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; R. J. Dwayne Miller

doi:10.1364/OE.16.003334

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

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

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Christoph T. Hebeisen, German Sciaini, Maher Harb, Ralph Ernstorfer, Thibault Dartigalongue, Sergei G. Kruglik, and R. J. Dwayne Miller, "Grating enhanced ponderomotive scattering for visualization and full characterization of femtosecond electron pulses," Opt. Express 16, 3334-3341 (2008)

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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.

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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]
A. H. Zewail, “4D ultrafast electron diffraction, crystallography, and microscopy,” Annu. Rev. Phys. Chem. 57, 65–103 (2006).
[Crossref] [PubMed]
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]
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]
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]
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]
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]
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]
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]
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]
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]
A. M. Michalik and J. E. Sipe, “Analytic model of electron pulse propagation in ultrafast electron diffraction experiments,” J. Appl. Phys. 99 (2006).
[Crossref]
T. W. B. Kibble, “Refraction of electron beams by intense electromagnetic waves,” Phys. Rev. Lett. 16, 1054–1056 (1966).
[Crossref]
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]
P. H. Bucksbaum, D. W. Schumacher, and M. Bashkansky, “High intensity Kapitza-Dirac Effect,” Phys. Rev. Lett. 61, 1182–1185 (1988).
[Crossref] [PubMed]
D. L. Freimund, K. Aflatooni, and H. Batelaan, “Observation of the Kapitza-Dirac effect,” Nature 413, 142–143 (2001).
[Crossref] [PubMed]
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]
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.”
S. B. van der Geer and M. J. de Loos, “The General Particle Tracer code,” URL http://www.pulsar.nl/gpt.
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]

2007 (1)

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]

2006 (6)

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]

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

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]

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

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]

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]

2005 (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]

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]

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]

2004 (1)

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]

2003 (1)

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]

2002 (1)

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]

2001 (2)

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]

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

1988 (1)

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

1966 (1)

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

1933 (1)

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]

Aflatooni, K.

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

Akre, R. A.

Allison, T. K.

Als-Nielsen, J.

Arthur, J.

Bashkansky, M.

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

Batelaan, H.

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

Baum, P.

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]

Berden, G.

Bergh, M.

Blome, C.

Bong, E.

Brennan, S.

Bucksbaum, P. H.

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

Burgy, F.

Caleman, C.

Campbell, G. H.

Cavalieri, A. L.

Cavalleri, A.

Chapman, H. N.

Dartigalongue, T.

de Loos, M. J.

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

Deyirmenjian, V. B.

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.”

Dirac, P. A. M.

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]

Duesterer, S.

Düsterer, S.

Dwyer, J. R.

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]

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]

Emma, P.

Ernstorfer, R.

Falcone, R. W.

Falcone, R.W.

Forget, P.

Frank, A.

Freimund, D. L.

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

Fritz, D. M.

Fuoss, P. H.

Gaffney, K. J.

Gillespie, W. A.

Hajdu, J.

Hansen, T. N.

Harb, M.

Hastings, J. B.

Hebeisen, C. T.

Hignette, O.

Huldt, G.

Hulin, D.

Ischebeck, R.

Jamison, S. P.

Jordan, R. E.

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]

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]

Kao, C. C.

Kapitza, P. L.

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]

Kibble, T. W. B.

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

Kieffer, J. C.

King, W. E.

Kiselev, S.

Knabbe, E.-A.

Krejcik, P.

Larsson, J.

Lee, R. W.

Lee, R.W.

Lee, S. H.

Lefebvre, E.

Lindenberg, A. M.

Lowney, D. P.

Luening, K.

MacLeod, A. M.

MacPhee, A. G.

Malka, V.

Matthews, T.

Michalik, A. M.

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

Miller, R. J. D.

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]

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]

Mills, D. M.

Pahl, R.

Phillips, P. J.

Phuoc, K. T.

Pukhov, A.

Raksi, F.

Reed, B.

Reis, D. A.

Rousse, A.

Rousseau, J. P.

Rudati, J.

Schlarb, H.

Schmerge, J. F.

Schmidt, B.

Schmüser, P.

