Abstract

In electro-optic sampling of terahertz pulses with a finite diameter, the probe pulse is subject to a lensing effect. The altered diffraction leads to an additional phase shift Δη in the far field compared to the case of a plane wave. It is demonstrated that Δη is in the same order of magnitude as the direct electro-optic phase shift at the exit of the detection crystal and thus also gives a significant contribution to the measured amplitude.

© 2009 Optical Society of America

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2008 (2)

J. Hebling, K.-L. Yeh, M. C. Hoffmann, B. Bartal, and K. A. Nelson, J. Opt. Soc. Am. B 25, B6 (2008).
[CrossRef]

Y. Shen, G. L. Carr, J. B. Murphy, T. Y. Tsang, X. Wang, and X. Yang, Phys. Rev. A 78, 043813 (2008).
[CrossRef]

2007 (1)

A. Schneider and P. Günter, Appl. Phys. Lett. 90, 121125 (2007).
[CrossRef]

2006 (2)

2005 (1)

2004 (1)

A. Schneider, I. Biaggio, and P. Günter, Appl. Phys. Lett. 84, 2229 (2004).
[CrossRef]

2001 (2)

1999 (2)

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

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

1996 (3)

Q. Wu and X.-C. Zhang, IEEE J. Sel. Top. Quantum Electron. 2, 693 (1996).
[CrossRef]

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 68, 1604 (1996).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

Bakker, H. J.

Bartal, B.

Bartel, T.

Biaggio, I.

A. Schneider, I. Biaggio, and P. Günter, Appl. Phys. Lett. 84, 2229 (2004).
[CrossRef]

Carr, G. L.

Y. Shen, G. L. Carr, J. B. Murphy, T. Y. Tsang, X. Wang, and X. Yang, Phys. Rev. A 78, 043813 (2008).
[CrossRef]

Chen, Q.

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, J. Opt. Soc. Am. B 18, 823 (2001).
[CrossRef]

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

Elsaesser, T.

Gaal, P.

Gallot, G.

Grischkowsky, D.

Günter, P.

A. Schneider and P. Günter, Appl. Phys. Lett. 90, 121125 (2007).
[CrossRef]

A. Schneider and P. Günter, Appl. Opt. 45, 6598 (2006).
[CrossRef] [PubMed]

A. Schneider, M. Stillhart, and P. Günter, Opt. Express 14, 5376 (2006).
[CrossRef] [PubMed]

A. Schneider, I. Biaggio, and P. Günter, Appl. Phys. Lett. 84, 2229 (2004).
[CrossRef]

Hebling, J.

Heinz, T. F.

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

Hoffmann, M. C.

Jiang, Z.

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, J. Opt. Soc. Am. B 18, 823 (2001).
[CrossRef]

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

Murphy, J. B.

Y. Shen, G. L. Carr, J. B. Murphy, T. Y. Tsang, X. Wang, and X. Yang, Phys. Rev. A 78, 043813 (2008).
[CrossRef]

Nahata, A.

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

Nelson, K. A.

Nienhuys, H.-K.

Planken, P. C. M.

Reimann, K.

Schneider, A.

A. Schneider and P. Günter, Appl. Phys. Lett. 90, 121125 (2007).
[CrossRef]

A. Schneider and P. Günter, Appl. Opt. 45, 6598 (2006).
[CrossRef] [PubMed]

A. Schneider, M. Stillhart, and P. Günter, Opt. Express 14, 5376 (2006).
[CrossRef] [PubMed]

A. Schneider, I. Biaggio, and P. Günter, Appl. Phys. Lett. 84, 2229 (2004).
[CrossRef]

Shen, Y.

Y. Shen, G. L. Carr, J. B. Murphy, T. Y. Tsang, X. Wang, and X. Yang, Phys. Rev. A 78, 043813 (2008).
[CrossRef]

Stillhart, M.

Sun, F. G.

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

Tani, M.

Tsang, T. Y.

Y. Shen, G. L. Carr, J. B. Murphy, T. Y. Tsang, X. Wang, and X. Yang, Phys. Rev. A 78, 043813 (2008).
[CrossRef]

Wang, X.

