Abstract

Three dimensional information of the Gouy phase shift in a converging spherical terahertz (THz) beam is directly observed by using a THz balanced electro-optic holographic imaging system. The major properties of the Gouy phase shift are presented, including the longitudinal and transverse distributions, relationships with the frequency and the f-number, influence on the THz polarization. The imaging technique supplies an accurate and comprehensive measurement method for observing and understanding the Gouy phase shift.

© 2013 OSA

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  1. A. E. Siegman, Lasers (Mill Valley, Califorina, 1986), Chap. 17.
  2. J. L. Johnson, T. D. Dorney, and D. M. Mittleman, “Enhanced depth resolution in terahertz imaging using phase-shift interferometry,” Appl. Phys. Lett.78(6), 835–837 (2001).
    [CrossRef]
  3. K. I. Popov, A. F. Pegoraro, A. Stolow, and L. Ramunno, “Image formation in CARS microscopy: effect of the Gouy phase shift,” Opt. Express19(7), 5902–5911 (2011).
    [CrossRef] [PubMed]
  4. N. Shivaram, A. Roberts, L. Xu, and A. Sandhu, “In situ spatial mapping of Gouy phase slip for high-detail attosecond pump-probe measurements,” Opt. Lett.35(20), 3312–3314 (2010).
    [CrossRef] [PubMed]
  5. R. W. Boyd, “Intuitive explanation of the phase anomaly of focused light beams,” J. Opt. Soc. Am.70(7), 877–880 (1980).
    [CrossRef]
  6. P. Hariharan and P. A. Robinson, “The Gouy phase shift as a geometrical quantum effect,” J. Mod. Opt.43(2), 219–221 (1996).
  7. S. M. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett.26(8), 485–487 (2001).
    [CrossRef] [PubMed]
  8. R. Simon and N. Mukunda, “Bargmann invariant and the geometry of the Gouy effect,” Phys. Rev. Lett.70(7), 880–883 (1993).
    [CrossRef] [PubMed]
  9. T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun.283(18), 3371–3375 (2010).
    [CrossRef]
  10. J. H. Chow, G. de Vine, M. B. Gray, and D. E. McClelland, “Measurement of Gouy phase evolution by use of spatial mode interference,” Opt. Lett.29(20), 2339–2341 (2004).
    [CrossRef] [PubMed]
  11. F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett.92(11), 113001 (2004).
    [CrossRef] [PubMed]
  12. J. Hamazaki, Y. Mineta, K. Oka, and R. Morita, “Direct observation of Gouy phase shift in a propagating optical vortex,” Opt. Express14(18), 8382–8392 (2006).
    [CrossRef] [PubMed]
  13. P. Bon, B. Rolly, N. Bonod, J. Wenger, B. Stout, S. Monneret, and H. Rigneault, “Imaging the Gouy phase shift in photonic jets with a wavefront sensor,” Opt. Lett.37(17), 3531–3533 (2012).
    [CrossRef] [PubMed]
  14. A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett.83(17), 3410–3413 (1999).
    [CrossRef]
  15. R. W. McGowan, R. A. Cheville, and D. Grischkowsky, “Direct observation of the Gouy phase shift in THz impulse ranging,” Appl. Phys. Lett.76(6), 670–672 (2000).
    [CrossRef]
  16. W. Zhu, A. Agrawal, and A. Nahata, “Direct measurement of the Gouy phase shift for surface plasmon-polaritons,” Opt. Express15(16), 9995–10001 (2007).
    [CrossRef] [PubMed]
  17. Q. Wu, T. D. Hewitt, and X. C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett.69(8), 1026–1028 (1996).
    [CrossRef]
  18. X. K. Wang, Y. Cui, D. Hu, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz quasi-near-field real-time imaging,” Opt. Commun.282(24), 4683–4687 (2009).
    [CrossRef]
  19. X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun.283(23), 4626–4632 (2010).
    [CrossRef]
  20. X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz polarization real-time imaging based on balanced electro-optic detection,” J. Opt. Soc. Am. A27(11), 2387–2393 (2010).
    [CrossRef] [PubMed]
  21. X. K. Wang, W. Xiong, W. F. Sun, and Y. Zhang, “Coaxial waveguide mode reconstruction and analysis with THz digital holography,” Opt. Express20(7), 7706–7715 (2012).
    [CrossRef] [PubMed]
  22. Z. P. Jiang, X. G. Xu, and X.-C. Zhang, “Improvement of terahertz imaging with a dynamic subtraction technique,” Appl. Opt.39(17), 2982–2987 (2000).
    [CrossRef] [PubMed]
  23. X. K. Wang, Y. Cui, W. F. Sun, Y. Zhang, and C. L. Zhang, “Terahertz pulse reflective focal-plane tomography,” Opt. Express15(22), 14369–14375 (2007).
    [CrossRef] [PubMed]
  24. M. Yi, K. Lee, J. D. Song, and J. Ahn, “Terahertz phase microscopy in the sub-wavelength regime,” Appl. Phys. Lett.100(16), 161110 (2012).
    [CrossRef]
  25. X. Y. Pang, T. D. Visser, and W. Wolf, “Phase anomaly and phase singularities of the field in the focal region of high-numerical aperture systems,” Opt. Commun.284(24), 5517–5522 (2011).
    [CrossRef]
  26. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 4.
  27. J. Lin, X.-C. Yuan, S. S. Kou, C. J. R. Sheppard, O. G. Rodríguez-Herrera, and J. C. Dainty, “Direct calculation of a three-dimensional diffracted field,” Opt. Lett.36(8), 1341–1343 (2011).
    [CrossRef] [PubMed]
  28. G. Lamouche, M. L. Dufour, B. Gauthier, and J. P. Monchalin, “Gouy phase anomaly in optical coherence tomography,” Opt. Commun.239(4-6), 297–301 (2004).
    [CrossRef]
  29. N. C. van der Valk, W. A. van der Marel, and P. C. M. Planken, “Terahertz polarization imaging,” Opt. Lett.30(20), 2802–2804 (2005).
    [CrossRef] [PubMed]
  30. Q. W. Zhan, “Second-order tilted wave interpretation of the Gouy phase shift under high numerical aperture uniform illumination,” Opt. Commun.242(4-6), 351–360 (2004).
    [CrossRef]

