Abstract

The THz emission point on a nonlinear electro-optical crystal for generating broadband THz radiation is modeled as a radiating Gaussian aperture. With the wavelengths of the infrared pump beam being much smaller than the wavelength components of the generated THz pulse, a THz sub-wavelength radiating aperture with Gaussian profile is effectively created. This paper comprehensively investigates Gaussian apertures in focused THz radiation generation in electro-optical crystals and illustrates the break-down of the paraxial approximation at low THz frequencies. The findings show that the shape of the radiation pattern causes a reduction in detectable THz radiation and hence contributes significantly to low signal-to-noise ratio in THz radiation generation. Whilst we have demonstrated the findings on optical rectification in this paper, the model may apply without a loss of generality to other types of apertures sources in THz radiation generation.

© 2010 Optical Society of America

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  1. G. Mourou, C. V. Stancampiano, V. Antonetti, and A. Orszag, “Picosecond microwave pulses generated with a subpicosecond laser-driven semiconductor switch,” Appl. Phys. Lett. 39, 295–296 (1981).
    [CrossRef]
  2. C. Fattinger, and D. Grischkowsky, “Point source terahertz optics,” Appl. Phys. Lett. 53, 1480–1482 (1988).
    [CrossRef]
  3. M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, “Optical rectification,” Phys. Rev. Lett. 9, 446–448 (1962).
    [CrossRef]
  4. X.-C. Zhang, Y. Jin, and X. F. Ma, “Coherent measurement of THz optical rectification from electro-optic crystals,” Appl. Phys. Lett. 61, 2764–2766 (1992).
    [CrossRef]
  5. A. Rice, Y. Jin, X. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from _110_ zinc-blende crystals,” Appl. Phys. Lett. 64, 1324–1326 (1994).
    [CrossRef]
  6. Q. Chen, and X.-C. Zhang, “Polarization modulation in optoelectronic generation and detection of terahertz beams,” Appl. Phys. Lett. 74, 3435–3437 (1999).
    [CrossRef]
  7. T. Yuan, S. P. Mickan, J. Xu, D. Abbott, and X.-C. Zhang “Towards an apertureless electro-optic T-ray microscope,” CLEO, 637 – 638 (2002).
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    [CrossRef]
  20. X. Xie, J. Xu, J. Dai, and X.-C. Zhang, “Enhancement of terahertz wave generation from laser induced plasma,” Appl. Phys. Lett. 90, 141104 (2007).
    [CrossRef]

2008 (1)

2007 (2)

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

X. Xie, J. Xu, J. Dai, and X.-C. Zhang, “Enhancement of terahertz wave generation from laser induced plasma,” Appl. Phys. Lett. 90, 141104 (2007).
[CrossRef]

2006 (1)

Q. Xing, L. Lang, Z. Tian, N. Zhang, S. Li, K. Wang, L. Chai, and Q. Wang, “The effect of two-photon absorption and optical excitation area on the generation of THz radiation,” Opt. Commun. 267, 422–426 (2006).
[CrossRef]

2005 (1)

1999 (2)

J. Xu, and X.-C. Zhang, “Optical rectification in an area with a diameter comparable to or smaller than the center wavelength of terahertz radiation,” Opt. Lett. 27, 1067–1069 (1999).
[CrossRef]

Q. Chen, and X.-C. Zhang, “Polarization modulation in optoelectronic generation and detection of terahertz beams,” Appl. Phys. Lett. 74, 3435–3437 (1999).
[CrossRef]

1996 (1)

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
[CrossRef]

1994 (1)

A. Rice, Y. Jin, X. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from _110_ zinc-blende crystals,” Appl. Phys. Lett. 64, 1324–1326 (1994).
[CrossRef]

1992 (1)

X.-C. Zhang, Y. Jin, and X. F. Ma, “Coherent measurement of THz optical rectification from electro-optic crystals,” Appl. Phys. Lett. 61, 2764–2766 (1992).
[CrossRef]

1988 (1)

C. Fattinger, and D. Grischkowsky, “Point source terahertz optics,” Appl. Phys. Lett. 53, 1480–1482 (1988).
[CrossRef]

1981 (1)

G. Mourou, C. V. Stancampiano, V. Antonetti, and A. Orszag, “Picosecond microwave pulses generated with a subpicosecond laser-driven semiconductor switch,” Appl. Phys. Lett. 39, 295–296 (1981).
[CrossRef]

1962 (1)

M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, “Optical rectification,” Phys. Rev. Lett. 9, 446–448 (1962).
[CrossRef]

Abbott, D.

