1. Introduction

In an effort to understand various dynamical processes in nature, much research has been devoted to the advancement of ultrashort optical pulse generation and time-resolved experimentation [1]. Alongside these developments arise new techniques for optical pulse measurement and characterization [2–4]. In analogy to the evolution in ultrafast optical science, concomitant progress in ultrashort electron pulse generation and measurement is essential to the advancement of time-resolved studies employing electron pulses. Ultrafast electron-based systems provide much higher spatial resolution while maintaining femtosecond temporal resolution, thus offering the possibility of investigating intricate atomic/molecular dynamical processes; an excellent review of this subject can be found in [5]. Common methods for generating femtosecond electron packets utilize photocathodes and high-voltage DC or RF biasing grids [6–8]. Electronic streaking techniques, often used to characterize these electron pulses, also rely on fast high-voltage transients to deflect the electron pulses. While electronic streaking has been successful for generating and characterizing electron pulses having durations on the order of hundreds of femtoseconds [6], inherently large beam traversal paths coupled with space-charge effects impose limitations on the maximum attainable temporal resolution. As a result, alternative methods for producing and characterizing ultrashort electron pulses are sought after. In particular, all-optical generation offers much higher electric fields for electron acceleration, eliminates the requirement of high-voltage biasing, can preserve phase synchronization between optical-pump and electron-probe pulses, and allows for compact electron pulse sources.

Theoretical investigations into using optical pulses to selectively disperse segments of an electron pulse have been outlined [9,10]. Such schemes would require extremely large intensities in the >30 TW/cm² range to achieve the necessary electric fields (>10⁸ V/cm) required for deflection of keV energy electrons. However, recent studies have indicated that surface plasmon (SP) excitations are an effective means for electron acceleration. Experimental [11] and theoretical [12] investigations have shown that enhanced electric fields of up to 2.8×10⁹ V/cm can be generated in large interaction areas of 1 cm² using significantly reduced laser excitation intensities near 30 GW/cm² [13]. The high-gradient field of the evanescent plasmon wave resulted in a large ponderomotive force and subsequent acceleration of the synchronously photo-emitted electron bunch to energies up to 2 keV. While the feasibility of such SP-based accelerator geometries has been demonstrated, alternative travelling wave configurations and electron injection schemes for SP acceleration have not been fully explored.

In this paper, we model a novel all-optical technique for femtosecond gating of electron beams/pulses. The key process is the excitation of SP waves at a vacuum-metal interface using femtosecond laser pulses. Since the SP field is produced on an ultrafast timescale, a large fraction of an incoming electron beam can be sliced to yield electron packets having durations comparable to that of the excitation optical pulse. It is demonstrated that the deflected electron packets are highly directional and exhibit a large degree of microbunching, with durations of only a few optical cycles. Further analysis of angle-resolved energy spectra of the electrons reveals that their final velocities are highly correlated with exit angle. By varying the delay between the launching of the SP and the incident electron pulse, the same SP-gating mechanism can also be employed for temporal characterization of an incoming electron pulse. This technique holds promise for generation and characterization of ultrashort electron bunches below 100 fs.

