Abstract

We present a new approach (demonstrated experimentally and through modeling) to characterize the spectral envelope of a terahertz (THz) pulse in a single shot. The coherent THz pulse is produced by a femtosecond electron bunch and contains information on the bunch duration. The technique, involving a single low-power laser probe pulse, is an extension of the conventional spectral encoding method (limited in time resolution to hundreds of femtoseconds) into a regime only limited in resolution by the laser pulse length (tens of femtoseconds). While only the bunch duration is retrieved (and not the exact charge profile), such a measurement provides a useful and critical parameter for optimization of the electron accelerator.

© 2008 Optical Society of America

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  1. W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
    [CrossRef] [PubMed]
  2. J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, Phys. Rev. Lett. 96, 014801 (2006).
    [CrossRef] [PubMed]
  3. G. Gallot and D. Grischkowsky, J. Opt. Soc. Am. B 16, 1204 (1999).
    [CrossRef]
  4. S. P. Jamison, A. M. MacLeod, G. Berden, D. A. Jaroszynski, and W. A. Gillespie, Opt. Lett. 31, 1753 (2006).
    [CrossRef] [PubMed]
  5. J. Shan, A. S. Weling, E. Knoesel, L. Bartels, M. Bonn, A. Nahata, G. A. Reider, and T. F. Heinz, Opt. Lett. 25, 426 (2000).
    [CrossRef]
  6. S. P. Jamison, J. Shen, A. M. MacLeod, W. A. Gillespie, and D. A. Jaroszynski, Opt. Lett. 28, 1710 (2003).
    [CrossRef] [PubMed]
  7. J. van Tilborg, C. B. Schroeder, Cs. Tóth, C. G. R. Geddes, E. Esarey, and W. P. Leemans, Opt. Lett. 32, 313 (2007).
    [CrossRef] [PubMed]
  8. K. Y. Kim, B. Yellampalle, A. J. Taylor, G. Rodriguez, and J. H. Glownia, Opt. Lett. 32, 1968 (2007).
    [CrossRef] [PubMed]
  9. F. G. Sun, Z. Jiang, and X.-C. Zhang, Appl. Phys. Lett. 73, 2233 (1998).
    [CrossRef]
  10. Z. Jiang and X.-C. Zhang, Appl. Phys. Lett. 72, 1945 (1998).
    [CrossRef]
  11. B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, Appl. Phys. Lett. 87, 211109 (2005).
    [CrossRef]
  12. J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, E. Esarey, and W. P. Leemans, Phys. Plasmas 13, 056704 (2006).
    [CrossRef]
  13. Z. Jiang, F. G. Sun, Q. Chen, and X.-C. Zhang, Appl. Phys. Lett. 74, 1191 (1999).
    [CrossRef]
  14. C. B. Schroeder, E. Esarey, J. van Tilborg, and W. P. Leemans, Phys. Rev. E 69, 016501 (2004).
    [CrossRef]

2007 (2)

2006 (3)

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, Phys. Rev. Lett. 96, 014801 (2006).
[CrossRef] [PubMed]

S. P. Jamison, A. M. MacLeod, G. Berden, D. A. Jaroszynski, and W. A. Gillespie, Opt. Lett. 31, 1753 (2006).
[CrossRef] [PubMed]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, E. Esarey, and W. P. Leemans, Phys. Plasmas 13, 056704 (2006).
[CrossRef]

2005 (1)

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, Appl. Phys. Lett. 87, 211109 (2005).
[CrossRef]

2004 (1)

C. B. Schroeder, E. Esarey, J. van Tilborg, and W. P. Leemans, Phys. Rev. E 69, 016501 (2004).
[CrossRef]

2003 (2)

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

S. P. Jamison, J. Shen, A. M. MacLeod, W. A. Gillespie, and D. A. Jaroszynski, Opt. Lett. 28, 1710 (2003).
[CrossRef] [PubMed]

2000 (1)

1999 (2)

G. Gallot and D. Grischkowsky, J. Opt. Soc. Am. B 16, 1204 (1999).
[CrossRef]

Z. Jiang, F. G. Sun, Q. Chen, and X.-C. Zhang, Appl. Phys. Lett. 74, 1191 (1999).
[CrossRef]

1998 (2)

F. G. Sun, Z. Jiang, and X.-C. Zhang, Appl. Phys. Lett. 73, 2233 (1998).
[CrossRef]

Z. Jiang and X.-C. Zhang, Appl. Phys. Lett. 72, 1945 (1998).
[CrossRef]

Auerbach, D.

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

Bartels, L.

Berden, G.

Bonn, M.

Byrd, J.

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

Carnahan, M. A.

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

Chen, Q.

Z. Jiang, F. G. Sun, Q. Chen, and X.-C. Zhang, Appl. Phys. Lett. 74, 1191 (1999).
[CrossRef]

Esarey, E.

