Abstract

We present experimental evidence for a photothermoelastic response in zincblende crystals illuminated by quantum cascade laser sources in the frequency range 2.2–2.9 THz. Results obtained using an optically balanced sampling arrangement indicate a mechanism whereby the stress distribution established through localized heating of the crystal induces a change in optical birefringence via the photoelastic response of the crystal. A full mathematic model of this photothermoelastic mechanism in (110)-orientated crystals is presented, and shown to agree well with experimental measurements of the magnitude, and the orientational and spatial dependencies of the sampled signal in ZnTe and GaP crystals.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. C. Nuss and J. Orenstein, Millimeter and Submillimeter Wave Spectroscopy of Solids (Springer, 1998).
  2. M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Terahertz spectroscopy,” J. Phys. Chem. B 106, 7146–7159 (2002).
    [CrossRef]
  3. C. A. Schmuttenmaer, “Exploring dynamics in the far-infrared with terahertz spectroscopy,” Chem. Rev. 104, 1759–1780 (2004).
    [CrossRef]
  4. A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
    [CrossRef]
  5. P. Y. Han and X.-C. Zhang, “Free-space coherent broadband terahertz time-domain spectroscopy,” Meas. Sci. Technol. 12, 1747–1756 (2001).
    [CrossRef]
  6. Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
    [CrossRef]
  7. Q. Wu and X. C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68, 1604–1606 (1996).
    [CrossRef]
  8. Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, “Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am. B 18, 823–831 (2001).
    [CrossRef]
  9. N. C. J. van der Valk, T. Wenckebach, and P. C. M. Planken, “Full mathematical description of electro-optic detection in optically isotropic crystals,” J. Opt. Soc. Am. B 21, 622–631 (2004).
    [CrossRef]
  10. Z. Jiang and X.-C. Zhang, “Terahertz imaging via electro-optic effect,” IEEE Trans. Microw. Theory Tech. 47, 2644–2650 (1999).
    [CrossRef]
  11. Q. Wu, T. D. Hewitt, and X. C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996).
    [CrossRef]
  12. M. Usami, M. Yamashita, K. Fukushima, C. Otani, and K. Kawase, “Terahertz wideband spectroscopic imaging based on two-dimensional electro-optic sampling technique,” Appl. Phys. Lett. 86, 141109 (2005).
    [CrossRef]
  13. R. Rungsawang, O. Marshall, J. R. Freeman, H. E. Beere, S. Malik, J. Alton, S. Barbieri, and D. A. Ritchie, “Intensity detection of terahertz quantum cascade laser radiation using electro-optic sampling,” Appl. Phys. Lett. 93, 191111 (2008).
    [CrossRef]
  14. J. Darmo, M. Martl, and K. Unterrainer, “Quasi phase-matched terahertz detector,” Electron. Lett. 46, 788–790 (2010).
    [CrossRef]
  15. D. Oustinov, N. Jukam, R. Rungsawang, J. Madéo, S. Barbieri, P. Filloux, C. Sirtori, X. Marcadet, J. Tignon, and S. Dhillon, “Phase seeding of a terahertz quantum cascade laser,” Nat. Commun. 1, 1–6 (2010).
    [CrossRef]
  16. J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
    [CrossRef]
  17. S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
    [CrossRef]
  18. 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]
  19. J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
    [CrossRef]
  20. A. van Kolck, M. Amanti, M. Fischer, M. Beck, J. Faist, and J. Lloyd-Hughes, “Thermo-optic detection of terahertz radiation from a quantum cascade laser,” Appl. Phys. Lett. 97, 251103 (2010).
    [CrossRef]
  21. S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
    [CrossRef]
  22. M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11, 125022 (2009).
    [CrossRef]
  23. Z. Jiang, F. G. Sun, Q. Chen, and X. C. Zhang, “Electro-optic sampling near zero optical transmission point,” Appl. Phys. Lett. 74, 1191–1193 (1999).
    [CrossRef]
  24. P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18, 313–317 (2001).
    [CrossRef]
  25. R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infrared Radiation, 2nd ed. (Oxford University, 1968).
  26. V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, G. N. Kulipanov, G. L. Kuryshev, A. N. Matveenko, A. K. Petrov, V. M. Popik, M. A. Scheglov, O. A. Shevchenko, and N. A. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res., Sect. A 543, 102–109 (2005).
    [CrossRef]
  27. S. Adachi, Handbook on Physical Properties of Semiconductors (Kluwer Academic, 2004), Vol. 3.
  28. G. Ghosh, “Temperature dispersion of refractive indices in semiconductors,” J. Appl. Phys. 79, 9388–9389 (1996).
    [CrossRef]
  29. M. Bass, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. 4.
  30. B. A. Boley and J. H. Weiner, Theory of Thermal Stresses (Wiley, 1960).
  31. J. F. Nye, Physical Properties of Crystals (Clarendon, 1957).
  32. B. A. Auld, Acoustic Fields and Waves in Solids, 2nd ed. (Krieger, 1990), Vol. 1.
  33. M. Yamada, K. Yamamoto, and K. Abe, “Elastic and photoelastic constants of ZnTe measured by Brillouin scattering,” J. Phys. D 10, 1309–1313 (1977).
    [CrossRef]
  34. M. E. Levinštejn, S. Rumyantsev, and M. Shur, Handbook Series on Semiconductor Parameters (World Scientific, 1999), Vol. 2.
  35. M. Yamada, K. Wasa, and C. Hamaguchi, “Brillouin scattering in GaP,” Jpn. J. Appl. Phys. 15, 1107–1111 (1976).
    [CrossRef]
  36. W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
    [CrossRef]