2. Plasmon-based electron gating geometry and model description

The excitation of SP waves provides a novel and effective method for accelerating charged particles via the ponderomotive interaction [11,12]. Briefly, the underlying arrangement for launching SP waves is illustrated in Fig. 1. An ultrashort optical pulse, of duration τ_p and fluence F, enters a dielectric prism and strikes a thin metal film that has been deposited on the prism’s surface. For an ideal film thickness, d, nearly perfect coupling between the electromagnetic wave and the SP oscillations can be achieved by tuning the incident angle of the excitation laser beam to match the SP resonance angle. Accordingly, the electromagnetic energy is transferred to the SP wave having electric field distribution of the form E_SP (z,t) =η E_l(t)exp(-γ z) , where E_l is the electric field of the laser pulse, γ ^-l is the evanescent decay length into vacuum, η is the electric field enhancement factor, and z is the distance from the metal surface. To generate ultrashort electron pulses, electrons are injected in this high SP field. Shown in Fig. 1, a continuous stream of electrons is directed towards the metal film and enters the SP field at an angle of incidence, θ. Once the electrons interact with the SP wave, they will experience the effective time-average ponderomotive force over many cycles of the SP field. The direction of the ponderomotive force is along the largest SP field gradient and, in this arrangement, is approximately normal to the metal film surface. If the kinetic energy of an incident electron is less than the ponderomotive potential, U_SP , created by the SP field, then the electron will be deflected and depart the surface at angle, α, also shown in Fig. 1. An electron beam, however, is comprised of many electrons, having various arrival times and locations with respect to the peak of the SP field. In the region of spatial overlap between the electron beam and the SP field, only a finite portion of the electron beam will experience a change in momentum and will be redirected away form the prism’s surface. The spatial extent of the sliced section will depend on magnitude of E_SP , the duration of the optical excitation pulse, and θ. It should be noted, however, that direct photoemission from the metal surface may influence the gating process via space-charge interaction. To circumvent the photoemission and eliminate this possibility, the surface of the metal can be engineered in such a way so as to inhibit photoemission processes, while maintaining E_SP . For example, an ultrathin large band-gap material can be deposited over the metal to prevent multiphoton electron emission.

 

Fig. 1. Arrangement for electron pulse gating using SP waves. (left) An external electron beam is directed toward a metal-coated prism surface at angleθ, measured from the surface normal. The electrons comprising the input beam are deflected and depart the interaction region at an angle α. Varying the delay between the launching of the SP and an incident electron packet allows the same SP-gating mechanism to be utilized for temporal characterization of electron pulses. (right) Potential experimental arrangement for realizing electron beam gating using SP waves, which consists of a laser source, an electron source, a timing mechanism to synchronize the optical and electron pulses, and an electron spectrometer for energy discrimination.

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For a finite duration electron packet, the relative delay between the electron beam and optical pulse becomes an important parameter in determining the efficiency and selectivity of the optical deflection mechanism. This relationship between the deflection efficiency and relative delay between the optical and electron pulses can be applied to ultrafast electron pulse duration measurement. In analogy to optical-optical correlation for the measurement of ultrafast laser pulses, electron-optical cross correlation allows for temporal characterization of electron pulses. For electron-optical cross correlation, the deflected charge is a function of the relative delay, τ between the optical and electron pulses. Depending on the magnitude of the E_SP , electron deflection will be conditional in nature: the electrons are either deflected or not deflected from the metal surface. Hence, the SP wave can be described by a window function of the form

where Θ(t) is the Heaviside step function and t ₀ is the width of the rectangular window. For illustrative purposes, we assume a Gaussian form for the temporal envelope of the SP wave of width τ_p . Thus, the functional form of the width of the window function is given by

I ₀ is the peak intensity of the SP wave and I_th is the minimum intensity required for ponderomotive electron deflection and is given by I_th =4m_eω ² K / e ², where K, m_e , and e are the kinetic energy, mass, and charge of the electron, respectively. For a relative delay, τ the deflected charge can be described through the cross-correlation function

where ρ_elec is time-varying charge density of the electron pulse.