Y. Shen, G. L. Carr, J. B. Murphy, T. Y. Tsang, X. Wang, and X. Yang, Phys. Rev. A 78, 043813 (2008).
[CrossRef]

Weling, A. S.

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

Wenckebach, T.

Woerner, M.

Wu, Q.

Q. Wu and X.-C. Zhang, IEEE J. Sel. Top. Quantum Electron. 2, 693 (1996).
[CrossRef]

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 68, 1604 (1996).
[CrossRef]

Yang, X.

Y. Shen, G. L. Carr, J. B. Murphy, T. Y. Tsang, X. Wang, and X. Yang, Phys. Rev. A 78, 043813 (2008).
[CrossRef]

Yariv, A.

A. Yariv and P. Yeh, Photonics, 6th ed. (Oxford University Press, 2007).

Yeh, K.-L.

Yeh, P.

A. Yariv and P. Yeh, Photonics, 6th ed. (Oxford University Press, 2007).

Zhang, X.-C.

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, J. Opt. Soc. Am. B 18, 823 (2001).
[CrossRef]

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

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 68, 1604 (1996).
[CrossRef]

Q. Wu and X.-C. Zhang, IEEE J. Sel. Top. Quantum Electron. 2, 693 (1996).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (5)

A. Schneider, I. Biaggio, and P. Günter, Appl. Phys. Lett. 84, 2229 (2004).
[CrossRef]

A. Schneider and P. Günter, Appl. Phys. Lett. 90, 121125 (2007).
[CrossRef]

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 68, 1604 (1996).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

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

IEEE J. Sel. Top. Quantum Electron. (1)

Q. Wu and X.-C. Zhang, IEEE J. Sel. Top. Quantum Electron. 2, 693 (1996).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

Y. Shen, G. L. Carr, J. B. Murphy, T. Y. Tsang, X. Wang, and X. Yang, Phys. Rev. A 78, 043813 (2008).
[CrossRef]

Other (1)

A. Yariv and P. Yeh, Photonics, 6th ed. (Oxford University Press, 2007).

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Figures (2)

Fig. 1
Fig. 1

Definition of the coordinate systems and orientation of the crystal axes. The beams propagate along z = z . x and y are the main axes of the crystal’s indicatrix in the presence of a terahertz electric field in the x direction.

Fig. 2
Fig. 2

Difference signal D of the balanced photodetectors as a function of the terahertz electric field E from Eq. (6). Solid curve, finite size of the terahertz pulse (radius σ = 0.3 mm ). Dotted curve, plane terahertz wave ( σ ) , the standard solution. The EO crystal is a 0.5 mm thick plate of ZnTe. The other parameters are indicated in the text.

Equations (10)

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Δ ϕ x , y ( E ) = ϕ x , y ( E ) ϕ x , y ( E = 0 ) = ± k 0 d n 3 2 r E ,
Δ ϕ ( ρ ) = ( 1 ρ 2 2 σ 2 ) k 0 d Δ n ( ρ = 0 ) ,
f = σ 2 d Δ n ( ρ = 0 ) .
J = ( A x 2 + A y 2 ) 1 2 [ A x e i ( ϕ x + π 4 ) A y e i ( ϕ y π 4 ) ] .
J = [ 2 ( A x 2 + A y 2 ) ] 1 2 [ A x e i ( δ + π 4 ) + A y e i ( δ + π 4 ) A x e i ( δ + π 4 ) + A y e i ( δ + π 4 ) ] .
D = J y 2 J x 2 = 2 A x A y A x 2 + A y 2 sin ( 2 δ ) .
E ( z ) = E 0 W 0 W ( z ) exp ( i [ k 0 z η ( z ) ] ) ,
q ( E ) = z ( E ) + i z 0 ( E ) = q i 1 f 1 ( E ) q i + l ,
δ = k 0 d n 3 r E + Δ η x Δ η y .
δ = d n 3 r E [ k 0 + P ( 2 σ 2 ) ] .

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