Abstract

We analyze three different techniques, namely, interferometry, polarization gating, and the Talbot effect to record two-dimensional images of propagating coherent terahertz waveforms in LiNbO3. Polarization gating yields significant improvements in the accuracy of waveform reproduction and sensitivity compared to Talbot imaging, which has been extensively used to date.

© 2008 Optical Society of America

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  1. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).
  3. K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2005).
  4. W. Kuang, W. J. Kim, and J. D. O'Brien, “Finite-difference time domain method for nonorthogonal unit-cell two-dimensional photonic crystals,” J. Lightwave Technol. 25, 2612-2617 (2007).
    [CrossRef]
  5. M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Phase mapping of optical fields in integrated optical waveguide structures,” J. Lightwave Technol. 19, 1169-1176 (2001).
    [CrossRef]
  6. M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294-297 (2000).
    [CrossRef] [PubMed]
  7. E. Flück, M. Hammer, A. M. Otter, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Amplitude and phase evolution of optical fields inside periodic photonic structures,” J. Lightwave Technol. 21, 1-10 (2003).
    [CrossRef]
  8. P. Kramper, M. Kafesaki, C. M. Soukoulis, A. Birner, F. Müller, U. Gösele, R. B. Wehrspohn, J. Mlynek, and V. Sandoghdar, “Near-field visualization of light confinement in a photonic crystal microresonator,” Opt. Lett. 29, 1-10 (2004).
    [CrossRef]
  9. S. I. Bozhevolnyi, V. S. Volkov, T. Sndergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, “Near-field imaging of light propagation in photonic crystal waveguides: explicit role of bloch harmonics,” Phys. Rev. B 66, 235204 (2002).
    [CrossRef]
  10. H. Gersen, T. J. Karle, R., J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
    [CrossRef] [PubMed]
  11. K.Sakai, ed., Terahertz Optoelectronics (Springer, 2005).
    [CrossRef]
  12. B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26-33 (2002).
    [CrossRef]
  13. P. H. Siegel, “Terahertz technology,” IEEE Trans. Microwave Theory Tech. 50, 910-928 (2002).
    [CrossRef]
  14. 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]
  15. T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
    [CrossRef]
  16. D. A. Kleinman and D. H. Auston, “Theory of electrooptic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20, 964-970 (1984).
    [CrossRef]
  17. A. G. Stepanov, J. Hebling, and J. Kuhl, “The generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23-26 (2005).
    [CrossRef]
  18. D. W. Ward, E. R. Statz, and K. A. Nelson, “Fabrication of polaritonic structures in linbo3 and litao3 using femtosecond laser machining,” Appl. Phys. A 86, 49-54 (2007).
    [CrossRef]
  19. R. M. Koehl, S. Adachi, and K. A. Nelson, “Direct visualization of collective wavepacket dynamics,” J. Phys. Chem. A 103, 10260-10267 (1999).
    [CrossRef]
  20. G. Sagnac, “L'ether lumineux demontre par l'effet du vent relatif d'ether dans un interferometre en rotation uniforme,” Compt. Rend. 157, 708-710 (1913).
  21. F. Pockels, “On the effect of an electrostatic field on the optical behavior of piezoelectric crystals,” Abh. Gott. 39, 1-7 (1894).
  22. F. Talbot, “Fact relating to optical science no. IV,” Philos. Mag. 9, 401-407 (1836).
    [CrossRef]
  23. J. Shan, A. S. Weling, E. Knoesel, L. Bartels, M. Bonn, A. Nahata, G. A. Reider, and T. F. Heinz, “Single-shot measurement of terahertz electromagnetic pulses by use of electro-optic sampling,” Opt. Lett. 25, 426-428 (2000).
    [CrossRef]
  24. K.-L. Yeh.T. Hornung, J. C. Vaughan, and K. A. Nelson, “THz amplification in high-dielectric materials,” in Ultrafast Phenomena XV, P.Corkum, D.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007), pp. 802-804.
    [CrossRef]
  25. T. P. Dougherty, G. P. Wiederrecht, and K. A. Nelson, “Impulsive stimulated Raman scattering experiments in the polariton regime,” J. Opt. Soc. Am. B 9, 2179-2189 (1992).
    [CrossRef]
  26. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford Classic Texts, 1998).
  27. D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555-1558 (1984).
    [CrossRef]
  28. J. K. Wahlstrand and R. Merlin, “Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons,” Phys. Rev. B 68, 054301 (2003).
    [CrossRef]
  29. D. H. Auston and M. C. Nuss, “Electrooptical generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24, 184-197 (1988).
    [CrossRef]
  30. T. Feurer, J. C. Vaughan, T. Hornung, and K. A. Nelson, “Typesetting of THz waveforms,” Opt. Lett. 29, 1802-1804 (2002).
    [CrossRef]
  31. J. F. Nye, Physical Properties of Crystals (Oxford U. Press, 1985).

