Abstract

Four phase-sensitive imaging methods (Talbot, phase contrast, Sagnac, and polarization gating) used for detecting terahertz-frequency waves in structured lithium niobate slabs are compared analytically and experimentally. It is demonstrated that both phase contrast and a self-compensating polarization gating geometry can generate in-focus images of the sample and quantitatively measure the terahertz electric field. Of these two methods polarization gating has better signal-to-noise ratio and so is preferred for most situations, while phase contrast imaging has better spatial resolution and so is preferred for measurements involving fine structures or near-field effects.

© 2010 Optical Society of America

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  1. Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, 2009).
  2. 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]
  3. K.-H. Lin, C. A. Werley, and K. A. Nelson, “Generation of multicycle THz phonon-polariton waves in a planar waveguide by tilted optical pulse fronts,” Appl. Phys. Lett. 95, 103304 (2009).
    [CrossRef]
  4. T. Feurer, J. C. Vaughan, and K. A. Nelson, “Spatiotemporal coherent control of lattice vibrational waves,” Science 299, 374–377 (2003).
    [CrossRef] [PubMed]
  5. T. Hornung, K. L. Yeh, and K. A. Nelson, “Terahertz nonlinear response in lithium niobate,” in Ultrafast Phenomena XV, P.Corkum, D.M.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007).
    [CrossRef]
  6. N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, “Integrated diffractive THz elements,” Appl. Phys. Lett. 82, 674–676 (2003).
    [CrossRef]
  7. N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, “Terahertz polariton propagation in patterned materials,” Nature Mater. 1, 95–98 (2002).
    [CrossRef]
  8. E. R. Statz, D. W. Ward, and K. A. Nelson, “Phonon-polariton excitation in ferroelectric slab waveguides and photonic crystals,” in Ultrafast Phenomena XV, P.Corkum, D.M.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007), pp. 784–786.
    [CrossRef]
  9. P. Peier, S. Pilz, and T. Feurer, “Time-resolved coherent imaging of a THz multilayer response,” J. Opt. Soc. Am. B 26, 1649–1655 (2009).
    [CrossRef]
  10. 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 (2006).
    [CrossRef]
  11. R. M. Koehl, S. Adachi, and K. A. Nelson, “Direct visualization of collective wavepacket dynamics,” J. Phys. Chem. A 103, 10260–10267 (1999).
    [CrossRef]
  12. 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]
  13. P. Peier, S. Pilz, F. Müller, K. A. Nelson, and T. Feurer, “Analysis of phase contrast imaging of terahertz phonon-polaritons,” J. Opt. Soc. Am. B 25, B70–B75 (2008).
    [CrossRef]
  14. Q. Wu, C. A. Werley, K.-H. Lin, A. Dorn, M. G. Bawendi, and K. A. Nelson, “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide,” Opt. Express 17, 9219–9225 (2009).
    [CrossRef] [PubMed]
  15. T. P. Dougherty, G. P. Wiederrecht, and K. A. Nelson, “Impulsive stimulated Raman scattering experiments in the polariton regime,” J. Opt. Soc. Am. 9, 2179–2189 (1992).
    [CrossRef]
  16. In reality the signal at the camera is a magnified inverted image of the phase pattern after the sample: P(−mx,−mz)∝Δϕ(x,z). This scaling and inversion of the field is not important for understanding the concepts in this paper, so the magnification factor will be omitted from equations in the text. Said in another way, the analysis assumes a non-inverting imaging system with a magnification of 1.
  17. H. F. Talbot, “Facts relating to optical science no. IV,” Philos. Mag. 9, 401–407 (1836).
  18. K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, E.Wolf ed., (Elsevier, 1989), Vol. 27, pp. 1–108.
    [CrossRef]
  19. F. Zernike, “Phase contrast: a new method for the microscopic observation of transparent objects,” Physica (Amsterdam) 9, 686–698 (1942).
    [CrossRef]
  20. F. Zernike, “How I discovered phase contrast,” Science 121, 345–349 (1955).
    [CrossRef] [PubMed]
  21. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005), Chap. 8.
  22. 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).
  23. M. C. Gabriel, N. A. Whitaker, Jr., C. W. Dirk, M. G. Kuzyk, and M. Thakur, “Measurement of ultrafast optical nonlinearities using a modified Sagnac interferometer,” Opt. Lett. 16, 1334–1336 (1991).
    [CrossRef] [PubMed]
  24. T. Tachizaki, T. Muroya, O. Matsudaa, Y. Sugawara, D. H. Hurley, and O. B. Wright, “Scanning ultrafast Sagnac interferometry for imaging two-dimensional surface wave propagation,” Rev. Sci. Instrum. 77, 043713 (2006).
    [CrossRef]
  25. B. I. Greene and R. C. Farrow, “Direct measurement of a subpicosecond birefringent response in CS2,” J. Chem. Phys. 77, 4779–4780 (1982).
    [CrossRef]
  26. S. Kinoshita, Y. Kai, M. Yamaguchi, and T. Yagi, “Direct comparison between ultrafast optical Kerr effect and high-resolution light scattering spectroscopy,” Phys. Rev. Lett. 75, 148–151 (1995).
    [CrossRef] [PubMed]
  27. D. Auston and M. Nuss, “Electrooptic generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24, 184–197 (1988).
    [CrossRef]
  28. 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]
  29. 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]
  30. Z. Jiang and X.-C. Zhang, “Terahertz Imaging via Electrooptic Effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (1999).
    [CrossRef]
  31. A. Yariv and P. Yeh, Photonics, Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, 2007).
  32. A. A. Goshtasby, 2-D and 3-D Image Registration (Wiley, 2005), Chap. 5.
  33. N. J. Cronin, Microwave and Optical Waveguides (Institute of Physics, 1995).