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

Alexander, M.

A. Rice, Y. Jin, X. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from _110_ zinc-blende crystals,” Appl. Phys. Lett. 64, 1324–1326 (1994).
[CrossRef]

Antonetti, V.

G. Mourou, C. V. Stancampiano, V. Antonetti, and A. Orszag, “Picosecond microwave pulses generated with a subpicosecond laser-driven semiconductor switch,” Appl. Phys. Lett. 39, 295–296 (1981).
[CrossRef]

Atakaramians, S.

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

Balakrishnan, J.

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

Bass, M.

M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, “Optical rectification,” Phys. Rev. Lett. 9, 446–448 (1962).
[CrossRef]

Bliss, D.

A. Rice, Y. Jin, X. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from _110_ zinc-blende crystals,” Appl. Phys. Lett. 64, 1324–1326 (1994).
[CrossRef]

Boccara, C.

Chai, L.

Q. Xing, L. Lang, Z. Tian, N. Zhang, S. Li, K. Wang, L. Chai, and Q. Wang, “The effect of two-photon absorption and optical excitation area on the generation of THz radiation,” Opt. Commun. 267, 422–426 (2006).
[CrossRef]

Chen, Q.

Q. Chen, and X.-C. Zhang, “Polarization modulation in optoelectronic generation and detection of terahertz beams,” Appl. Phys. Lett. 74, 3435–3437 (1999).
[CrossRef]

Dai, J.

X. Xie, J. Xu, J. Dai, and X.-C. Zhang, “Enhancement of terahertz wave generation from laser induced plasma,” Appl. Phys. Lett. 90, 141104 (2007).
[CrossRef]

Dakovski, G.

Fattinger, C.

C. Fattinger, and D. Grischkowsky, “Point source terahertz optics,” Appl. Phys. Lett. 53, 1480–1482 (1988).
[CrossRef]

Ferguson, B.

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

Fischer, B. M.

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

Franken, P. A.

M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, “Optical rectification,” Phys. Rev. Lett. 9, 446–448 (1962).
[CrossRef]

Gresillon, S.

Grischkowsky, D.

C. Fattinger, and D. Grischkowsky, “Point source terahertz optics,” Appl. Phys. Lett. 53, 1480–1482 (1988).
[CrossRef]

Heinz, T. F.

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
[CrossRef]

Jin, Y.

A. Rice, Y. Jin, X. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from _110_ zinc-blende crystals,” Appl. Phys. Lett. 64, 1324–1326 (1994).
[CrossRef]

X.-C. Zhang, Y. Jin, and X. F. Ma, “Coherent measurement of THz optical rectification from electro-optic crystals,” Appl. Phys. Lett. 61, 2764–2766 (1992).
[CrossRef]

Jones, I.

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

Kubera, B.

Lang, L.

Q. Xing, L. Lang, Z. Tian, N. Zhang, S. Li, K. Wang, L. Chai, and Q. Wang, “The effect of two-photon absorption and optical excitation area on the generation of THz radiation,” Opt. Commun. 267, 422–426 (2006).
[CrossRef]

Larkin, J.

A. Rice, Y. Jin, X. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from _110_ zinc-blende crystals,” Appl. Phys. Lett. 64, 1324–1326 (1994).
[CrossRef]

Lecaque, R.

Li, S.

Q. Xing, L. Lang, Z. Tian, N. Zhang, S. Li, K. Wang, L. Chai, and Q. Wang, “The effect of two-photon absorption and optical excitation area on the generation of THz radiation,” Opt. Commun. 267, 422–426 (2006).
[CrossRef]

Lin, H.

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

Ma, X.

A. Rice, Y. Jin, X. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from _110_ zinc-blende crystals,” Appl. Phys. Lett. 64, 1324–1326 (1994).
[CrossRef]

Ma, X. F.

X.-C. Zhang, Y. Jin, and X. F. Ma, “Coherent measurement of THz optical rectification from electro-optic crystals,” Appl. Phys. Lett. 61, 2764–2766 (1992).
[CrossRef]

Mickan, S. P.

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

Mourou, G.