2007

W. Kuang, W. J. Kim, and J. D. O'Brien, “Finite-difference time domain method for nonorthogonal unit-cell two-dimensional photonic crystals,” J. Lightwave Technol. 25, 2612-2617 (2007).
[CrossRef]

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

D. W. Ward, E. R. Statz, and K. A. Nelson, “Fabrication of polaritonic structures in linbo3 and litao3 using femtosecond laser machining,” Appl. Phys. A 86, 49-54 (2007).
[CrossRef]

2005

A. G. Stepanov, J. Hebling, and J. Kuhl, “The generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23-26 (2005).
[CrossRef]

H. Gersen, T. J. Karle, R., J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

2004

P. Kramper, M. Kafesaki, C. M. Soukoulis, A. Birner, F. Müller, U. Gösele, R. B. Wehrspohn, J. Mlynek, and V. Sandoghdar, “Near-field visualization of light confinement in a photonic crystal microresonator,” Opt. Lett. 29, 1-10 (2004).
[CrossRef]

2003

E. Flück, M. Hammer, A. M. Otter, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Amplitude and phase evolution of optical fields inside periodic photonic structures,” J. Lightwave Technol. 21, 1-10 (2003).
[CrossRef]

J. K. Wahlstrand and R. Merlin, “Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons,” Phys. Rev. B 68, 054301 (2003).
[CrossRef]

2002

T. Feurer, J. C. Vaughan, T. Hornung, and K. A. Nelson, “Typesetting of THz waveforms,” Opt. Lett. 29, 1802-1804 (2002).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, T. Sndergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, “Near-field imaging of light propagation in photonic crystal waveguides: explicit role of bloch harmonics,” Phys. Rev. B 66, 235204 (2002).
[CrossRef]

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26-33 (2002).
[CrossRef]

P. H. Siegel, “Terahertz technology,” IEEE Trans. Microwave Theory Tech. 50, 910-928 (2002).
[CrossRef]

2001

2000

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294-297 (2000).
[CrossRef] [PubMed]

J. Shan, A. S. Weling, E. Knoesel, L. Bartels, M. Bonn, A. Nahata, G. A. Reider, and T. F. Heinz, “Single-shot measurement of terahertz electromagnetic pulses by use of electro-optic sampling,” Opt. Lett. 25, 426-428 (2000).
[CrossRef]

1999

R. M. Koehl, S. Adachi, and K. A. Nelson, “Direct visualization of collective wavepacket dynamics,” J. Phys. Chem. A 103, 10260-10267 (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]

1992

1988

D. H. Auston and M. C. Nuss, “Electrooptical generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24, 184-197 (1988).
[CrossRef]

1984

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555-1558 (1984).
[CrossRef]

D. A. Kleinman and D. H. Auston, “Theory of electrooptic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20, 964-970 (1984).
[CrossRef]

1913

G. Sagnac, “L'ether lumineux demontre par l'effet du vent relatif d'ether dans un interferometre en rotation uniforme,” Compt. Rend. 157, 708-710 (1913).

1894

F. Pockels, “On the effect of an electrostatic field on the optical behavior of piezoelectric crystals,” Abh. Gott. 39, 1-7 (1894).

1836

F. Talbot, “Fact relating to optical science no. IV,” Philos. Mag. 9, 401-407 (1836).
[CrossRef]

Adachi, S.