2009 (3)

2008 (1)

2007 (1)

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]

2006 (2)

T. Tachizaki, T. Muroya, O. Matsudaa, Y. Sugawara, D. H. Hurley, and O. B. Wright, “Scanning ultrafast Sagnac interferometry for imaging two-dimensional surface wave propagation,” Rev. Sci. Instrum. 77, 043713 (2006).
[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 (2006).
[CrossRef]

2004 (1)

2003 (3)

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]

T. Feurer, J. C. Vaughan, and K. A. Nelson, “Spatiotemporal coherent control of lattice vibrational waves,” Science 299, 374–377 (2003).
[CrossRef] [PubMed]

N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, “Integrated diffractive THz elements,” Appl. Phys. Lett. 82, 674–676 (2003).
[CrossRef]

2002 (1)

N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, “Terahertz polariton propagation in patterned materials,” Nature Mater. 1, 95–98 (2002).
[CrossRef]

1999 (2)

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

Z. Jiang and X.-C. Zhang, “Terahertz Imaging via Electrooptic Effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (1999).
[CrossRef]

1996 (1)

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]

1995 (1)

S. Kinoshita, Y. Kai, M. Yamaguchi, and T. Yagi, “Direct comparison between ultrafast optical Kerr effect and high-resolution light scattering spectroscopy,” Phys. Rev. Lett. 75, 148–151 (1995).
[CrossRef] [PubMed]

1992 (1)

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

1991 (1)

1988 (1)

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

1982 (1)

B. I. Greene and R. C. Farrow, “Direct measurement of a subpicosecond birefringent response in CS2,” J. Chem. Phys. 77, 4779–4780 (1982).
[CrossRef]

1955 (1)

F. Zernike, “How I discovered phase contrast,” Science 121, 345–349 (1955).
[CrossRef] [PubMed]

1942 (1)

F. Zernike, “Phase contrast: a new method for the microscopic observation of transparent objects,” Physica (Amsterdam) 9, 686–698 (1942).
[CrossRef]

1913 (1)

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).

