Abstract

By revisiting the theory of terahertz pulse detection schemes employing a chirped optical probe pulse, we address and resolve a conflict that exists in literature. In this report, we show that the equation governing the detected field depends upon the experimental scheme, and in the limit of small bandwidth, that this expression differs from the conventionally used equation through a phase factor. We experimentally verify this equation using a spectral in-line interferometry approach. We also briefly discuss the implications of our new equations for single-shot terahertz retrieval schemes.

© 2007 Optical Society of America

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  1. Q. Wu and X.-C. Zhang, "Free-space electro-optic sampling of terahertz beams," Appl. Phys. Lett. 67, 3523-3525 (1995).
    [CrossRef]
  2. I. Wilke, A. M. MacLeod,W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, "Single-shot electron-beam bunch length measurements." Phys. Rev. Lett. 88, 124801-4 (2002).
    [CrossRef] [PubMed]
  3. G. Berden, S. P. Jamison, A. M. MacLeod, W. A. Gillespie, B. Redlich, and A. F. G. van der Meer, "Electro-optic technique with improved time resolution for real-time, nondestructive, single-shot measurements of femtosecond electron bunch profiles." Phys. Rev. Lett. 93, 114802-4 (2004).
    [CrossRef] [PubMed]
  4. J. van Tilborg, C. B. Schroeder, C. V. Filip, C. Toth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, "Temporal characterization of femtosecond laser-plasma-accelerated electron bunches using terahertz radiation." Phys. Rev. Lett. 96, 014801-4 (2006).
    [CrossRef] [PubMed]
  5. K. Y. Kim, B. Yellampelle, J. H. Glownia, A. J. Taylor, and G. Rodriguez, "Terahertz-frequency electrical conductivity measurements of ultrashort laser-ablated plasmas," Proc. SPIE 6261 II, 6261Q (2006).
  6. L. Bentson, P. Bolton, E. Bong, P. Emma, J. Galayda, J. Hastings, P. Krejcik, C. Rago, J. Rifkin, and C. M. Spencer, "FEL research and development at the SLAC sub-picosecond photon source, SPPS," Nucl. Instrum. Methods Phys. Res.,  507, 205-209 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  10. K. Y. Kim, B. Yellampalle, G. Rodriguez, R. D. Averitt, A. J. Taylor, and J. H. Glownia, "Single-shot, interferometric, high-resolution, terahertz field diagnostic," Appl. Phys. Lett. 88, 1-3 (2006).
  11. B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, "Algorithm for high-resolution singleshot THz measurement using in-line spectral interferometry with chirped pulses." Appl. Phys. Lett. 87, 211109-1 (2005).
    [CrossRef]
  12. S. P. Jamison, A. M. MacLeod, G. Berden, D. A. Jaroszynski, and W. A. Gillespie, "Temporally resolved electrooptic effect." Opt. Lett. 31, 1753-5 (2006).
    [CrossRef] [PubMed]
  13. G. Gallot and D. Grischkowsky, "Electro-optic detection of terahertz radiation." J. Opt. Soc. Am. B 16, 1204-12 (1999).
    [CrossRef]
  14. Z. Jiang, F. G. Sun, Q. Chen, and X. C. Zhang, "Electro-optic sampling near zero optical transmission point." Appl. Phys. Lett. 74, 1191-3 (1999).
    [CrossRef]
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2006 (3)

J. van Tilborg, C. B. Schroeder, C. V. Filip, C. Toth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, "Temporal characterization of femtosecond laser-plasma-accelerated electron bunches using terahertz radiation." Phys. Rev. Lett. 96, 014801-4 (2006).
[CrossRef] [PubMed]

K. Y. Kim, B. Yellampalle, G. Rodriguez, R. D. Averitt, A. J. Taylor, and J. H. Glownia, "Single-shot, interferometric, high-resolution, terahertz field diagnostic," Appl. Phys. Lett. 88, 1-3 (2006).