2012

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

2011

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

A. van Kolck, M. Amanti, M. Fischer, M. Beck, J. Faist, and J. Lloyd-Hughes, “Thermo-optic detection of terahertz radiation from a quantum cascade laser,” Appl. Phys. Lett. 97, 251103 (2010).
[CrossRef]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

J. Darmo, M. Martl, and K. Unterrainer, “Quasi phase-matched terahertz detector,” Electron. Lett. 46, 788–790 (2010).
[CrossRef]

D. Oustinov, N. Jukam, R. Rungsawang, J. Madéo, S. Barbieri, P. Filloux, C. Sirtori, X. Marcadet, J. Tignon, and S. Dhillon, “Phase seeding of a terahertz quantum cascade laser,” Nat. Commun. 1, 1–6 (2010).
[CrossRef]

2009

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11, 125022 (2009).
[CrossRef]

2008

R. Rungsawang, O. Marshall, J. R. Freeman, H. E. Beere, S. Malik, J. Alton, S. Barbieri, and D. A. Ritchie, “Intensity detection of terahertz quantum cascade laser radiation using electro-optic sampling,” Appl. Phys. Lett. 93, 191111 (2008).
[CrossRef]

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
[CrossRef]

2005

M. Usami, M. Yamashita, K. Fukushima, C. Otani, and K. Kawase, “Terahertz wideband spectroscopic imaging based on two-dimensional electro-optic sampling technique,” Appl. Phys. Lett. 86, 141109 (2005).
[CrossRef]

V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, G. N. Kulipanov, G. L. Kuryshev, A. N. Matveenko, A. K. Petrov, V. M. Popik, M. A. Scheglov, O. A. Shevchenko, and N. A. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res., Sect. A 543, 102–109 (2005).
[CrossRef]

2004

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[CrossRef]

C. A. Schmuttenmaer, “Exploring dynamics in the far-infrared with terahertz spectroscopy,” Chem. Rev. 104, 1759–1780 (2004).
[CrossRef]

N. C. J. van der Valk, T. Wenckebach, and P. C. M. Planken, “Full mathematical description of electro-optic detection in optically isotropic crystals,” J. Opt. Soc. Am. B 21, 622–631 (2004).
[CrossRef]

2002

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Terahertz spectroscopy,” J. Phys. Chem. B 106, 7146–7159 (2002).
[CrossRef]

2001

P. Y. Han and X.-C. Zhang, “Free-space coherent broadband terahertz time-domain spectroscopy,” Meas. Sci. Technol. 12, 1747–1756 (2001).
[CrossRef]

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, “Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am. B 18, 823–831 (2001).
[CrossRef]

P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18, 313–317 (2001).
[CrossRef]

1999

Z. Jiang, F. G. Sun, Q. Chen, and X. C. Zhang, “Electro-optic sampling near zero optical transmission point,” Appl. Phys. Lett. 74, 1191–1193 (1999).
[CrossRef]

Z. Jiang and X.-C. Zhang, “Terahertz imaging via electro-optic effect,” IEEE Trans. Microw. Theory Tech. 47, 2644–2650 (1999).
[CrossRef]

1996

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

Q. Wu and X. C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68, 1604–1606 (1996).
[CrossRef]

G. Ghosh, “Temperature dispersion of refractive indices in semiconductors,” J. Appl. Phys. 79, 9388–9389 (1996).
[CrossRef]

1995

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

1977

M. Yamada, K. Yamamoto, and K. Abe, “Elastic and photoelastic constants of ZnTe measured by Brillouin scattering,” J. Phys. D 10, 1309–1313 (1977).
[CrossRef]

1976

M. Yamada, K. Wasa, and C. Hamaguchi, “Brillouin scattering in GaP,” Jpn. J. Appl. Phys. 15, 1107–1111 (1976).
[CrossRef]

1965

W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[CrossRef]

Abe, K.

M. Yamada, K. Yamamoto, and K. Abe, “Elastic and photoelastic constants of ZnTe measured by Brillouin scattering,” J. Phys. D 10, 1309–1313 (1977).
[CrossRef]

Adachi, S.

S. Adachi, Handbook on Physical Properties of Semiconductors (Kluwer Academic, 2004), Vol. 3.

Alton, J.

R. Rungsawang, O. Marshall, J. R. Freeman, H. E. Beere, S. Malik, J. Alton, S. Barbieri, and D. A. Ritchie, “Intensity detection of terahertz quantum cascade laser radiation using electro-optic sampling,” Appl. Phys. Lett. 93, 191111 (2008).
[CrossRef]

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[CrossRef]

Amanti, M.

A. van Kolck, M. Amanti, M. Fischer, M. Beck, J. Faist, and J. Lloyd-Hughes, “Thermo-optic detection of terahertz radiation from a quantum cascade laser,” Appl. Phys. Lett. 97, 251103 (2010).
[CrossRef]

Amanti, M. I.

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11, 125022 (2009).
[CrossRef]

Auld, B. A.

B. A. Auld, Acoustic Fields and Waves in Solids, 2nd ed. (Krieger, 1990), Vol. 1.

Bakker, H. J.

