Abstract

Asynchronous electro-optic sampling (A-EOS) using two mode-locked lasers with slightly different pulse repetition rates has significantly advanced high-speed time-domain terahertz (THz) spectroscopy on several practical fronts. However, A-EOS also holds strong potential as a precision frequency measurement technique. By carefully considering A-EOS in the frequency domain as a pair of femtosecond frequency combs with a detuned comb spacing, we show there exists a unique one-to-one mapping between a THz frequency comb and the resulting radio frequency comb of the A-EOS signal. With reasonable frequency comb spacing (0.1 to 1 GHz) and detuning frequencies (1 to 50 kHz) of the combs’ repetition rates, interrogation bandwidths of >10THz centered between 10 to 100 THz (300 to 3000cm1) are possible. Furthermore, we calculate the effect of nonuniform spectral phase of the sampling pulse train and wave-vector mismatch within a ZnTe sampling crystal on the expected heterodyne beat signal.

© 2012 Optical Society of America

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    [CrossRef]
  2. Y. Hu, X. Wang, L. Guo, and C. Zhang, “Terahertz time-domain spectroscopic study of carbon monoxide,” Spectrosc. Spectr. Anal. 26, 1008–1011 (2006).
  3. D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67, 379–390 (1998).
    [CrossRef]
  4. G. Chang, C. J. Divin, C.-H. Liu, S. L. Williamson, A. Galvanauskas, and T. B. Norris, “Power scalable compact THz system based on an ultrafast Yb-doped fiber amplifier,” Opt. Express 14, 7909–7913 (2006).
    [CrossRef]
  5. 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]
  6. F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett. 29, 1542–1544 (2004).
    [CrossRef]
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    [CrossRef]
  8. R. V. Krems, W. C. Stwalley, and B. Friedrich, Cold Molecules: Theory, Experiment, Applications (CRC Press, 2009).
  9. A. C. Vutha, W. C. Campbell, Y. V. Gurevich, N. R. Hutzler, M. Parsons, D. Patterson, E. Petrik, B. Spaun, J. M. Doyle, G. Gabrielse, and D. DeMille, “Search for the electric dipole moment of the electron with thorium monoxide,” J. Phys. B At. Mol. Opt. Phys. 43, 074007 (2010).
    [CrossRef]
  10. J. J. Hudson, B. E. Sauer, M. R. Tarbutt, and E. A. Hinds, “Measurement of the electron electric dipole moment using YbF molecules,” Phys. Rev. Lett. 89, 023003 (2002).
    [CrossRef]
  11. T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88, 241104 (2006).
    [CrossRef]
  12. Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
    [CrossRef]
  13. S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
    [CrossRef]
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    [CrossRef]
  17. G. Gallot and D. Grischkowsky, “Electro-optic detection of terahertz radiation,” J. Opt. Soc. Am. B 16, 1204–1212 (1999).
    [CrossRef]
  18. Y. Shen, The Principles of Nonlinear Optics, Wiley Classics Library (Wiley-Interscience, 2003).
  19. E. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
    [CrossRef]
  20. F. O. Ilday, H. Lim, J. R. Buckley, and F. W. Wise, “Practical all-fiber source of high-power, 120 fs pulses at 1 μm,” Opt. Lett. 28, 1362–1364 (2003).
    [CrossRef]
  21. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
    [CrossRef]
  22. E. Palik, Handbook of Optical Constants of Solids (Academic, 1985), Vol. 1.
  23. S. Schiller, “Spectrometry with frequency combs,” Opt. Lett. 27, 766–768 (2002).
    [CrossRef]
  24. I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100, 013902 (2008).
    [CrossRef]

2011 (1)

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[CrossRef]

2010 (2)

A. C. Vutha, W. C. Campbell, Y. V. Gurevich, N. R. Hutzler, M. Parsons, D. Patterson, E. Petrik, B. Spaun, J. M. Doyle, G. Gabrielse, and D. DeMille, “Search for the electric dipole moment of the electron with thorium monoxide,” J. Phys. B At. Mol. Opt. Phys. 43, 074007 (2010).
[CrossRef]