1836 (1)

H. F. Talbot, “Facts relating to optical science no. IV,” Philos. Mag. 9, 401–407 (1836).

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.

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

Bawendi, M. G.

Cronin, N. J.

N. J. Cronin, Microwave and Optical Waveguides (Institute of Physics, 1995).

Dirk, C. W.

Dorn, A.

Dougherty, T. P.

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

Farrow, R. C.

B. I. Greene and R. C. Farrow, “Direct measurement of a subpicosecond birefringent response in CS2,” J. Chem. Phys. 77, 4779–4780 (1982).
[CrossRef]

Feurer, T.

P. Peier, S. Pilz, and T. Feurer, “Time-resolved coherent imaging of a THz multilayer response,” J. Opt. Soc. Am. B 26, 1649–1655 (2009).
[CrossRef]

P. Peier, S. Pilz, F. Müller, K. A. Nelson, and T. Feurer, “Analysis of phase contrast imaging of terahertz phonon-polaritons,” J. Opt. Soc. Am. B 25, B70–B75 (2008).
[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, and K. A. Nelson, “Spatiotemporal coherent control of lattice vibrational waves,” Science 299, 374–377 (2003).
[CrossRef] [PubMed]

N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, “Integrated diffractive THz elements,” Appl. Phys. Lett. 82, 674–676 (2003).
[CrossRef]

N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, “Terahertz polariton propagation in patterned materials,” Nature Mater. 1, 95–98 (2002).
[CrossRef]

Gabriel, M. C.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005), Chap. 8.

Goshtasby, A. A.

A. A. Goshtasby, 2-D and 3-D Image Registration (Wiley, 2005), Chap. 5.

Greene, B. I.

B. I. Greene and R. C. Farrow, “Direct measurement of a subpicosecond birefringent response in CS2,” J. Chem. Phys. 77, 4779–4780 (1982).
[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]

Hornung, T.

T. Hornung, K. L. Yeh, and K. A. Nelson, “Terahertz nonlinear response in lithium niobate,” in Ultrafast Phenomena XV, P.Corkum, D.M.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007).
[CrossRef]

Hurley, D. H.

T. Tachizaki, T. Muroya, O. Matsudaa, Y. Sugawara, D. H. Hurley, and O. B. Wright, “Scanning ultrafast Sagnac interferometry for imaging two-dimensional surface wave propagation,” Rev. Sci. Instrum. 77, 043713 (2006).
[CrossRef]

Jiang, Z.

Z. Jiang and X.-C. Zhang, “Terahertz Imaging via Electrooptic Effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (1999).
[CrossRef]

Kai, Y.

S. Kinoshita, Y. Kai, M. Yamaguchi, and T. Yagi, “Direct comparison between ultrafast optical Kerr effect and high-resolution light scattering spectroscopy,” Phys. Rev. Lett. 75, 148–151 (1995).
[CrossRef] [PubMed]

Kinoshita, S.

S. Kinoshita, Y. Kai, M. Yamaguchi, and T. Yagi, “Direct comparison between ultrafast optical Kerr effect and high-resolution light scattering spectroscopy,” Phys. Rev. Lett. 75, 148–151 (1995).
[CrossRef] [PubMed]

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]

Kuzyk, M. G.

Lee, Y. -S.

Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, 2009).

Lin, K. -H.

K.-H. Lin, C. A. Werley, and K. A. Nelson, “Generation of multicycle THz phonon-polariton waves in a planar waveguide by tilted optical pulse fronts,” Appl. Phys. Lett. 95, 103304 (2009).
[CrossRef]

Q. Wu, C. A. Werley, K.-H. Lin, A. Dorn, M. G. Bawendi, and K. A. Nelson, “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide,” Opt. Express 17, 9219–9225 (2009).
[CrossRef] [PubMed]

Matsudaa, O.