P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18, 313–317 (2001).
[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]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

D. Oustinov, N. Jukam, R. Rungsawang, J. Madéo, S. Barbieri, P. Filloux, C. Sirtori, X. Marcadet, J. Tignon, and S. Dhillon, “Phase seeding of a terahertz quantum cascade laser,” Nat. Commun. 1, 1–6 (2010).
[CrossRef]

R. Rungsawang, O. Marshall, J. R. Freeman, H. E. Beere, S. Malik, J. Alton, S. Barbieri, and D. A. Ritchie, “Intensity detection of terahertz quantum cascade laser radiation using electro-optic sampling,” Appl. Phys. Lett. 93, 191111 (2008).
[CrossRef]

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[CrossRef]

Bass, M.

M. Bass, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. 4.

Beard, M. C.

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Terahertz spectroscopy,” J. Phys. Chem. B 106, 7146–7159 (2002).
[CrossRef]

Beck, M.

A. van Kolck, M. Amanti, M. Fischer, M. Beck, J. Faist, and J. Lloyd-Hughes, “Thermo-optic detection of terahertz radiation from a quantum cascade laser,” Appl. Phys. Lett. 97, 251103 (2010).
[CrossRef]

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11, 125022 (2009).
[CrossRef]

Beere, H.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Beere, H. E.

R. Rungsawang, O. Marshall, J. R. Freeman, H. E. Beere, S. Malik, J. Alton, S. Barbieri, and D. A. Ritchie, “Intensity detection of terahertz quantum cascade laser radiation using electro-optic sampling,” Appl. Phys. Lett. 93, 191111 (2008).
[CrossRef]

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[CrossRef]

Boley, B. A.

B. A. Boley and J. H. Weiner, Theory of Thermal Stresses (Wiley, 1960).

Bond, W. L.

W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[CrossRef]

Burnett, A. D.

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
[CrossRef]

Cavalié, P.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

Chasmar, R. P.

R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infrared Radiation, 2nd ed. (Oxford University, 1968).

Chen, Q.

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, “Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am. B 18, 823–831 (2001).
[CrossRef]

Z. Jiang, F. G. Sun, Q. Chen, and X. C. Zhang, “Electro-optic sampling near zero optical transmission point,” Appl. Phys. Lett. 74, 1191–1193 (1999).
[CrossRef]

Cherkassky, V. S.

V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, G. N. Kulipanov, G. L. Kuryshev, A. N. Matveenko, A. K. Petrov, V. M. Popik, M. A. Scheglov, O. A. Shevchenko, and N. A. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res., Sect. A 543, 102–109 (2005).
[CrossRef]

Colombelli, R.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Cunningham, J. E.

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
[CrossRef]

Darmo, J.

J. Darmo, M. Martl, and K. Unterrainer, “Quasi phase-matched terahertz detector,” Electron. Lett. 46, 788–790 (2010).
[CrossRef]

Davies, A. G.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

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]

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
[CrossRef]

Dean, P.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

Dhillon, S.

D. Oustinov, N. Jukam, R. Rungsawang, J. Madéo, S. Barbieri, P. Filloux, C. Sirtori, X. Marcadet, J. Tignon, and S. Dhillon, “Phase seeding of a terahertz quantum cascade laser,” Nat. Commun. 1, 1–6 (2010).
[CrossRef]

Dhillon, S. S.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

Ding, L.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Faist, J.

A. van Kolck, M. Amanti, M. Fischer, M. Beck, J. Faist, and J. Lloyd-Hughes, “Thermo-optic detection of terahertz radiation from a quantum cascade laser,” Appl. Phys. Lett. 97, 251103 (2010).
[CrossRef]

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11, 125022 (2009).
[CrossRef]

Fan, W.

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
[CrossRef]

Filloux, P.

D. Oustinov, N. Jukam, R. Rungsawang, J. Madéo, S. Barbieri, P. Filloux, C. Sirtori, X. Marcadet, J. Tignon, and S. Dhillon, “Phase seeding of a terahertz quantum cascade laser,” Nat. Commun. 1, 1–6 (2010).
[CrossRef]

Fischer, M.

A. van Kolck, M. Amanti, M. Fischer, M. Beck, J. Faist, and J. Lloyd-Hughes, “Thermo-optic detection of terahertz radiation from a quantum cascade laser,” Appl. Phys. Lett. 97, 251103 (2010).
[CrossRef]

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11, 125022 (2009).
[CrossRef]

Fowler, J.

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[CrossRef]

Freeman, J. R.

R. Rungsawang, O. Marshall, J. R. Freeman, H. E. Beere, S. Malik, J. Alton, S. Barbieri, and D. A. Ritchie, “Intensity detection of terahertz quantum cascade laser radiation using electro-optic sampling,” Appl. Phys. Lett. 93, 191111 (2008).
[CrossRef]

Fukushima, K.

M. Usami, M. Yamashita, K. Fukushima, C. Otani, and K. Kawase, “Terahertz wideband spectroscopic imaging based on two-dimensional electro-optic sampling technique,” Appl. Phys. Lett. 86, 141109 (2005).
[CrossRef]

Gallo, P.

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11, 125022 (2009).
[CrossRef]

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]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Ghosh, G.

G. Ghosh, “Temperature dispersion of refractive indices in semiconductors,” J. Appl. Phys. 79, 9388–9389 (1996).
[CrossRef]

Hamaguchi, C.

M. Yamada, K. Wasa, and C. Hamaguchi, “Brillouin scattering in GaP,” Jpn. J. Appl. Phys. 15, 1107–1111 (1976).
[CrossRef]

Han, P. Y.

