Abstract

We apply phase contrast imaging to enable, sharply focused visualization of terahertz waves in electro-optic media. The approach allows quantitative characterization of THz waves in the 60 GHz – 4.5 THz frequency range in a thin dielectric slab and in-focus observation of THz waves in polaritonic structures.

© 2009 Optical Society of America

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References

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  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]
  2. 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]
  3. D. Auston and M. Nuss, "Electrooptic Generation and Detection of Femtosecond Electrical Transients," IEEE J. Quantum Electron. 24, 184-197 (1988).
    [CrossRef]
  4. A. G. Stepanov, J. Kuhl, I. Z. Kozma, E. Riedle, G. Almási, and J. Hebling, "Scaling up the energy of THz pulses created by optical rectification," Opt. Express 13, 5762-5768 (2005).
    [CrossRef] [PubMed]
  5. K. -L. Yeh, M. C. Hoffmann, J. Hebling, and KeithA. Nelson, "Generation of 10 ?J ultrashort terahertz pulses by optical rectification," Appl. Phys. Lett. 90, 171121 (2007).
    [CrossRef]
  6. T. Feurer, N. S. Stoyanov, D. W. Ward, and K. A. Nelson, "Direct Visualization of the Gouy Phase by Focusing Phonon Polaritons," Phys. Rev. Lett. 88, 257402 (2002).
    [CrossRef] [PubMed]
  7. T. Feurer, J. C. Vaughan, and K. A. Nelson, "Spatiotemporal Coherent Control of Lattice Vibrational Waves," Science 299, 374-377 (2003).
    [CrossRef] [PubMed]
  8. N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, "Terahertz polariton propagation in patterned materials," Nature Materials 1, 95-98 (2002).
    [CrossRef]
  9. N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, "Integrated diffractive terahertz elements," Appl. Phys. Lett. 82, 674-676 (2003).
    [CrossRef]
  10. J. P. Wolfe, Imaging phonons: acoustic wave propagation in solids (Cambridge University Press, Cambridge, 1998).
  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. Z. Jiang and X.-C. Zhang, "Terahertz Imaging via Electrooptic Effect," IEEE Trans. Microwave Theory Tech. 47, 2644-2650 (1999).
    [CrossRef]
  13. R. M. Koehl, S. Adachi, and K. A. Nelson, "Direct Visualization of Collective Wavepacket Dynamics," J. Phys. Chem. A 103, 10260-10267 (1999).
    [CrossRef]
  14. D. W. Ward, E. R. Statz, K. A. Nelson, R. M. Roth, and R. M. Osgood, "Terahertz wave generation and propagation in thin-film lithium niobate produced by crystal ion slicing," Appl. Phys. Lett. 86, 022908 (2005).
    [CrossRef]
  15. H. F. Talbot, "Facts relating to optical science no. IV," Philos. Mag. 9, 401-407 (1836).
  16. 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]
  17. F. Zernike, "How I discovered phase contrast," Science 121, 345-349 (1955).
    [CrossRef] [PubMed]
  18. F. Zernike, "Phase contrast: a new method for the microscopic observation of transparent objects," Physica 9686-698 (1942).
    [CrossRef]
  19. JosephW.  Goodman, Introduction to Fourier Optics, 3rd edition (Roberts & Company Publishers, Englewood, 2005), Chap. 8.
    [PubMed]
  20. N. J. Cronin, Microwave and Optical Waveguides (Institute of Physics Publisher, Philadelphia, 1995).
  21. D. W. Ward, E. R. Statz, and K. S. Nelson, "Fabrication of polaritonic structures in LiNbO3 and LiTaO3 using femtosecond laser machining," Appl. Phys. A 86, 49-54 (2007).
    [CrossRef]
  22. Joseph W.  Goodman, Introduction to Fourier Optics, 3rd edition (Roberts & Company Publishers, Englewood, 2005), Chap. 5.
    [PubMed]

2008 (1)

2007 (3)

D. W. Ward, E. R. Statz, and K. S. 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]

K. -L. Yeh, M. C. Hoffmann, J. Hebling, and KeithA. Nelson, "Generation of 10 ?J ultrashort terahertz pulses by optical rectification," Appl. Phys. Lett. 90, 171121 (2007).
[CrossRef]

2005 (2)

A. G. Stepanov, J. Kuhl, I. Z. Kozma, E. Riedle, G. Almási, and J. Hebling, "Scaling up the energy of THz pulses created by optical rectification," Opt. Express 13, 5762-5768 (2005).
[CrossRef] [PubMed]

D. W. Ward, E. R. Statz, K. A. Nelson, R. M. Roth, and R. M. Osgood, "Terahertz wave generation and propagation in thin-film lithium niobate produced by crystal ion slicing," Appl. Phys. Lett. 86, 022908 (2005).
[CrossRef]

2003 (2)

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 terahertz elements," Appl. Phys. Lett. 82, 674-676 (2003).
[CrossRef]

2002 (2)

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

T. Feurer, N. S. Stoyanov, D. W. Ward, and K. A. Nelson, "Direct Visualization of the Gouy Phase by Focusing Phonon Polaritons," Phys. Rev. Lett. 88, 257402 (2002).
[CrossRef] [PubMed]

1999 (2)

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

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]

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]

1988 (1)

D. Auston and M. Nuss, "Electrooptic Generation and Detection of Femtosecond Electrical Transients," IEEE J. Quantum Electron. 24, 184-197 (1988).
[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 9686-698 (1942).
[CrossRef]

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]

Almási, G.

