generated by short laser pulses with peak intensities of 8.0 × 1012 and 1.2 × 1013 W/cm2, demonstrating the shaping of PE spectra by the Coulomb repulsion between PEs, accumulating residual charges on the NP, and induced plasmonic electric fields. Compared to well-understood rescattering PE cutoff energies for strong-field photoemission from gaseous atomic targets (10× the ponderomotive energy), our measured and simulated PE spectra reveal a dramatic cutoff-energy increase of two orders of magnitude with a significantly higher contribution from direct photoemission. Our findings indicate that direct PEs reach up to 93 % of the rescattered electron cutoff energy, in contrast to 20 % for gaseous atoms, suggesting a novel scheme for the development of compact tunable tabletop electron sources.

Bidirectional residual current in monolayer graphene under few-cycle laser irradiation.

By numerically solving the time-dependent Schrödinger equation and semiconductor Bloch equations, the light-induced residual current in monolayer graphene driven by a circularly polarized few-cycle laser is investigated. An evident current direction reversal is disclosed when the amplitude of the driving electric field exceeds a certain threshold value, which is absent in recent investigation [Nature550, 224 (2017)10.1038/nature23900]. Here the internal physical mechanism for the current reversal is inter-optical-cycle interference under a suitable long laser wavelength. Moreover, the reversal-related laser field amplitude depends sensitively on the ratio of ponderomotive energy to photon energy.

Strong-field ionization of plasmonic nanoparticles

We modeled strong-field ionization of metal nanoparticles by intense infrared laser pulses, accounting for and distinguishing in photoelectron (PE) momentum distributions the effects of PE correlation, PE--residual-charge interactions, PE rescattering and recombination, and transient laser-induced plasmonic fields. Our numerical results for 5-, 30-, and 70-nm-diameter gold nanospheres and peak laser-pulse intensities of $8.0\ifmmode\times\else\texttimes\fi{}{10}^{12}$ and $1.2\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{4.pt}{0ex}}{\text{W/cm}}^{2}$ show how PE velocity-map images are distinctly shaped by PE Coulomb repulsion, residual-charge accumulations, and plasmonic near fields. In contrast to gaseous atomic targets and dielectric nanoparticles, we find very large PE cutoff energies, for both directly emitted and rescattered PEs, that exceed the incident laser-pulse ponderomotive energy by two orders of magnitude.

Quantitative determination of the electric field strength in a plasmon focus from ponderomotive energy shifts

Abstract Spectroscopic photoemission microscopy is used to detect and quantify a ponderomotive shift in the energy of electrons that are emitted from a surface plasmon polariton focus. The focus is formed on an atomically flat Au(111) surface by an Archimedean spiral and is spatiotemporally separated from the circularly polarized light pulse used to excite the spiral. A spectroscopic analysis of electrons emitted from the focus exhibits a peaked above-threshold electron emission spectrum. From the shift of the peaks as function of laser power the field strength of the surface plasmon polariton was quantitatively determined without free parameters. Estimations of the Keldysh parameter γ = 4.4 and the adiabaticity parameter δ = 4700 indicate that electron emission occurs in a regime of multiplasmon absorption and nonlocalized surface plasmon fields.

Laser cluster interaction in ambient magnetic fields for accelerating electrons in two stages without external injection

In the few-cycle pulse regime of laser-cluster interaction (intensity >10^{16},text{ W/cm}^{2}, wavelength > 780 nm), laser absorption is mostly collisionless and may happen via anharmonic resonance (AHR) process in the overdense (cluster) plasma potential. Many experiments, theory and simulation show average absorbed energy per cluster-electron ({mathcal {E}_A}) close to the electron’s ponderomotive energy (U_mathrm {p}) in the collisionless regime. In this work, by simple rigid sphere model (RSM) and detailed particle-in-cell (PIC) simulation, we show enhanced {mathcal {E}_A}approx 30–70U_mathrm {p}—a 15–30 fold increase—with an external (crossed) magnetic field near the electron-cyclotron resonance (ECR). Due to relativistic mass increase, electrons quickly deviate from the standard (non-relativistic) ECR, but time-dependent relativistic-ECR (RECR) happens which also contributes to enhanced {mathcal {E}_A}. Here laser is coupled to electrons in two stages, i.e, AHR and ECR/RECR. To probe further we retrieve the phase-difference Delta psi between the driving electric field and corresponding velocity component for each electron (in PIC and RSM). We find absorption by electron via AHR happens in a very short interval Delta tau for less than half a laser period where Delta psi remains close to pi (necessary condition for maximum laser absorption) and then Delta psi drops to its initial pi /2 (meaning no absorption) after such short-lived AHR. On the contrary, auxiliary magnetic field near the ECR modifies AHR scenario inside the cluster and also helps maintaining the required phase Delta psi approx pi for the liberated cluster-electron accompanied by frequency matching for ECR/RECR for a prolonged Delta tau (which covers 50–60% of the laser pulse through pulse maxima) even after AHR—leading to jump in {mathcal {E}_A}approx 30–70U_mathrm {p}. We note that to realize the second stage of enhanced energy coupling via ECR/RECR, the first stage via AHR is necessary.