P. Y. Han and X.-C. Zhang, “Free-space coherent broadband terahertz time-domain spectroscopy,” Meas. Sci. Technol. 12, 1747–1756 (2001).
[CrossRef]

Hewitt, T. D.

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

Ibrahim, M. S. M.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

Jiang, Z.

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, “Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am. B 18, 823–831 (2001).
[CrossRef]

Z. Jiang, F. G. Sun, Q. Chen, and X. C. Zhang, “Electro-optic sampling near zero optical transmission point,” Appl. Phys. Lett. 74, 1191–1193 (1999).
[CrossRef]

Z. Jiang and X.-C. Zhang, “Terahertz imaging via electro-optic effect,” IEEE Trans. Microw. Theory Tech. 47, 2644–2650 (1999).
[CrossRef]

Jones, F. E.

R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infrared Radiation, 2nd ed. (Oxford University, 1968).

Jukam, N.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

D. Oustinov, N. Jukam, R. Rungsawang, J. Madéo, S. Barbieri, P. Filloux, C. Sirtori, X. Marcadet, J. Tignon, and S. Dhillon, “Phase seeding of a terahertz quantum cascade laser,” Nat. Commun. 1, 1–6 (2010).
[CrossRef]

Kapon, E.

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11, 125022 (2009).
[CrossRef]

Kawase, K.

M. Usami, M. Yamashita, K. Fukushima, C. Otani, and K. Kawase, “Terahertz wideband spectroscopic imaging based on two-dimensional electro-optic sampling technique,” Appl. Phys. Lett. 86, 141109 (2005).
[CrossRef]

Khanna, S. P.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

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]

Knyazev, B. A.

V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, G. N. Kulipanov, G. L. Kuryshev, A. N. Matveenko, A. K. Petrov, V. M. Popik, M. A. Scheglov, O. A. Shevchenko, and N. A. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res., Sect. A 543, 102–109 (2005).
[CrossRef]

Kubarev, V. V.

V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, G. N. Kulipanov, G. L. Kuryshev, A. N. Matveenko, A. K. Petrov, V. M. Popik, M. A. Scheglov, O. A. Shevchenko, and N. A. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res., Sect. A 543, 102–109 (2005).
[CrossRef]

Kulipanov, G. N.

V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, G. N. Kulipanov, G. L. Kuryshev, A. N. Matveenko, A. K. Petrov, V. M. Popik, M. A. Scheglov, O. A. Shevchenko, and N. A. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res., Sect. A 543, 102–109 (2005).
[CrossRef]

Kuryshev, G. L.

V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, G. N. Kulipanov, G. L. Kuryshev, A. N. Matveenko, A. K. Petrov, V. M. Popik, M. A. Scheglov, O. A. Shevchenko, and N. A. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res., Sect. A 543, 102–109 (2005).
[CrossRef]

Levinštejn, M. E.

M. E. Levinštejn, S. Rumyantsev, and M. Shur, Handbook Series on Semiconductor Parameters (World Scientific, 1999), Vol. 2.

Linfield, E. H.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

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]

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
[CrossRef]

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[CrossRef]

Lloyd-Hughes, J.

A. van Kolck, M. Amanti, M. Fischer, M. Beck, J. Faist, and J. Lloyd-Hughes, “Thermo-optic detection of terahertz radiation from a quantum cascade laser,” Appl. Phys. Lett. 97, 251103 (2010).
[CrossRef]

Madéo, J.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

D. Oustinov, N. Jukam, R. Rungsawang, J. Madéo, S. Barbieri, P. Filloux, C. Sirtori, X. Marcadet, J. Tignon, and S. Dhillon, “Phase seeding of a terahertz quantum cascade laser,” Nat. Commun. 1, 1–6 (2010).
[CrossRef]

Maineult, W.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Malik, S.

R. Rungsawang, O. Marshall, J. R. Freeman, H. E. Beere, S. Malik, J. Alton, S. Barbieri, and D. A. Ritchie, “Intensity detection of terahertz quantum cascade laser radiation using electro-optic sampling,” Appl. Phys. Lett. 93, 191111 (2008).
[CrossRef]

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]

Marcadet, X.

D. Oustinov, N. Jukam, R. Rungsawang, J. Madéo, S. Barbieri, P. Filloux, C. Sirtori, X. Marcadet, J. Tignon, and S. Dhillon, “Phase seeding of a terahertz quantum cascade laser,” Nat. Commun. 1, 1–6 (2010).
[CrossRef]

Marshall, O.

R. Rungsawang, O. Marshall, J. R. Freeman, H. E. Beere, S. Malik, J. Alton, S. Barbieri, and D. A. Ritchie, “Intensity detection of terahertz quantum cascade laser radiation using electro-optic sampling,” Appl. Phys. Lett. 93, 191111 (2008).
[CrossRef]

Martl, M.

J. Darmo, M. Martl, and K. Unterrainer, “Quasi phase-matched terahertz detector,” Electron. Lett. 46, 788–790 (2010).
[CrossRef]

Matveenko, A. N.

V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, G. N. Kulipanov, G. L. Kuryshev, A. N. Matveenko, A. K. Petrov, V. M. Popik, M. A. Scheglov, O. A. Shevchenko, and N. A. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res., Sect. A 543, 102–109 (2005).
[CrossRef]

Maussang, K.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

Maysonnave, J.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

Nienhuys, H.-K.

P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18, 313–317 (2001).
[CrossRef]

Nuss, M. C.