Calculation of the deflected charge Q_deflected (τ) requires knowledge of the local spatial and temporal distribution of the electric field near the metal-vacuum interface. The dynamical electromagnetic field structure of the SP waves for the geometry described in Fig. 1 can be determined from Maxwell’s equations

and

where $\overrightarrow{E}$ is the electric field, $\overrightarrow{H}$ is the magnetic intensity, ε is the local permittivity, and μ₀ is the permeability of free space. Since an analytical solution is not obtainable for the metalcoated prism structure, direct numerical solution is employed in which equations (1) and (2) are discretized and solved on a finite mesh using the finite-difference time-domain technique [14]. The electromagnetic wave is initiated using the total field/scattered field formulation and a perfectly matched layer damps spurious reflections from the window boundaries [12]. To account for the frequency-dependent response of the metallic film, the Drude model [15] for the dielectric function is implemented:

where ω_p is the plasma frequency, v_d is the damping frequency, and ε₀ is the permittivity of free space. Equation (6) is incorporated into the model using the auxiliary differential equation method [12,14]. Once the electric and magnetic field values are calculated, they are used to determine the electrons trajectories through

where $\stackrel{\rightharpoonup }{v}$ is velocity of the electron. The incident electron beam/pulse is represented by ~10⁵ sample electron trajectories, which are assigned relative weights to account for the packet’s finite spatial extent and temporal duration. It should be noted that these trajectories do not physically represent actual electrons; rather, they simply allow a probabilistic calculation of the behaviour of the electron pulse by considering all possible particle trajectories.

To investigate the SP-gating process, we have used parameters that achievable under actual experimental conditions [13]. The excitation laser pulse has a central wavelength of λ=800 nm, τ_p =30 fs, and an incidence angle of 45°, while the metal parameters are taken to be those of a silver film: d = 50 nm, ω_p =5.73×10¹⁵ Hz, and v_d =1.3×10¹⁴ Hz [16]. The spatial step size of the square computational lattice is chosen to be ∆x, ∆y =5 nm with a corresponding temporal step ∆t = 5 as. The zero time is defined to be the peak of the excitation pulse striking the metal film and all absolute time values are given with respect to this temporal origin.

3. Results

The injection of electrons into the E_SP field and the subsequent ponderomotive photo-acceleration is a complex process. Several aspects of the deflected electron packets (e.g., angular and kinetic spectra, duration, etc.) are dependent on many variables including the magnitude of E_SP , the pulse duration of the excitation optical pulse, the incident angle, θ, and the specific time and location of electron entry into the SP wave. The following analysis elucidates the interaction of the incoming electron beam with the E_SP . Several aspects of the deflected electrons are investigated, which include: the kinetic energy spectra, the angular distributions, angle resolved spectra, and spatial and temporal distribution.

To illustrate the ponderomotive deflection process, several test electrons are directed towards the metal surface during the excitation of E_SP . Figure 2 illustrates representative trajectories of five K ₀ = 1 keV electrons launched at various times τ_e = -12, -6, 0, 6 and 12 fs with respect to the peak of the laser pulse. The test electrons are incident at θ = 45° and their paths are mapped as they traverse an E_SP that has a magnitude of 7.4×10⁹ V/cm. As the electrons approach the SP field, their initial constant velocities are significantly modified as evidenced by their ‘quivering’ motion. It is apparent that the electrons experience a time-average ponderomotive force in the direction of largest field gradient ∇|E_SP |². The pertinent parameter in determining whether an electron is deflected away from the surface is its velocity component along the film’s normal, v _⊥, or more specifically, the kinetic energy K _⊥ = m_e$v_{\perp }^2$/2 associated with this velocity component. Once an electron decelerates and reaches a critical point within the E_SP field, where K _⊥ balances the ponderomotive potential of the SP wave, U_SP , the instantaneous v _⊥(t) component will be reduced to zero and the electron has only a velocity component parallel to the film’s surface, v _∥. Eventually, v _⊥ will increase along the film’s normal as the electron is pushed away from the film surface.