Transition of the generation mechanism of high-order harmonics in an extended neon system

Using a time-dependent density functional theory method, we perform a systematic numerical study of the transition of high-order harmonic generation in neon (Ne) systems from an isolated Ne atom to an extended Ne system of solid density. We show that ionized electrons wander in such extended systems until they meet a nearby ion and collide with it. The maximum energy edge for the main feature of the high-order harmonic spectrum in this “wandering electron” picture is determined as Eedge = Ip + 8Up, where Ip is the ionization energy of Ne and Up is the ponderomotive energy delivered by the driving laser. The factor of 8 comes from the maximum kinetic energy of an ionized electron in the driving laser field. Beyond the atomic limit of high-order harmonic spectra, a multiplatform feature is observed, corresponding to re-collisions of ionized electrons with their nearby ions. It is also shown that a Ne simple cubic lattice of appropriate size provides a selection condition for the direction of polarization of high-order harmonics beyond the atomic limit, which may be further used to manipulate the emitted radiation.

Role of contrast of a relativistic femtosecond laser pulse interacting with solid and structured targets

We consider the effect of a pre-plasma layer inevitably present in experiments on the acceleration of electrons and ions during interaction of a relativistic femtosecond laser pulse with a dense plasma. The interaction regimes are identified in which the presence of such a layer can significantly increase the average and maximum energies of electrons. The regimes are discussed in which an artificial nanosecond prepulse makes it possible to produce a collimated electron beam with a high charge and an average energy of up to 10 ponderomotive energies in the direction of the reflected or incident laser beam. It is shown that the acceleration of ions, as a rule, requires an ultrahigh contrast of the laser pulse, since the parameters of the accelerated ion beams deteriorate significantly in the presence of preplasma or due to the evaporation of a thin-film target. The regimes of interaction of laser pulses with thick targets, in which heavy multiply charged ions can be accelerated by cleaning the surface with a prepulse, are also discussed. An essential part of the review is devoted to the interaction of radiation with micro- and nanostructured targets. Both the methods of their fabrication and the issues related to the interaction of a femtosecond laser pulse and its contrast with such structures are considered.

Two-dimensional electron returning trajectory in nonsequential double ionization by strong-field circularly polarized laser pulses

We investigate the features of electron returning trajectories in recollision-induced nonsequential double ionization by intense circularly polarized laser pulses within a classical ensemble model. We find typical two-dimensional returning trajectories of the first ionized electron that can be decomposed into local circular motion driven by the laser field and overall elliptical motion due to the Coulombic attraction of the parent ion. Such trajectories burst within a narrow time window of less than two laser cycles and end periodically with kinetic energies around the instantaneous ponderomotive energy after many laser cycles, which is very different from the well-known simple one-dimensional returning trajectories in the case of linear laser polarization.

Extreme Sub-Wavelength Structure Formation from Mid-IR Femtosecond Laser Interaction with Silicon.

Mid-infrared (MIR) wavelengths (2–10 m) open up a new paradigm for femtosecond laser–solid interactions. On a fundamental level, compared to the ubiquitous near-IR (NIR) or visible (VIS) laser interactions, MIR photon energies render semiconductors to behave like high bandgap materials, while driving conduction band electrons harder due to the scaling of the ponderomotive energy. From an applications perspective, many VIS/NIR opaque materials are transparent for MIR. This allows sub-surface modifications for waveguide writing while simultaneously extending interactions to higher order processes. Here, we present the formation of an extreme sub-wavelength structure formation (∼) on a single crystal silicon surface by a 3600 nm MIR femtosecond laser with a pulse duration of 200 fs. The 50–100 nm linear structures were aligned parallel to the laser polarization direction with a quasi-periodicity of 700 nm. The dependence of the structure on the native oxide, laser pulse number, and polarization were studied. The properties of the structures were studied using scanning electron microscopy (SEM), atomic force microscopy (AFM), cross-sectional transmission electron-microscopy (CS-TEM), electron diffraction (ED), and energy-dispersive X-ray spectroscopy (EDX). As traditional models for the formation of laser induced periodic surface structure do not explain this structure formation, new theoretical efforts are needed.