M. C. Nuss and J. Orenstein, Millimeter and Submillimeter Wave Spectroscopy of Solids (Springer, 1998).

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, 1957).

Orenstein, J.

M. C. Nuss and J. Orenstein, Millimeter and Submillimeter Wave Spectroscopy of Solids (Springer, 1998).

Otani, C.

M. Usami, M. Yamashita, K. Fukushima, C. Otani, and K. Kawase, “Terahertz wideband spectroscopic imaging based on two-dimensional electro-optic sampling technique,” Appl. Phys. Lett. 86, 141109 (2005).
[CrossRef]

Oustinov, D.

D. Oustinov, N. Jukam, R. Rungsawang, J. Madéo, S. Barbieri, P. Filloux, C. Sirtori, X. Marcadet, J. Tignon, and S. Dhillon, “Phase seeding of a terahertz quantum cascade laser,” Nat. Commun. 1, 1–6 (2010).
[CrossRef]

Petrov, A. K.

V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, G. N. Kulipanov, G. L. Kuryshev, A. N. Matveenko, A. K. Petrov, V. M. Popik, M. A. Scheglov, O. A. Shevchenko, and N. A. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res., Sect. A 543, 102–109 (2005).
[CrossRef]

Planken, P. C. M.

N. C. J. van der Valk, T. Wenckebach, and P. C. M. Planken, “Full mathematical description of electro-optic detection in optically isotropic crystals,” J. Opt. Soc. Am. B 21, 622–631 (2004).
[CrossRef]

P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18, 313–317 (2001).
[CrossRef]

Popik, V. M.

V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, G. N. Kulipanov, G. L. Kuryshev, A. N. Matveenko, A. K. Petrov, V. M. Popik, M. A. Scheglov, O. A. Shevchenko, and N. A. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res., Sect. A 543, 102–109 (2005).
[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]

Ritchie, D.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Ritchie, D. A.

R. Rungsawang, O. Marshall, J. R. Freeman, H. E. Beere, S. Malik, J. Alton, S. Barbieri, and D. A. Ritchie, “Intensity detection of terahertz quantum cascade laser radiation using electro-optic sampling,” Appl. Phys. Lett. 93, 191111 (2008).
[CrossRef]

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[CrossRef]

Rudra, A.

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11, 125022 (2009).
[CrossRef]

Rumyantsev, S.

M. E. Levinštejn, S. Rumyantsev, and M. Shur, Handbook Series on Semiconductor Parameters (World Scientific, 1999), Vol. 2.

Rungsawang, R.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

D. Oustinov, N. Jukam, R. Rungsawang, J. Madéo, S. Barbieri, P. Filloux, C. Sirtori, X. Marcadet, J. Tignon, and S. Dhillon, “Phase seeding of a terahertz quantum cascade laser,” Nat. Commun. 1, 1–6 (2010).
[CrossRef]

R. Rungsawang, O. Marshall, J. R. Freeman, H. E. Beere, S. Malik, J. Alton, S. Barbieri, and D. A. Ritchie, “Intensity detection of terahertz quantum cascade laser radiation using electro-optic sampling,” Appl. Phys. Lett. 93, 191111 (2008).
[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]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Scalari, G.

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11, 125022 (2009).
[CrossRef]

Scheglov, M. A.

V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, G. N. Kulipanov, G. L. Kuryshev, A. N. Matveenko, A. K. Petrov, V. M. Popik, M. A. Scheglov, O. A. Shevchenko, and N. A. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res., Sect. A 543, 102–109 (2005).
[CrossRef]

Schmuttenmaer, C. A.

C. A. Schmuttenmaer, “Exploring dynamics in the far-infrared with terahertz spectroscopy,” Chem. Rev. 104, 1759–1780 (2004).
[CrossRef]

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Terahertz spectroscopy,” J. Phys. Chem. B 106, 7146–7159 (2002).
[CrossRef]

Shevchenko, O. A.

V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, G. N. Kulipanov, G. L. Kuryshev, A. N. Matveenko, A. K. Petrov, V. M. Popik, M. A. Scheglov, O. A. Shevchenko, and N. A. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res., Sect. A 543, 102–109 (2005).
[CrossRef]

Shur, M.

M. E. Levinštejn, S. Rumyantsev, and M. Shur, Handbook Series on Semiconductor Parameters (World Scientific, 1999), Vol. 2.

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]

D. Oustinov, N. Jukam, R. Rungsawang, J. Madéo, S. Barbieri, P. Filloux, C. Sirtori, X. Marcadet, J. Tignon, and S. Dhillon, “Phase seeding of a terahertz quantum cascade laser,” Nat. Commun. 1, 1–6 (2010).
[CrossRef]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Smith, R. A.

R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infrared Radiation, 2nd ed. (Oxford University, 1968).

Steenson, D. P.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

Sun, F. G.

Z. Jiang, F. G. Sun, Q. Chen, and X. C. Zhang, “Electro-optic sampling near zero optical transmission point,” Appl. Phys. Lett. 74, 1191–1193 (1999).
[CrossRef]

Tani, M.

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, “Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am. B 18, 823–831 (2001).
[CrossRef]

Terazzi, R.

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11, 125022 (2009).
[CrossRef]

Tignon, J.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

D. Oustinov, N. Jukam, R. Rungsawang, J. Madéo, S. Barbieri, P. Filloux, C. Sirtori, X. Marcadet, J. Tignon, and S. Dhillon, “Phase seeding of a terahertz quantum cascade laser,” Nat. Commun. 1, 1–6 (2010).
[CrossRef]

Turner, G. M.

