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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 5 — Mar. 3, 2008
  • pp: 3334–3341
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Grating enhanced ponderomotive scattering for visualization and full characterization of femtosecond electron pulses

Christoph T. Hebeisen, German Sciaini, Maher Harb, Ralph Ernstorfer, Thibault Dartigalongue, Sergei G. Kruglik, and R. J. Dwayne Miller  »View Author Affiliations


Optics Express, Vol. 16, Issue 5, pp. 3334-3341 (2008)
http://dx.doi.org/10.1364/OE.16.003334


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Abstract

Real time views of atomic motion can be achieved using electron pulses as structural probes. The requisite time resolution requires knowledge of both the electron pulse duration and the exact timing of the excitation pulse and the electron probe to within 10–100 fs accuracy. By using an intensity grating to enhance the pondermotive force, we are now able to fully characterize electron pulses and to confirm many body simulations with laser pulse energies on the microjoule level. This development solves one of the last barriers to the highest possible time resolution for electron probes.

© 2008 Optical Society of America

To understand condensed phase dynamics, chemical, and biological processes at the most fundamental level, one would ideally like to observe structural dynamics as they occur at the atomic level [1

1. J. R. Dwyer, C. T. Hebeisen, R. Ernstorfer, M. Harb, V. B. Deyirmenjian, R. E. Jordan, and R. J. D. Miller, “Femtosecond electron diffraction: ‘making the molecular movie’,” Phil. Trans. Roy. Soc. A 364, 741–778 (2006). [CrossRef]

, 2

2. A. H. Zewail, “4D ultrafast electron diffraction, crystallography, and microscopy,” Annu. Rev. Phys. Chem. 57, 65–103 (2006). [CrossRef] [PubMed]

, 3

3. W. E. King, G. H. Campbell, A. Frank, B. Reed, J. F. Schmerge, B. J. Siwick, B. C. Stuart, and P. M. Weber, “Ultrafast electron microscopy in materials science, biology, and chemistry,” J. Appl. Phys 97, 111,101 (2005). [CrossRef]

]. In the last few years, enormous strides have been made in making such experiments possible, using ultrafast laser excitation pulses to trigger structural changes and either x-ray or electron probes to follow the induced atomic motions [4

4. B. J. Siwick, J. R. Dwyer, R. E. Jordan, and R. J. D. Miller, “An atomic-level view of melting using femtosecond electron diffraction,” Science 302, 1382–1385 (2003). [CrossRef] [PubMed]

, 5

5. A. M. Lindenberg, J. Larsson, K. Sokolowski-Tinten, K. J. Gaffney, C. Blome, O. Synnergren, J. Sheppard, C. Caleman, A. G. MacPhee, D. Weinstein, D. P. Lowney, T. K. Allison, T. Matthews, R. W. Falcone, A. L. Cavalieri, D. M. Fritz, S. H. Lee, P. H. Bucksbaum, D. A. Reis, J. Rudati, P. H. Fuoss, C. C. Kao, D. P. Siddons, R. Pahl, J. Als-Nielsen, S. Duesterer, R. Ischebeck, H. Schlarb, H. Schulte-Schrepping, T. Tschentscher, J. Schneider, D. von der Linde, O. Hignette, F. Sette, H. N. Chapman, R. W. Lee, T. N. Hansen, S. Techert, J. S. Wark, M. Bergh, G. Huldt, D. van der Spoel, N. Timneanu, J. Hajdu, R. A. Akre, E. Bong, P. Krejcik, J. Arthur, S. Brennan, K. Luening, and J. B. Hastings, “Atomic-scale visualization of inertial dynamics,” Science 308, 392–395 (2005). [CrossRef] [PubMed]

, 6

6. A. Rousse, K. T. Phuoc, R. Shah, A. Pukhov, E. Lefebvre, V. Malka, S. Kiselev, F. Burgy, J. P. Rousseau, D. Umstadter, and D. Hulin, “Production of a keV x-ray beam from synchrotron radiation in relativistic laser-plasma interaction,” Phys. Rev. Lett. 93 (2004). [CrossRef] [PubMed]

, 7

7. A. Cavalleri, C. Toth, C. W. Siders, J. A. Squier, F. Raksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett. 87 (2001). [CrossRef] [PubMed]

]. The required time resolution is on the order of 100 fs given by the approximate time it takes two atoms to move far enough apart to break a bond, or the periods of the most highly damped motions along structural relaxation coordinates [1

1. J. R. Dwyer, C. T. Hebeisen, R. Ernstorfer, M. Harb, V. B. Deyirmenjian, R. E. Jordan, and R. J. D. Miller, “Femtosecond electron diffraction: ‘making the molecular movie’,” Phil. Trans. Roy. Soc. A 364, 741–778 (2006). [CrossRef]