2012 (3)

2011 (3)

2010 (4)

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun.283(18), 3371–3375 (2010).
[CrossRef]

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun.283(23), 4626–4632 (2010).
[CrossRef]

N. Shivaram, A. Roberts, L. Xu, and A. Sandhu, “In situ spatial mapping of Gouy phase slip for high-detail attosecond pump-probe measurements,” Opt. Lett.35(20), 3312–3314 (2010).
[CrossRef] [PubMed]

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz polarization real-time imaging based on balanced electro-optic detection,” J. Opt. Soc. Am. A27(11), 2387–2393 (2010).
[CrossRef] [PubMed]

2009 (1)

X. K. Wang, Y. Cui, D. Hu, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz quasi-near-field real-time imaging,” Opt. Commun.282(24), 4683–4687 (2009).
[CrossRef]

2007 (2)

2006 (1)

2005 (1)

2004 (4)

J. H. Chow, G. de Vine, M. B. Gray, and D. E. McClelland, “Measurement of Gouy phase evolution by use of spatial mode interference,” Opt. Lett.29(20), 2339–2341 (2004).
[CrossRef] [PubMed]

G. Lamouche, M. L. Dufour, B. Gauthier, and J. P. Monchalin, “Gouy phase anomaly in optical coherence tomography,” Opt. Commun.239(4-6), 297–301 (2004).
[CrossRef]

Q. W. Zhan, “Second-order tilted wave interpretation of the Gouy phase shift under high numerical aperture uniform illumination,” Opt. Commun.242(4-6), 351–360 (2004).
[CrossRef]