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Terahertz spectroscopy,” J. Phys. Chem. B 106, 7146–7159 (2002).
[CrossRef]

Unterrainer, K.

J. Darmo, M. Martl, and K. Unterrainer, “Quasi phase-matched terahertz detector,” Electron. Lett. 46, 788–790 (2010).
[CrossRef]

Usami, M.

M. Usami, M. Yamashita, K. Fukushima, C. Otani, and K. Kawase, “Terahertz wideband spectroscopic imaging based on two-dimensional electro-optic sampling technique,” Appl. Phys. Lett. 86, 141109 (2005).
[CrossRef]

van der Valk, N. C. J.

N. C. J. van der Valk, T. Wenckebach, and P. C. M. Planken, “Full mathematical description of electro-optic detection in optically isotropic crystals,” J. Opt. Soc. Am. B 21, 622–631 (2004).
[CrossRef]

van Kolck, A.

A. van Kolck, M. Amanti, M. Fischer, M. Beck, J. Faist, and J. Lloyd-Hughes, “Thermo-optic detection of terahertz radiation from a quantum cascade laser,” Appl. Phys. Lett. 97, 251103 (2010).
[CrossRef]

Vinokurov, N. A.

V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, G. N. Kulipanov, G. L. Kuryshev, A. N. Matveenko, A. K. Petrov, V. M. Popik, M. A. Scheglov, O. A. Shevchenko, and N. A. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res., Sect. A 543, 102–109 (2005).
[CrossRef]

Wasa, K.

M. Yamada, K. Wasa, and C. Hamaguchi, “Brillouin scattering in GaP,” Jpn. J. Appl. Phys. 15, 1107–1111 (1976).
[CrossRef]

Weiner, J. H.

B. A. Boley and J. H. Weiner, Theory of Thermal Stresses (Wiley, 1960).

Wenckebach, T.

N. C. J. van der Valk, T. Wenckebach, and P. C. M. Planken, “Full mathematical description of electro-optic detection in optically isotropic crystals,” J. Opt. Soc. Am. B 21, 622–631 (2004).
[CrossRef]

P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18, 313–317 (2001).
[CrossRef]

Wu, Q.

Q. Wu and X. C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68, 1604–1606 (1996).
[CrossRef]

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

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

Yamada, M.

M. Yamada, K. Yamamoto, and K. Abe, “Elastic and photoelastic constants of ZnTe measured by Brillouin scattering,” J. Phys. D 10, 1309–1313 (1977).
[CrossRef]

M. Yamada, K. Wasa, and C. Hamaguchi, “Brillouin scattering in GaP,” Jpn. J. Appl. Phys. 15, 1107–1111 (1976).
[CrossRef]

Yamamoto, K.

M. Yamada, K. Yamamoto, and K. Abe, “Elastic and photoelastic constants of ZnTe measured by Brillouin scattering,” J. Phys. D 10, 1309–1313 (1977).
[CrossRef]

Yamashita, M.

M. Usami, M. Yamashita, K. Fukushima, C. Otani, and K. Kawase, “Terahertz wideband spectroscopic imaging based on two-dimensional electro-optic sampling technique,” Appl. Phys. Lett. 86, 141109 (2005).
[CrossRef]

Zhang, X. C.

Z. Jiang, F. G. Sun, Q. Chen, and X. C. Zhang, “Electro-optic sampling near zero optical transmission point,” Appl. Phys. Lett. 74, 1191–1193 (1999).
[CrossRef]

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

Q. Wu and X. C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68, 1604–1606 (1996).
[CrossRef]

Zhang, X.-C.

P. Y. Han and X.-C. Zhang, “Free-space coherent broadband terahertz time-domain spectroscopy,” Meas. Sci. Technol. 12, 1747–1756 (2001).
[CrossRef]

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, “Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am. B 18, 823–831 (2001).
[CrossRef]

Z. Jiang and X.-C. Zhang, “Terahertz imaging via electro-optic effect,” IEEE Trans. Microw. Theory Tech. 47, 2644–2650 (1999).
[CrossRef]

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

Appl. Phys. Lett.

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

Q. Wu and X. C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68, 1604–1606 (1996).
[CrossRef]

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

M. Usami, M. Yamashita, K. Fukushima, C. Otani, and K. Kawase, “Terahertz wideband spectroscopic imaging based on two-dimensional electro-optic sampling technique,” Appl. Phys. Lett. 86, 141109 (2005).
[CrossRef]

R. Rungsawang, O. Marshall, J. R. Freeman, H. E. Beere, S. Malik, J. Alton, S. Barbieri, and D. A. Ritchie, “Intensity detection of terahertz quantum cascade laser radiation using electro-optic sampling,” Appl. Phys. Lett. 93, 191111 (2008).
[CrossRef]

A. van Kolck, M. Amanti, M. Fischer, M. Beck, J. Faist, and J. Lloyd-Hughes, “Thermo-optic detection of terahertz radiation from a quantum cascade laser,” Appl. Phys. Lett. 97, 251103 (2010).
[CrossRef]

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[CrossRef]

Z. Jiang, F. G. Sun, Q. Chen, and X. C. Zhang, “Electro-optic sampling near zero optical transmission point,” Appl. Phys. Lett. 74, 1191–1193 (1999).
[CrossRef]

Chem. Rev.