]. Laser pulses shorter than this time scale are readily available. The technical challenge is making sufficiently intense x-ray or electron pulses on this timescale to secure sufficient signal in a few shots, which is mandated by sample constraints. To obtain the highest time resolution, one must not only be able to produce such pulses but also to characterize their durations and determine their exact timing with respect to the excitation pulse inducing the structural changes [1

1. J. R. Dwyer, C. T. Hebeisen, R. Ernstorfer, M. Harb, V. B. Deyirmenjian, R. E. Jordan, and R. J. D. Miller, “Femtosecond electron diffraction: ‘making the molecular movie’,” Phil. Trans. Roy. Soc. A 364, 741–778 (2006). [CrossRef]

, 3

3. W. E. King, G. H. Campbell, A. Frank, B. Reed, J. F. Schmerge, B. J. Siwick, B. C. Stuart, and P. M. Weber, “Ultrafast electron microscopy in materials science, biology, and chemistry,” J. Appl. Phys 97, 111,101 (2005). [CrossRef]

]. The latter issue is referred to as the t=0 problem. Both the pulse duration and the t=0 position need to be determined within 10–100 fs accuracy.

For x-rays produced by free electron lasers, these technical issues have only recently been overcome [8

8. G. Berden, W. A. Gillespie, S. P. Jamison, E.-A. Knabbe, A. M. MacLeod, A. F. G. van der Meer, P. J. Phillips, H. Schlarb, B. Schmidt, P. Schmüser, and B. Steffen, “Benchmarking of Electro-Optic Monitors for Femtosecond Electron Bunches,” Phys. Rev. Lett. 99 (2007). [CrossRef] [PubMed]

, 9

9. A. L. Cavalieri, D. M. Fritz, S. H. Lee, P. H. Bucksbaum, D. A. Reis, J. Rudati, D. M. Mills, P. H. Fuoss, G. B. Stephenson, C. C. Kao, D. P. Siddons, D. P. Lowney, A. G. MacPhee, D. Weinstein, R.W. Falcone, R. Pahl, J. Als-Nielsen, C. Blome, S. Düsterer, R. Ischebeck, H. Schlarb, H. Schulte-Schrepping, T. Tschentscher, J. Schneider, O. Hignette, F. Sette, K. Sokolowski-Tinten, H. N. Chapman, R.W. Lee, T. N. Hansen, O. Synnergren, J. Larsson, S. Techert, J. Sheppard, J. S. Wark, M. Bergh, C. Caleman, G. Huldt, D. van der Spoel, N. Timneanu, J. Hajdu, R. A. Akre, E. Bong, P. Emma, P. Krejcik, J. Arthur, S. Brennan, K. J. Gaffney, A. M. Lindenberg, K. Luening, and J. B. Hastings, “Clocking femtosecond x-rays,” Phys. Rev. Lett. 94 (2005). [PubMed]

]. By using electro-optic sampling of the relativistic electron beam for the x-ray pulse source, a time resolution of ≈100 fs has been achieved. For the 30–100 kV electron pulses used in electron diffraction, one can in principle use streak cameras or laser ponder-motive scattering to characterize the pulses. However, streak cameras are problematic for this application due to the physical length of the streaking plates needed to measure sub-picosecond pulses [10

10. B. J. Siwick, J. R. Dwyer, R. E. Jordan, and R. J. D. Miller, “Ultrafast electron optics: Propagation dynamics of femtosecond electron packets,” J. Appl. Phys. 92, 1643–1648 (2002). [CrossRef]

]; the duration of those pulses rapidly changes during propagation and hence while passing the streaking plates. The best time resolution for high electron number pulses would be around 1 ps. The t=0 position cannot be identified with streak camera technology at all. We have demonstrated pondermotive scattering with a high intensity laser pulse as a viable option for electron pulse characterization [11

11. C. T. Hebeisen, R. Ernstorfer, M. Harb, T. Dartigalongue, R. E. Jordan, and R. J. D. Miller, “Femtosecond electron pulse characterization using laser ponderomotive scattering,” Opt. Lett. 31, 3517–3519 (2006). [CrossRef] [PubMed]

]. The drawback of this approach is its pulse energy requirement in the 10 mJ range. This requirement defeats one of the major advantages of using electron diffraction; namely that it is a table top experiment. While it is possible to calibrate the electron gun at a major facility and maintain the same conditions for the electron pulse afterwards, each experiment requires different probe conditions that lead to changes in temporal characteristics of the electron pulses and timing. Given the high sensitivity of electron pulses to space charge effects [10