S. P. Jamison, A. M. MacLeod, G. Berden, D. A. Jaroszynski, and W. A. Gillespie, "Temporally resolved electrooptic effect." Opt. Lett. 31, 1753-5 (2006).
[CrossRef] [PubMed]

2005 (1)

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, "Algorithm for high-resolution singleshot THz measurement using in-line spectral interferometry with chirped pulses." Appl. Phys. Lett. 87, 211109-1 (2005).
[CrossRef]

2004 (1)

G. Berden, S. P. Jamison, A. M. MacLeod, W. A. Gillespie, B. Redlich, and A. F. G. van der Meer, "Electro-optic technique with improved time resolution for real-time, nondestructive, single-shot measurements of femtosecond electron bunch profiles." Phys. Rev. Lett. 93, 114802-4 (2004).
[CrossRef] [PubMed]

2003 (2)

S. P. Jamison, J. L. Shen, A. M. MacLeod, W. A. Gillespie, and D. A. Jaroszynski, "High-temporal-resolution, single-shot characterization of terahertz pulses." Opt. Lett. 28, 1710-12 (2003).
[CrossRef] [PubMed]

L. Bentson, P. Bolton, E. Bong, P. Emma, J. Galayda, J. Hastings, P. Krejcik, C. Rago, J. Rifkin, and C. M. Spencer, "FEL research and development at the SLAC sub-picosecond photon source, SPPS," Nucl. Instrum. Methods Phys. Res.,  507, 205-209 (2003).
[CrossRef]

2002 (2)

T. Srinivasan-Rao, M. Amin, V. Castillo, D. M. Lazarus, D. Nikas, C. Ozben, Y. K. Semertzidis, A. Stillman, T. Tsang, and L. Kowalski, "Novel single shot scheme to measure submillimeter electron bunch lengths using electro-optic technique - art. no. 042801," Phys. Rev. ST Accel. Beams 504, 042801-1-042801-7 (2002).

I. Wilke, A. M. MacLeod,W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, "Single-shot electron-beam bunch length measurements." Phys. Rev. Lett. 88, 124801-4 (2002).
[CrossRef] [PubMed]

1999 (2)

Z. Jiang, F. G. Sun, Q. Chen, and X. C. Zhang, "Electro-optic sampling near zero optical transmission point." Appl. Phys. Lett. 74, 1191-3 (1999).
[CrossRef]

G. Gallot and D. Grischkowsky, "Electro-optic detection of terahertz radiation." J. Opt. Soc. Am. B 16, 1204-12 (1999).
[CrossRef]

1998 (1)

Z. P. Jiang and X. C. Zhang, "Electro-optic measurement of THz field pulses with a chirped optical beam," Appl. Phys. Lett. 72, 1945-1947 (1998).
[CrossRef]

1995 (1)

Q. Wu and X.-C. Zhang, "Free-space electro-optic sampling of terahertz beams," Appl. Phys. Lett. 67, 3523-3525 (1995).
[CrossRef]

Amin, M.

T. Srinivasan-Rao, M. Amin, V. Castillo, D. M. Lazarus, D. Nikas, C. Ozben, Y. K. Semertzidis, A. Stillman, T. Tsang, and L. Kowalski, "Novel single shot scheme to measure submillimeter electron bunch lengths using electro-optic technique - art. no. 042801," Phys. Rev. ST Accel. Beams 504, 042801-1-042801-7 (2002).

Averitt, R. D.

K. Y. Kim, B. Yellampalle, G. Rodriguez, R. D. Averitt, A. J. Taylor, and J. H. Glownia, "Single-shot, interferometric, high-resolution, terahertz field diagnostic," Appl. Phys. Lett. 88, 1-3 (2006).

Bentson, L.

L. Bentson, P. Bolton, E. Bong, P. Emma, J. Galayda, J. Hastings, P. Krejcik, C. Rago, J. Rifkin, and C. M. Spencer, "FEL research and development at the SLAC sub-picosecond photon source, SPPS," Nucl. Instrum. Methods Phys. Res.,  507, 205-209 (2003).
[CrossRef]

Berden, G.

S. P. Jamison, A. M. MacLeod, G. Berden, D. A. Jaroszynski, and W. A. Gillespie, "Temporally resolved electrooptic effect." Opt. Lett. 31, 1753-5 (2006).
[CrossRef] [PubMed]

G. Berden, S. P. Jamison, A. M. MacLeod, W. A. Gillespie, B. Redlich, and A. F. G. van der Meer, "Electro-optic technique with improved time resolution for real-time, nondestructive, single-shot measurements of femtosecond electron bunch profiles." Phys. Rev. Lett. 93, 114802-4 (2004).
[CrossRef] [PubMed]

I. Wilke, A. M. MacLeod,W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, "Single-shot electron-beam bunch length measurements." Phys. Rev. Lett. 88, 124801-4 (2002).
[CrossRef] [PubMed]

Bolton, P.