J. van Tilborg, C. B. Schroeder, Cs. Tóth, C. G. R. Geddes, E. Esarey, and W. P. Leemans, Opt. Lett. 32, 313 (2007).
[CrossRef] [PubMed]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, Phys. Rev. Lett. 96, 014801 (2006).
[CrossRef] [PubMed]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, E. Esarey, and W. P. Leemans, Phys. Plasmas 13, 056704 (2006).
[CrossRef]

C. B. Schroeder, E. Esarey, J. van Tilborg, and W. P. Leemans, Phys. Rev. E 69, 016501 (2004).
[CrossRef]

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

Faure, J.

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

Filip, C. V.

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, Phys. Rev. Lett. 96, 014801 (2006).
[CrossRef] [PubMed]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, E. Esarey, and W. P. Leemans, Phys. Plasmas 13, 056704 (2006).
[CrossRef]

Fubiani, G.

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, E. Esarey, and W. P. Leemans, Phys. Plasmas 13, 056704 (2006).
[CrossRef]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, Phys. Rev. Lett. 96, 014801 (2006).
[CrossRef] [PubMed]

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

Gallot, G.

Geddes, C. G. R.

J. van Tilborg, C. B. Schroeder, Cs. Tóth, C. G. R. Geddes, E. Esarey, and W. P. Leemans, Opt. Lett. 32, 313 (2007).
[CrossRef] [PubMed]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, Phys. Rev. Lett. 96, 014801 (2006).
[CrossRef] [PubMed]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, E. Esarey, and W. P. Leemans, Phys. Plasmas 13, 056704 (2006).
[CrossRef]

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

Gillespie, W. A.

Glownia, J. H.

K. Y. Kim, B. Yellampalle, A. J. Taylor, G. Rodriguez, and J. H. Glownia, Opt. Lett. 32, 1968 (2007).
[CrossRef] [PubMed]

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, Appl. Phys. Lett. 87, 211109 (2005).
[CrossRef]

Grischkowsky, D.

Heinz, T. F.

Huber, R.

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, Phys. Rev. Lett. 96, 014801 (2006).
[CrossRef] [PubMed]

Jamison, S. P.

Jaroszynski, D. A.

Jiang, Z.

Z. Jiang, F. G. Sun, Q. Chen, and X.-C. Zhang, Appl. Phys. Lett. 74, 1191 (1999).
[CrossRef]

F. G. Sun, Z. Jiang, and X.-C. Zhang, Appl. Phys. Lett. 73, 2233 (1998).
[CrossRef]

Z. Jiang and X.-C. Zhang, Appl. Phys. Lett. 72, 1945 (1998).
[CrossRef]

Kaindl, R. A.

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, Phys. Rev. Lett. 96, 014801 (2006).
[CrossRef] [PubMed]

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

Kim, K. Y.

K. Y. Kim, B. Yellampalle, A. J. Taylor, G. Rodriguez, and J. H. Glownia, Opt. Lett. 32, 1968 (2007).
[CrossRef] [PubMed]

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, Appl. Phys. Lett. 87, 211109 (2005).
[CrossRef]

Knoesel, E.

Leemans, W. P.

J. van Tilborg, C. B. Schroeder, Cs. Tóth, C. G. R. Geddes, E. Esarey, and W. P. Leemans, Opt. Lett. 32, 313 (2007).
[CrossRef] [PubMed]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, Phys. Rev. Lett. 96, 014801 (2006).
[CrossRef] [PubMed]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, E. Esarey, and W. P. Leemans, Phys. Plasmas 13, 056704 (2006).
[CrossRef]

C. B. Schroeder, E. Esarey, J. van Tilborg, and W. P. Leemans, Phys. Rev. E 69, 016501 (2004).
[CrossRef]

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

MacLeod, A. M.

Marcelis, B.

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

Martin, M. C.

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

Nahata, A.

Reider, G. A.

Rodriguez, G.

K. Y. Kim, B. Yellampalle, A. J. Taylor, G. Rodriguez, and J. H. Glownia, Opt. Lett. 32, 1968 (2007).
[CrossRef] [PubMed]

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, Appl. Phys. Lett. 87, 211109 (2005).
[CrossRef]

Schroeder, C. B.

J. van Tilborg, C. B. Schroeder, Cs. Tóth, C. G. R. Geddes, E. Esarey, and W. P. Leemans, Opt. Lett. 32, 313 (2007).
[CrossRef] [PubMed]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, E. Esarey, and W. P. Leemans, Phys. Plasmas 13, 056704 (2006).
[CrossRef]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, Phys. Rev. Lett. 96, 014801 (2006).
[CrossRef] [PubMed]

C. B. Schroeder, E. Esarey, J. van Tilborg, and W. P. Leemans, Phys. Rev. E 69, 016501 (2004).
[CrossRef]

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

Shan, J.

Shen, J.

Sun, F. G.

Z. Jiang, F. G. Sun, Q. Chen, and X.-C. Zhang, Appl. Phys. Lett. 74, 1191 (1999).
[CrossRef]

F. G. Sun, Z. Jiang, and X.-C. Zhang, Appl. Phys. Lett. 73, 2233 (1998).
[CrossRef]

Taylor, A. J.

K. Y. Kim, B. Yellampalle, A. J. Taylor, G. Rodriguez, and J. H. Glownia, Opt. Lett. 32, 1968 (2007).
[CrossRef] [PubMed]

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, Appl. Phys. Lett. 87, 211109 (2005).
[CrossRef]

Tóth, Cs.

