Characterization of fast photoelectron packets in weak and strong laser fields in ultrafast electron microscopy

Ultramicroscopy 146 (2014) 97–102

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Characterization of fast photoelectron packets in weak and strong laser fields in ultrafast electron microscopy Dayne A. Plemmons a, Sang Tae Park b, Ahmed H. Zewail b, David J. Flannigan a,n a

Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, MN 55455, USA Physical Biology Center for Ultrafast Science & Technology, Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, USA b

art ic l e i nf o

a b s t r a c t

Article history: Received 14 May 2014 Received in revised form 29 July 2014 Accepted 3 August 2014 Available online 10 August 2014

The development of ultrafast electron microscopy (UEM) and variants thereof (e.g., photon-induced near-field electron microscopy, PINEM) has made it possible to image atomic-scale dynamics on the femtosecond timescale. Accessing the femtosecond regime with UEM currently relies on the generation of photoelectrons with an ultrafast laser pulse and operation in a stroboscopic pump-probe fashion. With this approach, temporal resolution is limited mainly by the durations of the pump laser pulse and probe electron packet. The ability to accurately determine the duration of the electron packets, and thus the instrument response function, is critically important for interpretation of dynamics occurring near the temporal resolution limit, in addition to quantifying the effects of the imaging mode. Here, we describe a technique for in situ characterization of ultrashort electron packets that makes use of coupling with photons in the evanescent near-field of the specimen. We show that within the weakly-interacting (i.e., low laser fluence) regime, the zero-loss peak temporal cross-section is precisely the convolution of electron packet and photon pulse profiles. Beyond this regime, we outline the effects of non-linear processes and show that temporal cross-sections of high-order peaks explicitly reveal the electron packet profile, while use of the zero-loss peak becomes increasingly unreliable. & 2014 Elsevier B.V. All rights reserved.

Keywords: Photon-induced near-field electron microscopy Instrument response function Ultrafast electron microscopy

1. Introduction Over the past decade, the area of time-resolved transmission electron microscopy has undergone substantial growth due largely to the development of new methods and instrumentation. Videorate capabilities have been in use for some time [1–4], and recent developments in direct detection technology have extended the detector temporal range down to hundreds of microseconds [5,6]. While such developments have opened new avenues of research, microsecond temporal resolutions are not sufficient for directly observing a wide range of atomic-scale structural dynamics. Indeed, time-resolved TEM studies conducted with video-rate detectors cannot reveal the origins of reactivity and structural transformations; modulation of bonding – which occurs on the femtosecond timescale – is the fundamental process that dictates such phenomena. In order to overcome the limits imposed by reliance on detectors for time-resolved experiments, and to extend the range to the femtosecond regime, an altogether different approach is needed. The advance that produced such an expansion of the temporal parameter

n

Corresponding author. Tel.: þ 1 612 625 3867 (office); fax: þ1 612 626 7246. E-mail address: fl[email protected] (D.J. Flannigan).

http://dx.doi.org/10.1016/j.ultramic.2014.08.001 0304-3991/& 2014 Elsevier B.V. All rights reserved.

space was extension of the stroboscopic pump-probe method to TEMs [7,8]. This is made possible via modification of a TEM such that optical access is provided to both the electron emission source and the specimen, thus enabling photon-pump/photoelectron-probe experiments to be conducted. This approach, known as ultrafast electron microscopy (UEM), has been successfully used to study a wide-range of materials and physical phenomena [9,10]. Essential to UEM is the generation of discrete femtosecond electron packets, and a variety of methods for accomplishing this have been explored [7,11–16]. An important aspect of emission source development is minimization of the duration of fast electron packets without degradation of the temporal or transverse coherence [17–21]. One approach in UEM that has been successfully employed is to populate each packet with (on average) one electron, thus circumventing the deleterious effects of Coulombic interactions [22–24]. For physical phenomena occurring on timescales approaching the temporal resolution, determination of the UEM instrument response function (IRF) is necessary for deconvolution of intrinsic excitation dynamics, and evaluation of methods for generating femtosecond electron packets requires quantification of the pulse properties, ideally at the specimen location. In addition, a robust and precise method is needed for determining time zero (i.e., temporal overlap of the photon pulse and electron packet at the specimen) [25–29]. One approach that has been developed for