L. Bentson, P. Bolton, E. Bong, P. Emma, J. Galayda, J. Hastings, P. Krejcik, C. Rago, J. Rifkin, and C. M. Spencer, "FEL research and development at the SLAC sub-picosecond photon source, SPPS," Nucl. Instrum. Methods Phys. Res.,  507, 205-209 (2003).
[CrossRef]

Bong, E.

L. Bentson, P. Bolton, E. Bong, P. Emma, J. Galayda, J. Hastings, P. Krejcik, C. Rago, J. Rifkin, and C. M. Spencer, "FEL research and development at the SLAC sub-picosecond photon source, SPPS," Nucl. Instrum. Methods Phys. Res.,  507, 205-209 (2003).
[CrossRef]

Castillo, V.

T. Srinivasan-Rao, M. Amin, V. Castillo, D. M. Lazarus, D. Nikas, C. Ozben, Y. K. Semertzidis, A. Stillman, T. Tsang, and L. Kowalski, "Novel single shot scheme to measure submillimeter electron bunch lengths using electro-optic technique - art. no. 042801," Phys. Rev. ST Accel. Beams 504, 042801-1-042801-7 (2002).

Chen, Q.

Z. Jiang, F. G. Sun, Q. Chen, and X. C. Zhang, "Electro-optic sampling near zero optical transmission point." Appl. Phys. Lett. 74, 1191-3 (1999).
[CrossRef]

Emma, P.

L. Bentson, P. Bolton, E. Bong, P. Emma, J. Galayda, J. Hastings, P. Krejcik, C. Rago, J. Rifkin, and C. M. Spencer, "FEL research and development at the SLAC sub-picosecond photon source, SPPS," Nucl. Instrum. Methods Phys. Res.,  507, 205-209 (2003).
[CrossRef]

Esarey, E.

J. van Tilborg, C. B. Schroeder, C. V. Filip, C. Toth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, "Temporal characterization of femtosecond laser-plasma-accelerated electron bunches using terahertz radiation." Phys. Rev. Lett. 96, 014801-4 (2006).
[CrossRef] [PubMed]

Filip, C. V.

J. van Tilborg, C. B. Schroeder, C. V. Filip, C. Toth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, "Temporal characterization of femtosecond laser-plasma-accelerated electron bunches using terahertz radiation." Phys. Rev. Lett. 96, 014801-4 (2006).
[CrossRef] [PubMed]

Fubiani, G.

J. van Tilborg, C. B. Schroeder, C. V. Filip, C. Toth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, "Temporal characterization of femtosecond laser-plasma-accelerated electron bunches using terahertz radiation." Phys. Rev. Lett. 96, 014801-4 (2006).
[CrossRef] [PubMed]

Galayda, J.

L. Bentson, P. Bolton, E. Bong, P. Emma, J. Galayda, J. Hastings, P. Krejcik, C. Rago, J. Rifkin, and C. M. Spencer, "FEL research and development at the SLAC sub-picosecond photon source, SPPS," Nucl. Instrum. Methods Phys. Res.,  507, 205-209 (2003).
[CrossRef]

Gallot, G.

Geddes, C. G. R.

J. van Tilborg, C. B. Schroeder, C. V. Filip, C. Toth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, "Temporal characterization of femtosecond laser-plasma-accelerated electron bunches using terahertz radiation." Phys. Rev. Lett. 96, 014801-4 (2006).
[CrossRef] [PubMed]

Gillespie, W. A.

S. P. Jamison, A. M. MacLeod, G. Berden, D. A. Jaroszynski, and W. A. Gillespie, "Temporally resolved electrooptic effect." Opt. Lett. 31, 1753-5 (2006).
[CrossRef] [PubMed]

G. Berden, S. P. Jamison, A. M. MacLeod, W. A. Gillespie, B. Redlich, and A. F. G. van der Meer, "Electro-optic technique with improved time resolution for real-time, nondestructive, single-shot measurements of femtosecond electron bunch profiles." Phys. Rev. Lett. 93, 114802-4 (2004).
[CrossRef] [PubMed]

S. P. Jamison, J. L. Shen, A. M. MacLeod, W. A. Gillespie, and D. A. Jaroszynski, "High-temporal-resolution, single-shot characterization of terahertz pulses." Opt. Lett. 28, 1710-12 (2003).
[CrossRef] [PubMed]

I. Wilke, A. M. MacLeod,W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, "Single-shot electron-beam bunch length measurements." Phys. Rev. Lett. 88, 124801-4 (2002).
[CrossRef] [PubMed]

Glownia, J. H.