R. M. Koehl, S. Adachi, and K. A. Nelson, “Direct visualization of collective wavepacket dynamics,” J. Phys. Chem. A 103, 10260-10267 (1999).
[CrossRef]

Auston, D. H.

D. H. Auston and M. C. Nuss, “Electrooptical generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24, 184-197 (1988).
[CrossRef]

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555-1558 (1984).
[CrossRef]

D. A. Kleinman and D. H. Auston, “Theory of electrooptic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20, 964-970 (1984).
[CrossRef]

Balistreri, M. L. M.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Phase mapping of optical fields in integrated optical waveguide structures,” J. Lightwave Technol. 19, 1169-1176 (2001).
[CrossRef]

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294-297 (2000).
[CrossRef] [PubMed]

Bartels, L.

Birner, A.

P. Kramper, M. Kafesaki, C. M. Soukoulis, A. Birner, F. Müller, U. Gösele, R. B. Wehrspohn, J. Mlynek, and V. Sandoghdar, “Near-field visualization of light confinement in a photonic crystal microresonator,” Opt. Lett. 29, 1-10 (2004).
[CrossRef]

Bogaerts, W.

H. Gersen, T. J. Karle, R., J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Boltasseva, A.

S. I. Bozhevolnyi, V. S. Volkov, T. Sndergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, “Near-field imaging of light propagation in photonic crystal waveguides: explicit role of bloch harmonics,” Phys. Rev. B 66, 235204 (2002).
[CrossRef]

Bonn, M.

Borel, P. I.

S. I. Bozhevolnyi, V. S. Volkov, T. Sndergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, “Near-field imaging of light propagation in photonic crystal waveguides: explicit role of bloch harmonics,” Phys. Rev. B 66, 235204 (2002).
[CrossRef]

Born, M.

M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford Classic Texts, 1998).

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, T. Sndergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, “Near-field imaging of light propagation in photonic crystal waveguides: explicit role of bloch harmonics,” Phys. Rev. B 66, 235204 (2002).
[CrossRef]

Cheung, K. P.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555-1558 (1984).
[CrossRef]

Dougherty, T. P.

Engelen, R. J. P.

H. Gersen, T. J. Karle, R., J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Ferguson, B.

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26-33 (2002).
[CrossRef]

Feurer, T.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

T. Feurer, J. C. Vaughan, T. Hornung, and K. A. Nelson, “Typesetting of THz waveforms,” Opt. Lett. 29, 1802-1804 (2002).
[CrossRef]

Flück, E.

E. Flück, M. Hammer, A. M. Otter, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Amplitude and phase evolution of optical fields inside periodic photonic structures,” J. Lightwave Technol. 21, 1-10 (2003).
[CrossRef]

Gersen, H.

H. Gersen, T. J. Karle, R., J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Gösele, U.

P. Kramper, M. Kafesaki, C. M. Soukoulis, A. Birner, F. Müller, U. Gösele, R. B. Wehrspohn, J. Mlynek, and V. Sandoghdar, “Near-field visualization of light confinement in a photonic crystal microresonator,” Opt. Lett. 29, 1-10 (2004).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

Hammer, M.

E. Flück, M. Hammer, A. M. Otter, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Amplitude and phase evolution of optical fields inside periodic photonic structures,” J. Lightwave Technol. 21, 1-10 (2003).
[CrossRef]

Hebling, J.

A. G. Stepanov, J. Hebling, and J. Kuhl, “The generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23-26 (2005).
[CrossRef]

Heinz, T. F.

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]

Hornung, T.

T. Feurer, J. C. Vaughan, T. Hornung, and K. A. Nelson, “Typesetting of THz waveforms,” Opt. Lett. 29, 1802-1804 (2002).
[CrossRef]

K.-L. Yeh.T. Hornung, J. C. Vaughan, and K. A. Nelson, “THz amplification in high-dielectric materials,” in Ultrafast Phenomena XV, P.Corkum, D.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007), pp. 802-804.
[CrossRef]

Huang, K.

M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford Classic Texts, 1998).

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Kafesaki, M.