D. G. Winters, P. Schlup, and R. A. Bartels, “Subpicosecond fiber-based soliton-tuned mid-infrared source in the 9.7–14.9 μm wavelength region,” Opt. Lett. 35, 2179–2181 (2010).
[CrossRef]

2008 (1)

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100, 013902 (2008).
[CrossRef]

2007 (1)

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb.” Nature 445, 627–630 (2007).
[CrossRef]

2006 (4)

Y. Hu, X. Wang, L. Guo, and C. Zhang, “Terahertz time-domain spectroscopic study of carbon monoxide,” Spectrosc. Spectr. Anal. 26, 1008–1011 (2006).

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88, 241104 (2006).
[CrossRef]

A. Bartels, A. Thoma, C. Janke, T. Dekorsy, A. Dreyhaupt, S. Winnerl, and M. Helm, “High-resolution THz spectrometer with kHz scan rates,” Opt. Express 14, 430–437 (2006).
[CrossRef]

G. Chang, C. J. Divin, C.-H. Liu, S. L. Williamson, A. Galvanauskas, and T. B. Norris, “Power scalable compact THz system based on an ultrafast Yb-doped fiber amplifier,” Opt. Express 14, 7909–7913 (2006).
[CrossRef]

2005 (1)

2004 (1)

2003 (1)

2002 (2)

S. Schiller, “Spectrometry with frequency combs,” Opt. Lett. 27, 766–768 (2002).
[CrossRef]

J. J. Hudson, B. E. Sauer, M. R. Tarbutt, and E. A. Hinds, “Measurement of the electron electric dipole moment using YbF molecules,” Phys. Rev. Lett. 89, 023003 (2002).
[CrossRef]

1999 (1)

1998 (1)

D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67, 379–390 (1998).
[CrossRef]

1996 (2)

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
[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]

1989 (1)

M. van Exter, C. Fattinger, and D. Grischkowsky, “High-brightness terahertz beams characterized with an ultrafast detector,” Appl. Phys. Lett. 55, 337–339 (1989).
[CrossRef]

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

1969 (1)

E. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
[CrossRef]

Araki, T.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88, 241104 (2006).
[CrossRef]

Baraniuk, R.

D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67, 379–390 (1998).
[CrossRef]

Barbieri, S.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[CrossRef]

Bartels, A.

Bartels, R. A.

Brehm, M.

Buckley, J. R.

Campbell, W. C.

A. C. Vutha, W. C. Campbell, Y. V. Gurevich, N. R. Hutzler, M. Parsons, D. Patterson, E. Petrik, B. Spaun, J. M. Doyle, G. Gabrielse, and D. DeMille, “Search for the electric dipole moment of the electron with thorium monoxide,” J. Phys. B At. Mol. Opt. Phys. 43, 074007 (2010).
[CrossRef]

Chang, G.

Coddington, I.

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100, 013902 (2008).
[CrossRef]

Davies, A. G.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[CrossRef]

Dekorsy, T.

DeMille, D.

A. C. Vutha, W. C. Campbell, Y. V. Gurevich, N. R. Hutzler, M. Parsons, D. Patterson, E. Petrik, B. Spaun, J. M. Doyle, G. Gabrielse, and D. DeMille, “Search for the electric dipole moment of the electron with thorium monoxide,” J. Phys. B At. Mol. Opt. Phys. 43, 074007 (2010).
[CrossRef]

Diddams, S. A.

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb.” Nature 445, 627–630 (2007).
[CrossRef]

Divin, C. J.

Doyle, J. M.

A. C. Vutha, W. C. Campbell, Y. V. Gurevich, N. R. Hutzler, M. Parsons, D. Patterson, E. Petrik, B. Spaun, J. M. Doyle, G. Gabrielse, and D. DeMille, “Search for the electric dipole moment of the electron with thorium monoxide,” J. Phys. B At. Mol. Opt. Phys. 43, 074007 (2010).
[CrossRef]

Dreyhaupt, A.