T. Tachizaki, T. Muroya, O. Matsudaa, Y. Sugawara, D. H. Hurley, and O. B. Wright, “Scanning ultrafast Sagnac interferometry for imaging two-dimensional surface wave propagation,” Rev. Sci. Instrum. 77, 043713 (2006).
[CrossRef]

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]

Müller, F.

Muroya, T.

T. Tachizaki, T. Muroya, O. Matsudaa, Y. Sugawara, D. H. Hurley, and O. B. Wright, “Scanning ultrafast Sagnac interferometry for imaging two-dimensional surface wave propagation,” Rev. Sci. Instrum. 77, 043713 (2006).
[CrossRef]

Nelson, K. A.

K.-H. Lin, C. A. Werley, and K. A. Nelson, “Generation of multicycle THz phonon-polariton waves in a planar waveguide by tilted optical pulse fronts,” Appl. Phys. Lett. 95, 103304 (2009).
[CrossRef]

Q. Wu, C. A. Werley, K.-H. Lin, A. Dorn, M. G. Bawendi, and K. A. Nelson, “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide,” Opt. Express 17, 9219–9225 (2009).
[CrossRef] [PubMed]

P. Peier, S. Pilz, F. Müller, K. A. Nelson, and T. Feurer, “Analysis of phase contrast imaging of terahertz phonon-polaritons,” J. Opt. Soc. Am. B 25, B70–B75 (2008).
[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 (2006).
[CrossRef]

N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, “Integrated diffractive THz elements,” Appl. Phys. Lett. 82, 674–676 (2003).
[CrossRef]

T. Feurer, J. C. Vaughan, and K. A. Nelson, “Spatiotemporal coherent control of lattice vibrational waves,” Science 299, 374–377 (2003).
[CrossRef] [PubMed]

N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, “Terahertz polariton propagation in patterned materials,” Nature Mater. 1, 95–98 (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. 9, 2179–2189 (1992).
[CrossRef]

E. R. Statz, D. W. Ward, and K. A. Nelson, “Phonon-polariton excitation in ferroelectric slab waveguides and photonic crystals,” in Ultrafast Phenomena XV, P.Corkum, D.M.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007), pp. 784–786.
[CrossRef]

T. Hornung, K. L. Yeh, and K. A. Nelson, “Terahertz nonlinear response in lithium niobate,” in Ultrafast Phenomena XV, P.Corkum, D.M.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007).
[CrossRef]

Nuss, M.

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

Patorski, K.

K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, E.Wolf ed., (Elsevier, 1989), Vol. 27, pp. 1–108.
[CrossRef]

Peier, P.

Pilz, S.

Planken, P. C. M.

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).

Statz, E. R.

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 (2006).
[CrossRef]

E. R. Statz, D. W. Ward, and K. A. Nelson, “Phonon-polariton excitation in ferroelectric slab waveguides and photonic crystals,” in Ultrafast Phenomena XV, P.Corkum, D.M.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007), pp. 784–786.
[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]

N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, “Integrated diffractive THz elements,” Appl. Phys. Lett. 82, 674–676 (2003).
[CrossRef]

N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, “Terahertz polariton propagation in patterned materials,” Nature Mater. 1, 95–98 (2002).
[CrossRef]

Sugawara, Y.

T. Tachizaki, T. Muroya, O. Matsudaa, Y. Sugawara, D. H. Hurley, and O. B. Wright, “Scanning ultrafast Sagnac interferometry for imaging two-dimensional surface wave propagation,” Rev. Sci. Instrum. 77, 043713 (2006).
[CrossRef]

Tachizaki, T.

T. Tachizaki, T. Muroya, O. Matsudaa, Y. Sugawara, D. H. Hurley, and O. B. Wright, “Scanning ultrafast Sagnac interferometry for imaging two-dimensional surface wave propagation,” Rev. Sci. Instrum. 77, 043713 (2006).
[CrossRef]

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science no. IV,” Philos. Mag. 9, 401–407 (1836).

Thakur, M.

van der Valk, N. C. J.