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett.92(11), 113001 (2004).
[CrossRef] [PubMed]

2001 (2)

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, “Enhanced depth resolution in terahertz imaging using phase-shift interferometry,” Appl. Phys. Lett.78(6), 835–837 (2001).
[CrossRef]

S. M. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett.26(8), 485–487 (2001).
[CrossRef] [PubMed]

2000 (2)

Z. P. Jiang, X. G. Xu, and X.-C. Zhang, “Improvement of terahertz imaging with a dynamic subtraction technique,” Appl. Opt.39(17), 2982–2987 (2000).
[CrossRef] [PubMed]

R. W. McGowan, R. A. Cheville, and D. Grischkowsky, “Direct observation of the Gouy phase shift in THz impulse ranging,” Appl. Phys. Lett.76(6), 670–672 (2000).
[CrossRef]

1999 (1)

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett.83(17), 3410–3413 (1999).
[CrossRef]

1996 (2)

P. Hariharan and P. A. Robinson, “The Gouy phase shift as a geometrical quantum effect,” J. Mod. Opt.43(2), 219–221 (1996).

Q. Wu, T. D. Hewitt, and X. C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett.69(8), 1026–1028 (1996).
[CrossRef]

1993 (1)

R. Simon and N. Mukunda, “Bargmann invariant and the geometry of the Gouy effect,” Phys. Rev. Lett.70(7), 880–883 (1993).
[CrossRef] [PubMed]

1980 (1)

Agrawal, A.

Ahn, J.

M. Yi, K. Lee, J. D. Song, and J. Ahn, “Terahertz phase microscopy in the sub-wavelength regime,” Appl. Phys. Lett.100(16), 161110 (2012).
[CrossRef]

Baltuska, A.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett.92(11), 113001 (2004).
[CrossRef] [PubMed]

Bon, P.

Bonod, N.

Boyd, R. W.

Cheville, R. A.

R. W. McGowan, R. A. Cheville, and D. Grischkowsky, “Direct observation of the Gouy phase shift in THz impulse ranging,” Appl. Phys. Lett.76(6), 670–672 (2000).
[CrossRef]

Chow, J. H.

Cui, Y.

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun.283(23), 4626–4632 (2010).
[CrossRef]

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz polarization real-time imaging based on balanced electro-optic detection,” J. Opt. Soc. Am. A27(11), 2387–2393 (2010).
[CrossRef] [PubMed]

X. K. Wang, Y. Cui, D. Hu, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz quasi-near-field real-time imaging,” Opt. Commun.282(24), 4683–4687 (2009).
[CrossRef]

X. K. Wang, Y. Cui, W. F. Sun, Y. Zhang, and C. L. Zhang, “Terahertz pulse reflective focal-plane tomography,” Opt. Express15(22), 14369–14375 (2007).
[CrossRef] [PubMed]

Dainty, J. C.

de Vine, G.

Dorney, T. D.

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, “Enhanced depth resolution in terahertz imaging using phase-shift interferometry,” Appl. Phys. Lett.78(6), 835–837 (2001).
[CrossRef]

Dufour, M. L.

G. Lamouche, M. L. Dufour, B. Gauthier, and J. P. Monchalin, “Gouy phase anomaly in optical coherence tomography,” Opt. Commun.239(4-6), 297–301 (2004).
[CrossRef]

Feng, S.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett.83(17), 3410–3413 (1999).
[CrossRef]

Feng, S. M.

Gauthier, B.

G. Lamouche, M. L. Dufour, B. Gauthier, and J. P. Monchalin, “Gouy phase anomaly in optical coherence tomography,” Opt. Commun.239(4-6), 297–301 (2004).
[CrossRef]

Goulielmakis, E.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett.92(11), 113001 (2004).
[CrossRef] [PubMed]

Gray, M. B.

Grischkowsky, D.