Fattinger, C.

M. van Exter, C. Fattinger, and D. Grischkowsky, “High-brightness terahertz beams characterized with an ultrafast detector,” Appl. Phys. Lett. 55, 337–339 (1989).
[CrossRef]

Friedrich, B.

R. V. Krems, W. C. Stwalley, and B. Friedrich, Cold Molecules: Theory, Experiment, Applications (CRC Press, 2009).

Gabrielse, G.

A. C. Vutha, W. C. Campbell, Y. V. Gurevich, N. R. Hutzler, M. Parsons, D. Patterson, E. Petrik, B. Spaun, J. M. Doyle, G. Gabrielse, and D. DeMille, “Search for the electric dipole moment of the electron with thorium monoxide,” J. Phys. B At. Mol. Opt. Phys. 43, 074007 (2010).
[CrossRef]

Gallot, G.

Galvanauskas, A.

Gellie, P.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[CrossRef]

Gohle, C.

Grischkowsky, D.

G. Gallot and D. Grischkowsky, “Electro-optic detection of terahertz radiation,” J. Opt. Soc. Am. B 16, 1204–1212 (1999).
[CrossRef]

M. van Exter, C. Fattinger, and D. Grischkowsky, “High-brightness terahertz beams characterized with an ultrafast detector,” Appl. Phys. Lett. 55, 337–339 (1989).
[CrossRef]

Guo, L.

Y. Hu, X. Wang, L. Guo, and C. Zhang, “Terahertz time-domain spectroscopic study of carbon monoxide,” Spectrosc. Spectr. Anal. 26, 1008–1011 (2006).

Gurevich, Y. V.

A. C. Vutha, W. C. Campbell, Y. V. Gurevich, N. R. Hutzler, M. Parsons, D. Patterson, E. Petrik, B. Spaun, J. M. Doyle, G. Gabrielse, and D. DeMille, “Search for the electric dipole moment of the electron with thorium monoxide,” J. Phys. B At. Mol. Opt. Phys. 43, 074007 (2010).
[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]

Helm, M.

Hinds, E. A.

J. J. Hudson, B. E. Sauer, M. R. Tarbutt, and E. A. Hinds, “Measurement of the electron electric dipole moment using YbF molecules,” Phys. Rev. Lett. 89, 023003 (2002).
[CrossRef]

Hollberg, L.

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb.” Nature 445, 627–630 (2007).
[CrossRef]

Holzwarth, R.

Hu, Y.

Y. Hu, X. Wang, L. Guo, and C. Zhang, “Terahertz time-domain spectroscopic study of carbon monoxide,” Spectrosc. Spectr. Anal. 26, 1008–1011 (2006).

Hudson, J. J.

J. J. Hudson, B. E. Sauer, M. R. Tarbutt, and E. A. Hinds, “Measurement of the electron electric dipole moment using YbF molecules,” Phys. Rev. Lett. 89, 023003 (2002).
[CrossRef]

Hutzler, N. R.

A. C. Vutha, W. C. Campbell, Y. V. Gurevich, N. R. Hutzler, M. Parsons, D. Patterson, E. Petrik, B. Spaun, J. M. Doyle, G. Gabrielse, and D. DeMille, “Search for the electric dipole moment of the electron with thorium monoxide,” J. Phys. B At. Mol. Opt. Phys. 43, 074007 (2010).
[CrossRef]

Ilday, F. O.

Jacobsen, R.

D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67, 379–390 (1998).
[CrossRef]

Janke, C.

Kabetani, Y.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88, 241104 (2006).
[CrossRef]

Keilmann, F.

Khanna, S. P.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[CrossRef]

Krems, R. V.

R. V. Krems, W. C. Stwalley, and B. Friedrich, Cold Molecules: Theory, Experiment, Applications (CRC Press, 2009).

Lim, H.

Linfield, E. H.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[CrossRef]

Litz, M.

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
[CrossRef]

Liu, C.-H.