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, and K. A. Nelson, “Spatiotemporal coherent control of lattice vibrational waves,” Science 299, 374–377 (2003).
[CrossRef] [PubMed]

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 (2006).
[CrossRef]

N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, “Integrated diffractive THz elements,” Appl. Phys. Lett. 82, 674–676 (2003).
[CrossRef]

N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, “Terahertz polariton propagation in patterned materials,” Nature Mater. 1, 95–98 (2002).
[CrossRef]

E. R. Statz, D. W. Ward, and K. A. Nelson, “Phonon-polariton excitation in ferroelectric slab waveguides and photonic crystals,” in Ultrafast Phenomena XV, P.Corkum, D.M.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007), pp. 784–786.
[CrossRef]

Wenckebach, T.

Werley, C. A.

Q. Wu, C. A. Werley, K.-H. Lin, A. Dorn, M. G. Bawendi, and K. A. Nelson, “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide,” Opt. Express 17, 9219–9225 (2009).
[CrossRef] [PubMed]

K.-H. Lin, C. A. Werley, and K. A. Nelson, “Generation of multicycle THz phonon-polariton waves in a planar waveguide by tilted optical pulse fronts,” Appl. Phys. Lett. 95, 103304 (2009).
[CrossRef]

Whitaker, N. A.

Wiederrecht, G. P.

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

Wright, O. B.

T. Tachizaki, T. Muroya, O. Matsudaa, Y. Sugawara, D. H. Hurley, and O. B. Wright, “Scanning ultrafast Sagnac interferometry for imaging two-dimensional surface wave propagation,” Rev. Sci. Instrum. 77, 043713 (2006).
[CrossRef]

Wu, Q.

Yagi, T.

S. Kinoshita, Y. Kai, M. Yamaguchi, and T. Yagi, “Direct comparison between ultrafast optical Kerr effect and high-resolution light scattering spectroscopy,” Phys. Rev. Lett. 75, 148–151 (1995).
[CrossRef] [PubMed]

Yamaguchi, M.

S. Kinoshita, Y. Kai, M. Yamaguchi, and T. Yagi, “Direct comparison between ultrafast optical Kerr effect and high-resolution light scattering spectroscopy,” Phys. Rev. Lett. 75, 148–151 (1995).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv and P. Yeh, Photonics, Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, 2007).

Yeh, K. L.

T. Hornung, K. L. Yeh, and K. A. Nelson, “Terahertz nonlinear response in lithium niobate,” in Ultrafast Phenomena XV, P.Corkum, D.M.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007).
[CrossRef]

Yeh, P.

A. Yariv and P. Yeh, Photonics, Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, 2007).

Zernike, F.

F. Zernike, “How I discovered phase contrast,” Science 121, 345–349 (1955).
[CrossRef] [PubMed]

F. Zernike, “Phase contrast: a new method for the microscopic observation of transparent objects,” Physica (Amsterdam) 9, 686–698 (1942).
[CrossRef]

Zhang, X. -C.

Z. Jiang and X.-C. Zhang, “Terahertz Imaging via Electrooptic Effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (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]

Annu. Rev. Mater. Res. (1)

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 (1)

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 (2006).
[CrossRef]

Appl. Phys. Lett. (3)

K.-H. Lin, C. A. Werley, and K. A. Nelson, “Generation of multicycle THz phonon-polariton waves in a planar waveguide by tilted optical pulse fronts,” Appl. Phys. Lett. 95, 103304 (2009).
[CrossRef]

N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, “Integrated diffractive THz elements,” Appl. Phys. Lett. 82, 674–676 (2003).
[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]

Compt. Rend. (1)

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. (1)

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

IEEE Trans. Microwave Theory Tech. (1)

Z. Jiang and X.-C. Zhang, “Terahertz Imaging via Electrooptic Effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (1999).
[CrossRef]

