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Characterization of ultrashort electron pulses by electron-laser pulse cross correlation Bradley J. Siwick,* Alexander A. Green, Christoph T. Hebeisen, and R. J. Dwayne Miller Departments of Chemistry and Physics, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada Received July 20, 2004 An all-optical method to determine the duration of ultrashort electron pulses is presented. This technique makes use of the laser pulse ponderomotive potential to effectively sample the temporal envelope of the electron pulse by sequentially scattering different sections of the pulse out of the main beam. Using laser pulse parameters that are easily accessible with modern tabletop chirped-pulse amplification laser sources, it is possible to measure the instantaneous duration of electron pulses shorter than 100 fs in the energy range that is most useful for electron diffraction studies, 10–300 keV. © 2005 Optical Society of America OCIS codes: 320.0320, 320.7100, 320.7120.
Ultrafast electron diffraction (UED) is a powerful technique for studying the structural dynamics of chemical and material systems at the atomic level, since the observable in a UED experiment is directly connected to the nuclear coordinates. The experimental temporal resolution is fundamentally tied to the duration of the electron pulses used in the investigations, and proper pulse characterization is important for determining the temporal response function of the diffractometer. Currently the only method available for measuring the duration of an ultrashort electron pulse is to use the techniques employed by streak cameras.1 Recently developed high-fluence femtosecond electron sources,2,3 however, produce pulses that have propagation characteristics, beam sizes, and temporal duration that make it impossible to fully characterize them in this manner. Moreover, to obtain access to the transition state structures involved in molecular processes there is a strong drive to decrease electron pulse duration further, to the ⬃100-fs level, while scaling to even higher pulse fluences. Thus, analogous to the evolution that has occurred in the characterization of optical pulses, a new means for fully characterizing electron pulses is needed. The physics of ultrashort electron pulse propagation is summarized in Fig. 1. Coulomb repulsion (space charge) makes the pulse duration a strong function of the photocathode-to-sample propagation time, tprop, and the pulse fluence, = N / A, where N is the total number of electrons contained in the pulse and A is the beam area. These pulse propagation calculations were made with a mean-field model4 that is in excellent quantitative agreement with full-scale many-body simulations and pulse duration measurements. The difficulties associated with streak camera measurements of the pulse duration arise from time resolution limitations and the positional specificity of the measurement. The time resolution of a streak camera is given by = / s, where is the beam size at the detector and s is the streak speed.1 The strong dependence of space-charge-induced broadening on and the practical UED requirement of several thousand electrons per pulse mean that electron-beam di0146-9592/05/091057-3/$15.00
ameters of more than 150 µm are typically used. An instrument response function of 250 fs then would require a streak speed of at least 6 ⫻ 108 m / s. Such sweep speeds can, in principle, be obtained by use of traveling-wave deflection structures on ⬍10-keV electron beams, but they become progressively more difficult with increasing electron energy. The issue of positional specificity arises from the propagation time spent traversing the deflection plates. An electron pulse of = 2 ⫻ 105 mm−2 will more than double its duration from 450 fs to 1.2 ps while propagating through deflection structures 4 cm in length if the structures are placed immediately after a 5-cm long, 30-keV electron gun (Fig. 1). Thus a measurement conducted in this manner cannot accurately determine the pulse duration at the sample plane, which is the quantity of interest, even if the temporal resolution is adequate. This will become an even more serious issue with further advances in electron source design. For example, electron pulse compression
Fig. 1. Space-charge-induced temporal broadening characteristics of a 30-keV electron pulse with an initial duration of 100 fs and a constant 200-µm beam diameter as a function of tprop and . This color map is accurate to better than ±50% over a beam diameter range of 100–500 µm, and an electron energy range of 30–120 keV. The pair of diagonal black and red lines marks the picosecond barrier for 30- and 60-keV electron pulses, respectively. © 2005 Optical Society of America
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Fig. 2. Geometry of the all-optical electron pulse duration measurement. Electron-beam cross sections are shown at various positions after the interaction region for a 600-fs electron pulse and the laser pulse parameters given in the text.
