Nonlinear Electron Dynamics Research Articles

Electron population dynamics in resonant non-linear x-ray absorption in nickel at a free-electron laser.

Free-electron lasers provide bright, ultrashort, and monochromatic x-ray pulses, enabling novel spectroscopic measurements not only with femtosecond temporal resolution: The high fluence of their x-ray pulses can also easily enter the regime of the non-linear x-ray-matter interaction. Entering this regime necessitates a rigorous analysis and reliable prediction of the relevant non-linear processes for future experiment designs. Here, we show non-linear changes in the -edge absorption of metallic nickel thin films, measured with fluences up to 60 J/cm2. We present a simple but predictive rate model that quantitatively describes spectral changes based on the evolution of electronic populations within the pulse duration. Despite its simplicity, the model reaches good agreement with experimental results over more than three orders of magnitude in fluence, while providing a straightforward understanding of the interplay of physical processes driving the non-linear changes. Our findings provide important insights for the design and evaluation of future high-fluence free-electron laser experiments and contribute to the understanding of non-linear electron dynamics in x-ray absorption processes in solids at the femtosecond timescale.

Uncovering extreme nonlinear dynamics in solids through time-domain field analysis

Time-domain analysis of harmonic fields with sub-cycle resolution is now experimentally viable due to the emergence of sensitive, on-chip techniques for petahertz-scale optical-field sampling. We demonstrate how such a time-domain, field-resolved analysis uncovers the extreme nonlinear electron dynamics responsible for high-harmonic generation within solids. Time-dependent density functional theory was used to simulate harmonic generation from a solid-state band-gap system driven by near- to mid-infrared waveforms. Particular attention was paid to regimes where both intraband and interband emission mechanisms play a critical role in shaping the nonlinear response. We show that a time-domain analysis of the harmonic radiation fields identifies the interplay between intra- and interband dynamical processes underlying the nonlinear light generation. With further analysis, we show that changes to the dominant emission regime can occur after only slight changes to the peak driving intensity and central driving wavelength. Time-domain analysis of harmonic fields also reveals, for the first time, the possibility of rapid changes in the dominant emission mechanism within the temporal window of the driving pulse envelope. Finally, we examine the experimental viability of performing time-domain analysis of harmonic fields with sub-cycle resolution using realistic parameters.

Thresholds between modulational stability, rogue waves and soliton regimes in saturable nonlinear media

We study a third-order nonlinear Schrödinger equation for saturable nonlinear media, which can represent either optical pulse propagation in 1D nonlinear waveguide arrays or electron dynamics in one-dimensional lattices. Here, we describe how stable uniform solutions can evolve into regimes in which they are localized and the influence of saturation on this transition. We observed regular and chaotic-like breathing dynamics as intermediate regimes, which have their domain of existence significantly altered by the saturation parameter. Critical nonlinear strengths separating the existing regimes are shown in phase diagrams, evidencing the role played by saturation. Numerical data and analytical approach show the nonlinear strength above which uniform solutions become breather solutions increasing with the saturation parameter. In the regular breathing regime, we reveal the breathing frequency for media with saturable nonlinearity displaying faster growth as it moves away from the critical point of uniform solutions. Furthermore, critical nonlinear strength separating the regimes of regular and chaotic-like breather solutions exhibits a decreasing behavior as the saturation parameter increases. The latter ones present clear signatures of emerging rogue waves, such as peaks showing long-tailed statistics. Thresholds of this regime are increased by the saturable nonlinearity. Thus, the regime of localized solutions, which we have shown to be well-described by bright soliton-like structures, becomes less accessible with increasing saturation.

The DREAM Endstation at the Linac Coherent Light Source

Free-electron lasers (FEL), with their ultrashort pulses, ultrahigh intensities, and high repetition rates at short wavelength, have provided new approaches to Atomic and Molecular Optical Science. One such approach is following the birth of a photo electron to observe ion dynamics on an ultrafast timescale. Such an approach presents the opportunity to decipher the photon-initiated structural dynamics of an isolated atomic and molecular species. It is a fundamental step towards understanding single- and non-linear multi-photon processes and coherent electron dynamics in atoms and molecules, ultimately leading to coherent control following FEL research breakthroughs in pulse shaping and polarization control. A key aspect for exploring photoinduced quantum phenomena is visualizing the collective motion of electrons and nuclei in a single reaction process, as dynamics in atoms/ions proceed at femtosecond (10−15 s) timescales while electronic dynamics take place in the attosecond timescale (10−18 s). Here, we report on the design of a Dynamic Reaction Microscope (DREAM) endstation located at the second interaction point of the Time-Resolved Molecular and Optical (TMO) instrument at the Linac Coherent Light Source (LCLS) capable of following the photon–matter interactions by detecting ions and electrons in coincidence. The DREAM endstation takes advantage of the pulse properties and high repetition rate of LCLS-II to perform gas-phase soft X-ray experiments in a wide spectrum of scientific domains. With its design ability to detect multi-ions and electrons in coincidence while operating in step with the high repetition rate of LCLS-II, the DREAM endstation takes advantage of the inherent momentum conservation of reaction product ions with participating electrons to reconstruct the original X-ray photon–matter interactions. In this report, we outline in detail the design of the DREAM endstation and its functionality, with scientific opportunities enabled by this state-of-the-art instrument.