J. Chem. Phys. (1)

B. I. Greene and R. C. Farrow, “Direct measurement of a subpicosecond birefringent response in CS2,” J. Chem. Phys. 77, 4779–4780 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Opt. Soc. Am. B (3)

J. Phys. Chem. A (1)

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

Nature Mater. (1)

N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, “Terahertz polariton propagation in patterned materials,” Nature Mater. 1, 95–98 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Philos. Mag. (1)

H. F. Talbot, “Facts relating to optical science no. IV,” Philos. Mag. 9, 401–407 (1836).

Phys. Rev. B (1)

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]

Phys. Rev. Lett. (1)

S. Kinoshita, Y. Kai, M. Yamaguchi, and T. Yagi, “Direct comparison between ultrafast optical Kerr effect and high-resolution light scattering spectroscopy,” Phys. Rev. Lett. 75, 148–151 (1995).
[CrossRef] [PubMed]

Physica (Amsterdam) (1)

F. Zernike, “Phase contrast: a new method for the microscopic observation of transparent objects,” Physica (Amsterdam) 9, 686–698 (1942).
[CrossRef]

Rev. Sci. Instrum. (1)

T. Tachizaki, T. Muroya, O. Matsudaa, Y. Sugawara, D. H. Hurley, and O. B. Wright, “Scanning ultrafast Sagnac interferometry for imaging two-dimensional surface wave propagation,” Rev. Sci. Instrum. 77, 043713 (2006).
[CrossRef]

Science (2)

F. Zernike, “How I discovered phase contrast,” Science 121, 345–349 (1955).
[CrossRef] [PubMed]

T. Feurer, J. C. Vaughan, and K. A. Nelson, “Spatiotemporal coherent control of lattice vibrational waves,” Science 299, 374–377 (2003).
[CrossRef] [PubMed]

Other (9)

T. Hornung, K. L. Yeh, and K. A. Nelson, “Terahertz nonlinear response in lithium niobate,” in Ultrafast Phenomena XV, P.Corkum, D.M.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007).
[CrossRef]

E. R. Statz, D. W. Ward, and K. A. Nelson, “Phonon-polariton excitation in ferroelectric slab waveguides and photonic crystals,” in Ultrafast Phenomena XV, P.Corkum, D.M.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2007), pp. 784–786.
[CrossRef]

In reality the signal at the camera is a magnified inverted image of the phase pattern after the sample: P(−mx,−mz)∝Δϕ(x,z). This scaling and inversion of the field is not important for understanding the concepts in this paper, so the magnification factor will be omitted from equations in the text. Said in another way, the analysis assumes a non-inverting imaging system with a magnification of 1.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005), Chap. 8.

K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, E.Wolf ed., (Elsevier, 1989), Vol. 27, pp. 1–108.
[CrossRef]

Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, 2009).

A. Yariv and P. Yeh, Photonics, Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, 2007).

A. A. Goshtasby, 2-D and 3-D Image Registration (Wiley, 2005), Chap. 5.

N. J. Cronin, Microwave and Optical Waveguides (Institute of Physics, 1995).

Supplementary Material (1)

» Media 1: AVI (1872 KB)     

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Figures (7)

Fig. 1
Fig. 1

(a)–(e) show polarization gating imaging frames from five time-points from a video clip (Media 1) of a rightward propagating terahertz wave interacting with large single-slit. The wave consists of two several-cycle wavepackets generated by two optical pulses of different intensities separated by 27 ps. Two air-gaps [trapezoidal shapes near top center and bottom center masked in light gray in (a) and Media 1] were generated by removing these regions from the LN slab using laser machining. A thin LN bridge, 3 wavelengths tall, remains. The terahertz wave passes through the gap and diffracts as it is emitted. (f) shows an E-field trace extracted by averaging over the vertical dimension of the dashed box in (e).