10. B. J. Siwick, J. R. Dwyer, R. E. Jordan, and R. J. D. Miller, “Ultrafast electron optics: Propagation dynamics of femtosecond electron packets,” J. Appl. Phys. 92, 1643–1648 (2002). [CrossRef]

, 12

12. A. M. Michalik and J. E. Sipe, “Analytic model of electron pulse propagation in ultrafast electron diffraction experiments,” J. Appl. Phys. 99 (2006). [CrossRef]

], an in situ method to characterize them is needed. Here we describe a new approach that solves this issue using laser pulse energies that are well within reach for conventional small scale femtosecond lasers and even compact all fibre systems.

The ponderomotive force is proportional to the gradient of the light intensity [13

13. T. W. B. Kibble, “Refraction of electron beams by intense electromagnetic waves,” Phys. Rev. Lett. 16, 1054–1056 (1966). [CrossRef]

]:

F(r,t)=e2λ28π2meε0c3I(r,t),
(1)

where e and me are the charge and mass of an electron, respectively, λ is the wavelength of the laser and I is the laser intensity. In a single propagating laser pulse, as used in our earlier experiments [11

11. C. T. Hebeisen, R. Ernstorfer, M. Harb, T. Dartigalongue, R. E. Jordan, and R. J. D. Miller, “Femtosecond electron pulse characterization using laser ponderomotive scattering,” Opt. Lett. 31, 3517–3519 (2006). [CrossRef] [PubMed]

], the ponderomotive force is due to the gradient of the envelope of the laser pulse, which varies on length scales given by the laser pulse duration longitudinally and the focal spot transversely. In order to reduce the energy required to create a strong scattering signal, we use two counterpropagating laser pulses that overlap at their intersection with the electron beam in space and in time. The use of standing waves of light to scatter electrons was proposed by Kapitza and Dirac in 1933 [14

14. P. L. Kapitza and P. A. M. Dirac, “The reflection of electrons from standing light waves,” P. Camb. Philos. Soc. 29, 297–300 (1933). [CrossRef]

] and has been realized to scatter [15

15. P. H. Bucksbaum, D. W. Schumacher, and M. Bashkansky, “High intensity Kapitza-Dirac Effect,” Phys. Rev. Lett. 61, 1182–1185 (1988). [CrossRef] [PubMed]

] and to diffract electrons [16

16. D. L. Freimund, K. Aflatooni, and H. Batelaan, “Observation of the Kapitza-Dirac effect,” Nature 413, 142–143 (2001). [CrossRef] [PubMed]

] at relatively low energy (30 eV and 380 eV, respectively). Possible applications to short pulse generation have also been discussed [17

17. P. Baum and A. H. Zewail, “Breaking resolution limits in ultrafast electron diffraction and microscopy,” P. Natl. Acad. Sci. USA 103, 16,105–16,110 (2006). [CrossRef]

]. For counterpropagating Gaussian laser pulses propagating in x-direction, the intensity is

I(r,t)=I02exp(ı(ωt+kx)(txc)24wt2)+
exp(ı(ωtkx)(t+xc)24wt2)2exp(y2+z22wf2),
(2)

where I 0 is the peak intensity of each laser pulse, k=2π/λ, ω=2πc/λ, and 22ln2wt and 22ln2wf are the laser pulse duration and the beam waist, respectively. The x-component of the ponderomotive force takes the following form on the x-axis:

Fx(x,y=0,z=0,t)=I0e2λ216π2meε0c3×
x[exp((txc)22wt2)+exp((t+xc)22wt2)+
2exp(t22wt2)exp(x22wt2c2)cos(2kx)].
(3)

The envelope of this force in the yz-plane is the same as for the intensity. The first two terms describe the laser pulses travelling in opposite directions and the last describes the standing wave. Since λwtc the derivative is dominated by the latter contribution.

Fx(x,y=0,z=0,t)
I0e2λ2πmeε0c3exp(t22wt2)exp(x22wt2c2)sin(2kx),
(4)

The setup is shown in Fig. 1. The electron gun has been described elsewhere [1

1. J. R. Dwyer, C. T. Hebeisen, R. Ernstorfer, M. Harb, V. B. Deyirmenjian, R. E. Jordan, and R. J. D. Miller, “Femtosecond electron diffraction: ‘making the molecular movie’,” Phil. Trans. Roy. Soc. A 364, 741–778 (2006). [CrossRef]

]. It has been modified to use the 500 nm, 50 fs output of a non-collinear optical parametric amplifier to drive the electron gun via two-photon photoemission. These pulses are significantly shorter than the initial laser pulse and their wavelength has been tuned close to the threshold above which no photoemission is observed. This minimizes the excess energy of the emitted electrons by allowing only the highest energy electrons to escape, thereby reducing longitudinal as well as transverse spread of the resulting electron pulses.