Ultrafast nonlinear absorption of TMDC quantum dots

We study theoretically absorption properties of MoS 2 quantum dots placed in an ultrashort and strong optical pulse with the duration of a few femtoseconds and the amplitude up to 1.5 V/Å. While the monolayer of MoS 2 has a bandgap of ≈ 1 . 8 eV , the quantum dots of MoS 2 have in-gap edge states, which open additional absorption channels. The absorbance of the system strongly depends on the amplitude of the pulse. At small amplitude, less than 0.5 V/Å, the absorbance varies by more than 20% with the frequency of the pulse. The system shows saturable absorption if the frequency of the pulse is larger than the bulk bandgap and reverse saturable absorption if the frequency of the pulse is in the bandgap. At large amplitudes, > 0 . 5 V/Å, of the pulse, the ultrafast absorbance of a quantum dot has a weak dependence on the pulse frequency. If the frequency of the pulse is less than the corresponding bulk bandgap, the absorbance has a nonmonotonic dependence on the pulse amplitude with the maximum at ≈ 0 . 5 V/Å. We also present the results for QDs of different TMDC materials, which show that at large field amplitude, > 0 . 5 V/Å, the absorbance is universal and has weak dependence on the type of TMDC. • Interaction of strong optical pulses with TMDC quantum dots. • Nonlinear ultrafast electron dynamics in TMDC quantum dots. • Universal high field behavior of quantum dot absorbance. • Controllable energy storage in quantum dots.

High-order harmonic generation from twisted bilayer graphene driven by a midinfrared laser field

Theoretical calculations of high-harmonic generation (HHG) from commensurate twisted bilayer graphene (tBLG) under intense laser fields are performed. The nonlinear electron dynamics in tBLG is considered by solving the Liouville--von Neumann equation for a single-particle density matrix, which combines the full energy bands and momentum matrix elements within the framework of tight-binding approximation. We show that the pump intensity determines the relative magnitude of two components of the harmonic spectrum parallel and perpendicular to driving polarization. The important dependence of HHG on twisted angles and crystal orientations is also presented. Especially in the absence of the relaxation process, the harmonic emission for twisted angles around 10 \ifmmode^\circ\else\textdegree\fi{} exhibits an evident decrease in efficiency per layer compared to monolayer graphene (MLG), which can be interpreted according to Fermi velocity modification. Our calculation also shows that the relative emission efficiency of different harmonic orders between tBLG and MLG contains redundant information on both the dephasing time and an empirical parameter characterizing the decay of the interlayer electron hopping, thus suggesting an all-optical method for the reconstruction of the two parameters. The reconstruction feasibility is successfully demonstrated by a simple optimization algorithm even if considering the possible experimental uncertainty of both driving pulse parameters and high-harmonic signals. Our results show that HHG spectroscopic characteristics in tBLG might serve as a fingerprint to identify the geometric stacking angle and the electronic interaction between adjacent layers, as well as the strong-field laser induced ultrafast dephasing process.

2D self-interacting magnetically confined electrons

We investigate the nonlinear dynamics of electrons in the presence of an external homogeneous magnetic field in 2 + 1 flat space-time dimensions. Two regimes of magnetic fields are examined: high laboratory fields and strong-QED fields. We provide the (nonlinear) ground-state Landau energy levels together with their respective eigenfunctions. We comment on the relevance of this (toy) model to reveal certain processes thought to occur near the surfaces of neutron stars.

Nonlinear Dynamics of Electrons in Electromagnetic and Gravitational Fields

The nonlinear dynamics of positrons in modified theories is considered in light of new hypotheses regarding the mass of charged particles and the mass of the graviton. Laws of the vertical movement of positrons in a constant magnetic field, a Barnhill–Schiff electric field, and the Earth’s gravitational field are obtained on the basis of calculations. Experiments are proposed to test these new hypotheses.

