Femtosecond Laser-Induced Ultrafast Electron Redistribution near a Microscale Metallic Filament

Abstract

In this study, a femtosecond laser beam is delivered to metal wire targets to generate suprathermal electron jets reaching energies of several hundreds of keV. During the process, it is observed that the mirror-imaging distribution of the beam focus with respect to the surface of the target displays highly asymmetric features and different dynamic responses. Especially, the exterior focus exhibits an extraordinary polarity reversal of the macroscopic current, while the interior focus behaves ordinarily. The former is attributed to the strong field at the focal point outside the surface, causing the secondary ionization and driving electrons back to the target, thereby reshaping the distribution of these high-energy hot electrons and the morphology of plasma jets. A numerical model is proposed to simulate the experimental observation and interpret the unexpected phenomenon. Furthermore, the particle-in-cell algorithm is also implemented to verify the results and present more details. This study seeks to emphasize the role of focal position in regulating the photoemission process, which may offer a fresh perspective for research in laser–material interactions and dynamics.

1. Introduction

Since the invention of the chirped pulse amplification (CPA) technique [1], the interaction between intense laser pulses and metals has been extensively investigated [2,3,4,5,6,7]. In these studies, the behaviour of photoemitted suprathermal electrons with energies reaching hundreds of keV, and the evolutionary dynamics of plasmas have become the central topics. Those high-energy suprathermal electrons not only serve as the key energy carriers in inertial confinement fusion schemes, e.g., “fast ignition”, but also drive the secondary radiation sources (e.g., ultrafast X-rays) and high-energy particle beams, demonstrating broad application prospects. Notable phenomena and experiments include laser-induced metallic plasma jets [8,9,10], novel electron sources based on laser-irradiated metal wires [11,12,13,14], wire-target plasma devices for fusion ignition [15,16,17], laser-driven collimated electron emission along wire [11,12,18,19,20], the generation of strong sub-terahertz surface waves on metal wires [21,22,23,24], and intense terahertz radiation from femtosecond-laser-driven wire-guided helical undulators [25]. Among these, the wire-based electron or radiation sources have demonstrated considerable potential applications, attracting accumulating interest.

In the meantime, theoretical investigations of laser–solid–plasma interactions have also been conducted. For example, Kluge et al. studied absorption mechanisms and hot electron generation in laser-produced plasmas [26]. Keldysh developed the ionization theory under the strong laser field approximation [27]. Later, more complete mathematical algorithms were proposed based on Keldysh theory [27]. A. Kasperczuk et al. employed X-ray interferometric imaging to study the influence of focal position on plasma jet morphology and electron density distribution in a defocused laser system [28]. Zhang et al. observed the photoemission current change at various positions outside the laser ablation spot. For the past decades [29], with the development and establishment of laser–solid interaction and radiation absorption mechanism [30,31,32], the understanding of laser–metal ionization becomes deeper and clearer [33,34,35,36,37,38]. However, these studies are primarily focused on the influence due to the laser beam intensity without regarding the beam focal position as a critical parameter. The subtle feature related to the current flow and beam distribution around the target is lacking in investigation, and the relevant simulation model is yet to be established [39,40]. In order to unveil the underlying microscopic mechanism of ultrafast electron redistribution, which has not been addressed in previous works, it triggers our motivation to elucidate the backflow dynamics and evolution process of suprathermal electrons in the vicinity of a microscopic metal wire, and to reveal the physics insight.

2. Materials and Methods

The experimental set-up is illustrated in Figure 1A Yb: CaF₂ laser amplifier delivering a pulse energy of 5 $\mathrm{m}\mathrm{J}$ at 100 Hz repetition frequency, with a central wavelength of 1030 nm and a pulse duration of 400 $\mathrm{f}\mathrm{s}$ (FWHM) is employed. The laser beam was expanded and then focused down to a spot size of 10 $\mathrm{\mu }\mathrm{m}$, achieving a peak intensity exceeding $5\times {10}^{17} \mathrm{W}/{\mathrm{c}\mathrm{m}}^2$. A half-wave plate combining a polarization cube is used to tune the pulse energy for the experiment while monitoring the shot-by-shot energy fluctuation simultaneously. A CCD camera is employed to take shots, imaging and calibrating the laser beam spot during the translation stage scan. Due to the tilted orientation of the metal wire (with respect to the axis of the motion), the beam waist (focal spot) could be accurately identified as it is positioned on the target surface. According to the coordinates of the translation stage, the relative position between the focal spot and the target surface could be readily derived and determined via optical geometry. The suprathermal electron energy is diagnosed using an online electron time-of-flight (e-TOF) energy spectrometer. The wire photoemission experiment is conducted within a vacuum chamber under a base pressure better than $1\times {10}^{-4} \mathrm{P}\mathrm{a}$ and at a constant ambient temperature of $25 °\mathrm{C}$.