Quantum estimation in strong fields: In situ ponderomotive sensing

We develop a new framework to optimize and understand uncertainty from in situ strong field measurements of laser field parameters. We present the first derivation of quantum and classical Fisher information for an electron undergoing strong-field ionization. This is used for parameter estimation and to characterize the uncertainty of the ponderomotive energy, directly proportional to laser intensity. In particular, the quantum and classical Fisher information for the momentum basis displays quadratic scaling over time. This can be linked to above-threshold ionization interference rings for measurements in the momentum basis and to the `ponderomotive phase' for the `ideal' quantum measurements. Preferential scaling is found for increasing laser pulse length and intensity. We use this to demonstrate for in situ measurements of laser intensity, that high resolution momentum spectroscopy has the capacity to reduce the uncertainty by over $25$ times compared to measurements employing the ionization rate, while using the `ideal' quantum measurement would reduce it by a further factor of $2.6$. A minimum uncertainty of the order $2.8 \times 10^{-3}~\%$ is theorized for this framework. Finally, we examine previous in situ measurements formulating a measurement that matches the experimental procedure and suggest how to improve this.

Radiation for laser-driven rescattering near the ultimate high-energy cutoff: The single-atom response and bremsstrahlung limit

The discovery of laser-driven rescattering and high harmonic radiation out to a maximum photon energy of 3.17 times the ponderomotive energy laid the groundwork for attosecond pulse generation and coherent x rays. As the laser field drives the interaction to higher energies, relativity and the Lorentz force from the laser magnetic field enter into the dynamics. Recent studies of laser rescattering have included these effects to give a quantitative description of rescattering dynamics in the high-energy limit, i.e., recollision energies of order 1,000 hartree (27 keV). In this high-energy limit, we treat the emitted high harmonic radiation from rescattering as a bremsstrahlung process. We find the highest-energy photons in the radiated energy spectra follow the rescattering electron energy near the ultimate cutoff. The effective charge from the ion core shielding does not affect the radiation yield at cutoff; however, the overall energy radiated does scale quadratically with the atomic number of the parent ion.

Theoretical investigation of the Freeman resonance in the dissociative ionization of H2+

The dissociative ionization of $H_2^+$ in linearly polarized, 400 nm laser pulses is simulated by solving a three-particle time-dependent Schr\"odinger equation in full dimensionality. The joint energy spectra (JES) are computed for $\cos^8$ and flat-top envelopes using the time-dependent surface flux (tSurff) methods. In JES, the energy sharing $n$ photon energies $\omega$ of nuclear kinetic energy release (KER) $E_N$ and electronic KER $E_e$ are well represented by $E_N+E_e=n\omega-U_p+E_0$ for $\cos^8$ pulses, but satisfy $E_N+E_e=n\omega+E_0$ for flat-top envelope, exposing a deviation of the ponderomotive energy $U_p$, which has been observed in experiments, where $E_0$ is the ground energy of $H_2^+$. The analysis of the wavefunction for electrons and protons after the pulse are presented, where we find $U_p$ is absorbed by the Freeman resonances between two excited ungerade states.

Exact solution of the 1D time-dependent Schrödinger equation for the emission of quasi-free electrons from a flat metal surface by a laser

We solve exactly the one-dimensional Schrödinger equation for ψ(x, t) describing the emission of electrons from a flat metal surface, located at x = 0, by a periodic electric field E cos(ωt) at x > 0, turned on at t = 0. We prove that for all physical initial conditions ψ(x, 0), the solution ψ(x, t) exists, and converges for long times, at a rate , to a periodic solution considered by Faisal et al (2005 Phys. Rev. A 72 023412). Using the exact solution, we compute ψ(x, t), for t > 0, via an exponentially convergent algorithm, taking as an initial condition a generalized eigenfunction representing a stationary state for E = 0. We find, among other things, that: (i) the time it takes the current to reach its asymptotic state may be large compared to the period of the laser; (ii) the current averaged over a period increases dramatically as ℏω becomes larger than the work function of the metal plus the ponderomotive energy in the field. For weak fields, the latter is negligible, and the transition is at the same frequency as in the Einstein photoelectric effect; (iii) the current at the interface exhibits a complex oscillatory behavior, with the number of oscillations in one period increasing with the laser intensity and period. These oscillations get damped strongly as x increases.