Electrons in intense laser fields with local phase, polarization, and skyrmionic textures

Laser fields can be shaped on a subwavelength scale as to have a specific distribution in spin angular momentum, orbital structure, or topology. We study how these various features affect the strongly nonlinear electron dynamics. Specifically, we derive closed expressions for the wave function of an unbound electron subject to a generally structured, intense laser field and demonstrate its use for imprinting the orbital angular momentum of a propagating optical vortex onto photoelectrons emitted from atoms and traveling through the optical vortex. It is also shown that photoelectrons can be accelerated or momentum textured when moving through a focused, intense laser field whose spin angular momentum is modulated as to have a radial polarization, which also implies the presence of a strong electrical longitudinal component. Further results are presented on the subwavelength spatiotemporal imaging of a laser field topology, as demonstrated explicitly for the field's spin and orbital distributions of lossless propagating optical skyrmions imaged by photoelectrons.

Dynamic pulse propagation modelling for predictive femtosecond-laser-microbonding of transparent materials.

A dynamic pulse propagation modeling for femtosecond laser bonding of Borofloat glass is presented. The temperature evolution and internal modifications are predicted by incorporating the nonlinear electron dynamics along with temperature dependent thermal properties. The modelling predicts the spatial and temporal distribution of absorption coefficient and plasma density that gives quantitative estimations of the heat affected zone and weld geometry. The impact of focusing condition on heat affected zone and weld geometry is investigated, which for the first time to our knowledge allows to numerically determine the desired relative position between the geometrical focus of a femtosecond-laser-pulse and the interface of the two substrates to be welded. The prediction of the modelling on the offset distance is applied to weld Borofloat glass plates having optical contact and can be applied to other dielectric solids.

Topological light fields for highly non-linear charge quantum dynamics and high harmonic generation.

We study theoretically the electron quantum dynamics in atoms driven by intense IR laser pulses that are phase and/or polarization structured. The extremely non-linear electron dynamics causes high harmonic emission, which we calculate, analyze, and characterize. Results are presented for three different types of structured lasers: radially polarized and azimuthally polarized beams and optical skyrmions. We identify a topological index that is inherent to the driving pulse topology and is taken over by the high harmonics. All harmonics are found to have the same topological index. For vector IR pulses as driving fields, the far-field emitted beam tightens with a higher topological order and remains unchanged when the atom is driven by an optical skyrmion.

Transport of moderately relativistic electron beam in dense plasma

Transport of moderate relativistic micro electron beam in overdense plasma is investigated using numerical simulation and analytical modeling. It is found that if the product of the initial beam current density jb and radius R0 is above a lower limit, which scales like , where ne is the plasma density, the beam will periodically self pinch and relax as it propagates. Otherwise the beam diverges. But if is too large, the pinching behavior becomes quite different. Such micro-beam transport behavior can be attributed to the nonlinear dynamics of the beam electrons in overdense plasma.

Nonlinear Migration Dynamics of Excess Electrons along Linear Oligopeptides Controlled by an Applied Electric Field.

Migration of an excess electron along linear oligopeptides governed by the external electric field (Eex ) which is against the inner dipole electric field is theoretically investigated, including the effects of Eex on the structural and electronic properties of electron migration. Two structural properties including electron-binding ability and the dipole moment of linear oligopeptides are sensitive to the Eex values and can be largely modulated by Eex due to the competition of Eex and the inner electric field and electron transfer caused by Eex . In the case of low Eex values, two structural properties decrease slightly, while for high Eex values, the electron-binding ability continually increases strongly, with dipole moments firstly increasing significantly and then increasing more slowly at higher Eex . Additionally, linear oligopeptides of different chain lengths influence the modulation extent of Eex and the longer the chain length is, the more sensitive modulation of Eex is. In addition, electronic properties represented by electron spin densities and singly occupied molecular orbital distributions vary with Eex intensities, leading to an unusual electron migration behavior. As Eex increases, an excess electron transfers from the N-terminus to the C-terminus and jumps over a neighboring dipole unit of two termini to other units, respectively, instead of transferring by means of a one-by-one dipole unit hopping mechanism. These findings not only promote a deeper understanding of the connection between Eex and structural and electronic properties of electron transfer behavior in peptides, but also provide a new insight into the modulation of electron migration along the oligopeptides.

“Diffusion” region of magnetic reconnection: electron orbits and the phase space mixing

Abstract. The nonlinear dynamics of electrons in the vicinity of magnetic field neutral lines during magnetic reconnection, deep inside the “diffusion” region where the electron motion is nonadiabatic, has been numerically analyzed. Test particle orbits are examined in that vicinity, for a prescribed planar two-dimensional magnetic field configuration and with a prescribed uniform electric field in the neutral line direction. On electron orbits, a strong particle acceleration occurs due to the reconnection electric field. Local instability of orbits in the neighborhood of the neutral line is pointed out. It combines with finiteness of orbits due to particle trapping by the magnetic field, and this should lead to the effect of mixing in the phase space, and the appearance of dynamical chaos. The latter may presumably be viewed as a mechanism producing finite “conductivity” in collisionless plasma near the neutral line. That conductivity is necessary to provide violation of the magnetic field frozen-in condition, i.e., for magnetic reconnection to occur in that region. Keywords. Magnetospheric physics (plasma sheet)

Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves

We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.