G. Mourou, C. V. Stancampiano, V. Antonetti, and A. Orszag, “Picosecond microwave pulses generated with a subpicosecond laser-driven semiconductor switch,” Appl. Phys. Lett. 39, 295–296 (1981).
[CrossRef]

Nahata, A.

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
[CrossRef]

Ng, B. W.-H.

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

Orszag, A.

G. Mourou, C. V. Stancampiano, V. Antonetti, and A. Orszag, “Picosecond microwave pulses generated with a subpicosecond laser-driven semiconductor switch,” Appl. Phys. Lett. 39, 295–296 (1981).
[CrossRef]

Png, G. M.

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

Rice, A.

A. Rice, Y. Jin, X. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from _110_ zinc-blende crystals,” Appl. Phys. Lett. 64, 1324–1326 (1994).
[CrossRef]

Shan, J.

Stancampiano, C. V.

G. Mourou, C. V. Stancampiano, V. Antonetti, and A. Orszag, “Picosecond microwave pulses generated with a subpicosecond laser-driven semiconductor switch,” Appl. Phys. Lett. 39, 295–296 (1981).
[CrossRef]

Tian, Z.

Q. Xing, L. Lang, Z. Tian, N. Zhang, S. Li, K. Wang, L. Chai, and Q. Wang, “The effect of two-photon absorption and optical excitation area on the generation of THz radiation,” Opt. Commun. 267, 422–426 (2006).
[CrossRef]

Ung, B. S. Y.

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

Wang, K.

Q. Xing, L. Lang, Z. Tian, N. Zhang, S. Li, K. Wang, L. Chai, and Q. Wang, “The effect of two-photon absorption and optical excitation area on the generation of THz radiation,” Opt. Commun. 267, 422–426 (2006).
[CrossRef]

Wang, Q.

Q. Xing, L. Lang, Z. Tian, N. Zhang, S. Li, K. Wang, L. Chai, and Q. Wang, “The effect of two-photon absorption and optical excitation area on the generation of THz radiation,” Opt. Commun. 267, 422–426 (2006).
[CrossRef]

Ward, J. F.

M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, “Optical rectification,” Phys. Rev. Lett. 9, 446–448 (1962).
[CrossRef]

Weinreich, G.

M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, “Optical rectification,” Phys. Rev. Lett. 9, 446–448 (1962).
[CrossRef]

Weling, A. S.

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
[CrossRef]

Withayachumnankul, W.

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

Xie, X.

X. Xie, J. Xu, J. Dai, and X.-C. Zhang, “Enhancement of terahertz wave generation from laser induced plasma,” Appl. Phys. Lett. 90, 141104 (2007).
[CrossRef]

Xing, Q.

Q. Xing, L. Lang, Z. Tian, N. Zhang, S. Li, K. Wang, L. Chai, and Q. Wang, “The effect of two-photon absorption and optical excitation area on the generation of THz radiation,” Opt. Commun. 267, 422–426 (2006).
[CrossRef]

Xu, J.

X. Xie, J. Xu, J. Dai, and X.-C. Zhang, “Enhancement of terahertz wave generation from laser induced plasma,” Appl. Phys. Lett. 90, 141104 (2007).
[CrossRef]

J. Xu, and X.-C. Zhang, “Optical rectification in an area with a diameter comparable to or smaller than the center wavelength of terahertz radiation,” Opt. Lett. 27, 1067–1069 (1999).
[CrossRef]

Yin, X.

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

Zhang, N.

Q. Xing, L. Lang, Z. Tian, N. Zhang, S. Li, K. Wang, L. Chai, and Q. Wang, “The effect of two-photon absorption and optical excitation area on the generation of THz radiation,” Opt. Commun. 267, 422–426 (2006).
[CrossRef]

Zhang, X.-C.