Manquest, C.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[CrossRef]

Mbele, V.

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb.” Nature 445, 627–630 (2007).
[CrossRef]

Mittleman, D.

D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67, 379–390 (1998).
[CrossRef]

Mourou, G.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[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]

Neelamani, R.

D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67, 379–390 (1998).
[CrossRef]

Newbury, N. R.

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100, 013902 (2008).
[CrossRef]

Norris, T. B.

Nuss, M.

D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67, 379–390 (1998).
[CrossRef]

Palik, E.

E. Palik, Handbook of Optical Constants of Solids (Academic, 1985), Vol. 1.

Parsons, M.

A. C. Vutha, W. C. Campbell, Y. V. Gurevich, N. R. Hutzler, M. Parsons, D. Patterson, E. Petrik, B. Spaun, J. M. Doyle, G. Gabrielse, and D. DeMille, “Search for the electric dipole moment of the electron with thorium monoxide,” J. Phys. B At. Mol. Opt. Phys. 43, 074007 (2010).
[CrossRef]

Patterson, D.

A. C. Vutha, W. C. Campbell, Y. V. Gurevich, N. R. Hutzler, M. Parsons, D. Patterson, E. Petrik, B. Spaun, J. M. Doyle, G. Gabrielse, and D. DeMille, “Search for the electric dipole moment of the electron with thorium monoxide,” J. Phys. B At. Mol. Opt. Phys. 43, 074007 (2010).
[CrossRef]

Petrik, E.

A. C. Vutha, W. C. Campbell, Y. V. Gurevich, N. R. Hutzler, M. Parsons, D. Patterson, E. Petrik, B. Spaun, J. M. Doyle, G. Gabrielse, and D. DeMille, “Search for the electric dipole moment of the electron with thorium monoxide,” J. Phys. B At. Mol. Opt. Phys. 43, 074007 (2010).
[CrossRef]

Ravaro, M.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[CrossRef]

Saneyoshi, E.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88, 241104 (2006).
[CrossRef]

Santarelli, G.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[CrossRef]

Sauer, B. E.

J. J. Hudson, B. E. Sauer, M. R. Tarbutt, and E. A. Hinds, “Measurement of the electron electric dipole moment using YbF molecules,” Phys. Rev. Lett. 89, 023003 (2002).
[CrossRef]

Schiller, S.

Schliesser, A.

Schlup, P.

Shen, Y.

Y. Shen, The Principles of Nonlinear Optics, Wiley Classics Library (Wiley-Interscience, 2003).

Sirtori, C.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[CrossRef]

Spaun, B.

A. C. Vutha, W. C. Campbell, Y. V. Gurevich, N. R. Hutzler, M. Parsons, D. Patterson, E. Petrik, B. Spaun, J. M. Doyle, G. Gabrielse, and D. DeMille, “Search for the electric dipole moment of the electron with thorium monoxide,” J. Phys. B At. Mol. Opt. Phys. 43, 074007 (2010).
[CrossRef]

Strickland, D.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Stwalley, W. C.

R. V. Krems, W. C. Stwalley, and B. Friedrich, Cold Molecules: Theory, Experiment, Applications (CRC Press, 2009).

Swann, W. C.

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100, 013902 (2008).
[CrossRef]

Tarbutt, M. R.

J. J. Hudson, B. E. Sauer, M. R. Tarbutt, and E. A. Hinds, “Measurement of the electron electric dipole moment using YbF molecules,” Phys. Rev. Lett. 89, 023003 (2002).
[CrossRef]

Thoma, A.

Treacy, E.

E. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
[CrossRef]

van der Weide, D.

van Exter, M.

M. van Exter, C. Fattinger, and D. Grischkowsky, “High-brightness terahertz beams characterized with an ultrafast detector,” Appl. Phys. Lett. 55, 337–339 (1989).
[CrossRef]

Vutha, A. C.