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table-top ultrafast electron diffraction setups is ponderomotive scattering in an intense laser field [30,31]. Such scattering produces a variation in the spatial intensity distribution on the detector, the time-dependent behavior of which is directly related to the electron packet properties [32,33]. To overcome the practical challenges associated with the necessary high-laser fluences in single-beam ponderomotive scattering, Kapitza–Dirac optical gratings have recently been demonstrated [21,34,35]. Here, we describe a method for measuring the femtosecond electron packet properties, as well as the overall UEM IRF, precisely at the specimen location and within both linear (weak) and non-linear (strong) interaction regimes. The method is based upon the photon-induced near-field effect, wherein freelypropagating electrons comprising the femtosecond probe packet absorb photons from the pump pulse at the specimen and populate discrete energy states [36,37]. In the weak-interaction regime (i.e., relatively low pump-laser fluence), the timedependent cross-section of the zero-loss peak (ZLP) is precisely the convolution of the electron and photon temporal profiles. We discuss the role of non-linear interactions outside of the weakinteraction regime and show that temporal cross-sections of highorder peaks in the energy spectrum explicitly reveal the electron packet profile, while the ZLP becomes increasingly unreliable. In addition, we show that this is an effective way to directly determine the IRF, wherein the measured response intrinsically contains all contributions from angular distribution, dispersion, etc. [23], thus leading to an overall temporal profile of packets containing on average one electron.

2. Background A schematic of a UEM configured for stroboscopic operation is shown in Fig. 1. The inset shows, conceptually, the generation of one time point (τ) and the method for assigning a single temporal value to pulses with a finite duration. The general experimental procedure is as follows. A femtosecond laser pulse is split into what are dubbed pump and probe beams. The pump beam (which may undergo nonlinear conversion depending upon the excitation of interest) is

directed onto the specimen and initiates the dynamics. The probe beam is directed into the Wehnelt cylinder of the electron gun after undergoing appropriate harmonic generation; ultraviolet pulses are used to generate photoelectron packets from the LaB6 emission source. The discrete, femtosecond photoelectron probe packets are then accelerated and directed down the column in the manner typical for standard TEMs with thermionic gun assemblies. One temporal point (τ) is generated by fixing the relative arrival times of the photon pump pulse and electron probe packet with a motorized optical delay stage. Additional points are generated by changing the position of the stage such that the arrival times now differ by τþΔτ. The variable time delay dictated by the position of the stage allows one to temporally scan (in this case) the photon pump pulse across the electron probe packet, each with a fixed spatial position (i.e., at the specimen location). One consequence of illumination of the specimen with the photon pump pulse is light scattering and near-field enhancement, the intensity and spatial arrangement of which depend upon the material properties and feature shape [38–40]. When spatiotemporally overlapped at the specimen, the freely-propagating electrons (with energy E, e.g., 200 keV and comprising the ZLP) in the probe packet can absorb photons (with energy ħω, e.g., 2.4 eV, where ħ is the reduced Planck constant and ω the angular frequency of light) in the pump pulse and transition into discrete excited states (E þnħω, where n is an integer). This process, known as the photon-induced near-field effect (PINEM), as well as the related electron-energy gain spectroscopy (EEGS), are described experimentally and theoretically in detail elsewhere [36,41–44]. In UEM, evidence for electron–photon coupling is experimentally observed in the low-loss region of the electronenergy spectrum. Precise spatiotemporal overlap at the specimen produces discrete peaks occurring at integer multiples of photon quanta to both the loss (  nħω) and what corresponds to the gain (þnħω) side of the ZLP [36,42,45]. In PINEM, electrons in the probe packet gain quanta of energy only in the presence of the photon pump pulse (and only when both are spatially overlapped at the specimen). The intensity response (i.e., electron counts) of the ZLP in the energy spectrum is therefore directly related to the cross-correlation of the photon (pump) pulses and electron (probe) packets. This is because the

Fig. 1. Condensed schematic of the ultrafast electron microscope (UEM) and overview of the experimental concept. The critical components are labeled, including the spectrometer, which is necessary for the particular method outlined here. The inset shows (i) an example of the temporal overlap of the photon pulse and electron packet separated in time by τ [Δp and Δe represent the photon pulse and electron packet temporal durations (full-width at half-maximum, FWHM), respectively], and (ii) a schematic of the spatial interaction region of Δp and Δe at the specimen, again separated in time by τ.

