Abstract

A detailed analysis of the relationship between the duration of the chirped probe pulse and the bipolar terahertz (THz) pulse length in the spectral encoding technique is carried out. We prove that there is an optimal chirped probe pulse length (or an optimal chirp rate of the chirped probe pulse) matched to the input THz pulse length and derive a rigorous relationship between them. We find that only under this restricted condition the THz signal can be correctly retrieved.

© 2008 Optical Society of America

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  1. S.P. Mickan and X.-C. Zhang, “T-ray sensing and imaging,” Interrnational Journal of High Speed Electronics and Systems, 12, 601 (2003).
  2. Q. Wu and X.-C. Zhang, “7 terahertz broadband GaP electro-optic sensor,” Appl. Phys. Lett. 70, 1784–1786 (1997).
    [Crossref]
  3. Zhiping 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]
  4. Jie. Shan, Aniruddha S. Weling, Ernst Knoesel, Ludwig Bartels, Mischa Bonn, Ajay Nahata, Georg A. Reider, and Tony F. Heinz, “single-shot measurement of terahertz electromagnetic pulses by use of electro-optic sampling,” Opt. Lett. 25, 426–428 (2000).
    [Crossref]
  5. Steven P. Jamison, Jingling Shen, A. M. Macleod, W. A. Gillespie, and D. A. Jaroszynski, “High-temporal-resolution, single-shot characterization of terahertz pulses,” Opt. Lett. 28, 1710–1712 (2003).
    [Crossref]
  6. B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownina, and A. J. Taylor, Appl. Phys. Lett. 87, 211109 (2005).
    [Crossref]
  7. 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, 041123 (2006).
  8. Jeroen van Tilborg, “Coherent terahertz radiation from laser-wakefield-accelerated electron beams”, Doctoral Dissertation, p. 76 (2006).
  9. F. G. Sun, Zhiping Jiang, and X.-C. Zhang, “Analysis of terahertz pulse measurement with a chirped probe beam,” Appl. Phys. Lett. 73, 2233–2235 (1998).
    [Crossref]
  10. J. R. Fletcher, “Distortion and uncertainty in chirped pulse THz spectrometers,” Opt. Express 10, 1425–1430 (2002).
    [PubMed]
  11. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, “Details of electro-optic terahertz detection with a chirped probe pulse,” Opt. Express 15, 1376–1383 (2007).
    [Crossref] [PubMed]

2007 (1)

2006 (2)

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, 041123 (2006).

Jeroen van Tilborg, “Coherent terahertz radiation from laser-wakefield-accelerated electron beams”, Doctoral Dissertation, p. 76 (2006).

2005 (1)

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

2003 (1)

2002 (1)

2000 (1)

1998 (2)

Zhiping 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]

F. G. Sun, Zhiping Jiang, and X.-C. Zhang, “Analysis of terahertz pulse measurement with a chirped probe beam,” Appl. Phys. Lett. 73, 2233–2235 (1998).
[Crossref]

1997 (1)

Q. Wu and X.-C. Zhang, “7 terahertz broadband GaP electro-optic sensor,” Appl. Phys. Lett. 70, 1784–1786 (1997).
[Crossref]

A. Reider, Georg

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, 041123 (2006).

Bartels, Ludwig

Bonn, Mischa

F. Heinz, Tony

Fletcher, J. R.

Gillespie, W. A.

Glownia, J. H.

Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, “Details of electro-optic terahertz detection with a chirped probe pulse,” Opt. Express 15, 1376–1383 (2007).
[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, 041123 (2006).

Glownina, J. H.

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

Jaroszynski, D. A.

Jiang, Zhiping

F. G. Sun, Zhiping Jiang, and X.-C. Zhang, “Analysis of terahertz pulse measurement with a chirped probe beam,” Appl. Phys. Lett. 73, 2233–2235 (1998).
[Crossref]

Zhiping 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]

Kim, K. Y.

Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, “Details of electro-optic terahertz detection with a chirped probe pulse,” Opt. Express 15, 1376–1383 (2007).
[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, 041123 (2006).

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

Knoesel, Ernst

Macleod, A. M.

Mickan, S.P.

S.P. Mickan and X.-C. Zhang, “T-ray sensing and imaging,” Interrnational Journal of High Speed Electronics and Systems, 12, 601 (2003).

Nahata, Ajay

P. Jamison, Steven

Rodriguez, G.

Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, “Details of electro-optic terahertz detection with a chirped probe pulse,” Opt. Express 15, 1376–1383 (2007).
[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, 041123 (2006).

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

S. Weling, Aniruddha

Shan, Jie.

Shen, Jingling

Sun, F. G.

F. G. Sun, Zhiping Jiang, and X.-C. Zhang, “Analysis of terahertz pulse measurement with a chirped probe beam,” Appl. Phys. Lett. 73, 2233–2235 (1998).
[Crossref]

Taylor, A. J.

Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, “Details of electro-optic terahertz detection with a chirped probe pulse,” Opt. Express 15, 1376–1383 (2007).
[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, 041123 (2006).