Fig. 1. (a) Optical setup. The laser pulse is split by a beam splitter (BS). A small part of the beam is used to produce visible light using a non-collinear optical parametric amplifier (NOPA), which, after a delay line, is used to drive the electron gun. The other part of the beam is split again after a focusing lens to form the grating at the focus intersecting the electron beam. One of the beams is sent through a delay line for compensation of the relative delay between the pulses. (b) Schematic view of the experiment geometry. When the laser pulse hits the photocathode, it creates an electron pulse which is accelerated by a DC electric field. The electron pulse is stripped of its outer electrons by a pinhole before it is scattered by the ponderomotive force of the intensity grating created by the two laser pulses.

The two laser pulses used to create the ponderomotive force profile need to overlap in space as well as in time with each other and with the electron pulse to produce a scattering signal. An elliptical pinhole is placed in the electron beam at 45° with respect to the electron and laser beams. Both laser beams are aligned on this pinhole. The temporal overlap between the electron pulse and the laser pulses is determined for each of the two arms by observing electron beam deformations by plasma generation on a metal surface [1

1. J. R. Dwyer, C. T. Hebeisen, R. Ernstorfer, M. Harb, V. B. Deyirmenjian, R. E. Jordan, and R. J. D. Miller, “Femtosecond electron diffraction: ‘making the molecular movie’,” Phil. Trans. Roy. Soc. A 364, 741–778 (2006). [CrossRef]

]. The delay between the pulses is adjusted to compensate the differences.

Images of the electron beam on the detector are shown in Fig. 2. The images taken at different electron pulse-laser pulse delays τ are analysed to give a time trace S(τ) [11

11. C. T. Hebeisen, R. Ernstorfer, M. Harb, T. Dartigalongue, R. E. Jordan, and R. J. D. Miller, “Femtosecond electron pulse characterization using laser ponderomotive scattering,” Opt. Lett. 31, 3517–3519 (2006). [CrossRef] [PubMed]

]:

S(τ)=XDτ(X,Y)dXdY,
(5)

where X and Y are the horizontal and vertical coordinates on the detector screen (origin at electron beam center) and Dτ (X,Y) is the number density of electrons detected in the image at time delay τ. A number of these time traces for different electron numbers per pulse are shown in Fig. 3.

Fig. 2. Detector images (animation, 528 kB) of the electron beam. The counter in the bottom right corner indicates the relative delay between the laser and electron pulses. The black spot in the electron beam is caused by detector damage. Conditions: 10,000 electrons per pulse, 135 µJ laser pulse energy, images integrated over 4000 pulses. [Media 1]

To illustrate that this time trace is a direct cross-correlation of the electron and laser pulses, we assume that the displacement that electrons experience due to the ponderomotive force is negligible over the size of the laser focus and therefore the force acting on an electron can be integrated along a straight line. If this condition is not met, the linearity of the signal with respect to the laser intensity could be compromised. The cumulative displacement along the trajectory would be reduced, leading to saturation and a broader time trace. For the parameters used in this study, the condition is not strictly met, however, experimental verification of the linearity of the signal vs. laser power did not reveal any signs of saturation. Since the distance from the beam crossing point to the detector is much longer than the laser spot size, the deflection of an electron at the detector is

ΔX=TdmeFx(x,y,z,t)dt
(6)

where Td is the propagation time to the detector. Here we assume that the direction of propagation of the electron is parallel to the z-axis. In practice, lateral velocity components are inevitable. Numerical simulations with 10,000 electrons per pulse show that under the present experimental conditions, the average transverse velocity just before the interaction with the grating is about 4×10-4 v where v is the velocity of the electrons in z-direction. The offset caused by this transverse velocity over the width of the grating is not a significant fraction of the grating pitch π/k.