Copper or tungsten wires with a diameter of 300 $\mathrm{\mu }\mathrm{m}$ were used as target materials. In each experimental run, a wire target was mounted on a high-precision in-vacuum manipulation stage via an insulating ceramic holder, providing translational accuracy of $~0.1 \mathrm{\mu }\mathrm{m}$ and rotational accuracy of $10 \mathrm{\mu }\mathrm{r}\mathrm{a}\mathrm{d}$ respectively. The laser beam propagates towards the metal wire approximately perpendicular within the interaction region, while the translation direction of the scanning stage was oriented at an angle of $10°$ relative to the wire axis. Thus, when the wire scans along with the stage, the relative position of the laser beam focus with respect to the wire surface would change during the motion, i.e., the scan of the translation stage in the x-direction $\Delta x$ leads to the tuning of the focal spot in the z-direction $\Delta z=\Delta x·tan10°$. Here ‘−’ is used to denote the focus moving towards inside the material, and ‘+’ to denote moving outside. As the focus of the laser beam is scanned from inside to outside the wire, highlighted by the various positions along the z-axis, −90 µm, 0 µm, 193 µm, 385 µm, the generated back-loop current, i.e., the photoemitted electron current, is measured simultaneously using a shielded cable connected via a vacuum feedthrough to a picoammeter. The experimental error could be carried out, which is primarily attributed to the laser energy fluctuation and the measurement uncertainty of the picoammeter. To characterize the stability of our system, the backflow current fluctuation was measured at a unique beam size, demonstrating that the peak-to-valley (PV) fluctuation remained ±5% within the average value.

3. Results and Discussion

Figure 2 displays the femtosecond laser-induced photoemission current for both copper (Cu) and tungsten (W) wires. When scanning the translation stage, it would change the beam focal position relative to the wire surface (in Figure 1B). The net photoemission current for both Cu and W wires measured at the orientation angle of 10° is shown and compared (Figure 2C). Meanwhile, the control signal acquired at $0°$ angle for W is sketched in the same plot (Figure 2B), where the focus remains precisely on the surface during the scan, and the measured current is close to a constant. In contrast, the signals for both Cu and W wires at 10° undergo significant change. As the focus moves from the interior towards the surface of the wire (z-position changes from −90 µm to 0 µm), the excitation current increases, reaching the positive maximum when the focus is on the surface, corresponding to the laser beam’s peak intensity. For the Cu case, as the beam waist moves away from the surface to the exterior region (z-position 0 µm to 193 µm), the current starts to decrease monotonously and changes sign at a certain distance, attaining a pronounced negative value. It indicates that, within this stage, the metal wire temporarily acquires electrons and reverses the direction of the net-charge flow. However, this trend wouldn’t continue all the time. At the z-position 193 µm and beyond, the current stops to become more negative, instead gradually returns to net-zero up to z-position 385 µm, and then turns to a small but positive value when the focus moves further away, restoring the regular photoemission. The above phenomenon, particularly the reversal feature of the net change flow in the microscale wire under the laser pulse illumination, challenges the conventional expectation and suggests a potential new dynamic algorithm for the electron redistribution.

To elucidate the underlying physics, data analysis is further conducted, and a numerical simulation model is developed. The scanning motion of the translation stage causes the change in the focal position along the z-direction, thus the laser beam intensity at the surface varies as:

$$I_s={\displaystyle \frac{I_p}{1+{(z/z_R)}^2}}$$

(1)

where ${\mathrm{I}}_{\mathrm{p}}$ denotes the peak intensity at the beam waist, ${\mathrm{z}}_{\mathrm{R}}$ is the Rayleigh length, and z represents the distance from the focus to the surface. The curvature of the wire surface is neglected, i.e., being treated as a flat plane, since the beam focal size (~10 μm) is much smaller than the wire diameter (300 μm). Considering the beam intensity in the experimental regime, the dominant ionization processes can be categorized into three types of dynamics: multiphoton ionization (MPI), tunnel ionization (TI), and over-the-barrier ionization (OBI). Thus, the Keldysh parameter γ [27] could be rewritten as:

$$\gamma =\omega \sqrt{{\displaystyle \frac{E_{0}c{ϵ}_0(1+z^2/{z_R}^2)}{I_p}}}$$

(2)

where ω is the angular frequency of the laser, ${\mathrm{E}}_0$ is the ionization energy of the material in wire, c is the speed of light, and ${\mathsf{ϵ}}_0$ is the vacuum permittivity. So $\mathsf{\gamma }\gg 1$ corresponds to the typical multiphoton absorption regime, while $\mathsf{\gamma }\ll 1$, tunnel ionization would dominate [30,31,32]. In Figure 3A, the specific contribution from the aforementioned three dynamics versus the beam intensity on the surface in the experiment is depicted. And the ionization rate from the surface ${\mathrm{w}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ could be calculated and expressed in terms of γ [27]:

$$w_{out}={\displaystyle \frac{\sqrt{6\pi }}{2}}\times \sqrt{{\displaystyle \frac{E_0\omega }{\gamma }}}\mathrm{e}\mathrm{x}\mathrm{p}(-{\displaystyle \frac{4}{3}}{\displaystyle \frac{E_0\gamma }{\omega }}[1-{\displaystyle \frac{1}{10}}{\gamma }^2])$$