K. Y. Kim, B. Yellampalle, G. Rodriguez, R. D. Averitt, A. J. Taylor, and J. H. Glownia, "Single-shot, interferometric, high-resolution, terahertz field diagnostic," Appl. Phys. Lett. 88, 1-3 (2006).

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, "Algorithm for high-resolution singleshot THz measurement using in-line spectral interferometry with chirped pulses." Appl. Phys. Lett. 87, 211109-1 (2005).
[CrossRef]

Grischkowsky, D.

Hastings, J.

L. Bentson, P. Bolton, E. Bong, P. Emma, J. Galayda, J. Hastings, P. Krejcik, C. Rago, J. Rifkin, and C. M. Spencer, "FEL research and development at the SLAC sub-picosecond photon source, SPPS," Nucl. Instrum. Methods Phys. Res.,  507, 205-209 (2003).
[CrossRef]

Huber, R.

J. van Tilborg, C. B. Schroeder, C. V. Filip, C. Toth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, "Temporal characterization of femtosecond laser-plasma-accelerated electron bunches using terahertz radiation." Phys. Rev. Lett. 96, 014801-4 (2006).
[CrossRef] [PubMed]

Jamison, S. P.

S. P. Jamison, A. M. MacLeod, G. Berden, D. A. Jaroszynski, and W. A. Gillespie, "Temporally resolved electrooptic effect." Opt. Lett. 31, 1753-5 (2006).
[CrossRef] [PubMed]

G. Berden, S. P. Jamison, A. M. MacLeod, W. A. Gillespie, B. Redlich, and A. F. G. van der Meer, "Electro-optic technique with improved time resolution for real-time, nondestructive, single-shot measurements of femtosecond electron bunch profiles." Phys. Rev. Lett. 93, 114802-4 (2004).
[CrossRef] [PubMed]

S. P. Jamison, J. L. Shen, A. M. MacLeod, W. A. Gillespie, and D. A. Jaroszynski, "High-temporal-resolution, single-shot characterization of terahertz pulses." Opt. Lett. 28, 1710-12 (2003).
[CrossRef] [PubMed]

Jaroszynski, D. A.

Jiang, Z.

Z. Jiang, F. G. Sun, Q. Chen, and X. C. Zhang, "Electro-optic sampling near zero optical transmission point." Appl. Phys. Lett. 74, 1191-3 (1999).
[CrossRef]

Jiang, Z. P.

Z. P. Jiang and X. C. Zhang, "Electro-optic measurement of THz field pulses with a chirped optical beam," Appl. Phys. Lett. 72, 1945-1947 (1998).
[CrossRef]

Kaindl, R. A.

J. van Tilborg, C. B. Schroeder, C. V. Filip, C. Toth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, "Temporal characterization of femtosecond laser-plasma-accelerated electron bunches using terahertz radiation." Phys. Rev. Lett. 96, 014801-4 (2006).
[CrossRef] [PubMed]

Kim, K. Y.

K. Y. Kim, B. Yellampalle, G. Rodriguez, R. D. Averitt, A. J. Taylor, and J. H. Glownia, "Single-shot, interferometric, high-resolution, terahertz field diagnostic," Appl. Phys. Lett. 88, 1-3 (2006).

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, "Algorithm for high-resolution singleshot THz measurement using in-line spectral interferometry with chirped pulses." Appl. Phys. Lett. 87, 211109-1 (2005).
[CrossRef]

Knippels, G. M. H.

I. Wilke, A. M. MacLeod,W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, "Single-shot electron-beam bunch length measurements." Phys. Rev. Lett. 88, 124801-4 (2002).
[CrossRef] [PubMed]

Kowalski, L.

T. Srinivasan-Rao, M. Amin, V. Castillo, D. M. Lazarus, D. Nikas, C. Ozben, Y. K. Semertzidis, A. Stillman, T. Tsang, and L. Kowalski, "Novel single shot scheme to measure submillimeter electron bunch lengths using electro-optic technique - art. no. 042801," Phys. Rev. ST Accel. Beams 504, 042801-1-042801-7 (2002).