According to Eq. 4 with the lateral envelope of the laser beam, Fx can be written as a product of a constant F 0 and of four functions each of which only depends on one of the variables t, x, y, z:

ft(t)=exp(t22wt2),fx(x)=exp(x22wt2c2)sin(2kx),
fy(y)=exp(y22wf2),fz(z)=exp(z22wf2).
(7)

Equation 5 can be rewritten as the sum of |X| over all electrons in a pulse. If the electron beam on the detector in absence of the grating is small, we can set XX. Using the electron density in the electron pulse at the beam crossover position ρ(r,t)=ρxy(x,y)ρt (t+τ-z/v) and Eq. 6 and Eq. 7, we obtain

S(τ)=F0ft(t)fx(x)fy(y)fz(z)×
ρxy(x,y)ρt(t+τzv)dtdxdydz
fz(z)ft(t)ρt(t+τzν)dzdt.
(8)

S(τ) can therefore be identified as a convolution of the temporal profiles of the electron pulse and the laser pulse and of the transverse spatial profile of the laser pulse as it is crossed by the electron pulse. As opposed to our earlier experiments [11

11. C. T. Hebeisen, R. Ernstorfer, M. Harb, T. Dartigalongue, R. E. Jordan, and R. J. D. Miller, “Femtosecond electron pulse characterization using laser ponderomotive scattering,” Opt. Lett. 31, 3517–3519 (2006). [CrossRef] [PubMed]

], the scattering potential is not moving through the electron beam, thereby eliminating the transverse spatial profile of the electron pulse from the convolution.

Fig. 3. Time traces with Gaussian fits. Vertical offset for clarity. While a Gaussian appears to be a good fit for traces of pulses with relatively few electrons, there are systematic deviations between the data and the fit for pulses with more electrons. The fits have widths of 1005 fs, 757 fs, 546 fs and 404 fs FWHM, respectively.

It is obvious from Fig. 3 that the width of the time trace and hence the electron pulse duration increases with the electron number density. Particularly for pulses containing large numbers of electrons i.e. long electron pulses whose shape dominates the corresponding time trace, the shape of the traces is non-Gaussian. The actual temporal shape of the electron pulse cannot be directly deconvolved from noisy experimental time-traces unless the other contributions to the convolution are small. However, the variance σ 2 ρ of the temporal shape ρt(t) of the electron pulse can be extracted from the experimental trace without prior knowledge of the non-Gaussian pulse shape by

σρ2=σtrace2σt2σf2ν2
(9)

where σ 2 trace, σ 2 t and σ 2 f are the variances of S(τ), ft(t) and fz(z), respectively.

A common measure for the pulse duration is the full width at half maximum with FWHM=22ln2σ for a Gaussian. This conversion does not apply to other pulse shapes but it is a useful value to estimate the effect of the pulse shape on the temporal resolution of a pumpprobe experiment. Therefore, we calculate the electron pulse duration T as T=22ln2σρ . The contributions that need to be deconvolved from the trace are the temporal laser pulse shape (210±10 fs FWHM sech2) and the spatial profile of the laser pulse at the focus in z direction (41±10μm310±80fsFWHM Gaussian for 55 keV electrons). Figure 4 shows the electron pulse duration as a function of the number of electrons per pulse. The sensitivity of the pulse duration to the electron number density clearly demonstrates the importance of this new in-situ measurement as a routine diagnostic tool.

Fig. 4. Electron pulse duration T vs. number of electrons per pulse; General Particle Tracer (GPT) simulations and measurements obtained in the described experiments.

The measured pulse durations are compared to simulations performed with the General Particle Tracer [19

19. S. B. van der Geer and M. J. de Loos, “The General Particle Tracer code,” URL http://www.pulsar.nl/gpt.

] software package. The parameters used in the simulations correspond to the current setup of the electron gun: Electrons are emitted from a gold photocathode with a 50 fs, 500 nm, 200 µm FWHM diameter laser pulse. In order to account for the two-photon process, the effective pulse duration used in the simulations is 35 fs and the diameter is 141 µm. An excess energy distribution of 0.1 eV width is assumed. The electrons are accelerated over a 6 mm gap to 55 keV. The anode is a 150 µm diameter pinhole and the electrons propagate freely for 26mm after that. A 30 µm diameter pinhole strips the electron pulse followed by another 7mm of free propagation before the laser interaction. Note that in our femtosecond electron diffraction experiments [20

20. M. Harb, R. Ernstorfer, T. Dartigalongue, C. T. Hebeisen, R. E. Jordan, and R. J. D. Miller, “Carrier Relaxation and Lattice Heating Dynamics in Silicon Revealed by Femtosecond Electron Diffraction,” J. Phys. Chem. B 110, 25,308–25,313 (2006). [CrossRef]

], the propagation distance to the sample is 9mm shorter than in this setup. This is not a limitation of this pulse characterization technique but was chosen to minimize the complexity of the setup.