When the SPs are excited with an ultrashort optical pulse, electrons on the leading or trailing edge of the optical pulse will experience a dynamical ponderomotive potential that depends on the specific arrival time of the electron. As a result, the angle, α, through which the electron is deflected will vary with τ_e . Figure 2 illustrates that electrons can exit the surface with both α>θ and α<θ, which correspond to the cases of kinetic energy loss or gain, respectively. Given that ∇|E_SP |² is along the film’s normal, only the electron velocity component along this direction, v _⊥, can be substantially altered through the interaction. The condition α<θ necessitates that the electron exits the interaction region with a kinetic energy K>K ₀. This is due to the fact that the electron enters a location over which the SP extends spatially, but at a time before the peak excitation of the plasmon. Even though the electron is within the evanescent penetration depth of the SP wave, this electron is allowed to ‘sample’ a ponderomotive potential that is greater than the minimum potential required for deflection. The opposite situation can also occur in which electrons enter the evanescent field during the trailing edge of the SP wave and suffer a reduction inv _⊥. This is evidenced by the trajectory having the largest delay of 12 fs, illustrated in Fig. 2, which exits the interaction with α>θ.

 

Fig. 2. Trajectories of five test electrons as they interact with an SP wave having a peak electric field amplitude of E_SP =7.4×10⁹ V/cm. The test electrons are delayed with respect to the peak of E_SP with launching times ofτ_e = -12 (orange), -6 (purple), 0 (blue), 6 (green) and 12 fs (red). Laser parameters: τ_p =30 fs, λ=800 nm, F=2.18 mJ/cm².

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The effective ponderomotive potential, and hence the amount of energy transferred to the impinging electron, is a function of the duration of the optical excitation pulse. To determine the effective U_SP of the SP wave as a function of angle of incidence, electrons are directed toward the metal film surface at various θ. By incrementing E_SP for a given θ, the threshold electric field required for electron deflection can be measured and in turn, the effective ponderomotive potential of the SP wave can be determined. The situation is clearly depicted in Fig. 3(a)–3(f) for various θ ranging from 0 to 75°. Individual K₀ =1 keV test electrons are direct towards the metal film at peak excitation of the plasmon, which ensures that the maximum surface field will be sampled. The threshold electric field, $E_{\mathit{\text{SP}}}^{\mathit{\text{TH}}}$ , required for electron deflection is defined as the minimum E_SP required such that the electron trajectory does not cross the metal-vacuum boundary. Each panel in Fig. 3 illustrates electron trajectories for field values above and below such threshold values. It should be noted that, for U_SP < K _⊥, the electron’s traced path crosses the plane of the film surface and is absorbed, however, the trajectory is shown for illustrative purposes. Conversely, if E_SP is above the threshold required for deflection, U_SP > K _⊥ will ensure that the electron has its v _⊥ component altered such that the electron is deflected away. For each case that the electron is deflected, its new velocity component along the film normal is greater than or equal to its initial velocity along the film normal. Notably, at such $E_{\mathit{\text{SP}}}^{\mathit{\text{TH}}}$ , the deflection angles α~ θ- 12°. For θ = 0°, however, the difference between the deflected angle and the incident angle is the largest at 17°. This effect is due to the finite wavevector of the SP wave: as the SP wave propagates along the metal film, the direction of largest gradient, as observed by the electron, acquires a slight tilt with respect to the film surface and preferentially forces the electron along this direction. The results shown here indicate that it may be possible, experimentally, to use electrons and their subsequent deflection to probe the magnitude of the surface electric field, which currently, is a challenging parameter to measure.

 

Fig. 3. Electrons interacting with the SP wave for various θ of (a) 75°, (b) 60°, (c) 45°, (d) 30°, (e) 15°, and (f) 0°. For each panel, two electron trajectories are plotted corresponding to the cases of K _⊥ < U_SP (solid blue) and K _⊥ > U_SP (dashed red). The arrows indicate the direction of the electrons as they approach and exit E_SP . Laser parameters: τ_p =30 fs, λ=800 nm.