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

van Tilborg, Jeroen

Jeroen van Tilborg, “Coherent terahertz radiation from laser-wakefield-accelerated electron beams”, Doctoral Dissertation, p. 76 (2006).

Wu, Q.

Q. Wu and X.-C. Zhang, “7 terahertz broadband GaP electro-optic sensor,” Appl. Phys. Lett. 70, 1784–1786 (1997).
[Crossref]

Yellampalle,

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, 041123 (2006).

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

Zhang, X.-C.

Zhiping 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]

F. G. Sun, Zhiping Jiang, and X.-C. Zhang, “Analysis of terahertz pulse measurement with a chirped probe beam,” Appl. Phys. Lett. 73, 2233–2235 (1998).
[Crossref]

Q. Wu and X.-C. Zhang, “7 terahertz broadband GaP electro-optic sensor,” Appl. Phys. Lett. 70, 1784–1786 (1997).
[Crossref]

S.P. Mickan and X.-C. Zhang, “T-ray sensing and imaging,” Interrnational Journal of High Speed Electronics and Systems, 12, 601 (2003).

Appl. Phys. Lett. (5)

Q. Wu and X.-C. Zhang, “7 terahertz broadband GaP electro-optic sensor,” Appl. Phys. Lett. 70, 1784–1786 (1997).
[Crossref]

Zhiping 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]

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownina, and A. J. Taylor, Appl. Phys. Lett. 87, 211109 (2005).
[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, 041123 (2006).

F. G. Sun, Zhiping Jiang, and X.-C. Zhang, “Analysis of terahertz pulse measurement with a chirped probe beam,” Appl. Phys. Lett. 73, 2233–2235 (1998).
[Crossref]

Doctoral Dissertation, (1)

Jeroen van Tilborg, “Coherent terahertz radiation from laser-wakefield-accelerated electron beams”, Doctoral Dissertation, p. 76 (2006).

Opt. Express (2)

Opt. Lett. (2)

Other (1)

S.P. Mickan and X.-C. Zhang, “T-ray sensing and imaging,” Interrnational Journal of High Speed Electronics and Systems, 12, 601 (2003).

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Figures (3)

Fig. 1.
Fig. 1.

An example of the oscillation function f(t′/T 0) (solid line) as well as an original THz field (dashed line) when m = 6.

Fig. 2.
Fig. 2.

Relationship (solid line) between the dimensionless optimal chirped pulse length n and the input dimensionless THz pulse length m. The restricted condition T cT 2/T 0 or T≥(T 0 T c)½ described by Sun’s theory is also shown as the area under the curve n=m 2 (or T c=T 2/T 0, dashed line) and the curve itself compared with the optimal T c curve.

Fig. 3.
Fig. 3.

(Color on line) Retrieved THz waveforms vs the original THz waveforms (black dotted lines) with T 0=25fs in (a) and T 0=10fs in (b). The red solid lines are the retrieved THz waveforms calculated according equation (6) under the conditions of input THz pulse length T = 0.5ps (m =20 when T 0=25fs and m =50 when T '=10fs) and their corresponding optimal chirped pulse lengths T co =2.6437ps when T 0=25fs, T co = 4.1943ps when T 0=10fs, respectively, which are calculated from equation (7). The retrieved THz fields calculated according to the equation (6) with T c = T co/2, T c = T co/4, T c = 2T co, and T c = 4T co are also shown in each figure.

Equations (8)

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S ( ω 1 ) = E c ( ω 1 ) E s * ( ω 1 ) + E s * ( ω 1 ) E s ( ω 1 ) .
S ( t ) = kγf ( t / T 0 ) ( t T 1 ) exp [ ( t ′2 T 2 ) χ ]
γ = 2 π T 0 2 n 1 ( n 4 + n 2 ) 1 / 2 [ ( m 2 + n 2 ) 2 + n 2 ] 3 / 2 [ ( m 2 n 2 + n 4 + n 2 ) 2 + m 4 n 2 ] 1 / 4
f ( t / T 0 ) = n 1 cos { 1 2 arctg n 3 m 2 n 2 + m 2 + n 2 n 3 ( 2 m 2 + n 2 ) ( 1 + n 2 ) [ ( m 2 + n 2 ) + m 4 n 2 ] t T 0 2 }
( m 2 + n 2 ) sin { 1 2 arctg n 3 m 2 n 2 + m 2 + n 2 n 3 ( 2 m 2 + n 2 ) ( 1 + n 2 ) [ ( m 2 + n 2 ) + m 4 n 2 ] t T 0 2 }
χ = m 2 1 + n 2 + m 4 n 2 + m 6 ( m 2 + n 2 ) 2 + m 4 n 2
S n ( t ) = S ( t ) f ( t / T 0 ) = ( t T 1 ) exp [ ( t ′2 T 2 ) χ ]
n = { 1 3 [ 2 ( 6 m 6 + 4 m 4 8 m 2 + 1 ) 1 / 2 cos β 3 ( m 2 1 ) ] } 1 / 2

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