(3)

Moreover, in the experimental beam intensity range, the theory of ultra-intense laser–solid interactions [33,34,35,36,37,38] is implemented to calculate the laser absorption by the target, mainly involving four mechanisms: vacuum heating (VH), resonance absorption (RA), inverse bremsstrahlung (IB) absorption, and $\mathrm{J}\times \mathrm{B}$ absorption. The competition among these mechanisms varies with beam intensity, making it difficult to determine the absolute absorption efficiency directly. Then, as illustrated in Figure 3B, the total net current in copper wire excited by the laser pulse could be deconvoluted into two components: ${\mathrm{J}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ and ${\mathrm{J}}_{\mathrm{i}\mathrm{n}}$, where ${\mathrm{J}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ represents the regular current directly excited by the laser at the metal surface, emitting outward from the surface, while ${\mathrm{J}}_{\mathrm{i}\mathrm{n}}$ denotes the current flowing inward to the surface. The latter is regarded as the primary cause of the unexpected macroscopic current reversal observed in our experiment, and it is mainly due to the electron population being pulled back to the surface by the drag force from the beam focus located exterior to the wire (refer to Figure 1B). During the process for the laser focus moving from the interior to the surface, ${\mathrm{J}}_{\mathrm{i}\mathrm{n}}=0$, and ${\mathrm{J}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ should be symmetric around the focus in the z-direction. At this stage, the outward excitation efficiency ${\mathrm{f}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ can be inversely fitted using the back-loop current data for z = −90 µm to 0 µm. Incorporating the factor ${\mathrm{f}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ and the ionization rate ${\mathrm{w}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$, ${\mathrm{J}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ is calculated:

$$J_{out}=e{w}_{out}{f}_{out}\tau f_{rep}$$

(4)

where e is the electron charge, $\mathsf{\tau }$ and ${\mathrm{f}}_{\mathrm{r}\mathrm{e}\mathrm{p}}$ represent the pulse duration and repetition frequency of the laser respectively. Via this scheme, ${\mathrm{J}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ values at various positions can be calculated, and shown as the red curve in Figure 3B.

In the following section, let us turn to the analysis of ${\mathrm{J}}_{\mathrm{i}\mathrm{n}}$, and explore its origin. During the process for z = 0 µm to 193 µm, the focus moves away from the surface into the space. Within this stage, the beam focus remains relatively close to the surface, and a significant population of electrons and ions is generated and persists near the interaction point (the beam focus). Especially, the ions evaporated from the surface would undergo the secondary ionization under the intense field strength of the laser pulse, liberating a large number of new electrons, which are then pulled back towards the surface along the laser propagation direction. This makes the net current of the wire reverse to a negative value, and explains where ${\mathrm{J}}_{\mathrm{i}\mathrm{n}}$ comes from.

Using Equations (2) and (3) and considering the laser beam intensity at various z positions, the secondary ionization rate at the exterior beam focus ${\mathrm{w}}_{\mathrm{i}\mathrm{n}}$ can be calculated and the algorithm is depicted in Figure 1B. Referring to the laser–plasma absorption theory [40], the dominant mechanism is expected to be $\mathrm{J}\times \mathrm{B}$ absorption primarily, with absorption efficiency ${\mathrm{f}}_{\mathrm{i}\mathrm{n}}\approx {\mathrm{f}}_{\mathrm{j}\mathrm{b}}\propto \sqrt{1+{\displaystyle \frac{{\mathrm{I}}_{\mathrm{p}}{\mathsf{\lambda }}^2}{1.37\times {10}^{18}}}}-1$. So the magnitude of the backflow (inward flow) current can be calculated by:

$$J_{in}=e{w}_{in}\tau f_{rep}{f}_{in}{R}_k$$

(5)

where ${\mathrm{R}}_{\mathrm{k}}$ denotes the factor 1$/(1+{(\mathrm{z}/{\mathrm{z}}_{\mathrm{R}})}^2)$, ${\mathrm{w}}_{\mathrm{i}\mathrm{n}}$ is defined previously as the ionization excitation rate at the focal point (refer to supplemental materials for more details). Apparently, the ionization rate ${\mathrm{w}}_{\mathrm{i}\mathrm{n}}$ would influence the magnitude of ${\mathrm{J}}_{\mathrm{i}\mathrm{n}}$, which changes the overall surface ionization mechanism, showing asymmetric features for the interior and exterior focal conditions, referring to Figure 3C.