P. Kramper, M. Kafesaki, C. M. Soukoulis, A. Birner, F. Müller, U. Gösele, R. B. Wehrspohn, J. Mlynek, and V. Sandoghdar, “Near-field visualization of light confinement in a photonic crystal microresonator,” Opt. Lett. 29, 1-10 (2004).
[CrossRef]

Karle, T. J.

H. Gersen, T. J. Karle, R., J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Kim, W. J.

Kleinman, D. A.

D. A. Kleinman and D. H. Auston, “Theory of electrooptic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20, 964-970 (1984).
[CrossRef]

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555-1558 (1984).
[CrossRef]

Knoesel, E.

Koehl, R. M.

R. M. Koehl, S. Adachi, and K. A. Nelson, “Direct visualization of collective wavepacket dynamics,” J. Phys. Chem. A 103, 10260-10267 (1999).
[CrossRef]

Korterik, J. P.

H. Gersen, T. J. Karle, R., J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

E. Flück, M. Hammer, A. M. Otter, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Amplitude and phase evolution of optical fields inside periodic photonic structures,” J. Lightwave Technol. 21, 1-10 (2003).
[CrossRef]

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Phase mapping of optical fields in integrated optical waveguide structures,” J. Lightwave Technol. 19, 1169-1176 (2001).
[CrossRef]

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294-297 (2000).
[CrossRef] [PubMed]

Kramper, P.

P. Kramper, M. Kafesaki, C. M. Soukoulis, A. Birner, F. Müller, U. Gösele, R. B. Wehrspohn, J. Mlynek, and V. Sandoghdar, “Near-field visualization of light confinement in a photonic crystal microresonator,” Opt. Lett. 29, 1-10 (2004).
[CrossRef]

Krauss, T. F.

H. Gersen, T. J. Karle, R., J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Kristensen, M.

S. I. Bozhevolnyi, V. S. Volkov, T. Sndergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, “Near-field imaging of light propagation in photonic crystal waveguides: explicit role of bloch harmonics,” Phys. Rev. B 66, 235204 (2002).
[CrossRef]

Kuang, W.

Kuhl, J.

A. G. Stepanov, J. Hebling, and J. Kuhl, “The generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23-26 (2005).
[CrossRef]

Kuipers, L.

H. Gersen, T. J. Karle, R., J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

E. Flück, M. Hammer, A. M. Otter, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Amplitude and phase evolution of optical fields inside periodic photonic structures,” J. Lightwave Technol. 21, 1-10 (2003).
[CrossRef]

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Phase mapping of optical fields in integrated optical waveguide structures,” J. Lightwave Technol. 19, 1169-1176 (2001).
[CrossRef]

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294-297 (2000).
[CrossRef] [PubMed]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Merlin, R.

J. K. Wahlstrand and R. Merlin, “Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons,” Phys. Rev. B 68, 054301 (2003).
[CrossRef]

Mlynek, J.

P. Kramper, M. Kafesaki, C. M. Soukoulis, A. Birner, F. Müller, U. Gösele, R. B. Wehrspohn, J. Mlynek, and V. Sandoghdar, “Near-field visualization of light confinement in a photonic crystal microresonator,” Opt. Lett. 29, 1-10 (2004).
[CrossRef]

Müller, F.

P. Kramper, M. Kafesaki, C. M. Soukoulis, A. Birner, F. Müller, U. Gösele, R. B. Wehrspohn, J. Mlynek, and V. Sandoghdar, “Near-field visualization of light confinement in a photonic crystal microresonator,” Opt. Lett. 29, 1-10 (2004).
[CrossRef]

Nahata, A.

Nelson, K. A.

D. W. Ward, E. R. Statz, and K. A. Nelson, “Fabrication of polaritonic structures in linbo3 and litao3 using femtosecond laser machining,” Appl. Phys. A 86, 49-54 (2007).
[CrossRef]

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

T. Feurer, J. C. Vaughan, T. Hornung, and K. A. Nelson, “Typesetting of THz waveforms,” Opt. Lett. 29, 1802-1804 (2002).
[CrossRef]

R. M. Koehl, S. Adachi, and K. A. Nelson, “Direct visualization of collective wavepacket dynamics,” J. Phys. Chem. A 103, 10260-10267 (1999).
[CrossRef]

T. P. Dougherty, G. P. Wiederrecht, and K. A. Nelson, “Impulsive stimulated Raman scattering experiments in the polariton regime,” J. Opt. Soc. Am. B 9, 2179-2189 (1992).
[CrossRef]

K.-L. Yeh.T. Hornung, J. C. Vaughan, and K. A. Nelson, “THz amplification in high-dielectric materials,” in Ultrafast Phenomena XV, P.Corkum, D.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007), pp. 802-804.
[CrossRef]

Nuss, M. C.