C. A. Schmuttenmaer, “Exploring dynamics in the far-infrared with terahertz spectroscopy,” Chem. Rev. 104, 1759–1780 (2004).
[CrossRef]

Electron. Lett.

J. Darmo, M. Martl, and K. Unterrainer, “Quasi phase-matched terahertz detector,” Electron. Lett. 46, 788–790 (2010).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

Z. Jiang and X.-C. Zhang, “Terahertz imaging via electro-optic effect,” IEEE Trans. Microw. Theory Tech. 47, 2644–2650 (1999).
[CrossRef]

J. Appl. Phys.

W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[CrossRef]

G. Ghosh, “Temperature dispersion of refractive indices in semiconductors,” J. Appl. Phys. 79, 9388–9389 (1996).
[CrossRef]

J. Opt. Soc. Am. B

P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18, 313–317 (2001).
[CrossRef]

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, “Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am. B 18, 823–831 (2001).
[CrossRef]

N. C. J. van der Valk, T. Wenckebach, and P. C. M. Planken, “Full mathematical description of electro-optic detection in optically isotropic crystals,” J. Opt. Soc. Am. B 21, 622–631 (2004).
[CrossRef]

J. Phys. Chem. B

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Terahertz spectroscopy,” J. Phys. Chem. B 106, 7146–7159 (2002).
[CrossRef]

J. Phys. D

M. Yamada, K. Yamamoto, and K. Abe, “Elastic and photoelastic constants of ZnTe measured by Brillouin scattering,” J. Phys. D 10, 1309–1313 (1977).
[CrossRef]

Jpn. J. Appl. Phys.

M. Yamada, K. Wasa, and C. Hamaguchi, “Brillouin scattering in GaP,” Jpn. J. Appl. Phys. 15, 1107–1111 (1976).
[CrossRef]

Mater. Today

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
[CrossRef]

Meas. Sci. Technol.

P. Y. Han and X.-C. Zhang, “Free-space coherent broadband terahertz time-domain spectroscopy,” Meas. Sci. Technol. 12, 1747–1756 (2001).
[CrossRef]

Nat. Commun.

D. Oustinov, N. Jukam, R. Rungsawang, J. Madéo, S. Barbieri, P. Filloux, C. Sirtori, X. Marcadet, J. Tignon, and S. Dhillon, “Phase seeding of a terahertz quantum cascade laser,” Nat. Commun. 1, 1–6 (2010).
[CrossRef]

Nat. Photonics

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

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]

New J. Phys.

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11, 125022 (2009).
[CrossRef]

Nucl. Instrum. Methods Phys. Res., Sect. A

V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, G. N. Kulipanov, G. L. Kuryshev, A. N. Matveenko, A. K. Petrov, V. M. Popik, M. A. Scheglov, O. A. Shevchenko, and N. A. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res., Sect. A 543, 102–109 (2005).
[CrossRef]

Opt. Express

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, R. Rungsawang, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, S. S. Dhillon, and J. Tignon, “Measuring the sampling coherence of a terahertz quantum cascade laser,” Opt. Express 20, 16662–16670 (2012).
[CrossRef]

Opt. Lett.

J. Maysonnave, N. Jukam, M. S. M. Ibrahim, K. Maussang, J. Madéo, P. Cavalié, P. Dean, S. P. Khanna, D. P. Steenson, E. H. Linfield, A. G. Davies, J. Tignon, and S. S. Dhillon, “Integrated injection seeded terahertz source and amplifier for time-domain spectroscopy,” Opt. Lett. 37, 731–733 (2012).
[CrossRef]

Other

M. C. Nuss and J. Orenstein, Millimeter and Submillimeter Wave Spectroscopy of Solids (Springer, 1998).

S. Adachi, Handbook on Physical Properties of Semiconductors (Kluwer Academic, 2004), Vol. 3.

R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infrared Radiation, 2nd ed. (Oxford University, 1968).

M. Bass, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. 4.

B. A. Boley and J. H. Weiner, Theory of Thermal Stresses (Wiley, 1960).

J. F. Nye, Physical Properties of Crystals (Clarendon, 1957).

B. A. Auld, Acoustic Fields and Waves in Solids, 2nd ed. (Krieger, 1990), Vol. 1.

M. E. Levinštejn, S. Rumyantsev, and M. Shur, Handbook Series on Semiconductor Parameters (World Scientific, 1999), Vol. 2.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

(a) Experimental apparatus for optical sampling of the birefringence induced in a crystal by THz radiation. C, crystal; λ/4, quarter-wave plate; WP, Wollaston prism; P, optical polarizer; TP, THz polarizer. (b) Geometry of the (110) zincblende crystal showing the crystallographic axes (xyz), the Cartesian (yz), and cylindrical (r,φ) axes in the (110) plane of the crystal, and the principal axes of the index ellipsoid (YZ). The x and y directions are bisected by the normal to the page. All other axes shown are in the plane of the page. Also shown are the angles ψ and θ of the polarization directions of the THz and probe beams relative to the [1, 1, 0] direction.

Fig. 2.
Fig. 2.

(a) Phase delays measured as a function of modulation frequency for a 1.9mm-thick ZnTe crystal, using QCL devices emitting at 2.2 THz (red), 2.6 THz (blue), and 2.9 THz (black), and also for a 0.5 mm ZnTe crystal at 2.2 THz (green). The error bars have been calculated based on three repeated measurements. The solid lines are fits to Eq. (6). (b) Corresponding temperature modulation at the crystal surface predicted using Eq. (7).

Fig. 3.
Fig. 3.