Nonlinear dynamics of electrons interacting with oblique whistler mode chorus in the magnetosphere

AbstractWe perform test particle simulations for relativistic electrons interacting with a whistler mode chorus packet propagating at oblique angles. By confirming that the energy transport of oblique lower band chorus is nearly along the ambient magnetic field, we apply the gyroaveraging method in calculating equations of motion of electrons. We trace evolution of a delta function of relativistic electrons in a phase space of kinetic energy and equatorial pitch angle and obtain numerical Green's functions of the chorus wave‐particle interactions. Examining the Green's functions in a wide range of kinetic energies, we find that Landau resonance can accelerate MeV electrons efficiently and that higher nth resonances such as n =− 1 and n = 2 also contribute to acceleration of electrons at high equatorial pitch angles (∼70°) and high energies (∼2 MeV). We investigate the rate of energy gain of the cyclotron resonance acceleration and the Landau resonance acceleration and find that the perpendicular component of wave electric field dominates both accelerations for MeV electrons. Furthermore, the proximity between the parallel components of Vp and Vg of oblique whistler mode waves and the nonlinear trapping condition make the interaction time of Landau resonance much longer than that of n = 1 cyclotron resonance, resulting in efficient acceleration of MeV electrons.

Dielectric coats effect on the third harmonic generation by a metallic nanoparticle lattice exposed to intense laser radiation

In this work, we theoretically study the effect of coating of metallic nanoparticles on the third harmonic generation in a periodic three-dimensional lattice. Taking into account the effects of dielectric shell of nanoparticles and microscopic electromagnetic fields on the nonlinear dynamics of electrons, equations describing the laser–nanoparticle interaction are derived in the non-relativistic approximation. We pay special attention on the effects of the thickness and the kind of shell of nanoparticles upon the third harmonic efficiency. It is found that in some frequency areas, existence of shell can amplify the microscopic fields in the place of conduction electrons, which can lead to the improvement of harmonic generation. This amplification could be essential if the frequency region related to the shell effect improvement coincides with that of the plasmon resonance.

Pulse train dependence of electron dynamics during resonant femtosecond laser nonlinear ionization of a Na4 cluster

In this study, a real-time and real-space time-dependent density functional theory (TDDFT) is applied to describe nonlinear electron–photon interactions during a resonant femtosecond laser pulse train photoionization of a Na4 cluster. The effects of key pulse train parameters, such as the spatial/temporal pulse energy distribution, pulse number per train, pulse separation and pulse phase on resonant absorption, are discussed. The calculations show that the resonant effect and the nonlinear electron dynamics, including energy absorption, electron emission, dipole response and ionization probability, can be controlled by shaping the ultrafast laser pulse train.

Nonlinear plasmonics in a two-dimensional plasma layer

The nonlinear electron dynamics in a two-dimensional (2D) plasma layer are investigated theoretically and numerically. In contrast to the Langmuir oscillations in a three-dimensional (3D) plasma, a well-known feature of the 2D system is the square root dependence of the frequency on the wavenumber, which leads to unique dispersive properties of 2D plasmons. It is found that for large amplitude plasmonic waves there is a nonlinear frequency upshift similar to that of periodic gravity waves (Stokes waves). The periodic wave train is subject to a modulational instability, leading to sidebands growing exponentially in time. Numerical simulations show the breakup of a 2D wave train into localized wave packets and later into wave turbulence with immersed large amplitude solitary spikes. The results are applied to systems involving massless Dirac fermions in graphene as well as to sheets of electrons on liquid helium.

Nonlinear electron dynamics of gold ultrathin films induced by intense terahertz waves

Linear and nonlinear electron dynamics of polycrystalline gold (Au) ultrathin films with thicknesses ranging from 1.4 to 5.8 nm were investigated via transmittance terahertz (THz) spectroscopy with intense electric field transients. We prepared ultrathin films with low surface roughness formed on a Si–(7 × 7) reconstructed surface, leading to the observation of monotonic decrease in THz transmittance with respect to film thickness. Furthermore, at all tested thicknesses, the transmittance decreased nonlinearly by 10%–30% with the application if high-intensity THz electric fields. Based on a Drude-model analysis, we found a significant decrease in the damping constant induced by the THz electric field, indicating that electrons are driven beyond the polycrystalline grain boundaries in Au thin films, and consequently leading to the suppression of the electron–boundary scattering rate.