schemes can only be expected to refocus the pulse temporally through a narrow range of positions. Hence it is important to be able to determine the instantaneous electron pulse duration, and for this purpose new approaches akin to the nonlinear optical methods used for laser pulses are required. In this Letter we propose such an all-optical method for the characterization of ultrashort electron pulses. It is well known that the net change in momentum of a free electron interacting with a plane wave in vacuum is zero. However, it has been demonstrated that if there are inhomogeneities in the field distribution the averaged motion of an electron includes a drift component toward regions of lower field intensity in addition to the high-frequency quiver oscillations.5 The ponderomotive force, Fp, that gives rise to this drift motion emerges naturally from the cycle-averaged Lorentz force,6 and at low intensities 共I ⬍ ⬃ 1018 W / cm2兲, where the quiver motion of the electron is nonrelativistic and the magnetic field term in the Lorentz force can be neglected, Fp = − ⵜ Up. Here Up is the laser pulse ponderomotive potential (LPP), Up共r,t兲 =
e 2 2 8 2m ⑀ oc 3
I共r,t兲,
Several applications for this interaction have been proposed or implemented in other contexts.7–9 Since the effect of the LPP is to expel electrons from regions of high intensity, the interaction can be used to sample the temporal envelope of a femtosecond electron pulse by sequentially scattering different sections of the electron pulse out of the main beam and measuring the associated reduction in beam intensity. An effective geometry for performing such measurements is shown in Fig. 2. The electron beam is sent through an aperture, Al, and then intersects with a well-characterized laser pulse at 90°. A distance l downstream from the interaction point the electron beam passes through another aperture, A2, that blocks the detection of the scattered electrons. Different sections of the electron pulse can be sliced out of the main beam by delaying the arrival of the laser pulse by a time with respect to the electron pulse at the intersection point. The detector, placed after A2, can be either an electron image intensifier of the types used in UED experiments or a Faraday cup attached to a sensitive electrometer. To model the situation presented in Fig. 2, we performed Monte Carlo simulations in which the equation of motion for 30-keV free electrons interacting with the LPP was integrated numerically. Initial electron positions were randomly generated by use of Gaussian distributions for the transverse and temporal coordinates. By repeatedly solving the equations of motion for this distribution of initial conditions, the effect of the LPP on the portion of the electron pulse transmitted through A1 can be built up one electron at a time. Figure 3 shows the results of these Monte Carlo simulations for several e−2 full width 共e−2 FW兲 electron pulse durations and Gaussian fits to the calculated responses. The drop in the measured intensity with laser interaction, Io − Im, has been normalized with respect to the electron-beam intensity with no laser interaction, Io; i.e.,
共1兲
e is the electron charge, m is the electron rest mass, ⑀o is the permittivity of free space, c is the speed of light, and and I are the wavelength and intensity of the laser pulse, respectively. The magnitude of Up is equal to half the quiver energy of the electron in the oscillating field, and at 800 nm Up ⬇ 6 ⫻ 10−14 I eV (I in W / cm2). In the intensity range 1015 – 1017 W / cm2, easily accessible to modern chirped-pulse amplification lasers, the LPP provides a repulsive potential that ranges from tens to thousands of electron volts.
Fig. 3. Electron–laser pulse cross correlation. The reduction in electron-beam intensity transmitted through A2 is sensitive to and the duration of the electron pulse at the interaction point (see the legend). The impulse response of the measurement (inset) is ⬃300 fs e−2 FW for the parameters A1 = wl = 30 m, l = 200 fs (dashed curve), but only ⬃80 fs e−2 FW for A1 = wl = 10 m, l = 60 fs (solid curve).