Auston, D.

D. Auston and M. Nuss, "Electrooptic Generation and Detection of Femtosecond Electrical Transients," IEEE J. Quantum Electron. 24, 184-197 (1988).
[CrossRef]

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]

Feurer, T.

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 terahertz 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 Materials 1, 95-98 (2002).
[CrossRef]

T. Feurer, N. S. Stoyanov, D. W. Ward, and K. A. Nelson, "Direct Visualization of the Gouy Phase by Focusing Phonon Polaritons," Phys. Rev. Lett. 88, 257402 (2002).
[CrossRef] [PubMed]

Hebling, J.

K. -L. Yeh, M. C. Hoffmann, J. Hebling, and KeithA. Nelson, "Generation of 10 ?J ultrashort terahertz pulses by optical rectification," Appl. Phys. Lett. 90, 171121 (2007).
[CrossRef]

A. G. Stepanov, J. Kuhl, I. Z. Kozma, E. Riedle, G. Almási, and J. Hebling, "Scaling up the energy of THz pulses created by optical rectification," Opt. Express 13, 5762-5768 (2005).
[CrossRef] [PubMed]

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]

Hoffmann, M. C.

K. -L. Yeh, M. C. Hoffmann, J. Hebling, and KeithA. Nelson, "Generation of 10 ?J ultrashort terahertz pulses by optical rectification," Appl. Phys. Lett. 90, 171121 (2007).
[CrossRef]

Jiang, Z.

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

Keith, J.

K. -L. Yeh, M. C. Hoffmann, J. Hebling, and KeithA. Nelson, "Generation of 10 ?J ultrashort terahertz pulses by optical rectification," Appl. Phys. Lett. 90, 171121 (2007).
[CrossRef]

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]

Kozma, I. Z.

Kuhl, J.

Müller, F.

Nelson, K. A.

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, K. A. Nelson, R. M. Roth, and R. M. Osgood, "Terahertz wave generation and propagation in thin-film lithium niobate produced by crystal ion slicing," Appl. Phys. Lett. 86, 022908 (2005).
[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 terahertz 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 Materials 1, 95-98 (2002).
[CrossRef]

T. Feurer, N. S. Stoyanov, D. W. Ward, and K. A. Nelson, "Direct Visualization of the Gouy Phase by Focusing Phonon Polaritons," Phys. Rev. Lett. 88, 257402 (2002).
[CrossRef] [PubMed]

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]

Nelson, K. S.

D. W. Ward, E. R. Statz, and K. S. Nelson, "Fabrication of polaritonic structures in LiNbO3 and LiTaO3 using femtosecond laser machining," Appl. Phys. A 86, 49-54 (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]

Osgood, R. M.

D. W. Ward, E. R. Statz, K. A. Nelson, R. M. Roth, and R. M. Osgood, "Terahertz wave generation and propagation in thin-film lithium niobate produced by crystal ion slicing," Appl. Phys. Lett. 86, 022908 (2005).
[CrossRef]

Peier, P.

Pilz, S.

Riedle, E.

Roth, R. M.

D. W. Ward, E. R. Statz, K. A. Nelson, R. M. Roth, and R. M. Osgood, "Terahertz wave generation and propagation in thin-film lithium niobate produced by crystal ion slicing," Appl. Phys. Lett. 86, 022908 (2005).
[CrossRef]

Statz, E. R.

D. W. Ward, E. R. Statz, and K. S. 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]

D. W. Ward, E. R. Statz, K. A. Nelson, R. M. Roth, and R. M. Osgood, "Terahertz wave generation and propagation in thin-film lithium niobate produced by crystal ion slicing," Appl. Phys. Lett. 86, 022908 (2005).
[CrossRef]

Stepanov, A. G.

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 terahertz 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 Materials 1, 95-98 (2002).
[CrossRef]

T. Feurer, N. S. Stoyanov, D. W. Ward, and K. A. Nelson, "Direct Visualization of the Gouy Phase by Focusing Phonon Polaritons," Phys. Rev. Lett. 88, 257402 (2002).
[CrossRef] [PubMed]

Talbot, H. F.