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In a quasi-static situation, where the E_SP field is turned on for a long period of time (i.e. longer than the interaction time between the electron and E_SP ), the ponderomotive potential can be calculate using U_SP = e ² E^{SP 2} /(4m_eω ²) [17]. However, the plasmon field is generated from an ultrashort pulse and therefore the effective ponderomotive potential will be reduced. Moreover, electrons can be incident at arbitrary angles and the effective ponderomotive potential will vary accordingly with θ. These two effects can be incorporated into a modified equation describing the threshold value of ponderomotive potential

where β is a constant accounting for the finite duration of the SP wave [17]. Figure 4 illustrates the simulated U_TH as a function of θ as calculated from the $E_{\mathit{\text{SP}}}^{\mathit{\text{TH}}}$ values. Good agreement between the model calculations and Eq. (8) is achieved with β =2.1, indicating that the effective ponderomotive potential is reduced by over a factor of 2 as compared to the quasi-static value. A distinct trade-off emerges in that a longer optical pulse can be used to lower the required U_TH , however, at the expenditure of increasing the duration of the deflected electron packet. It is also important to note the significantly reduced UTH near 90°. To avoid the generation of electrons via photoemission, θ can be sufficiently large (~ 90°) such that the laser beam intensity is reduced to ≥ 1 GW/cm², which in turn, would reduced the number of photoelectrons produced at the metal surface.

 

Fig. 4. Comparison of threshold values of the ponderomotive potential required for electron deflection as calculated from the model (red circles) and Eq. (8) (solid blue line).

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To characterize a femtosecond electron packet generated via the SP-gating process, a continuous beam of electrons is directed toward the metal film with θ=45° and K₀ = 1 keV. Several snap-shots at times ranging from t=-20 fs to 130 fs are shown in Fig. 5, illustrating the result of the interaction between the incoming electron beam and the surface plasmon electric field of E_SP =7.4×10⁹ V/cm. Initially (t<-20 fs), electrons incident upon the metal are not deflected, as E_SP has not reached its peak value. These electrons can either reflect off the surface of the metal film or generate secondary electrons. In either case, such electrons are not synchronized with the laser pulse and would appear as a DC offset in the deflected current. Once the optical pulse couples to the SP wave (t=0), the ponderomotive force exerted by E_SP deflects electrons and a significant portion of the original electron beam has been sliced and redirected away from the prism surface.

Further examination of the spatial distribution of the deflected electron pulse indicates a high degree of spatial microbunching, with an average distance between peaks equal to half the wavelength (~400 nm) of the optical excitation pulse. To observe the temporal characteristics of the microbunches, the electron packet is sampled and illustrated in Fig. 6 for five sampling locations both perpendicular and parallel to the metal surface. For detection along the perpendicular direction, each curve of Fig. 6(a) has the same overall pulse shape comprising a fast rise of ~10 fs and a slow fall of ~72 fs with no indication of microbunching. As the detector distance from the metal surface is increased, the full-width at half-maximum (FWHM) of the electron density curves increase from 34 to 43 and to 44 fs for distances of 1.0, 1.5, and 2.0 µm, respectively. Figure 6(b) illustrates the variation of the FWHM with distance along a direction 22° away from the surface normal (see the inset of Fig. 7(a)). These results indicate that the deflected electron packet’s energy distribution is non-monoenergetic. Furthermore, as the distance of the detector increases, the amplitude of each curve decreases, suggesting that the electrons comprising the packet do not depart the surface at the same α. The variation of total number of deflected electrons with distance is shown in Fig. 6(c) along the direction 22° away from the surface normal. However, as shown in Fig. 6(d), the measured temporal profiles parallel to the film surface reveal broad envelopes (160 fs) with an underlying waveform composed of eight ultrashort packets corresponding approximately to the number of electron field oscillations of E_SP . The average duration of these subsidiary pulses is 13 fs, and span the range from 7 to 23 fs. Interestingly, the packets’ durations increase with time, signifying that the duration of the underlying packets are a function of the time spent in E_SP . It is interesting to note that, even though there is no velocity matching between the electrons and the SP wave, electrons acquire a preferential spatial distribution from electromagnetic fields of the plasmon.