The observed electron pulse durations are in good agreement with calculations both with respect to duration and dependence on electron number. The relatively small systematic deviation may be caused by imperfections of the experiment, e.g. pedestals in the temporal profile of the laser pulse. Also, the finite size of the undisturbed electron beam on the detector (just under 1/4 the size of the scattered electron distribution) leads to a slight broadening of the time traces. Shorter, cleaned up laser pulses, tighter focusing of the laser as well as focusing of the electron beam on the detector will shorten the system response of the pulse characterization and reduce errors in the pulse shapes for the deconvolution. The intrinsic system response is determined mostly by the electron transit time across the focus (310 fs presently). A 10 µm focus and 20 fs laser pulse would give a system response of 80 fs and 10 fs accuracy to the t=0 position with pulse energies of 10 µJ.

In conclusion, we have demonstrated a method for the full characterization of femtosecond electron pulses. Using grating enhanced pondermotive scattering, the scattered electrons are imaged to give direct visualization of the laser-electron pulse interaction with modest laser input power. This new approach permits routine characterization of both duration and t=0 position of electron pulses for pump-probe experiments. This information is critical to attaining the highest time resolution possible in the use of femtosecond electron pulses for diffraction and imaging applications in atomically resolved structural dynamics [1

1. J. R. Dwyer, C. T. Hebeisen, R. Ernstorfer, M. Harb, V. B. Deyirmenjian, R. E. Jordan, and R. J. D. Miller, “Femtosecond electron diffraction: ‘making the molecular movie’,” Phil. Trans. Roy. Soc. A 364, 741–778 (2006). [CrossRef]

]. Equally important, this method enables in-situ measurements directly at the sample position. The measurements largely confirm n-body simulations performed with the General Particle Tracer n-body code. This illustrates that the many body effects and assumptions on the initial electron distribution are taken into account reasonably well, and can be used with some confidence in advancing electron source brightness.

Acknowledgments

Funding for this projectwas provided by the Natural Science and Engineering Research Council of Canada.

References and links

1.

J. R. Dwyer, C. T. Hebeisen, R. Ernstorfer, M. Harb, V. B. Deyirmenjian, R. E. Jordan, and R. J. D. Miller, “Femtosecond electron diffraction: ‘making the molecular movie’,” Phil. Trans. Roy. Soc. A 364, 741–778 (2006). [CrossRef]

2.

A. H. Zewail, “4D ultrafast electron diffraction, crystallography, and microscopy,” Annu. Rev. Phys. Chem. 57, 65–103 (2006). [CrossRef] [PubMed]

3.

W. E. King, G. H. Campbell, A. Frank, B. Reed, J. F. Schmerge, B. J. Siwick, B. C. Stuart, and P. M. Weber, “Ultrafast electron microscopy in materials science, biology, and chemistry,” J. Appl. Phys 97, 111,101 (2005). [CrossRef]

4.

B. J. Siwick, J. R. Dwyer, R. E. Jordan, and R. J. D. Miller, “An atomic-level view of melting using femtosecond electron diffraction,” Science 302, 1382–1385 (2003). [CrossRef] [PubMed]

5.

A. M. Lindenberg, J. Larsson, K. Sokolowski-Tinten, K. J. Gaffney, C. Blome, O. Synnergren, J. Sheppard, C. Caleman, A. G. MacPhee, D. Weinstein, D. P. Lowney, T. K. Allison, T. Matthews, R. W. Falcone, A. L. Cavalieri, D. M. Fritz, S. H. Lee, P. H. Bucksbaum, D. A. Reis, J. Rudati, P. H. Fuoss, C. C. Kao, D. P. Siddons, R. Pahl, J. Als-Nielsen, S. Duesterer, R. Ischebeck, H. Schlarb, H. Schulte-Schrepping, T. Tschentscher, J. Schneider, D. von der Linde, O. Hignette, F. Sette, H. N. Chapman, R. W. Lee, T. N. Hansen, S. Techert, J. S. Wark, M. Bergh, G. Huldt, D. van der Spoel, N. Timneanu, J. Hajdu, R. A. Akre, E. Bong, P. Krejcik, J. Arthur, S. Brennan, K. Luening, and J. B. Hastings, “Atomic-scale visualization of inertial dynamics,” Science 308, 392–395 (2005). [CrossRef] [PubMed]

6.

A. Rousse, K. T. Phuoc, R. Shah, A. Pukhov, E. Lefebvre, V. Malka, S. Kiselev, F. Burgy, J. P. Rousseau, D. Umstadter, and D. Hulin, “Production of a keV x-ray beam from synchrotron radiation in relativistic laser-plasma interaction,” Phys. Rev. Lett. 93 (2004). [CrossRef] [PubMed]

7.

A. Cavalleri, C. Toth, C. W. Siders, J. A. Squier, F. Raksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett. 87 (2001). [CrossRef] [PubMed]

8.