Krejcik, P.

L. Bentson, P. Bolton, E. Bong, P. Emma, J. Galayda, J. Hastings, P. Krejcik, C. Rago, J. Rifkin, and C. M. Spencer, "FEL research and development at the SLAC sub-picosecond photon source, SPPS," Nucl. Instrum. Methods Phys. Res.,  507, 205-209 (2003).
[CrossRef]

Lazarus, D. M.

T. Srinivasan-Rao, M. Amin, V. Castillo, D. M. Lazarus, D. Nikas, C. Ozben, Y. K. Semertzidis, A. Stillman, T. Tsang, and L. Kowalski, "Novel single shot scheme to measure submillimeter electron bunch lengths using electro-optic technique - art. no. 042801," Phys. Rev. ST Accel. Beams 504, 042801-1-042801-7 (2002).

Leemans, W. P.

J. van Tilborg, C. B. Schroeder, C. V. Filip, C. Toth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, "Temporal characterization of femtosecond laser-plasma-accelerated electron bunches using terahertz radiation." Phys. Rev. Lett. 96, 014801-4 (2006).
[CrossRef] [PubMed]

MacLeod, A. M.

S. P. Jamison, A. M. MacLeod, G. Berden, D. A. Jaroszynski, and W. A. Gillespie, "Temporally resolved electrooptic effect." Opt. Lett. 31, 1753-5 (2006).
[CrossRef] [PubMed]

G. Berden, S. P. Jamison, A. M. MacLeod, W. A. Gillespie, B. Redlich, and A. F. G. van der Meer, "Electro-optic technique with improved time resolution for real-time, nondestructive, single-shot measurements of femtosecond electron bunch profiles." Phys. Rev. Lett. 93, 114802-4 (2004).
[CrossRef] [PubMed]

S. P. Jamison, J. L. Shen, A. M. MacLeod, W. A. Gillespie, and D. A. Jaroszynski, "High-temporal-resolution, single-shot characterization of terahertz pulses." Opt. Lett. 28, 1710-12 (2003).
[CrossRef] [PubMed]

I. Wilke, A. M. MacLeod,W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, "Single-shot electron-beam bunch length measurements." Phys. Rev. Lett. 88, 124801-4 (2002).
[CrossRef] [PubMed]

Nikas, D.

T. Srinivasan-Rao, M. Amin, V. Castillo, D. M. Lazarus, D. Nikas, C. Ozben, Y. K. Semertzidis, A. Stillman, T. Tsang, and L. Kowalski, "Novel single shot scheme to measure submillimeter electron bunch lengths using electro-optic technique - art. no. 042801," Phys. Rev. ST Accel. Beams 504, 042801-1-042801-7 (2002).

Ozben, C.

T. Srinivasan-Rao, M. Amin, V. Castillo, D. M. Lazarus, D. Nikas, C. Ozben, Y. K. Semertzidis, A. Stillman, T. Tsang, and L. Kowalski, "Novel single shot scheme to measure submillimeter electron bunch lengths using electro-optic technique - art. no. 042801," Phys. Rev. ST Accel. Beams 504, 042801-1-042801-7 (2002).

Rago, C.

L. Bentson, P. Bolton, E. Bong, P. Emma, J. Galayda, J. Hastings, P. Krejcik, C. Rago, J. Rifkin, and C. M. Spencer, "FEL research and development at the SLAC sub-picosecond photon source, SPPS," Nucl. Instrum. Methods Phys. Res.,  507, 205-209 (2003).
[CrossRef]

Redlich, B.

G. Berden, S. P. Jamison, A. M. MacLeod, W. A. Gillespie, B. Redlich, and A. F. G. van der Meer, "Electro-optic technique with improved time resolution for real-time, nondestructive, single-shot measurements of femtosecond electron bunch profiles." Phys. Rev. Lett. 93, 114802-4 (2004).
[CrossRef] [PubMed]

Rifkin, J.

L. Bentson, P. Bolton, E. Bong, P. Emma, J. Galayda, J. Hastings, P. Krejcik, C. Rago, J. Rifkin, and C. M. Spencer, "FEL research and development at the SLAC sub-picosecond photon source, SPPS," Nucl. Instrum. Methods Phys. Res.,  507, 205-209 (2003).
[CrossRef]

Rodriguez, G.