X. Xie, J. Xu, J. Dai, and X.-C. Zhang, “Enhancement of terahertz wave generation from laser induced plasma,” Appl. Phys. Lett. 90, 141104 (2007).
[CrossRef]

J. Xu, and X.-C. Zhang, “Optical rectification in an area with a diameter comparable to or smaller than the center wavelength of terahertz radiation,” Opt. Lett. 27, 1067–1069 (1999).
[CrossRef]

Q. Chen, and X.-C. Zhang, “Polarization modulation in optoelectronic generation and detection of terahertz beams,” Appl. Phys. Lett. 74, 3435–3437 (1999).
[CrossRef]

A. Rice, Y. Jin, X. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from _110_ zinc-blende crystals,” Appl. Phys. Lett. 64, 1324–1326 (1994).
[CrossRef]

X.-C. Zhang, Y. Jin, and X. F. Ma, “Coherent measurement of THz optical rectification from electro-optic crystals,” Appl. Phys. Lett. 61, 2764–2766 (1992).
[CrossRef]

Appl. Phys. Lett. (7)

X.-C. Zhang, Y. Jin, and X. F. Ma, “Coherent measurement of THz optical rectification from electro-optic crystals,” Appl. Phys. Lett. 61, 2764–2766 (1992).
[CrossRef]

A. Rice, Y. Jin, X. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from _110_ zinc-blende crystals,” Appl. Phys. Lett. 64, 1324–1326 (1994).
[CrossRef]

Q. Chen, and X.-C. Zhang, “Polarization modulation in optoelectronic generation and detection of terahertz beams,” Appl. Phys. Lett. 74, 3435–3437 (1999).
[CrossRef]

G. Mourou, C. V. Stancampiano, V. Antonetti, and A. Orszag, “Picosecond microwave pulses generated with a subpicosecond laser-driven semiconductor switch,” Appl. Phys. Lett. 39, 295–296 (1981).
[CrossRef]

C. Fattinger, and D. Grischkowsky, “Point source terahertz optics,” Appl. Phys. Lett. 53, 1480–1482 (1988).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
[CrossRef]

X. Xie, J. Xu, J. Dai, and X.-C. Zhang, “Enhancement of terahertz wave generation from laser induced plasma,” Appl. Phys. Lett. 90, 141104 (2007).
[CrossRef]

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

Opt. Commun. (1)

Q. Xing, L. Lang, Z. Tian, N. Zhang, S. Li, K. Wang, L. Chai, and Q. Wang, “The effect of two-photon absorption and optical excitation area on the generation of THz radiation,” Opt. Commun. 267, 422–426 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, “Optical rectification,” Phys. Rev. Lett. 9, 446–448 (1962).
[CrossRef]

Proc. IEEE (1)

W. Withayachumnankul, G. M. Png, X. Yin, S. Atakaramians, I. Jones, H. Lin, B. S. Y. Ung, J. Balakrishnan, B. W.-H. Ng, B. Ferguson, S. P. Mickan, B. M. Fischer, and D. Abbott, “T-ray sensing and imaging,” Proc. IEEE 95, 1528–1558 (2007).
[CrossRef]

Other (7)

B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, 1991).
[CrossRef]

S. J. Orfanidis, Electromagnetic Waves and Antennas (http://www.ece.rutgers.edu/orfanidi/ewa/ch17.pdf, 2008).

C. Fumeaux, D. Baumann, S. Atakaramians, and E. Li “Considerations on paraxial Gaussian beam source conditions for time-domain full-wave simulations,” 25th Annual Review of Progress in Applied Computational Electromagnetics, 401 – 406 (2009).

T. Yuan, S. P. Mickan, J. Xu, D. Abbott, and X.-C. Zhang “Towards an apertureless electro-optic T-ray microscope,” CLEO, 637 – 638 (2002).

T. Hattori, K. Tukamoto, R. Rungsawang, and H. Nakatsuka, “Knife edge measurement of tightly focused terahertz pulses,” The 8th International Workshop on Femtosecond Technology, 1 (2001).

C. A. Balanis, Antenna Theory: Analysis and Design (John Wiley & Sons, 1997).

A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

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Figures (13)

Fig. 1.
Fig. 1.

A THz time domain spectroscopy hybrid setup comprising of a Zomega ZnTe 〈110〉 crystal as emitter and a University of Freiburg, Germany manufactured photoconductive antenna as detector. The inset zooms in on the crystal to knife setup. The pump laser beam is focused into a 1 mm thick ZnTe crystal by means of an optical lens. The emitted THz is sliced along the x-axis by translating a sharp razor blade in the far-field region from the crystal back surface. By doing so, the THz knife-edge profile composed of different frequency components is mapped out.

Fig. 2.
Fig. 2.

(a) The THz waveform generated with the THz time domain spectroscopy setup. The time-domain representation is averaged over 10 pulses. (b) Spectrum of the pulse. The setup achieved a SNR of 100 dB and a bandwidth of approximately 3 THz.