A. C. Vutha, W. C. Campbell, Y. V. Gurevich, N. R. Hutzler, M. Parsons, D. Patterson, E. Petrik, B. Spaun, J. M. Doyle, G. Gabrielse, and D. DeMille, “Search for the electric dipole moment of the electron with thorium monoxide,” J. Phys. B At. Mol. Opt. Phys. 43, 074007 (2010).
[CrossRef]

Wang, X.

Y. Hu, X. Wang, L. Guo, and C. Zhang, “Terahertz time-domain spectroscopic study of carbon monoxide,” Spectrosc. Spectr. Anal. 26, 1008–1011 (2006).

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]

Williamson, S. L.

Winnerl, S.

Winters, D. G.

Wise, F. W.

Wu, Q.

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
[CrossRef]

Yasui, T.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88, 241104 (2006).
[CrossRef]

Yokoyama, S.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88, 241104 (2006).
[CrossRef]

Zhang, C.

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Figures (7)

Fig. 1.
Fig. 1.

Overview of the multifrequency heterodyne detection scheme. A-EOS results in a scaled copy of the original THz FC being created adjacent in frequency to each element of the LO optical comb. Further mixing of these sidebands with the LO comb during the direct heterodyne detection process produces a comb of rf frequencies, periodic in the pulse repetition rate of the LO comb and symmetric about half the pulse repetition rate. Careful analysis (see text) shows that each rf comb element arises from a single THz FC comb element, such that the full spectral content of the original THz FC is contained within a frequency range less than half the LO pulse repetition rate, where it may be recovered electronically.

Fig. 2.
Fig. 2.

Experimental configuration. An optical FFC generates a THz FC through DFG. After a sample is probed with the THz FC, an LO FFC with a detuned repetition rate electro-optically samples the signal THz FC. Following a polarizer, direct detection of the sampled LO FFC completes an element-by-element mapping from the THz regime to the rf domain.

Fig. 3.
Fig. 3.

(a) Optical spectrum of the local oscillator (LO) FFC after SFG. In the SFG process, the Nth THz FC element writes a sideband onto the Mth LO FFC element, producing a modulation at a frequency near the (M+N)th LO FFC element. (b) Radio frequency spectrum of directly detected photocurrent due to the A-EOS LO FFC. Four bands of heterodyne beats are formed. Of interest are the middle two bands (which are conjugate pairs) as each rf beat within these bands is created by a unique element of the THz FC. (c) Optical spectrum of the LO FFC after DFG. Similar to SFG, the process of DFG writes a group of sidebands onto the LO FFC (see text) and, after direct detection of the sampled LO, there is the same unique mapping of a particular THz FC element to a unique rf heterodyne beat as shown in (b).

Fig. 4.
Fig. 4.

The normalized heterodyne rf signal amplitude and phase due to a THz FC element at 0.85 THz predicted by Eq. (15) for various LO FFC spectral phase profiles. The LO FFC is initially transformed limited (160 fs centered at 1030 nm) but receives spectral phase due to GDD, third-order dispersion (TOD), and NLP (on upper axis) prior to sampling the THz FC.

Fig. 5.
Fig. 5.

Amplitude and phase of the EOS sidebands written onto the LO FFC by a THz FC element at 0.85 THz as a function of optical wavelength. The LO FFC has a central wavelength of 1030 nm and an optical bandwidth of 7 nm (dashed curve).

Fig. 6.
Fig. 6.

Calculated heterodyne beat signal for a THz frequency of 0.85 THz, as a function of nonlinear crystal length for a ZnTe detection crystal, and an LO FFC of 7 nm bandwidth, centered at 1030 nm.

Fig. 7.
Fig. 7.

Maximum detectable THz frequency of A-EOS scheme for various detuning factors, Δfr, as a function of laser repetition rate, fr. The limitation on the bandwidth is imposed by the overlap of the various rf frequency bands shown in Fig. 3(b).