K. Y. Kim, B. Yellampalle, G. Rodriguez, R. D. Averitt, A. J. Taylor, and J. H. Glownia, "Single-shot, interferometric, high-resolution, terahertz field diagnostic," Appl. Phys. Lett. 88, 1-3 (2006).

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, "Algorithm for high-resolution singleshot THz measurement using in-line spectral interferometry with chirped pulses." Appl. Phys. Lett. 87, 211109-1 (2005).
[CrossRef]

Schroeder, C. B.

J. van Tilborg, C. B. Schroeder, C. V. Filip, C. Toth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, "Temporal characterization of femtosecond laser-plasma-accelerated electron bunches using terahertz radiation." Phys. Rev. Lett. 96, 014801-4 (2006).
[CrossRef] [PubMed]

Semertzidis, Y. K.

T. Srinivasan-Rao, M. Amin, V. Castillo, D. M. Lazarus, D. Nikas, C. Ozben, Y. K. Semertzidis, A. Stillman, T. Tsang, and L. Kowalski, "Novel single shot scheme to measure submillimeter electron bunch lengths using electro-optic technique - art. no. 042801," Phys. Rev. ST Accel. Beams 504, 042801-1-042801-7 (2002).

Shen, J. L.

Spencer, C. M.

L. Bentson, P. Bolton, E. Bong, P. Emma, J. Galayda, J. Hastings, P. Krejcik, C. Rago, J. Rifkin, and C. M. Spencer, "FEL research and development at the SLAC sub-picosecond photon source, SPPS," Nucl. Instrum. Methods Phys. Res.,  507, 205-209 (2003).
[CrossRef]

Srinivasan-Rao, T.

T. Srinivasan-Rao, M. Amin, V. Castillo, D. M. Lazarus, D. Nikas, C. Ozben, Y. K. Semertzidis, A. Stillman, T. Tsang, and L. Kowalski, "Novel single shot scheme to measure submillimeter electron bunch lengths using electro-optic technique - art. no. 042801," Phys. Rev. ST Accel. Beams 504, 042801-1-042801-7 (2002).

Stillman, A.

T. Srinivasan-Rao, M. Amin, V. Castillo, D. M. Lazarus, D. Nikas, C. Ozben, Y. K. Semertzidis, A. Stillman, T. Tsang, and L. Kowalski, "Novel single shot scheme to measure submillimeter electron bunch lengths using electro-optic technique - art. no. 042801," Phys. Rev. ST Accel. Beams 504, 042801-1-042801-7 (2002).

Sun, F. G.

Z. Jiang, F. G. Sun, Q. Chen, and X. C. Zhang, "Electro-optic sampling near zero optical transmission point." Appl. Phys. Lett. 74, 1191-3 (1999).
[CrossRef]

Taylor, A. J.

K. Y. Kim, B. Yellampalle, G. Rodriguez, R. D. Averitt, A. J. Taylor, and J. H. Glownia, "Single-shot, interferometric, high-resolution, terahertz field diagnostic," Appl. Phys. Lett. 88, 1-3 (2006).

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, "Algorithm for high-resolution singleshot THz measurement using in-line spectral interferometry with chirped pulses." Appl. Phys. Lett. 87, 211109-1 (2005).
[CrossRef]

Toth, C.

J. van Tilborg, C. B. Schroeder, C. V. Filip, C. Toth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, "Temporal characterization of femtosecond laser-plasma-accelerated electron bunches using terahertz radiation." Phys. Rev. Lett. 96, 014801-4 (2006).
[CrossRef] [PubMed]

Tsang, T.

T. Srinivasan-Rao, M. Amin, V. Castillo, D. M. Lazarus, D. Nikas, C. Ozben, Y. K. Semertzidis, A. Stillman, T. Tsang, and L. Kowalski, "Novel single shot scheme to measure submillimeter electron bunch lengths using electro-optic technique - art. no. 042801," Phys. Rev. ST Accel. Beams 504, 042801-1-042801-7 (2002).

van der Meer, A. F. G.

G. Berden, S. P. Jamison, A. M. MacLeod, W. A. Gillespie, B. Redlich, and A. F. G. van der Meer, "Electro-optic technique with improved time resolution for real-time, nondestructive, single-shot measurements of femtosecond electron bunch profiles." Phys. Rev. Lett. 93, 114802-4 (2004).
[CrossRef] [PubMed]

I. Wilke, A. M. MacLeod,W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, "Single-shot electron-beam bunch length measurements." Phys. Rev. Lett. 88, 124801-4 (2002).
[CrossRef] [PubMed]

van Tilborg, J.