D. H. Auston and M. C. Nuss, “Electrooptical generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24, 184-197 (1988).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford U. Press, 1985).

O'Brien, J. D.

Otter, A. M.

E. Flück, M. Hammer, A. M. Otter, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Amplitude and phase evolution of optical fields inside periodic photonic structures,” J. Lightwave Technol. 21, 1-10 (2003).
[CrossRef]

Pockels, F.

F. Pockels, “On the effect of an electrostatic field on the optical behavior of piezoelectric crystals,” Abh. Gott. 39, 1-7 (1894).

Reider, G. A.

Sagnac, G.

G. Sagnac, “L'ether lumineux demontre par l'effet du vent relatif d'ether dans un interferometre en rotation uniforme,” Compt. Rend. 157, 708-710 (1913).

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2005).

Sandoghdar, V.

P. Kramper, M. Kafesaki, C. M. Soukoulis, A. Birner, F. Müller, U. Gösele, R. B. Wehrspohn, J. Mlynek, and V. Sandoghdar, “Near-field visualization of light confinement in a photonic crystal microresonator,” Opt. Lett. 29, 1-10 (2004).
[CrossRef]

Shan, J.

Siegel, P. H.

P. H. Siegel, “Terahertz technology,” IEEE Trans. Microwave Theory Tech. 50, 910-928 (2002).
[CrossRef]

Sndergaard, T.

S. I. Bozhevolnyi, V. S. Volkov, T. Sndergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, “Near-field imaging of light propagation in photonic crystal waveguides: explicit role of bloch harmonics,” Phys. Rev. B 66, 235204 (2002).
[CrossRef]

Soukoulis, C. M.

P. Kramper, M. Kafesaki, C. M. Soukoulis, A. Birner, F. Müller, U. Gösele, R. B. Wehrspohn, J. Mlynek, and V. Sandoghdar, “Near-field visualization of light confinement in a photonic crystal microresonator,” Opt. Lett. 29, 1-10 (2004).
[CrossRef]

Statz, E. R.

D. W. Ward, E. R. Statz, and K. A. Nelson, “Fabrication of polaritonic structures in linbo3 and litao3 using femtosecond laser machining,” Appl. Phys. A 86, 49-54 (2007).
[CrossRef]

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

Stepanov, A. G.

A. G. Stepanov, J. Hebling, and J. Kuhl, “The generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23-26 (2005).
[CrossRef]

Stoyanov, N. S.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

Talbot, F.

F. Talbot, “Fact relating to optical science no. IV,” Philos. Mag. 9, 401-407 (1836).
[CrossRef]

Valdmanis, J. A.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555-1558 (1984).
[CrossRef]

van Hulst, N. F.

H. Gersen, T. J. Karle, R., J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

E. Flück, M. Hammer, A. M. Otter, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Amplitude and phase evolution of optical fields inside periodic photonic structures,” J. Lightwave Technol. 21, 1-10 (2003).
[CrossRef]

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Phase mapping of optical fields in integrated optical waveguide structures,” J. Lightwave Technol. 19, 1169-1176 (2001).
[CrossRef]

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294-297 (2000).
[CrossRef] [PubMed]

Vaughan, J. C.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

T. Feurer, J. C. Vaughan, T. Hornung, and K. A. Nelson, “Typesetting of THz waveforms,” Opt. Lett. 29, 1802-1804 (2002).
[CrossRef]

K.-L. Yeh.T. Hornung, J. C. Vaughan, and K. A. Nelson, “THz amplification in high-dielectric materials,” in Ultrafast Phenomena XV, P.Corkum, D.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007), pp. 802-804.
[CrossRef]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, T. Sndergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, “Near-field imaging of light propagation in photonic crystal waveguides: explicit role of bloch harmonics,” Phys. Rev. B 66, 235204 (2002).
[CrossRef]

Wahlstrand, J. K.