Fig. 2
Fig. 2

Experimental setups. (a) Optical components common to all four imaging techniques. (b) The pumping geometry showing that the terahertz wave propagates in the plane of the LN slab, orthogonal to the generating pump light. (c) Talbot imaging. (d) Phase contrast imaging. (e) Sagnac imaging; the dashed line follows one edge of the beam through the interferometer. (f) Polarization gating. Instead of 400 nm light from second-harmonic generation in a BBO crystal, the probe was 532 nm light generated from a NOPA.

Fig. 3
Fig. 3

Space-time plots from each imaging method showing a broadband terahertz wave propagating in a 53 μ m thick, 1 cm wide, unstructured LN slab. The color scale indicates the relative value of the electric field. (a) Talbot imaging. (b) Phase contrast imaging. (c) Sagnac imaging. (d) Polarization gating imaging.

Fig. 4
Fig. 4

Experimental dispersion curve measured by taking the two-dimensional Fourier transform of the polarization gating space-time trace from Fig. 3d. The dispersion curves for the first three waveguide modes are visible.

Fig. 5
Fig. 5

Measured wave vector content of the images, calculated by taking the dispersion curves like the one shown in Fig. 4 and integrating over the frequency axis. The amplitude is proportional to the actual wave vector content multiplied by the instrument response.

Fig. 6
Fig. 6

Raw images of a Y-coupler structure imaged through (a) the phase contrast setup and (b) the polarization gating setup. Modulation in the background intensity of the phase contrast image is apparent, while it is smooth and unmodulated for the polarization gating image. The two images in (b) result from the two polarizations that have been imaged onto the same CCD chip.

Fig. 7
Fig. 7

Mode- and frequency-dependent sensitivity for a 53 μ m LN slab. Sensitivity is defined as the actual phase shift induced in the probe as it propagates through the LN slab normalized by the phase shift that would be expected for a DC electric field.

Equations (12)

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P PC ( x , z ) Δ I ( x , z ) I 0 ( x , z ) 2 Δ ϕ PC ( x , z ) ,
E ( x , z ) = E CW ( x , z ) exp [ i Δ ϕ ( x , z ) + i α ( x , z ) ] + E CCW ( x , z ) .
I ( x , z ) = E E = I CW ( x , z ) + I CCW ( x , z ) + 2 E CW ( x , z ) E CCW ( x , z ) cos [ Δ ϕ ( x , z ) + α ( x , z ) ] .
P SI ( x , z ) Δ I ( x , z ) I 0 ( x , z ) 2 E CW ( x , z ) E CCW ( x , z ) I CW ( x , z ) + I CCW ( x , z ) Δ ϕ SI ( x , z ) .
I ± ( x , z ) = I 0 ± ( x , z ) [ 1 ± sin ( Δ ϕ ( x , z ) ) ] ,
P PG ( x , z ) I + ( x , z ) I 0 + ( x , z ) I ( x , z ) I 0 ( x , z ) 2 Δ ϕ PG ( x , z ) .
Δ ϕ PC ( x , z ) = 2 π λ opt Δ n e o ( x , z ) = 2 π λ opt r 33 n e o 3 2 E THz ( x , z ) ,
Δ ϕ PG ( x , z ) = 2 π λ opt [ Δ n e o ( x , z ) Δ n o ( x , z ) ] = 2 π λ opt r 33 n e o 3 r 13 n o 3 2 E THz ( x , z ) .
P PC ( x , z ) P PG ( x , z ) = 2 Δ ϕ PC ( x , z ) 2 Δ ϕ PG ( x , z ) = r 33 n e o 3 r 33 n e o 3 r 13 n o 3 1.6 ,
d Δ ϕ ( x , z ) = ω opt c Δ n ( x , y , z ) d y = ω opt c n e o 3 r 33 2 E THz ( x , y , z ) d y .
Δ ϕ ( ω THz , m ) = ω opt c n e o 3 r 33 2 / 2 / 2 E T ( y , ω THz , m ) cos ( ω THz n e o c y + ψ 0 ) d y ,
E T ( y , ω THz , m ) = E 0   cos k y ( ω THz , m ) y + m π / 2 .

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