J. van Tilborg, C. B. Schroeder, C. V. Filip, C. Toth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, "Temporal characterization of femtosecond laser-plasma-accelerated electron bunches using terahertz radiation." Phys. Rev. Lett. 96, 014801-4 (2006).
[CrossRef] [PubMed]

Wilke, I.

I. Wilke, A. M. MacLeod,W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, "Single-shot electron-beam bunch length measurements." Phys. Rev. Lett. 88, 124801-4 (2002).
[CrossRef] [PubMed]

Wu, Q.

Q. Wu and X.-C. Zhang, "Free-space electro-optic sampling of terahertz beams," Appl. Phys. Lett. 67, 3523-3525 (1995).
[CrossRef]

Yellampalle, B.

K. Y. Kim, B. Yellampalle, G. Rodriguez, R. D. Averitt, A. J. Taylor, and J. H. Glownia, "Single-shot, interferometric, high-resolution, terahertz field diagnostic," Appl. Phys. Lett. 88, 1-3 (2006).

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, "Algorithm for high-resolution singleshot THz measurement using in-line spectral interferometry with chirped pulses." Appl. Phys. Lett. 87, 211109-1 (2005).
[CrossRef]

Zhang, X. C.

Z. Jiang, F. G. Sun, Q. Chen, and X. C. Zhang, "Electro-optic sampling near zero optical transmission point." Appl. Phys. Lett. 74, 1191-3 (1999).
[CrossRef]

Z. P. Jiang and X. C. Zhang, "Electro-optic measurement of THz field pulses with a chirped optical beam," Appl. Phys. Lett. 72, 1945-1947 (1998).
[CrossRef]

Zhang, X.-C.

Q. Wu and X.-C. Zhang, "Free-space electro-optic sampling of terahertz beams," Appl. Phys. Lett. 67, 3523-3525 (1995).
[CrossRef]

Appl. Phys. Lett. (5)

Q. Wu and X.-C. Zhang, "Free-space electro-optic sampling of terahertz beams," Appl. Phys. Lett. 67, 3523-3525 (1995).
[CrossRef]

Z. P. Jiang and X. C. Zhang, "Electro-optic measurement of THz field pulses with a chirped optical beam," Appl. Phys. Lett. 72, 1945-1947 (1998).
[CrossRef]

Z. Jiang, F. G. Sun, Q. Chen, and X. C. Zhang, "Electro-optic sampling near zero optical transmission point." Appl. Phys. Lett. 74, 1191-3 (1999).
[CrossRef]

K. Y. Kim, B. Yellampalle, G. Rodriguez, R. D. Averitt, A. J. Taylor, and J. H. Glownia, "Single-shot, interferometric, high-resolution, terahertz field diagnostic," Appl. Phys. Lett. 88, 1-3 (2006).

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, "Algorithm for high-resolution singleshot THz measurement using in-line spectral interferometry with chirped pulses." Appl. Phys. Lett. 87, 211109-1 (2005).
[CrossRef]

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

Nucl. Instrum. Methods Phys. Res. (1)

L. Bentson, P. Bolton, E. Bong, P. Emma, J. Galayda, J. Hastings, P. Krejcik, C. Rago, J. Rifkin, and C. M. Spencer, "FEL research and development at the SLAC sub-picosecond photon source, SPPS," Nucl. Instrum. Methods Phys. Res.,  507, 205-209 (2003).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (3)

I. Wilke, A. M. MacLeod,W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, "Single-shot electron-beam bunch length measurements." Phys. Rev. Lett. 88, 124801-4 (2002).
[CrossRef] [PubMed]

G. Berden, S. P. Jamison, A. M. MacLeod, W. A. Gillespie, B. Redlich, and A. F. G. van der Meer, "Electro-optic technique with improved time resolution for real-time, nondestructive, single-shot measurements of femtosecond electron bunch profiles." Phys. Rev. Lett. 93, 114802-4 (2004).
[CrossRef] [PubMed]

J. van Tilborg, C. B. Schroeder, C. V. Filip, C. Toth, C. G. R. Geddes, G. Fubiani, R. Huber, R. A. Kaindl, E. Esarey, and W. P. Leemans, "Temporal characterization of femtosecond laser-plasma-accelerated electron bunches using terahertz radiation." Phys. Rev. Lett. 96, 014801-4 (2006).
[CrossRef] [PubMed]

