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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References

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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. J. Shan, A. S. Weling, E. Knoesel, L. Bartels, M. Bonn, A. Nahata, G. A. Reider, and T. F. Heinz, "Single-shot measurement of terahertz electromagnetic pulses by use of electro-optic sampling,"Opt. Lett. 25, 426-428 (2000).
    [CrossRef]
  5. S. P. Jamison, J. Shen, A. M. Macleod and 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 (1)

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).

2005 (1)

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

2003 (2)

S. P. Jamison, J. Shen, A. M. Macleod and W. A. Gillespie, and D. A. Jaroszynski, "High-temporal-resolution, single-shot characterization of terahertz pulses," Opt. Lett. 28, 1710-1712 (2003).
[CrossRef]

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

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]

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).

Fletcher, J. R.

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, 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]

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, 041123 (2006).

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

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).

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, 041123 (2006).

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

Steven,

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.

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]

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.

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

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

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]

Interrnational Journal of High Speed Electronics and Systems (1)

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

Opt. Express (2)

Opt. Lett. (2)

Other (1)

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

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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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