R. W. McGowan, R. A. Cheville, and D. Grischkowsky, “Direct observation of the Gouy phase shift in THz impulse ranging,” Appl. Phys. Lett.76(6), 670–672 (2000).
[CrossRef]

Hamazaki, J.

Hariharan, P.

P. Hariharan and P. A. Robinson, “The Gouy phase shift as a geometrical quantum effect,” J. Mod. Opt.43(2), 219–221 (1996).

Hewitt, T. D.

Q. Wu, T. D. Hewitt, and X. C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett.69(8), 1026–1028 (1996).
[CrossRef]

Hu, D.

X. K. Wang, Y. Cui, D. Hu, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz quasi-near-field real-time imaging,” Opt. Commun.282(24), 4683–4687 (2009).
[CrossRef]

Jiang, Z. P.

Johnson, J. L.

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, “Enhanced depth resolution in terahertz imaging using phase-shift interferometry,” Appl. Phys. Lett.78(6), 835–837 (2001).
[CrossRef]

Kou, S. S.

Krausz, F.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett.92(11), 113001 (2004).
[CrossRef] [PubMed]

Lamouche, G.

G. Lamouche, M. L. Dufour, B. Gauthier, and J. P. Monchalin, “Gouy phase anomaly in optical coherence tomography,” Opt. Commun.239(4-6), 297–301 (2004).
[CrossRef]

Lee, K.

M. Yi, K. Lee, J. D. Song, and J. Ahn, “Terahertz phase microscopy in the sub-wavelength regime,” Appl. Phys. Lett.100(16), 161110 (2012).
[CrossRef]

Lezius, M.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett.92(11), 113001 (2004).
[CrossRef] [PubMed]

Lin, J.

Lindner, F.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett.92(11), 113001 (2004).
[CrossRef] [PubMed]

McClelland, D. E.

McGowan, R. W.

R. W. McGowan, R. A. Cheville, and D. Grischkowsky, “Direct observation of the Gouy phase shift in THz impulse ranging,” Appl. Phys. Lett.76(6), 670–672 (2000).
[CrossRef]

Mineta, Y.

Mittleman, D. M.

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, “Enhanced depth resolution in terahertz imaging using phase-shift interferometry,” Appl. Phys. Lett.78(6), 835–837 (2001).
[CrossRef]

Monchalin, J. P.

G. Lamouche, M. L. Dufour, B. Gauthier, and J. P. Monchalin, “Gouy phase anomaly in optical coherence tomography,” Opt. Commun.239(4-6), 297–301 (2004).
[CrossRef]

Monneret, S.

Morita, R.

Mukunda, N.

R. Simon and N. Mukunda, “Bargmann invariant and the geometry of the Gouy effect,” Phys. Rev. Lett.70(7), 880–883 (1993).
[CrossRef] [PubMed]

Nahata, A.

Oka, K.

Pang, X. Y.

X. Y. Pang, T. D. Visser, and W. Wolf, “Phase anomaly and phase singularities of the field in the focal region of high-numerical aperture systems,” Opt. Commun.284(24), 5517–5522 (2011).
[CrossRef]

Paulus, G. G.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett.92(11), 113001 (2004).
[CrossRef] [PubMed]

Pegoraro, A. F.

Planken, P. C. M.

Popov, K. I.

Ramunno, L.

Rigneault, H.

Roberts, A.

Robinson, P. A.

P. Hariharan and P. A. Robinson, “The Gouy phase shift as a geometrical quantum effect,” J. Mod. Opt.43(2), 219–221 (1996).

Rodríguez-Herrera, O. G.

Rolly, B.

Rudd, J. V.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett.83(17), 3410–3413 (1999).
[CrossRef]

Ruffin, A. B.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett.83(17), 3410–3413 (1999).
[CrossRef]

Sandhu, A.

Sheppard, C. J. R.

Shivaram, N.

Simon, R.