(a) Contour plot showing the spatial variation of the photodiode signal ΔI/Ip in the yz plane of the ZnTe crystal. The origin (0,0) corresponds to the center of the THz beam. For these measurements θ=0 and the polarization direction of the THz field ψ=0. (b) Spatial variation of the (normalized) photodiode signal calculated using the photothermoelastic model for the same experimental conditions.

Fig. 4.
Fig. 4.

(a) Spatial variation of the modulation of the birefringence in the yz plane of the ZnTe crystal, calculated using the photothermoelastic model and cast in terms of the coefficient β defined by Eq. (5). (b) Spatial variation of the angle α obtained via Eq. (16). The origin (0,0) corresponds to the center of the THz beam. 

Fig. 5.
Fig. 5.

Photodiode signal ΔI/Ip (black squares) measured for different polarization directions θ of the probe beam. Also shown (blue line) is the functional form ΔIcos2(2θ). These measurements were taken at the position corresponding to the maximum signal attained in Fig. 3(a), and with the polarization direction of the THz field ψ=0.

Fig. 6.
Fig. 6.

Phase delays measured as a function of modulation frequency for a 1-mm-thick GaP crystal, using a QCL device emitting at 2.2 THz.

Fig. 7.
Fig. 7.

Spatial variation of the photodiode signal ΔI/Ip in the yz plane of the ZnTe crystal, calculated assuming only a thermally induced EO effect. The signal is displayed on the same numerical scale as Fig. 3(b).

Equations (54)

Equations on this page are rendered with MathJax. Learn more.

δ=0L2πΔn(x)dxλ.
ΔI=Ipsin(2(αθ))cos(2θ)sin(δ),
ρCπw02dT(x,t)dt=(1R)αP0eαxGT(x,t).
ΔT(x)=(1R)αP0eαxG2+(ρCπw02ω)2.
Δn(x)=βΔT(x).
δ=2πβλ(1R)(1eαL)P0G2+(ρCπw02ω)2,
δ=2πβ(1eαL)αλΔT(0).
β(JF+HF22)(n2n3n2n3,),
I=Ip(η+sin2(δ02)),
σrr(r,x)=αthY[1b20bΔT(r,x)rdr1r20rΔT(r,x)rdr]
σφφ(r,x)=αthY[1b20bΔT(r,x)rdr+1r20rΔT(r,x)rdrΔT(r,x)],
(σ1σ2σ3σ4σ5σ6)=(0σrrcos2(φ)+σφφsin2(φ)σrrsin2(φ)+σφφcos2(φ)(σrrσφφ)sin(φ)+cos(φ)00),
ΔBi=pijsjkσk,
(ΔB1ΔB2ΔB3ΔB4ΔB5ΔB6)=(σ2(p12s11+p13s13)+σ3(p12s13+p13s33)σ2(p11s11+p13s13)+σ3(p11s13+p13s33)σ2(p13s11+p33s13)+σ3(p13s13+p33s33)σ4p44s4400).
x2(1n12+ΔB1)+y2(1n22+ΔB2)+z2(1n32+ΔB3)+2yzΔB4=1.
tan(2α)=2ΔB4ΔB2ΔB3.
x=X,
y=Ycos(α)Zsin(α),
z=Zcos(α)+Ysin(α).
X2[1n12+ΔB1]+Y2[(1n22+ΔB2)cos2(α)+(1n32+ΔB3)sin2(α)+2ΔB4sin(α)cos(α)]+Z2[(1n22+ΔB2)sin2(α)+(1n32+ΔB3)cos2(α)+2ΔB4sin(α)cos(α)]=1,
ΔnY=n32[ΔB2cos2(α)+ΔB3sin2(α)+2ΔB4sin(α)cos(α)],
ΔnZ=n32[ΔB2sin2(α)+ΔB3cos2(α)2ΔB4sin(α)cos(α)].
Δn(r,x)=ΔnYΔnZ=n32[(ΔB2ΔB3)22ΔB4+2ΔB4]sin(2α),
ΔT(r,x)=2(1R)αP0eαxe2r2/w02G2+(ρCπw02ω)2.
F=αthYn3p44s44(1eαL)ρC.
Di=dijσj.
E2=d14ε(σrrσφφ)sin(φ)cos(φ)
E3=d142ϵ[σrrcos2(φ)+σφφsin2(φ)],
ET=E22+E32,
tan(ψE)=E2E3.
Δn(r,x)=n3r41ET21+3sin2(ψE),
tan(2α)=2tan(ψE).
c=(c11c12c12000c12c11c12000c12c12c11000000c44000000c44000000c44),
s=(s11s12s12000s12s11s12000s12s12s11000000s44000000s44000000s44),
s11=c11+c12(c11c12)(c11+2c12),
s12=c12(c11c12)(c11+2c12),
s44=1c44.
s=NsM1,
s=(s11s12s13000s12s11s13000s13s13s33000000s44000000s44000000s66),
s11=(s11+s12)2+s444,
s12=(s11+s12)2s444,
s13=s12,
s33=s11,
s44=s44,
s66=2(s11s12).
p=(p11p12p12000p12p11p12000p12p12p11000000p44000000p44000000p44).
p=MpN1,
p=(p11p12p13000p12p11p13000p13p13p33000000p44000000p44000000p66),
p11=(p11+p12)2+p44,
p12=(p11+p12)2p44,
p13=p12,
p33=p11,
p44=p44,
p66=(p11p12)2.

Metrics