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lifetimes of the plasmonic effects that lead to generation of the evanescent near-field are much shorter than the photon pulse durations typically employed in UEM (i.e., lifetimes of one to 10 fs compared to pulse durations of 100 to 500 fs). That is, the temporal envelope of the near-field directly follows the photon pulse. As such, and akin to optical auto-correlation, this interaction can in theory be used to sample and characterize the temporal envelope of the electron packets by varying the (temporal) overlap (at a fixed spatial position) of the pump and probe and measuring the associated intensity response of the ZLP [37,46–49]. Because interaction between the freely-propagating electrons and the photons can occur only in the near-field of the specimen, appropriate deconvolution allows for electron packet characterization precisely at the specimen location.

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weak-interaction limit, the Gaussian temporal widths of nthqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ 2e þ ðσ 2p =nÞ, where

order peaks [side-bands in Fig. 2(a,b)] are σ n 

σ is the standard deviation and Δ¼2[2 ln(2)]0.5  σ. Notably, nth-order states are populated within an effective pffiffiffi optical pulse length range of ðσ p = nÞ; nth-order transitions are probable only for delays in which there is sufficient overlap for n transition events to occur. As also observed in the recentlyreported laser-streaking approach [50], higher orders show decreasing temporal widths, as the threshold intensity is an exceedingly small portion of the laser pulse. In principle, any of the higher-order peaks (n4 1) could be separated by using the effective optical pulse duration to obtain the temporal profile of the electron packet, though the ZLP is typically chosen due to its relatively large signal.

3. Calculations

3.2. Effects of increasing interaction strength

3.1. Energy spectra and the instrument response function

In the weak-interaction limit, linear depletion of the ZLP results in a temporal signal that is precisely the convolution of the incident electron packet and photon pulse profiles. Higher-order peaks are populated in a similar manner, though the probabilities are low, and the time window for these transitions becomes increasingly narrow. In this weak-interaction regime, direct determination of electron packet properties from low-loss energy spectra is not hampered by inherent artifacts introduced by nonlinear effects. For increasing interaction strengths, however, broadening of the temporal widths and deviation from Gaussian behavior have been observed [42]. These artifacts are the direct result of non-linear effects that occur at the increased fluences often employed in UEM experiments. In general, electron–photon coupling behavior is dependent on both the intensity of the pump laser pulse and the optical properties of the specimen, which gives rise to the evanescent near-field. The interaction parameter (Ω), defined as the argument of the Bessel function in Eq. (3), encompasses these dependencies for arbitrary fluences and specimens. For example, laser fluences on the order of 1 mJ/cm2 yield interaction parameters ranging from 4.7 to 7.5 for varying materials and structures [42]. For a focused electron beam, the oscillatory nature of the fluence dependence results in alternating depletion and population of peaks for different interaction strengths, as illustrated in Fig. 3(a). For example, in the weak-interaction limit, only one PINEM event is likely to occur, meaning that the vast majority of electrons depleted from the ZLP populate the first-order peaks. As the interaction strength increases, the likelihood of two transition events becomes dominant, and the first-order peak is depleted in favor of the second-order and zero-loss peaks. Further increase in interaction strength yields higher probabilities for a greater number of transition events. A multistate analog to the Rabi oscillation in a two-level system, this non-linear interaction gives rise to temporal signals that deviate from Gaussian shape in regions of maximum electron–photon coupling. Shown in Fig. 3(c), the observed temporal behavior of the first-order peak diverges from the cross-correlation of the electron packet and photon pulse to a non-Gaussian temporal profile with increasing interaction parameter (e.g., Ω ¼2–18). This is due to depletion of the firstorder states for delays in which a greater number of transition events are likely to occur. In practice, pulse characterization often takes place under parallel-beam (electron) illumination, where resulting low-loss energy spectra are the summation of interactions over the entire beam cross-section. For example, we consider here a 250 nm spherical nanostructure in which the Fourier component of the electric field parallel to the electron propagation decays exponentially with distance (see the Supplemental Material for details).