Schneider, J.

Schulte-Schrepping, H.

Schumacher, D. W.

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

Sette, F.

Shah, R.

Sheppard, J.

Siddons, D. P.

Siders, C. W.

Sipe, J. E.

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

Siwick, B. J.

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]

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]

Sokolowski-Tinten, K.

Squier, J. A.

Steffen, B.

Stephenson, G. B.

Stuart, B. C.

Synnergren, O.

Techert, S.

Timneanu, N.

Toth, C.

Tschentscher, T.

Umstadter, D.

van der Geer, S. B.

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

van der Meer, A. F. G.

van der Spoel, D.

von der Linde, D.

Wark, J. S.

Weber, P. M.

Weinstein, D.

Zewail, A. H.

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

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]

Annu. Rev. Phys. Chem. (1)

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

J. Appl. Phys (1)

J. Appl. Phys. (2)

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]

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

J. Phys. Chem. B (1)

Nature (1)

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

Opt. Lett. (1)

P. Camb. Philos. Soc. (1)

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]

P. Natl. Acad. Sci. USA (1)

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]

Phil. Trans. Roy. Soc. A (1)

Phys. Rev. Lett. (6)

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

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

Science (2)

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]

Other (2)

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

Supplementary Material (1)

» Media 1: AVI (3540 KB)

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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.

Download Full Size | PPT Slide | PDF

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]

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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.

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Fig. 4.

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

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Equations (16)

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F (r, t) = - \frac{e^{2} λ^{2}}{8 π^{2} m_{e} ε_{0} c^{3}} \nabla I (r, t),

I (r, t) = \frac{I_{0}}{2} ∣ \exp (ı (- ω t + k x) - \frac{{(t - \frac{x}{c})}^{2}}{4 w_{t}^{2}}) +

{\exp (ı (- ω t - k x) - \frac{{(t + \frac{x}{c})}^{2}}{4 w_{t}^{2}}) ∣}^{2} \exp (- \frac{y^{2} + z^{2}}{2 w_{f}^{2}}),

F_{x} (x, y = 0, z = 0, t) = - \frac{I_{0} e^{2} λ^{2}}{16 π^{2} m_{e} ε_{0} c^{3}} \times

\frac{\partial}{\partial x} [\exp (- \frac{{(t - \frac{x}{c})}^{2}}{2 w_{t}^{2}}) + \exp (- \frac{{(t + \frac{x}{c})}^{2}}{2 w_{t}^{2}}) +

2 \exp (- \frac{t^{2}}{2 w_{t}^{2}}) \exp (- \frac{x^{2}}{2 w_{t}^{2} c^{2}}) \cos (2 k x)] .

F_{x} (x, y = 0, z = 0, t) \approx

\frac{I_{0} e^{2} λ}{2 π m_{e} ε_{0} c^{3}} \exp (- \frac{t^{2}}{2 w_{t}^{2}}) \exp (- \frac{x^{2}}{2 w_{t}^{2} c^{2}}) \sin (2 kx),

S (τ) = \int ∣ X ∣ D_{τ} (X, Y) d X d Y,

Δ X = \frac{T_{d}}{m_{e}} \int F_{x} (x, y, z, t) d t

f_{t} (t) = \exp (- \frac{t^{2}}{2 w_{t}^{2}}), f_{x} (x) = \exp (- \frac{x^{2}}{2 w_{t}^{2} c^{2}}) \sin (2 k x),

f_{y} (y) = \exp (- \frac{y^{2}}{2 w_{f}^{2}}), f_{z} (z) = \exp (- \frac{z^{2}}{2 w_{f}^{2}}) .

S (τ) = \int F_{0} f_{t} (t) ∣ f_{x} (x) ∣ f_{y} (y) f_{z} (z) \times

ρ_{xy} (x, y) ρ_{t} (t + τ - \frac{z}{v}) d t d x d y d z

\propto \int f_{z} (z) f_{t} (t) ρ_{t} (t + τ - \frac{z}{ν}) d z d t .

σ_{ρ}^{2} = σ_{trace}^{2} - σ_{t}^{2} - \frac{σ_{f}^{2}}{ν^{2}}