We present a theoretical and experimental investigation of the THz pulse phase measured by a broadband heterodyne detection method via field-induced second-harmonic generation in ambient air. The dependence of the detected THz phase spectra on the positions of the wire shaped electrodes scanning along the detection plasma is discussed. An additional phase shift around the beam focus is observed. Theoretical deductions reveal that it is caused by the Gouy shift of the optical probe beam and THz beam during the heterodyne detection process.

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1. J. Dai, X. Xie, and X.-C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett.97(10), 103903 (2006). [CrossRef] [PubMed]
2. X. Xie, J. Dai, and X.-C. Zhang, “Coherent control of THz wave generation in ambient air,” Phys. Rev. Lett.96(7), 075005 (2006). [CrossRef] [PubMed]
3. D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett.25(16), 1210–1212 (2000). [CrossRef] [PubMed]
4. J. Dai, X. Xie, and X.-C. Zhang, “Terahertz wave amplification in gases with the excitation of femtosecond laser pulses,” Appl. Phys. Lett.91(21), 211102 (2007). [CrossRef]
5. J. Dai and X.-C. Zhang, “Terahertz wave generation from gas plasma using a phase compensator with attosecond phase-control accuracy,” Appl. Phys. Lett.94(2), 021117 (2009). [CrossRef]
6. H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett.103(2), 023902 (2009). [CrossRef] [PubMed]
7. J. Dai, N. Karpowicz, and X.-C. Zhang, “Coherent polarization control of terahertz waves generated from two-color laser-induced gas plasma,” Phys. Rev. Lett.103(2), 023001 (2009). [CrossRef] [PubMed]
8. Y. Liu, A. Houard, B. Prade, S. Akturk, A. Mysyrowicz, and V. T. Tikhonchuk, “Terahertz radiation source in air based on bifilamentation of femtosecond laser pulses,” Phys. Rev. Lett.99(13), 135002 (2007). [CrossRef] [PubMed]
9. N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire ‘terahertz gap’,” Appl. Phys. Lett.92(1), 011131 (2008). [CrossRef]
10. X. Lu, N. Karpowicz, Y. Chen, and X.-C. Zhang, “Systematic study of broadband terahertz gas sensor,” Appl. Phys. Lett.93(26), 261106 (2008). [CrossRef]
11. X. Lu, N. Karpowicz, and X.-C. Zhang, “Broadband terahertz detection with selected gases,” J. Opt. Soc. Am. B26(9), A66–A73 (2009). [CrossRef]
12. L. Zhang, H. Zhong, C. Deng, C. Zhang, and Y. Zhao, “Terahertz wave reference-free phase imaging for identification of explosives,” Appl. Phys. Lett.92(9), 091117 (2008). [CrossRef]
13. H. Zhong, C. Zhang, L. Zhang, Y. Zhao, and X.-C. Zhang, “A phase feature extraction technique for terahertz reflection spectroscopy,” Appl. Phys. Lett.92(22), 221106 (2008). [CrossRef]
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. McGowan, R. Cheville, and D. Grischkowsky, “Direct observation of the Gouy phase shift in THz impulses 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. H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett.71(17), 2725–2728 (1993). [CrossRef] [PubMed]
18. M. Kress, T. Löffler, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett.29(10), 1120–1122 (2004). [CrossRef] [PubMed]
19. A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of terahertz radiation from laser filaments in air by a static electric field,” Phys. Rev. Lett.100(25), 255006 (2008). [CrossRef] [PubMed]
20. R. W. Boyd, Nonlinear Optics (Academic, 1992).

Appl. Phys. Lett.

• J. Dai, X. Xie, and X.-C. Zhang, “Terahertz wave amplification in gases with the excitation of femtosecond laser pulses,” Appl. Phys. Lett.91(21), 211102 (2007). [CrossRef]
• J. Dai and X.-C. Zhang, “Terahertz wave generation from gas plasma using a phase compensator with attosecond phase-control accuracy,” Appl. Phys. Lett.94(2), 021117 (2009). [CrossRef]
• N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire ‘terahertz gap’,” Appl. Phys. Lett.92(1), 011131 (2008). [CrossRef]
• X. Lu, N. Karpowicz, Y. Chen, and X.-C. Zhang, “Systematic study of broadband terahertz gas sensor,” Appl. Phys. Lett.93(26), 261106 (2008). [CrossRef]
• L. Zhang, H. Zhong, C. Deng, C. Zhang, and Y. Zhao, “Terahertz wave reference-free phase imaging for identification of explosives,” Appl. Phys. Lett.92(9), 091117 (2008). [CrossRef]
• H. Zhong, C. Zhang, L. Zhang, Y. Zhao, and X.-C. Zhang, “A phase feature extraction technique for terahertz reflection spectroscopy,” Appl. Phys. Lett.92(22), 221106 (2008). [CrossRef]
• R. McGowan, R. Cheville, and D. Grischkowsky, “Direct observation of the Gouy phase shift in THz impulses ranging,” Appl. Phys. Lett.76(6), 670–672 (2000). [CrossRef]

J. Opt. Soc. Am. B

• X. Lu, N. Karpowicz, and X.-C. Zhang, “Broadband terahertz detection with selected gases,” J. Opt. Soc. Am. B26(9), A66–A73 (2009). [CrossRef]

Opt. Express

• 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]

Opt. Lett.

• M. Kress, T. Löffler, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett.29(10), 1120–1122 (2004). [CrossRef] [PubMed]
• D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett.25(16), 1210–1212 (2000). [CrossRef] [PubMed]

Phys. Rev. Lett.

• A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of terahertz radiation from laser filaments in air by a static electric field,” Phys. Rev. Lett.100(25), 255006 (2008). [CrossRef] [PubMed]
• H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett.71(17), 2725–2728 (1993). [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]
• J. Dai, X. Xie, and X.-C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett.97(10), 103903 (2006). [CrossRef] [PubMed]
• X. Xie, J. Dai, and X.-C. Zhang, “Coherent control of THz wave generation in ambient air,” Phys. Rev. Lett.96(7), 075005 (2006). [CrossRef] [PubMed]
• H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett.103(2), 023902 (2009). [CrossRef] [PubMed]
• J. Dai, N. Karpowicz, and X.-C. Zhang, “Coherent polarization control of terahertz waves generated from two-color laser-induced gas plasma,” Phys. Rev. Lett.103(2), 023001 (2009). [CrossRef] [PubMed]
• Y. Liu, A. Houard, B. Prade, S. Akturk, A. Mysyrowicz, and V. T. Tikhonchuk, “Terahertz radiation source in air based on bifilamentation of femtosecond laser pulses,” Phys. Rev. Lett.99(13), 135002 (2007). [CrossRef] [PubMed]

Other

• R. W. Boyd, Nonlinear Optics (Academic, 1992).

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