Determining the relation of the observed temporal behavior of low-loss energy spectra to the true photoelectron packet properties requires examination of the intensity dependence of PINEM transitions. Considering a first-order transition probability that is linearly proportional to the evanescent field intensity, Q 1 ðtÞ ¼ αI p ðtÞ, the probability density of the electron packet that has gained one photon of energy is given by Eq. (1). P 1 ðt; τÞ ¼ Q 1 ðtÞP e ðt þτÞ ¼ αI p ðtÞP e ðt þ τÞ

ð1Þ

Here, Pe(t) is the probability density of the electron packet, Ip(t) is the intensity profile of the pump laser pulse, and τ is the time delay. Integration over the entire electron packet then yields a first-order population (Eq. (2)). Z 1 P 1 ðτÞ ¼ αI p ðtÞP e ðt þτÞdt ¼ αfI p P e gðτÞ ð2Þ 1

In Eq. (2),  signifies cross-correlation. Thus, for electron– photon coupling in the linear regime, the temporal dependence of both the first-order peak and the ZLP, P0(τ) ¼1–2P1(τ), is proportional to the cross-correlation of the electron packet and photon pulse, which is by definition the UEM IRF. After properly accounting for any significant time-independent electron energy losses due to inelastic scattering processes in the specimen, the UEM IRF is explicitly revealed. At laser fluences typically employed in UEM experiments, electrons can absorb multiple photons, and as a result, population of nth-order states (where n 41) also contributes to depletion of the ZLP. Nevertheless, theoretical examination of the PINEM effect indicates that the linear approximation is indeed valid in the weak-interaction limit. That is, it is valid when the Bessel function of the first kind describing the intensity dependence of the PINEM transition probabilities can be approximated to the first term in the Taylor series shown in Eq. (3) [42]. Q n ¼ jJ n ðβI p ðtÞ1=2 Þj2 

pffiffiffiffiffiffiffiffiffiffiffi β2n I p ðtÞn for βI p ðtÞ1=2 ⪡ n þ 1 2n n!

ð3Þ

In Eq. (3), β is a proportionality constant representing the amplitude of scattered light at the spatial frequency required for coupling (see the Supplemental Material), and Jn is an nth-order Bessel function of the first kind. The effects on the energy distribution when in the weak-interaction limit are illustrated in Fig. 2, where varying overlap produces a significant depletion of the ZLP around zero time delay. The resulting temporal crosssection [Fig. 2(c)] takes on an inverted Gaussian shape with a qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi total FWHM of Δ0  Δ2e þ Δ2p , which is a convolution of the electron packet and photon pulse durations. Furthermore, in the

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Fig. 2. Pulse characterization via the photon-induced near-field effect. (a,b) Calculated time/energy phase space plots. Narrowing of the temporal widths for higher order peaks is evident in (a), while depletion of the ZLP around zero time delay can be seen in (b). (c) Temporal cross-section of the ZLP. In the weak-interaction limit, the temporal dependence of the zero energy-loss cross-section (Δo) is the convolution of the electron packet (Δe) and photon pulse (Δp) temporal profiles.

1=2

Fig. 3. Fluence dependence of the PINEM effect. (a,b) Intensities of low-order PINEM peaks at maximum pulse overlap versus interaction strength (Ω p I 0 ) for (a) focused and (b) parallel electron beams (367 nm beam waist). The oscillatory nature of the fluence dependence is evident in (a) but is absent in (b) due to spatial integration. The dashed lines guide the eye to linearity in the weak-interaction limit. (c,d) First-order peak temporal cross-sections. For a focused beam (c) the first-order peak is depleted near maximum pulse overlap resulting in non-Gaussian cross-sections. For a parallel beam (d), this effect is less pronounced but becomes significant at higher fluences.

As such, the oscillatory nature of the interaction-parameter dependence is effectively averaged out [Fig. 3(b)]; effectively-linear coupling occurs over a greater range of interaction parameters [depicted by the dashed line in Fig. 3(b)]. Note, however, that low-order peaks can still exhibit appreciable deviation from Gaussian shape under parallel beam illumination at high fluence due to depletion within the next effective optical pulse range [Fig. 3(d)]. Artifacts of the nonlinear PINEM process generally appear as a broadened temporal signal in experimental plots and thus do not accurately portray the intrinsic pulse properties. For electron packets with durations comparable to the pump laser pulse, broadening of the ZLP signal by up to 30% is expected to occur for applicable fluences (see Fig. S1 in the Supplemental Material). Ideally, characterization of pulse properties would take place in the weak-interaction limit where low-loss energy behavior explicitly identifies temporal properties of incident pulses. Operating in the weak-interaction limit, however, produces lower counts and is therefore more susceptible to noise.