May 1, 2005 / Vol. 30, No. 9 / OPTICS LETTERS
⌬I = 共Io − Im兲 / Io. The laser pulse parameters used in the simulation were 200 µJ of pulse energy, = 800 nm, spot size wl = A1 = 30 m e−2 FW, and pulse duration l = 200 fs e−2 FW. Aperture A2 was taken to be a 50-µm slit with the short axis in the z direction, and was placed at l = 10 cm from the interaction point. Since ⌬I is sensitive to the delay between the two pulses as well as their temporal duration, this measurement effectively provides a cross correlation of the electron and laser pulses. By deconvolving the impulse response of the measurement (300 fs, discussed below) using the Gaussian approximation, we recover the following pulse durations: 222, 398, 592, 794, and 986 fs in descending order. The recovered values agree with the actual electron pulse durations to better than 2% in all cases except the shortest pulse (200 fs), where the discrepancy is 11%. The impulse response of this technique is defined by the overlap integral of the laser and electron pulses through the interaction region. Thus it is possible to improve the temporal resolution of the method by reducing the size of the temporal slices taken at each delay by decreasing the size of A1 with concomitant reduction in the laser pulse duration and focus. This is evident from the inset in Fig. 3, in which the calculated impulse response (cross correlation for an electron pulse with a delta function temporal profile) for two sets of parameters is also shown. It is important to note that these response functions are not limited by jitter when one is measuring the output of photoactivated electron sources. In such systems each laser pulse is divided into two parts, one used to produce the electron pulse and the other used in the cross correlation. This ensures that the two pulses can be synchronized at the interaction region with timing jitter well below 100 fs and that extensive signal averaging is possible with this technique. This contrasts with the case of streak camera measurements, which, because of deflection plate trigger jitter, are essentially single shot in nature. The interesting pattern of scattered electrons (Fig. 2) results from the intensity gradients (forces) experienced by the electrons during interaction with the laser pulse. For the laser pulse parameters used in the simulations above the temporal (y axis) to transverse (x and z axes) aspect ratio is 2:1, so the dominant intensity gradients are in the ±z direction when averaged over the interaction region (gradients in the ±x direction cancel). This results in the band of scattered electron intensity that is visible in the cross sections along the z axis. Electrons interacting primarily with the leading and trailing edges of the laser pulse also obtain significant momentum in the ±y direction and are responsible for the rest of the scattered electron distribution. The exact spatial distribution can in principle provide additional information on the pulse profile. Note that higher energy electrons will be scattered less efficiently by the LPP, and it will be necessary to use higher intensities to observe the same effect. However, the pulse energies
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available from modern chirped-pulse amplification laser sources make this technique easily applicable to the electron energy range most used for electron diffraction, 10–300 keV, by scaling the laser pulse energy and focus. Modification of the theory to the relativistic laser intensity regime 共I ⬎ 1018 W / cm2兲 will extend its applicability further, possibly to characterize electron pulses from mega-electron-volt rf electron guns and electron bunches in synchrotrons and free-electron lasers. Note that, because of normalization with respect to Io, this technique is insensitive to space-chargeinduced temporal and transverse broadening occurring in the A1 – A2 region, provided that interaction with the laser pulse takes place immediately after A1. However, to ensure that the ponderomotive interaction is the dominant effect reducing electron transmission through A2, the number of electrons in the interaction region should be kept to only a few hundred per pulse by appropriate choice of A1 for femtosecond electron pulses. The unique feature of this electron–LPP crosscorrelation method is the ability to determine the instantaneous duration of electron pulses below even 100 fs in the energy range most applicable to electron diffraction studies, 10–300 keV. Further advances in ultrashort electron source development through the use of pulse compression will rely heavily on such a technique. Adaptations of this method could also be made to determine = 0 in a UED experiment or other related electron-laser-based experiments requiring high time resolution. This work was supported by the Natural Science and Engineering Research Council of Canada.
*Present address, FOM Institute for Atomic and Molecular Physics (AMOLF), Kruislaan 407, 1098 SJ, Amsterdam, the Netherlands; e-mail,
[email protected]. References 1. P. Gallant, P. Forget, F. Dorchies, Z. Jiang, J. C. Kieffer, P. A. Jaanimagi, J. C. Rebuffie, C. Goulmy, J. F. Pelletier, and M. Sutton, Rev. Sci. Instrum. 71, 3627 (2000). 2. B. J. Siwick, J. R. Dwyer, R. E. Jordan, and R. J. D. Miller, Science 302, 1382 (2003). 3. B. J. Siwick, J. R. Dwyer, R. E. Jordan, and R. J. D. Miller, Chem. Phys. 299, 285 (2004). 4. B. J. Siwick, J. R. Dwyer, R. E. Jordan, and R. J. D. Miller, J. Appl. Phys. 92, 1643 (2002). 5. P. H. Bucksbaum, M. Bashkansky, and T. J. McIlrath, Phys. Rev. Lett. 58, 349 (1987). 6. T. W. B. Kibble, Phys. Rev. 150, 1060 (1966). 7. G. V. Stupakov and M. S. Zolotorev, Phys. Rev. Lett. 86, 5274 (2001). 8. J. L. Chaloupka, and D. D. Meyerhofer, Phys. Rev. Lett. 83, 4538 (1999). 9. V. I. Balykin, M. V. Subbotin, and V. S. Letokhov, Opt. Commun. 129, 177 (1996).