Fig. 3.
Fig. 3.

Main steps to modelling are summarised, clockwise, as follows: (a) Model the THz radiation generation as an aperture with Gaussian intensity distribution and a beam waist identical to that of the IR pump beam. (b) Using the equivalence principle, introduce equivalent electric and magnetic sources in the source aperture. (c) Discretization of the aperture area in a grid. (d) Perform a near-field to far-field transformation, computing the radiation integrals on the basis of the discretized source distribution. (e) Project the far-field intensity distribution on a screen, taking into account the decay of intensity as a function of distance. Truncate the projection at the acceptance angle θ win of the parabolic mirrors. This is highlighted by the green dashed lines. (f) Perform a numerical knife-edge measurement on the field intensity projected on the screen. (g) The resulting curve corresponds to the measured knife-edge intensity profile. It is noted that the sharp truncation of the acceptance angle neglects diffraction effects.

Fig. 4.
Fig. 4.

(a) The power spectrum of the THz waveforms acquired with a knife-edge scanned at a distance of 0.75 mm from the crystal. With each movement of the knife, the THz field becomes weaker until when the THz radiation is entirely blocked by the knife. This can be seen at x = 5 mm, where the knife has not obstructed the THz beam, as opposed to x = 7 mm, where the THz radiation is totally blocked. (b) Selected frequency components are shown at different knife positions. The knife-edge profile is also shown to illustrate the integrated spatial distribution of the THz pulse at selected frequencies are unaffected by water vapor absorption and noise that occur at high THz frequencies.

Fig. 5.
Fig. 5.

(a) The radiation pattern and (b) the knife-edge profile at 0.375 THz. The beam waist w0 is approximately λ/5 leading to a pattern resembling the obliquity factor.

Fig. 6.
Fig. 6.

(a) The radiation pattern and (b) the knife-edge profile at 0.712 THz. The beam waist w0 is approximately λ/3 starting to approach paraxial Gaussian beam pattern towards the front.

Fig. 7.
Fig. 7.

(a) The radiation pattern and (b) the knife-edge profile at 1.35 THz. The beam waist w0 is approximately 0.7λ approaching a paraxial Gaussian pattern. Angle of divergence is 27°.

Fig. 8.
Fig. 8.

(a) The radiation pattern and (b) the knife-edge profile at 1.5 THz. The beam waist w0 is exactly 0.75λ approaching a paraxial Gaussian pattern. Angle of divergence is 24°.

Fig. 9.
Fig. 9.

(a) The radiation pattern and (b) the knife-edge profile at 1.91 THz. The beam waist w0 is approximately λ approaching a paraxial Gaussian pattern, with the back lobes sightly greater than −40 dB. Angle of divergence is 19°.

Fig. 10.
Fig. 10.

(a) The radiation pattern and (b) the knife-edge profile at 2.14 THz. The beam waist w0 is approximately 1.1λ closely resembling the paraxial Gaussian pattern, except for the back lobes less than −40 dB. Angle of divergence is 17°.

Fig. 11.
Fig. 11.

(a) The radiation pattern and (b) the knife-edge profile at 2.51 THz. The beam waist w0 is approximately 1.25λ closely resembling the paraxial Gaussian pattern, except for the back lobes less than −40 dB. Angle of divergence is 14°.

Fig. 12.
Fig. 12.

The goodness of the fit is demonstrated by fitting the knife-edge profile at 2.51 THz with the numerical model of 2.51 THz and 0.375 THz respectively. The latter is chosen to show a distinctive difference between the fits and the validity of the fitting criterion. For curve fitting, the free-parameters (beam waist and effective location of the source) are within a realistic range of values, and the resulting knife-edge curves must apply simultaneously to all the selected frequency components.

Fig. 13.
Fig. 13.

The detectable THz power percentage over the total generated THz power, with the normalized IR pump beam waist, w0/λ, on the x-axis for 3 different acceptance angle θ win = 10°, θ win = 20° and θ win = 30°.

Equations (5)

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A obl ( θ ) = ( 1 + cos θ ) 2 .
E i , y = E 0 e r 2 w 0 2
H i , x = E i , y η 0 ,
M S = n ̂ s × E i
J S = n ̂ s × H i .

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