G. Berden, W. A. Gillespie, S. P. Jamison, E.-A. Knabbe, A. M. MacLeod, A. F. G. van der Meer, P. J. Phillips, H. Schlarb, B. Schmidt, P. Schmüser, and B. Steffen, “Benchmarking of Electro-Optic Monitors for Femtosecond Electron Bunches,” Phys. Rev. Lett. 99 (2007). [CrossRef] [PubMed]

9.

A. L. Cavalieri, D. M. Fritz, S. H. Lee, P. H. Bucksbaum, D. A. Reis, J. Rudati, D. M. Mills, P. H. Fuoss, G. B. Stephenson, C. C. Kao, D. P. Siddons, D. P. Lowney, A. G. MacPhee, D. Weinstein, R.W. Falcone, R. Pahl, J. Als-Nielsen, C. Blome, S. Düsterer, R. Ischebeck, H. Schlarb, H. Schulte-Schrepping, T. Tschentscher, J. Schneider, O. Hignette, F. Sette, K. Sokolowski-Tinten, H. N. Chapman, R.W. Lee, T. N. Hansen, O. Synnergren, J. Larsson, S. Techert, J. Sheppard, J. S. Wark, M. Bergh, C. Caleman, G. Huldt, D. van der Spoel, N. Timneanu, J. Hajdu, R. A. Akre, E. Bong, P. Emma, P. Krejcik, J. Arthur, S. Brennan, K. J. Gaffney, A. M. Lindenberg, K. Luening, and J. B. Hastings, “Clocking femtosecond x-rays,” Phys. Rev. Lett. 94 (2005). [PubMed]

10.

B. J. Siwick, J. R. Dwyer, R. E. Jordan, and R. J. D. Miller, “Ultrafast electron optics: Propagation dynamics of femtosecond electron packets,” J. Appl. Phys. 92, 1643–1648 (2002). [CrossRef]

11.

C. T. Hebeisen, R. Ernstorfer, M. Harb, T. Dartigalongue, R. E. Jordan, and R. J. D. Miller, “Femtosecond electron pulse characterization using laser ponderomotive scattering,” Opt. Lett. 31, 3517–3519 (2006). [CrossRef] [PubMed]

12.

A. M. Michalik and J. E. Sipe, “Analytic model of electron pulse propagation in ultrafast electron diffraction experiments,” J. Appl. Phys. 99 (2006). [CrossRef]

13.

T. W. B. Kibble, “Refraction of electron beams by intense electromagnetic waves,” Phys. Rev. Lett. 16, 1054–1056 (1966). [CrossRef]

14.

P. L. Kapitza and P. A. M. Dirac, “The reflection of electrons from standing light waves,” P. Camb. Philos. Soc. 29, 297–300 (1933). [CrossRef]

15.

P. H. Bucksbaum, D. W. Schumacher, and M. Bashkansky, “High intensity Kapitza-Dirac Effect,” Phys. Rev. Lett. 61, 1182–1185 (1988). [CrossRef] [PubMed]

16.

D. L. Freimund, K. Aflatooni, and H. Batelaan, “Observation of the Kapitza-Dirac effect,” Nature 413, 142–143 (2001). [CrossRef] [PubMed]

17.

P. Baum and A. H. Zewail, “Breaking resolution limits in ultrafast electron diffraction and microscopy,” P. Natl. Acad. Sci. USA 103, 16,105–16,110 (2006). [CrossRef]

18.

V. B. Deyirmenjian, Department of Physics, University of Toronto, 60 St. George St., Toronto, ON, M5S 1A7 Canada, J. E. Sipe and R. J. D. Miller are preparing a manuscript to be called “A new source for ultrafast electron diffraction experiments.”

19.

S. B. van der Geer and M. J. de Loos, “The General Particle Tracer code,” URL http://www.pulsar.nl/gpt.

20.

M. Harb, R. Ernstorfer, T. Dartigalongue, C. T. Hebeisen, R. E. Jordan, and R. J. D. Miller, “Carrier Relaxation and Lattice Heating Dynamics in Silicon Revealed by Femtosecond Electron Diffraction,” J. Phys. Chem. B 110, 25,308–25,313 (2006). [CrossRef]

OCIS Codes
(320.2250) Ultrafast optics : Femtosecond phenomena
(320.5550) Ultrafast optics : Pulses

ToC Category:
Ultrafast Optics

History
Original Manuscript: January 9, 2008
Revised Manuscript: February 22, 2008
Manuscript Accepted: February 23, 2008
Published: February 27, 2008