Equations (16)

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ELO(z,t)=MALO(z,ωM)exp(iωMt),
ωM=2π(Mfr+f0),
ETHz(z,t)=NATHz(z,ΩN)exp(iΩNt).
ΩN=2πN(fr+Δfr).
PΩNωM+ΩN(z)=χ(2)(ωM+ΩN;ωM,ΩN)ALO(z,ωM)ATHz(z,ΩN),
PΩNωPΩN(z)=χ(2)(ωPΩN;ωP,ΩN)ALO(z,ωP)ATHz*(z,ΩN),
[z+β(ωM+ΩN)]AEOS(z,ωM+ΩN)=2πic2(ωM+ΩN)2k(ωM+N)PΩNωM+ΩN(z)exp(iΔk+z[β(ΩN)+β(ωM)]z).
[z+β(ωPΩN)]AEOS(z,ωPΩN)=2πic2(ωPΩN)2k(ωPN)PΩNωPΩN(z)exp(iΔkz[β(ΩN)+β(ωP)]z),
AEOS(l,ωM+ΩN)=2πic2(ωM+ΩN)2k(ωM+N)χ(2)(ωM+ΩN;ωM,ΩN)×exp(iΔk+l)1iΔk+exp(β(ωM+ΩN)l)ALO(ωM)ATHz(ΩN)
AEOS(l,ωPΩN)=2πic2(ωPΩN)2k(ωPN)χ(2)(ωPΩN;ωP,ΩN)×exp(iΔkl)1iΔkexp(β(ωPΩN)l)ALO(ωP)ATHz*(ΩN)
EEOS,ΩNSFG(l,t)=M[2πic2(ωM+ΩN)2k(ωM+N)χ(2)(ωM+ΩN;ωM,ΩN)×exp((iΔk+l))1iΔk+exp(β(ωM+ΩN)l)ALO(ωM)ATHz(ΩN)×exp(2iπ((M+N)fr+NΔfr)t)],
EEOS,ΩNDFG(l,t)=P[2πic2(ωPΩN)2k(ωPN)χ(2)(ωPΩN;ωP,ΩN)×exp((iΔkl))1iΔkexp(β(ωPΩN)l)ALO(ωP)ATHz*(ΩN)×exp(2πi((PN)frNΔfr)t)].
EEOS,ΩN(l,t)=M[2πic2(ωM+ΩN)2k(ωM+N)χ(2)(ωM+ΩN;ωM,ΩN)exp((iΔk+l))1iΔk+×ALO(ωM)ATHz(ΩN)exp(2πi((M+N)fr+NΔfr)t)+(ωM+2N+1ΩN)2k(ωM+N+1)χ(2)(ωM+2N+1ΩN;ωM+2N+1,ΩN)exp(iΔkl)1iΔk×ALO(ωM+2N+1)ATHz*(ΩN)exp(2πi((M+N+1)frNΔfr)t)].
SΩN(l,t)2πic2M[((ωM+ΩN)2k(ωM+N)χ(2)(ωM+ΩN;ωM,ΩN)exp(iΔk+l)1iΔk+×ALO(ωM)ATHz(ΩN)ALO*(ωM+N)exp(2πi[((M+N)(M+N))fr+NΔfr]t))+((ωM+2N+1ΩN)2k(ωM+N+1)χ(2)(ωM+2N+1ΩN;ωM+2N+1,ΩN)exp(iΔkl)1iΔk×ALO*(ωM+2N+1)ATHz(ΩN)ALO(ωM+N+1)×exp(2πi[((M+N+1)(M+N+1))fr+NΔfr]t))].
SΩNATHz(ΩN)exp(2πiNΔfrt)2πic2M[(ωM+ΩN)2k(ωM+N)χ(2)(ωM+ΩN;ωM,ΩN)exp(iΔk+l)1iΔk+×ALO(ωM)ALO(ωM+N)+(ωM+2N+1ΩN)2k(ωM+N+1)χ(2)(ωM+2N+1ΩN;ωM+2N+1,ΩN)exp(iΔkl)1iΔkALO*(ωM+2N+1)ALO(ωM+N+1)].
ATHz(ΩN)exp(2πiNΔfrt)=ATHz(ΩN)exp(iΩNΔfrfrt).

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