J. K. Wahlstrand and R. Merlin, “Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons,” Phys. Rev. B 68, 054301 (2003).
[CrossRef]

Ward, D. W.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

D. W. Ward, E. R. Statz, and K. A. Nelson, “Fabrication of polaritonic structures in linbo3 and litao3 using femtosecond laser machining,” Appl. Phys. A 86, 49-54 (2007).
[CrossRef]

Wehrspohn, R. B.

P. Kramper, M. Kafesaki, C. M. Soukoulis, A. Birner, F. Müller, U. Gösele, R. B. Wehrspohn, J. Mlynek, and V. Sandoghdar, “Near-field visualization of light confinement in a photonic crystal microresonator,” Opt. Lett. 29, 1-10 (2004).
[CrossRef]

Weling, A. S.

Wiederrecht, G. P.

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Wu, Q.

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]

Yeh., K.-L.

K.-L. Yeh.T. Hornung, J. C. Vaughan, and K. A. Nelson, “THz amplification in high-dielectric materials,” in Ultrafast Phenomena XV, P.Corkum, D.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007), pp. 802-804.
[CrossRef]

Zhang, X.-C.

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26-33 (2002).
[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]

Abh. Gott.

F. Pockels, “On the effect of an electrostatic field on the optical behavior of piezoelectric crystals,” Abh. Gott. 39, 1-7 (1894).

Annu. Rev. Mater. Res.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

Appl. Phys. A

D. W. Ward, E. R. Statz, and K. A. Nelson, “Fabrication of polaritonic structures in linbo3 and litao3 using femtosecond laser machining,” Appl. Phys. A 86, 49-54 (2007).
[CrossRef]

Appl. Phys. B

A. G. Stepanov, J. Hebling, and J. Kuhl, “The generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23-26 (2005).
[CrossRef]

Appl. Phys. Lett.

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]

Compt. Rend.

G. Sagnac, “L'ether lumineux demontre par l'effet du vent relatif d'ether dans un interferometre en rotation uniforme,” Compt. Rend. 157, 708-710 (1913).

IEEE J. Quantum Electron.

D. H. Auston and M. C. Nuss, “Electrooptical generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24, 184-197 (1988).
[CrossRef]

D. A. Kleinman and D. H. Auston, “Theory of electrooptic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20, 964-970 (1984).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

P. H. Siegel, “Terahertz technology,” IEEE Trans. Microwave Theory Tech. 50, 910-928 (2002).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

J. Phys. Chem. A

R. M. Koehl, S. Adachi, and K. A. Nelson, “Direct visualization of collective wavepacket dynamics,” J. Phys. Chem. A 103, 10260-10267 (1999).
[CrossRef]

Nat. Mater.

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26-33 (2002).
[CrossRef]

Opt. Lett.

Philos. Mag.

F. Talbot, “Fact relating to optical science no. IV,” Philos. Mag. 9, 401-407 (1836).
[CrossRef]

Phys. Rev. B

J. K. Wahlstrand and R. Merlin, “Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons,” Phys. Rev. B 68, 054301 (2003).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, T. Sndergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, “Near-field imaging of light propagation in photonic crystal waveguides: explicit role of bloch harmonics,” Phys. Rev. B 66, 235204 (2002).
[CrossRef]

Phys. Rev. Lett.

H. Gersen, T. J. Karle, R., J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294-297 (2000).
[CrossRef] [PubMed]

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555-1558 (1984).
[CrossRef]

Other

M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford Classic Texts, 1998).

K.-L. Yeh.T. Hornung, J. C. Vaughan, and K. A. Nelson, “THz amplification in high-dielectric materials,” in Ultrafast Phenomena XV, P.Corkum, D.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007), pp. 802-804.
[CrossRef]

J. F. Nye, Physical Properties of Crystals (Oxford U. Press, 1985).

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2005).