 

Fig. 5. Snapshots of the SP-gating of an electron beam at various times ranging from -20 fs to 130 fs. The white arrow indicates the direction of the wave vector of the incident laser pulse, while the black arrow indicates the propagation direction of the electron beam. Laser parameters: τ_p =30 fs, λ=800 nm, F=2.18 mJ/cm².

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Fig. 6. (a) Number of deflected electrons as a function of time at various sample locations at perpendicular distances of 1.0, 1.5, and 2.0 μm away from the metal film surface. (b) Variation of the FWHM of the electron packet as a function of distance away from the prism surface along a direction 22° from the surface normal. (c) Variation of the total number of deflected electrons as a function of distance away from the prism surface along a direction 22° away from the surface normal. (d) Number of deflected electrons as a function of time at two locations along the film surface for distances of 3.0 and 4.0 μm away from the center of the metal surface. Legends in (a) and (d) contain illustrations depicting the location of the detector with respect to the prism surface. It should be noted that in (a) and (d) the curves have been offset vertically for clarity. Laser parameters: τ_p =30 fs, λ=800 nm, F=2.18 mJ/cm².

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Fig. 7. (a) Kinetic energy spectra of the sliced electron beam depicted in Fig. 6. The peak has a central value of 330 eV and a FWHM of 179 eV. The inset shows the angular distribution of the sliced electron beam and its relation to the surface of the prism. Directionality of the sliced beam is evidenced by the peak at 22°, which has an angular half-width of 21°. (b) Angle-resolved energy spectra reveal distinct energy bands that follow K~K _∥ (1+cot² α) for various K _∥ values ranging from 204 to 417 eV. Laser parameters: τ_p =30 fs, λ=800 nm, F=2.18 mJ/cm².

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The energy spectrum of the sliced electron pulse is shown in Fig. 7(a). Here, it is observed that the initial mono-energetic spectrum of K ₀=1 keV electrons has broadened significantly following its interaction with the SP field. The large peak occurring at 330 eV with a FWHM of 179 eV indicates that significant portions of the electrons lose energy during the deflection process. However, an approximately equal number of electrons have gained energy, up to 4 keV, from E_SP . Of particular interest is the angular distribution shown in the inset of Fig. 7(a) which illustrates the number of deflected electrons as a function of exit angle, α. The highly directional nature of the deflected packet is observed with a peak at 22° and an angular half-width of 21°. Interestingly, a significant number of electrons have final velocity vectors parallel to the film surface, indicating that some electrons are decelerated to the critical point where v _⊥~ 0. The directional characteristic of the sliced electron packet can be utilized to spatially filter the deflected electron beam and discriminate against background electrons. Moreover, angle-resolved spectra shown in Fig. 7(b) clearly exemplify the large correlation between final energy and direction of the deflected electron packet. A closer examination of Fig. 7(b) reveals seven distinct energy bands indicating that the electrons are grouped with respect to their energies. As a approaches 90°, the energy bands asymptotically converge to values near 330 eV as shown in Fig. 7(a). The overall characteristic of these energy bands can be determined by considering that the ponderomotive force is nearly parallel to the normal of the metal film surface. Through simple analysis and the assuming that dv _∥/dt ≈ 0, the dependence of final energy on outgoing angle can be derived to be K ~ K _∥ (1+cot² α) for an individual energy band. The good agreement between K, calculated from this equation, and the model energy bands is shown in the inset in Fig. 7(b). In principle, the electron bunches can be separated according to their energy by employing an electron energy analyzer (shown in Fig. 1).