During the process for z position 193–385 µm, as the focus moves further away, ${\mathrm{R}}_{\mathrm{k}}$ decreases rapidly, leading to ${\mathrm{J}}_{\mathrm{i}\mathrm{n}}$ diminishing gradually down to nearly zero; ${\mathrm{J}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ would decrease concurrently since the laser intensity diminishes. Thus, the dominant ionization mechanism transfers from tunnelling ionization (TI) to multiphoton ionization (MPI). The calculated ${\mathrm{J}}_{\mathrm{i}\mathrm{n}}$ in Figure 3B indicates reaching its maximum value at z = 193 μm and decaying down to zero at z = 385 $\mathrm{\mu }\mathrm{m}$, while the total net current $\mathrm{J}={\mathrm{J}}_{\mathrm{o}\mathrm{u}\mathrm{t}}-{\mathrm{J}}_{\mathrm{i}\mathrm{n}}$ in theory (blue dashed line) agrees pretty well with the measured data in the experiment (solid red sphere). Detailed calculation of $J_{out}$ and $J_{in}$ is provided in Appendix A.

Furthermore, the particle-in-cell (PIC) algorithm [41] is employed to simulate the experiment, scanning the laser focal positions −90 µm, 0 µm, 193 µm, 385 µm with respect to the copper wire’s surface. The simulation is equipped with parameters at the experimental conditions: laser wavelength of 1030 nm, pulse duration of 400 fs, focal spot size of 10 µm, Rayleigh range of 305 µm, and in a tungsten target, employing a time interval of 10 fs. The panels in the left column of Figure 4 illustrate the distribution of the laser electric field ${\mathrm{E}}_{\mathrm{y}}$ around the wire, showing the beam focus located at various positions (with respect to the surface). Meanwhile, the corresponding photo-electron distributions are displayed in the right panels. (i) When the focus is at position z = −90 µm, the hot electrons exhibit a homogenous divergence feature in all directions. At this stage, the inward flow current component ${\mathrm{J}}_{\mathrm{i}\mathrm{n}}$ is zero. (ii) As the focus moves to the wire surface (z = 0 µm), the hot electrons distribution keeps homogenous, while the outward current ${\mathrm{J}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ reaches the maximum, but ${\mathrm{J}}_{\mathrm{i}\mathrm{n}}$ remains small and negligible. (iii) At focal position 193 µm, the hot electron distribution changes significantly, exhibiting an electron-vacant region near the focus, with a distinct “bifurcation” pattern. This feature is regarded as the secondary ionization process, associated with ${\mathrm{J}}_{\mathrm{i}\mathrm{n}}$ attaining its maximal backward flow to the surface. (iv) When the focus proceeds to position 385 µm, the electron density around the wire surface diminishes considerably down to zero, since both ${\mathrm{J}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ and ${\mathrm{J}}_{\mathrm{i}\mathrm{n}}$ decrease as the focus moves away from the surface, reducing the laser beam intensity significantly.

The above electron distribution features (i) to (iv) demonstrate that the PIC simulation is in excellent agreement with the experimental result. Notably, the deformed electron distribution and “bifurcation” pattern at position z = 193 µm is consistent with the schematic illustration depicted in Figure 1B, interpreted by the secondary-ionization and electron inward fluxing scheme. Furthermore, the normal average current from the simulation is approximately 20% higher than the experiment. This discrepancy may be attributed to the competition among different nonlinear absorption mechanisms, preventing the achievement of the theoretical limit. For the case where the beam focus is located on the target surface, the typical energy range of hot electrons could be derived, exhibiting a broad spectral feature, from several tens to several hundreds of keV, reproducing the experimental findings (inserted curve in Figure 1).

4. Conclusions

In summary, this work reveals, besides the laser beam intensity, how the beam focal position would influence the photo-electron excitation behaviour and dynamics at the metallic filament target. We carried out a systematic experiment to measure the current flow to calibrate the observed phenomena, and in the meantime, established a theoretical model based on secondary excitation and PIC algorithm to simulate the observed feature, aiming to explore the underlying dynamic mechanism, which was not well understood in previous works. Our analysis attributes the asymmetric feature in exterior/interior foci to the secondary-ionization-driven electron backflow, which cancels the outward current and causes polarity reversal. The simulation exhibits excellent agreement with the experimental data. The excitation scheme proposed in this study refines and expands the understanding of electron excitation behaviour in defocused laser–solid interaction systems, elucidating the essential factors which determine the hot electron distribution and plasma jet dynamics in the laser–metal interaction.