K.Sakai, ed., Terahertz Optoelectronics (Springer, 2005).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Top view of the pump pulse focused to a line parallel to the z axis. The pump produces a Cherenkov-type terahertz radiation pattern resembling a single-cycle waveform. The generated terahertz field is probed by a phase-matched probe pulse that illuminates one half of the crystal area. The pump and probe pulses are separated by a specific time delay τ.

Fig. 2
Fig. 2

Terahertz electric field modulates the phase of the probe pulse and the phase modulation is converted to an amplitude image through (a) interferometry, (b) polarization gating, or (c) Talbot imaging: c, crystal; l, lens; p, polarizer; λ 4 , quarter-wave plate; cam, CCD camera. The probe region is next to the pump with the arrow indicating the polariton wave propagation toward the probe region. Sometimes the whole crystal is probed and the polariton waves on both sides of the pump beam are observed.

Fig. 3
Fig. 3

Talbot imaging setup. The phase object and the CCD camera may be displaced by distances Δ 0 and Δ 1 , respectively, from their ideal positions on either side of the lens.

Fig. 4
Fig. 4

Sagnac interferometer. (a) Simulated (solid curve) and measured profile (dashed-dotted curve) of the terahertz waveform. (b) Spectral amplitudes calculated from (a).

Fig. 5
Fig. 5

Polarization gating. (a) Simulated (solid curve) and measured profile (dashed-dotted curve) of the terahertz waveform. (b) Spectral amplitudes calculated from (a).

Fig. 6
Fig. 6

(a) Assumed terahertz waveform and (b) corresponding spectral amplitude. (c) Simulated Talbot profiles based on the waveform shown in (a) as a function of x and the camera displacement Δ 1 . (d) Corresponding spectra. (e) Measured Talbot profiles for a 100 μ m thick crystal and (f) corresponding spectra.

Fig. 7
Fig. 7

Simulated spectra for three different camera displacements Δ 1 are compared to the spectrum of the input function (Mexican hat wavelet). All spectra are normalized to 1. The relative amplitudes are 1 for Δ 1 = 0.1 , 6 for Δ 1 = 1.0 , and 740 for Δ 1 = 50.0 mm (with magnification).

Fig. 8
Fig. 8

(a) Assumed terahertz waveform and (b) corresponding spectral amplitude. (c) Simulated Talbot profiles based on the waveform shown in (a) as a function of x and the camera displacement Δ 1 . (d) Corresponding spectra. (e) Measured Talbot profiles for a 3 mm thick crystal and (f) corresponding spectra.

Fig. 9
Fig. 9

Comparing Talbot imaging (dashed curve), interferometry (dotted curve), and polarization gating (solid curve) shows that the best signal-to-noise level is found for polarization gating.

Equations (11)

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ϕ z ( x ) = ω c [ n eo 1 2 r 33 n eo 3 E THz ( x ) ] L ,
ϕ x ( x ) = ω c [ n o 1 2 r 13 n o 3 E THz ( x ) ] L ,
I ( x ) exp [ i ϕ z ( x ) ] + exp [ i ξ ( x ) ] 2 .
V 1 ( x ) = i 2 sin Δ ϕ ( x ) δ ϕ 2 ( 1 1 ) ,
Δ ϕ ( x ) = ω 2 c ( r 33 n eo 3 r 13 n o 3 ) L E THz ( x )
I ( x ) δ ϕ 2 4 + δ ϕ 2 Δ ϕ ( x ) .
E ( x ) exp ( i k 2 ( f + Δ 1 ) x 2 ) d k x E ̃ 0 ( k x ) exp ( i α 2 k x 2 + i β x k x ) ,
α 2 = 1 2 k f ( Δ 0 + Δ 1 ) + Δ 0 Δ 1 f + Δ 1 , β = f f + Δ 1 ,
E 0 ( x ) = exp [ i ϕ z ( x ) ] .
E 0 ( x ) = exp ( i a x e b 2 x 2 ) 1 + i a x e b 2 x 2 ,
E ( x ) = exp ( i k 2 ( f + Δ 1 ) x 2 ) [ 1 i a β b 3 γ 3 x exp ( β 2 γ 2 x 2 ) ]

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