Citation
Christoph T. Hebeisen, German Sciaini, Maher Harb, Ralph Ernstorfer, Thibault Dartigalongue, Sergei G. Kruglik, and R. J. D. Miller, "Grating enhanced ponderomotive scattering for visualization and full characterization of femtosecond electron pulses," Opt. Express 16, 3334-3341 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-5-3334


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References

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  7. A. Cavalleri, C. Toth, C. W. Siders, J. A. Squier, F. Raksi, P. Forget, and J. C. Kieffer, "Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition," Phys. Rev. Lett. 87 (2001). [CrossRef] [PubMed]
  8. G. Berden, W. A. Gillespie, S. P. Jamison, E.-A. Knabbe, A. M. MacLeod, A. F. G. van der Meer, P. J. Phillips, H. Schlarb, B. Schmidt, P. Schmuser, and B. Steffen, "Benchmarking of Electro-Optic Monitors for Femtosecond Electron Bunches," Phys. Rev. Lett. 99 (2007). [CrossRef] [PubMed]
  9. A. L. Cavalieri, D. M. Fritz, S. H. Lee, P. H. Bucksbaum, D. A. Reis, J. Rudati, D. M. Mills, P. H. Fuoss, G. B. Stephenson, C. C. Kao, D. P. Siddons, D. P. Lowney, A. G. MacPhee, D. Weinstein, R.W. Falcone, R. Pahl, J. Als-Nielsen, C. Blome, S. Dusterer, R. Ischebeck, H. Schlarb, H. Schulte-Schrepping, T. Tschentscher, J. Schneider, O. Hignette, F. Sette, K. Sokolowski-Tinten, H. N. Chapman, R.W. Lee, T. N. Hansen, O. Synnergren, J. Larsson, S. Techert, J. Sheppard, J. S. Wark, M. Bergh, C. Caleman, G. Huldt, D. van der Spoel, N. Timneanu, J. Hajdu, R. A. Akre, E. Bong, P. Emma, P. Krejcik, J. Arthur, S. Brennan, K. J. Gaffney, A. M. Lindenberg, K. Luening, and J. B. Hastings, "Clocking femtosecond x-rays," Phys. Rev. Lett. 94 (2005). [PubMed]
  10. B. J. Siwick, J. R. Dwyer, R. E. Jordan, and R. J. D. Miller, "Ultrafast electron optics: Propagation dynamics of femtosecond electron packets," J. Appl. Phys. 92, 1643-1648 (2002). [CrossRef]
  11. C. T. Hebeisen, R. Ernstorfer, M. Harb, T. Dartigalongue, R. E. Jordan, and R. J. D. Miller, "Femtosecond electron pulse characterization using laser ponderomotive scattering," Opt. Lett. 31, 3517-3519 (2006). [CrossRef] [PubMed]
  12. A. M. Michalik and J. E. Sipe, "Analytic model of electron pulse propagation in ultrafast electron diffraction experiments," J. Appl. Phys. 99 (2006). [CrossRef]
  13. T. W. B. Kibble, "Refraction of electron beams by intense electromagnetic waves," Phys. Rev. Lett. 16, 1054-1056 (1966). [CrossRef]
  14. P. L. Kapitza and P. A. M. Dirac, "The reflection of electrons from standing light waves," P. Camb. Philos. Soc. 29, 297-300 (1933). [CrossRef]
  15. P. H. Bucksbaum, D. W. Schumacher, and M. Bashkansky, "High intensity Kapitza-Dirac Effect," Phys. Rev. Lett. 61, 1182-1185 (1988). [CrossRef] [PubMed]
  16. D. L. Freimund, K. Aflatooni, and H. Batelaan, "Observation of the Kapitza-Dirac effect," Nature 413, 142-143 (2001). [CrossRef] [PubMed]
  17. P. Baum and A. H. Zewail, "Breaking resolution limits in ultrafast electron diffraction and microscopy," P. Natl. Acad. Sci. USA 103, 16,105-16,110 (2006). [CrossRef]
  18. V. B. Deyirmenjian, Department of Physics, University of Toronto, 60 St. George St., Toronto, ON, M5S 1A7 Canada, J. E. Sipe and R. J. D. Miller are preparing a manuscript to be called "A new source for ultrafast electron diffraction experiments."
  19. S. B. van der Geer and M. J. de Loos, "The General Particle Tracer code," URL http://www.pulsar.nl/gpt.
  20. M. Harb, R. Ernstorfer, T. Dartigalongue, C. T. Hebeisen, R. E. Jordan, and R. J. D. Miller, "Carrier Relaxation and Lattice Heating Dynamics in Silicon Revealed by Femtosecond Electron Diffraction," J. Phys. Chem. B 110, 25,308-25,313 (2006). [CrossRef]

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