R. Simon and N. Mukunda, “Bargmann invariant and the geometry of the Gouy effect,” Phys. Rev. Lett.70(7), 880–883 (1993).
[CrossRef] [PubMed]

Song, J. D.

M. Yi, K. Lee, J. D. Song, and J. Ahn, “Terahertz phase microscopy in the sub-wavelength regime,” Appl. Phys. Lett.100(16), 161110 (2012).
[CrossRef]

Stolow, A.

Stout, B.

Sun, W. F.

van der Marel, W. A.

van der Valk, N. C.

Visser, T. D.

X. Y. Pang, T. D. Visser, and W. Wolf, “Phase anomaly and phase singularities of the field in the focal region of high-numerical aperture systems,” Opt. Commun.284(24), 5517–5522 (2011).
[CrossRef]

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun.283(18), 3371–3375 (2010).
[CrossRef]

Walther, H.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett.92(11), 113001 (2004).
[CrossRef] [PubMed]

Wang, X. K.

Wenger, J.

Whitaker, J. F.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett.83(17), 3410–3413 (1999).
[CrossRef]

Winful, H. G.

S. M. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett.26(8), 485–487 (2001).
[CrossRef] [PubMed]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett.83(17), 3410–3413 (1999).
[CrossRef]

Wolf, E.

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun.283(18), 3371–3375 (2010).
[CrossRef]

Wolf, W.

X. Y. Pang, T. D. Visser, and W. Wolf, “Phase anomaly and phase singularities of the field in the focal region of high-numerical aperture systems,” Opt. Commun.284(24), 5517–5522 (2011).
[CrossRef]

Wu, Q.

Q. Wu, T. D. Hewitt, and X. C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett.69(8), 1026–1028 (1996).
[CrossRef]

Xiong, W.

Xu, L.

Xu, X. G.

Ye, J. S.

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz polarization real-time imaging based on balanced electro-optic detection,” J. Opt. Soc. Am. A27(11), 2387–2393 (2010).
[CrossRef] [PubMed]

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun.283(23), 4626–4632 (2010).
[CrossRef]

X. K. Wang, Y. Cui, D. Hu, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz quasi-near-field real-time imaging,” Opt. Commun.282(24), 4683–4687 (2009).
[CrossRef]

Yi, M.

M. Yi, K. Lee, J. D. Song, and J. Ahn, “Terahertz phase microscopy in the sub-wavelength regime,” Appl. Phys. Lett.100(16), 161110 (2012).
[CrossRef]

Yuan, X.-C.

Zhan, Q. W.

Q. W. Zhan, “Second-order tilted wave interpretation of the Gouy phase shift under high numerical aperture uniform illumination,” Opt. Commun.242(4-6), 351–360 (2004).
[CrossRef]

Zhang, C. L.

Zhang, X. C.

Q. Wu, T. D. Hewitt, and X. C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett.69(8), 1026–1028 (1996).
[CrossRef]

Zhang, X.-C.

Zhang, Y.

Zhu, W.

Appl. Opt. (1)

Appl. Phys. Lett. (4)

M. Yi, K. Lee, J. D. Song, and J. Ahn, “Terahertz phase microscopy in the sub-wavelength regime,” Appl. Phys. Lett.100(16), 161110 (2012).
[CrossRef]

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, “Enhanced depth resolution in terahertz imaging using phase-shift interferometry,” Appl. Phys. Lett.78(6), 835–837 (2001).
[CrossRef]

R. W. McGowan, R. A. Cheville, and D. Grischkowsky, “Direct observation of the Gouy phase shift in THz impulse ranging,” Appl. Phys. Lett.76(6), 670–672 (2000).
[CrossRef]

Q. Wu, T. D. Hewitt, and X. C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett.69(8), 1026–1028 (1996).
[CrossRef]

J. Mod. Opt. (1)

P. Hariharan and P. A. Robinson, “The Gouy phase shift as a geometrical quantum effect,” J. Mod. Opt.43(2), 219–221 (1996).