Phys. Rev. ST Accel. Beams (1)

T. Srinivasan-Rao, M. Amin, V. Castillo, D. M. Lazarus, D. Nikas, C. Ozben, Y. K. Semertzidis, A. Stillman, T. Tsang, and L. Kowalski, "Novel single shot scheme to measure submillimeter electron bunch lengths using electro-optic technique - art. no. 042801," Phys. Rev. ST Accel. Beams 504, 042801-1-042801-7 (2002).

Other (4)

K. Y. Kim, B. Yellampelle, J. H. Glownia, A. J. Taylor, and G. Rodriguez, "Terahertz-frequency electrical conductivity measurements of ultrashort laser-ablated plasmas," Proc. SPIE 6261 II, 6261Q (2006).

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford University Press, 1997).

D. J. Claude and R. Wolfgang, Ultrashort Laser Pulse Phenomena : Fundamentals Techniques and Applications on a Femtosecond Time Scale (Academic Press, 1996).
[PubMed]

B. Yellampalle, K. Y. Kim, R. D. Averitt, G. Rodriguez, J. H. Glownia, and A. J. Taylor, "Single-shot highresolution THz field reconstruction using phase-retrieval," in Ultrafast Phenomena XV: Proceedings of the 15th International Conference (2006).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic of experimental scheme for the verification of EO effect with chirped pulse. (b) Set-up for direct characterization of THz field.

Fig. 2.
Fig. 2.

(a) Background spectrum, |Ẽopt|2, of chirped optical probe in absence of THz field. (b) Modulated probe, |Ẽout|2, in presence of THz field. (c) Temporal intensity profile of the probe pulse calculated using |Ẽopt|2 and the spectral phase. (d) THz field measured directly using a short optical probe pulse.

Fig. 3.
Fig. 3.

The blue curve is the directly measured spectral difference for a residual birefringence case (θ=0). The red curves are calculated spectral difference using (a) Eq. (8) and (b) using Eq. (6) of Ref [12] for various delays (T).

Fig. 4.
Fig. 4.

Comparison of directly measured difference spectra (blue lines) with the calculated difference spectra (red lines) using Eq. (8) for four different cases. (a) Residual birefringence (θ=0), (b) QWP at small angle ( θ = π 4 ) , (c) HWP at small angle ( θ = π 2 ) , and (d) detuned analyzer ( θ = π 2 ) .

Equations (12)

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E ˜ y ( ω ) = E ˜ opt ( ω ) B y [ E ˜ THz eff * E ˜ opt ] ( ω ) ,
E ˜ x ( ω ) = B x [ E ˜ THz eff * E ˜ opt ] ( ω ) .
[ E ˜ out x E ˜ out y ] = [ cos ( θ d ) 0 0 sin ( θ d ) ] M 2 M 1 [ E ˜ x E ˜ y ] ,
M 1,2 = [ a 1,2 i b 1,2 i b 1,2 a 1,2 * ] .
E ˜ out ( ω ) = E ˜ opt ( ω ) + ωα exp ( ) [ E ˜ THz eff * E ˜ opt ] ( ω ) ,
E out ( t ) = E opt ( t ) exp ( ) d dt [ E THz eff ( t ) E opt ( t ) ] .
E ˜ out ( ω ) = E ˜ opt ( ω ) + a exp ( ) [ E ˜ THz eff * E ˜ opt ] ( ω ) ,
E out ( t ) = E opt ( t ) [ 1 + a exp ( ) E THz eff ( t ) ] .
d dt [ E THz eff ( t ) E opt ( t ) ] = exp ( i ω 0 t ) d dt [ A THz ( t ) A opt ( t ) ] + i ω 0 exp ( i ω 0 t ) A THz ( t ) A opt ( t ) .
d dt [ A THz ( t ) A opt ( t ) ] << ω 0 A THz ( t ) A opt ( t ) ,
B ω , t = E ˜ opt * ( ω ) E opt ( t ) e iωt + + E ˜ opt ( ω ) E opt * ( t ) e iωt .
Δ = 1 N i = 0 N E out ( t ) = E opt ( t ) [ 1 + a exp ( ) E THz eff ( t ) ] ,

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