3.3. Circumventing fluence-dependent artifacts One approach for determining electron packet durations in arbitrary interaction regimes is to utilize weak-interaction behavior of high-order peaks. Because these peaks experience narrowing effective-optical-pulse duration and show weakinteraction behavior at higher fluences, temporal peak widths for increasing n converge to the electron packet duration   qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i:e:; lim σ 2e þ ðσ 2p =nÞ ¼ σ e . Thus, temporal cross-sections of n-1

high-order PINEM side bands are expected to reflect the intrinsic properties of the electron packets; accurate electron packet properties can be efficiently extracted from these features. In practice, the limit discussed above can be obtained from linear-regression analysis – plotting σ 2n obtained from experiments versus n  1 and determining the y-intercept as σ 2e . Fig. 4 shows such an analysis for σ 2n versus n  1 for several interaction strengths

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4. Conclusions

Fig. 4. Electron packet properties in select interaction regimes. Shown is the square of the calculated temporal widths of PINEM side bands (σn) plotted versus n  1. The dashed lines are linear best fits to the calculated points and are labeled with the corresponding interaction strength (Ω), which increases from 0.5 to 15.

Here, we have described a robust method for in situ ultrafast electron packet and photon pulse characterization – in both the linear and the non-linear regimes – with temporal resolution limited only by plasmon lifetimes (i.e., on the order of 10 fs). Current UEM experimental setups and instrument configurations are amenable to the described method owing to the sensitivity of the PINEM effect, especially in the near-collinear propagation geometry. Because electron–photon coupling occurs only in the evanescent near-fields, measured pulse properties are precisely those occurring at the specimen location; effects of angular distribution and dispersion on temporal coherence are all contained in the measurement. Linear-regression analysis of the nonlinear (i.e., strong-interaction) regime demonstrates the importance of proper identification of the experimental parameter space in order to ensure that measurements are accurate. Finally, this in situ method can be used for simultaneous characterization of the instrument response and the specimen dynamics, thus providing a means to extract the initial ultrafast response to excitation, as well as an accurate determination of time zero.

Acknowledgments Table 1 Temporal pulse properties (σx)a as a function of interaction strength (Ω) determined from linear regression analysis of the numerical simulation.b Ω

σpc (fs)

σec (fs)

σ0d (fs)

0.5 2 4 5 10 15

1507 1 1577 4 1767 8 1857 11 222 7 23 2437 30

300.0 7 0.5 3007 2 299 7 4 299 7 6 299 7 12 302 7 16

335.5637 0.001 337.747 0.02 343.187 0.07 345.0 7 0.1 356.77 0.2 364.47 0.3

a x ¼p, e, or 0, where p ¼ photon pulse, e¼ electron pulse, and 0¼ convoluted pulses. b Simulated using temporal widths of σp ¼ 150 fs and σe ¼300 fs (see the methods section in the Supplemental Material). c Obtained from linear regression (see Section 3.3). d Obtained fitting the ZLP cross-section. Note the width of the convolution ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffifrom is σ 0 ¼ σ 2p þ σ 2e ¼335.41 fs.

DP and DJF acknowledge support from 3M in the form of a Nontenured Faculty Award (Grant #13673369) and from the Donors of the American Chemical Society Petroleum Research Fund in the form of a Doctoral New Investigator Grant PRF# 53116DNI7. STP and AHZ acknowledge support from the National Science Foundation and the Air Force Office of Scientific Research in the Center for Physical Biology funded by the Gordon and Betty Moore Foundation.

Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.ultramic.2014.08.001.

References (Ω). A variety of information can be extracted from such a plot, including – and perhaps most importantly – accurate determination of the electron packet duration regardless of the fluence. Linearity of the data gives an estimation of the interaction strength and thus the accuracy of time-dependent ZLP plots in relation to the actual UEM IRF. Increased curvature indicates higher interaction strengths; however, a linear regime always remains for small n  1 within the weak-interaction limit. The slopes of the best-fit lines in Fig. 4 provide an in situ estimation of the photon pulse duration for comparison with (currently) external auto-correlation measurements. Table 1 compares the photon pulse and electron packet durations obtained by linear-regression analysis with the theoretically-observed temporal width of the ZLP. Although the observed peak widths of the ZLP broaden due to non-linear effects at high interaction strengths, electron packet properties predicted from linear regression remain accurate. Indeed, because linearity always holds for small n  1, accurate photon pulse durations for arbitrary interactions could also be extracted by including only points within the linear regime in the regression analysis (not included here in order to maintain clarity). Thus, this analysis effectively suppresses broadening effects in observed data giving a more accurate depiction of pulse properties and the UEM IRF.

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