J. van Tilborg, C. B. Schroeder, Cs. Tóth, C. G. R. Geddes, E. Esarey, and W. P. Leemans, Opt. Lett. 32, 313 (2007).
[CrossRef] [PubMed]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, E. Esarey, and W. P. Leemans, Phys. Plasmas 13, 056704 (2006).
[CrossRef]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, Phys. Rev. Lett. 96, 014801 (2006).
[CrossRef] [PubMed]

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

van Tilborg, J.

J. van Tilborg, C. B. Schroeder, Cs. Tóth, C. G. R. Geddes, E. Esarey, and W. P. Leemans, Opt. Lett. 32, 313 (2007).
[CrossRef] [PubMed]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, E. Esarey, and W. P. Leemans, Phys. Plasmas 13, 056704 (2006).
[CrossRef]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, Phys. Rev. Lett. 96, 014801 (2006).
[CrossRef] [PubMed]

C. B. Schroeder, E. Esarey, J. van Tilborg, and W. P. Leemans, Phys. Rev. E 69, 016501 (2004).
[CrossRef]

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

Weling, A. S.

Yellampalle, B.

K. Y. Kim, B. Yellampalle, A. J. Taylor, G. Rodriguez, and J. H. Glownia, Opt. Lett. 32, 1968 (2007).
[CrossRef] [PubMed]

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, Appl. Phys. Lett. 87, 211109 (2005).
[CrossRef]

Zhang, X.-C.

Z. Jiang, F. G. Sun, Q. Chen, and X.-C. Zhang, Appl. Phys. Lett. 74, 1191 (1999).
[CrossRef]

F. G. Sun, Z. Jiang, and X.-C. Zhang, Appl. Phys. Lett. 73, 2233 (1998).
[CrossRef]

Z. Jiang and X.-C. Zhang, Appl. Phys. Lett. 72, 1945 (1998).
[CrossRef]

Appl. Phys. Lett. (4)

F. G. Sun, Z. Jiang, and X.-C. Zhang, Appl. Phys. Lett. 73, 2233 (1998).
[CrossRef]

Z. Jiang and X.-C. Zhang, Appl. Phys. Lett. 72, 1945 (1998).
[CrossRef]

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, Appl. Phys. Lett. 87, 211109 (2005).
[CrossRef]

Z. Jiang, F. G. Sun, Q. Chen, and X.-C. Zhang, Appl. Phys. Lett. 74, 1191 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (5)

Phys. Plasmas (1)

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, E. Esarey, and W. P. Leemans, Phys. Plasmas 13, 056704 (2006).
[CrossRef]

Phys. Rev. E (1)

C. B. Schroeder, E. Esarey, J. van Tilborg, and W. P. Leemans, Phys. Rev. E 69, 016501 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802 (2003).
[CrossRef] [PubMed]

J. van Tilborg, C. B. Schroeder, C. V. Filip, Cs. Tóth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, Phys. Rev. Lett. 96, 014801 (2006).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Few-cycle THz pulse E THz ( t ) is emitted as LWFA-produced electron bunches exit the plasma–vacuum boundary. The THz field induces birefringence in the EO crystal, which is probed by a chirped laser pulse E L ( t ) . The modulated laser spectrum I m ( λ ) = E m ( λ ) 2 contains information of the THz pulse.

Fig. 2
Fig. 2

(a) Modeled spectral interferograms I m , norm ( λ ) for various parameters for τ FL , δ, and b. Through the wavelength-to-time parameter substitution λ t * in I m , norm ( λ ) the function I m , inst ( t * ) is obtained, with its Fourier transformation I m , inst ( ν * ) plotted in (b). Note that the envelopes of the three curves in (b) match the original THz spectrum Γ THz ( ν ) (black dashed curve).

Fig. 3
Fig. 3

Experimentally obtained modulated laser spectra I m ( λ ) are normalized [yielding I m , norm ( λ ) ] and plotted in (b) and (d). After the coordinate substitution λ t * [yielding I m , inst ( t * ) ], the Fourier-transformed curves I m , inst ( ν * ) are plotted in (a) and (c). Also displayed in (a) and (c) as the black dashed curves are the THz spectra Γ THz ( ν ) , based on coherent emission from a 50 fs (rms) electron bunch. Modeled curves for a 30 and 70 fs bunch are also shown in (c) to highlight the optimum fit for a 50 fs bunch.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

E L ( t ) = exp [ ( 1 ι b 2 ) t 2 2 τ FL 2 ( 1 + b 2 4 ) ] exp [ ι ω 0 t ] ,
ω inst ( t ) = ω 0 + b 2 τ FL 2 ( 1 + b 2 4 ) t .
E m ( t ) = 1 2 E L ( t ) [ cos δ cos ξ + ι sin δ sin ξ + cos δ sin ξ e ı Γ THz ( t ) + ι sin δ cos ξ e ı Γ THz ( t ) ] ,
I m ( t ) = E m ( t ) 2 = E L ( t ) 2 [ 1 + sin Γ THz ( t ) ] 2 .

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