To demonstrate that the aforementioned technique can be employed for electron-optical cross-correlation, the electron beam is replaced with an ultrashort electron pulse. Here, the deflected charge is a function of the relative delay, τ, between the optical and electron pulses. The situation is clearly depicted in Fig. 8 which illustrates a K ₀=1 keV, 50 fs electron pulse interacting with the surface plasmon electric field of E_SP =7.4×10⁹ V/cm for τ =0. The deflected electron pulse demonstrates much of the same behaviour as the electron packet sliced from the previously discussed electron beam; however, now the deflection efficiency is function of the temporal overlap of the electron pulse with the SP wave. Figure 9 illustrates the cross-correlated deflected charge, Q_deflected (τ), as a function of τ calculated for various E_SP . The overall shapes of each curve are Gaussian with FWHM of 72, 90, and 100 fs for E_SP of 3.7×10⁹ V/cm, 7.4×10⁹ V/cm, and 1.9×10¹⁰ V/cm, respectively. As described previously, the width of the cross-correlation function depends on the intensity of the SP wave, and is verified by the increase of the FWHM with increasing E_SP . Furthermore, the amount of Q_deflected(τ) is also a function of E_SP , where an increase of E_SP results in an increase of the amplitude of the correlation function. For the largest Q_deflected (τ) shown in Fig. 9, 33% of the incoming electrons have been deflected. Complete deflection of the incident electron pulse can be achieved by choosing E_SP sufficiently large (≫$E_{\mathit{\text{SP}}}^{\mathit{\text{TH}}}$ ), however, in such a case no inference can be made of the electron pulse duration. Conversely, increased temporal resolution can be achieved at the cost of a diminishing deflected signal level (see Fig. 9). Thus, a trade-off between the temporal width of the correlation and the amount of deflected charge emerges. An electron pulse representing a delta-function can be used to establish the resolution of the cross-correlation process. Figure 10 illustrates various cross-correlations corresponding to a 30 fs optical excitation pulse and various electron pulses having durations ranging from 5 to 200 fs. As the duration of the electron pulses are reduced, the FWHM of the curves approach a constant value of 77 fs corresponding to the temporal convolution width. This convolution width would be a function of the energy of the incident electron beam, θ, and the optical pulse duration. It should be noted that it is essential to operate in a electron density regime (<10⁴ A/cm² [18]) where the space-charge forces of the electron pulse are negligible in comparison to the ponderomotive force exerted by E_SP . Higher density electron beams requires the addition of a space-charge model in our calculations [19].

 

Fig. 8. (2.4 MB) Movie of the SP-gating of an electron pulse at various times ranging from -20 fs to 130 fs for a relative delay of τ=0. The arrows indicate the direction of the propagation of the electron and optical pulses. Laser parameters: τ_p =30 fs, λ=800 nm, F=2.18 mJ/cm².

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Fig. 9. Cross-correlation between an SP excited with a 30 fs optical pulse and a 50 fs electron pulse for various E_SP of 3.7×10⁹ V/cm, 7.4×10⁹ V/cm, and 1.9×10¹⁰ V/cm. Laser parameters: τ_p =30 fs, λ=800 nm.

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Fig. 10. Cross-correlation between an SP excited with a 30 fs optical pulse and electron pulses with durations ranging from 5 to 200 fs. The resolution of the system determined from the 5 fs electron pulse is 77 fs. Laser parameters: τ_p =30 fs, λ=800 nm, F=2.18 mJ/cm².

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4. Conclusion

We have proposed and theoretically investigated a novel method for electron beam slicing using SP waves. Since the generation of the SP field relies on ultrashort optical pulses, a large portion of an incident electron beam can be temporally gated with a precision limited only by the ponderomotive interaction, and results in an electron pulse having a temporal duration similar to that of the optical pulse. The sliced electron pulse is highly directional and investigation of its spatial distribution reveals a large degree of microbunching. Angle-resolved energy spectra reveal discrete energy bands, illustrating that the deflected electron energy and angle are interrelated. Furthermore, it is shown that the SP gating mechanism can be utilized for temporal characterization of ultrashort electron bunches below 100 fs. It is expected that even shorter duration electron bunches can be created by using a shorter wavelength for excitation of the SP wave.