J. Opt. Soc. Am. (1)

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

Opt. Commun. (6)

X. K. Wang, Y. Cui, D. Hu, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz quasi-near-field real-time imaging,” Opt. Commun.282(24), 4683–4687 (2009).
[CrossRef]

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun.283(23), 4626–4632 (2010).
[CrossRef]

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun.283(18), 3371–3375 (2010).
[CrossRef]

X. Y. Pang, T. D. Visser, and W. Wolf, “Phase anomaly and phase singularities of the field in the focal region of high-numerical aperture systems,” Opt. Commun.284(24), 5517–5522 (2011).
[CrossRef]

G. Lamouche, M. L. Dufour, B. Gauthier, and J. P. Monchalin, “Gouy phase anomaly in optical coherence tomography,” Opt. Commun.239(4-6), 297–301 (2004).
[CrossRef]

Q. W. Zhan, “Second-order tilted wave interpretation of the Gouy phase shift under high numerical aperture uniform illumination,” Opt. Commun.242(4-6), 351–360 (2004).
[CrossRef]

Opt. Express (5)

Opt. Lett. (6)

Phys. Rev. Lett. (3)

R. Simon and N. Mukunda, “Bargmann invariant and the geometry of the Gouy effect,” Phys. Rev. Lett.70(7), 880–883 (1993).
[CrossRef] [PubMed]

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett.92(11), 113001 (2004).
[CrossRef] [PubMed]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett.83(17), 3410–3413 (1999).
[CrossRef]

Other (2)

A. E. Siegman, Lasers (Mill Valley, Califorina, 1986), Chap. 17.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 4.

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Figures (6)

Fig. 1
Fig. 1

(a) THz balanced electro-optic (EO) holographic imaging system. The inset shows the Z-scan measurement of complex amplitude distribution around the focal point of the high density polyethylene lens (HDPL). (b) Normalized intensity distribution of the 1.3 THz component on the X-Z plane.

Fig. 2
Fig. 2

Experimental and simulated three dimensional information of the Gouy phase shift for 1.3 THz radiation. (a)-(c) are the unwrapped transverse phase distributions at Z = −22 mm, 0 mm and 28 mm, respectively. (d) is the longitudinal phase distribution on the X-Z plane. (e)-(g) are the simulated transverse phase maps at Z = −22 mm, 0 mm, and 28 mm, respectively. (h) is the simulated longitudinal phase map.

Fig. 3
Fig. 3

Longitudinal (a) and transverse (b) distributions of the Gouy phase shift. The blue circular dotted line is the experimental result. The red solid line is the simulation result. The green dashed line is the calculated result by using the analytic expression of the Gouy phase shift.

Fig. 4
Fig. 4

Gouy phase shifts for difference spectral components. (a)-(d) are the longitudinal phase maps at 0.7 THz, 1.0 THz, 1.6 THz, and 1.9 THz. (e) and (f) are the longitudinal and transverse distributions of the Gouy phase shifts extracted from (a)-(d).

Fig. 5
Fig. 5

Axial energy ratios with 0.7 THz, 1.0 THz, 1.3 THz, 1.6 THz, and 1.9 THz components.

Fig. 6
Fig. 6

Gouy phase shift with a 100 mm focal length HDPL. (a) and (b) are the longitudinal intensity and phase distributions of the 1.3 THz component on the X-Z plane. (c) and (d) show the axial phase distributions and the transverse phase differences with the 100 mm and the 50 mm focal length HDPLs.

Equations (3)

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U 1 ( x,y )=exp[ ( x 2 + y 2 ) w 2 ],
U 2 ( x,y )=exp[ ( x 2 + y 2 ) w 2 ]exp[ j k 2f ( x 2 + y 2 ) ],
U z ( x z , y z )= 1 jλz U 2 ( x,y )exp{ j k 2d [ ( x x z ) 2 + ( y y z ) 2 ] } dxdy,

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