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

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]

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. S. Nelson, "Fabrication of polaritonic structures in LiNbO3 and LiTaO3 using femtosecond laser machining," Appl. Phys. A 86, 49-54 (2007).
[CrossRef]

D. W. Ward, E. R. Statz, K. A. Nelson, R. M. Roth, and R. M. Osgood, "Terahertz wave generation and propagation in thin-film lithium niobate produced by crystal ion slicing," Appl. Phys. Lett. 86, 022908 (2005).
[CrossRef]

N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, "Integrated diffractive terahertz 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 Materials 1, 95-98 (2002).
[CrossRef]

T. Feurer, N. S. Stoyanov, D. W. Ward, and K. A. Nelson, "Direct Visualization of the Gouy Phase by Focusing Phonon Polaritons," Phys. Rev. Lett. 88, 257402 (2002).
[CrossRef] [PubMed]

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]

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, M. C. Hoffmann, J. Hebling, and KeithA. Nelson, "Generation of 10 ?J ultrashort terahertz pulses by optical rectification," Appl. Phys. Lett. 90, 171121 (2007).
[CrossRef]

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 9686-698 (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. S. Nelson, "Fabrication of polaritonic structures in LiNbO3 and LiTaO3 using femtosecond laser machining," Appl. Phys. A 86, 49-54 (2007).
[CrossRef]

Appl. Phys. Lett. (4)

K. -L. Yeh, M. C. Hoffmann, J. Hebling, and KeithA. Nelson, "Generation of 10 ?J ultrashort terahertz pulses by optical rectification," Appl. Phys. Lett. 90, 171121 (2007).
[CrossRef]

N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, "Integrated diffractive terahertz 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]

D. W. Ward, E. R. Statz, K. A. Nelson, R. M. Roth, and R. M. Osgood, "Terahertz wave generation and propagation in thin-film lithium niobate produced by crystal ion slicing," Appl. Phys. Lett. 86, 022908 (2005).
[CrossRef]

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. 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 (1)

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 Materials (1)

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

Opt. Express (1)

Philos. Mag. (1)

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

Phys. Rev. Lett. (1)

T. Feurer, N. S. Stoyanov, D. W. Ward, and K. A. Nelson, "Direct Visualization of the Gouy Phase by Focusing Phonon Polaritons," Phys. Rev. Lett. 88, 257402 (2002).
[CrossRef] [PubMed]

Physica (1)

F. Zernike, "Phase contrast: a new method for the microscopic observation of transparent objects," Physica 9686-698 (1942).
[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 (4)

J. P. Wolfe, Imaging phonons: acoustic wave propagation in solids (Cambridge University Press, Cambridge, 1998).

JosephW.  Goodman, Introduction to Fourier Optics, 3rd edition (Roberts & Company Publishers, Englewood, 2005), Chap. 8.
[PubMed]

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

Joseph W.  Goodman, Introduction to Fourier Optics, 3rd edition (Roberts & Company Publishers, Englewood, 2005), Chap. 5.
[PubMed]

Supplementary Material (2)

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup. (a) Schematic diagram. The sample, a 53 μm slab of LiNbO3, is imaged onto the camera using two lenses, and the phase plate is placed in the Fourier plane of the first lens. The 800 nm pump (red) and 400 nm probe (blue) are nearly collinear when they hit the sample. In our setup, f 1 = f 2 = 15 cm. (b) The pumping geometry. The 800 nm beam propagates through the crystal, orthogonal to its surface, polarized along z. The THz response, also polarized along z, propagates in the plane of the waveguide. (c) A bright-field image of the phase plate. The depressed square is 30 um across and 215 nm deep. The metal arrows (black in the Fig. 1 (c)) aid in alignment.

Fig. 2.
Fig. 2.

(a) (Media 1) Image of a THz field in a 53-μm LN crystal slab 42 ps after excitation by a cylindrically focused pump pulse. The chirping of the pulse because of waveguide dispersion and the first three waveguide modes are apparent. (b) The field profile from (a), averaged over the vertical dimension. Initial field strengths are higher but dispersion quickly broadens the pulse and lowers peak field amplitudes.

Fig. 3.
Fig. 3.

(a) E-field evolution as a function of space and time. The sides of the image correspond to the edges of the crystal. The colorbar has been scaled to enhance weaker signals; the maximum field strength at early times exceeds 10 kV/cm. (b) One quadrant of the 2D Fourier transform of the boxed region in (a). This gives the dispersion curve with the propagation constant β along the horizontal axis (β = kx for the coordinate system shown in Fig. 1(b)). The colorbar gives the normalized spectral intensity on a log scale. The first three waveguide modes are clearly visible. Overlaid on the experimental data are the theoretical dispersion curves for air (dark blue), bulk lithium niobate (light blue) and the first three waveguide modes for a 53 um slab (dashed green). There were no free parameters in this theoretical model.

Fig. 4.
Fig. 4.

(Media 2) The z-component of the THz E-field in a structured, 53 μm LN substrate.

Equations (4)

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Δϕopt(x,z)=2πλoptΔn(x,z)=2πλoptneo3r332ETHz(x,z)
I(x,z)=I0 (x,z) [12Δϕ(x,z)]
Δϕopt(x,z)=12(1S(x,z)R(x,z))=12 ΔI(x,z)I0(x,z)
u(x,y)=U0(kx,ky)|kx=2πx/λf,kz=2πz/λf

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