Abstract

We report the measurement of terahertz (THz) radiation, generated via optical rectification in a 20μm thick ZnTe crystal, as a function of the size of optical excitation. The result shows that, before the onset of significant higher-order nonlinear processes, the THz emission obtained with a fixed excitation power is largely size independent for excitation sizes smaller than the THz wavelength. This experimental finding is well described by a theoretical model including the generation of THz radiation through optical rectification from a subwavelength source and its propagation into the far field. The characteristic size dependence of the radiation from a subwavelength THz source is advantageous for use in apertureless near-field microscopy.

© 2005 Optical Society of America

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References

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  1. D. R. Grischkowsky, "Nonlinear generation of sub-psec pulses of THz electromagnetic radiation by optoelectronics--applications to time-domain spectroscopy," in Frontiers in Nonlinear Optics, H.Walther, N.Koroteev, and M.O.Scully, eds. (Institute of Physics, 1993), pp. 196-227.
  2. D. H. Auston, "Ultrafast optoelectronics," in Ultrashort Laser Pulses: Generation and Applications, 2nd ed., W.Kaiser, ed. (Springer-Verlag, 1993), pp. 183-235 and references therein.
  3. J. Shan, A. Nahata, and T. F. Heinz, "Terahertz time-domain spectroscopy based on nonlinear optics," J. Nonlinear Opt. Phys. Mater. 11, 31-48 (2002).
    [CrossRef]
  4. B. B. Hu and M. C. Nuss, "Imaging with terahertz waves," Opt. Lett. 20, 1716-1718 (1995).
    [CrossRef] [PubMed]
  5. D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, "T-ray imaging," IEEE J. Sel. Top. Quantum Electron. 2, 679-692 (1996).
    [CrossRef]
  6. S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, "THz near-field imaging," Opt. Commun. 150, 22-26 (1998).
    [CrossRef]
  7. Z. Jiang and X.-C. Zhang, "2D measurement and spatio-temporal coupling of few-cycle THz pulses," Opt. Express 5, 243-248 (1999).
    [CrossRef] [PubMed]
  8. T. Yuan, J. Z. Xu, and X.-C. Zhang, "Development of terahertz wave microscopes," Infrared Phys. Technol. 45, 417-425 (2004), and references therein.
    [CrossRef]
  9. O. Mitrofanov, M. Lee, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, J. D. Wynn, and J. F. Federici, "Terahertz pulse propagation through small apertures," Appl. Phys. Lett. 79, 907-909 (2001).
    [CrossRef]
  10. Q. Chen, Z. Jiang, G. X. Xu, and X.-C. Zhang, "Near-field terahertz imaging with a dynamic aperture," Opt. Lett. 25, 1122-1124 (2000).
    [CrossRef]
  11. H. T. Chen, R. Kersting, and G. C. Cho, "Terahertz imaging with nanometer resolution," Appl. Phys. Lett. 83, 3009-3011 (2003).
    [CrossRef]
  12. N. C. J. van der Valk and P. C. M. Planken, "Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip," Appl. Phys. Lett. 81, 1558-1560 (2002).
    [CrossRef]
  13. K. L. Wang, A. Barkan, and D. M. Mittleman, "Propagation effects in apertureless near-field optical antennas," Appl. Phys. Lett. 84, 305-307 (2004).
    [CrossRef]
  14. K. L. Wang, D. M. Mittleman, N. C. J. Van der Valk, and P. C. M. Planken, "Antenna effects in terahertz apertureless near-field optical microscopy," Appl. Phys. Lett. 85, 2715-2717 (2004).
    [CrossRef]
  15. H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944).
    [CrossRef]
  16. J. Z. Xu and X.-C. Zhang, "Optical rectification in an area with a diameter comparable to or smaller than the center wavelength of terahertz radiation," Opt. Lett. 27, 1067-1069 (2002).
    [CrossRef]
  17. J. R. Morris and Y. R. Shen, "Theory of far-infrared generation by optical mixing," Phys. Rev. A 15, 1143-1156 (1977).
    [CrossRef]
  18. D. Côté, J. E. Sipe, and H. M. van Driel, "Simple method for calculating the propagation of terahertz radiation in experimental geometries," J. Opt. Soc. Am. B 20, 1374-1385 (2003).
    [CrossRef]
  19. B. Kubera, G. L. Dakovski, and J. Shan, "Numerical study of apertureless terahertz near-field microscopy based on nonlinear optics" (available from the authors at the address on the title page).
  20. J. H. Bechtel and W. L. Smith, "Two-photon absorption in semiconductors with picosecond laser pulses," Phys. Rev. B 13, 3515-3522 (1976).
    [CrossRef]
  21. D. Côté, N. Laman, and H. M. van Driel, "Rectification and shift currents in GaAs," Appl. Phys. Lett. 80, 905-907 (2002).
    [CrossRef]

2004

T. Yuan, J. Z. Xu, and X.-C. Zhang, "Development of terahertz wave microscopes," Infrared Phys. Technol. 45, 417-425 (2004), and references therein.
[CrossRef]

K. L. Wang, A. Barkan, and D. M. Mittleman, "Propagation effects in apertureless near-field optical antennas," Appl. Phys. Lett. 84, 305-307 (2004).
[CrossRef]

K. L. Wang, D. M. Mittleman, N. C. J. Van der Valk, and P. C. M. Planken, "Antenna effects in terahertz apertureless near-field optical microscopy," Appl. Phys. Lett. 85, 2715-2717 (2004).
[CrossRef]

2003

2002

N. C. J. van der Valk and P. C. M. Planken, "Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip," Appl. Phys. Lett. 81, 1558-1560 (2002).
[CrossRef]

J. Shan, A. Nahata, and T. F. Heinz, "Terahertz time-domain spectroscopy based on nonlinear optics," J. Nonlinear Opt. Phys. Mater. 11, 31-48 (2002).
[CrossRef]

D. Côté, N. Laman, and H. M. van Driel, "Rectification and shift currents in GaAs," Appl. Phys. Lett. 80, 905-907 (2002).
[CrossRef]

J. Z. Xu and X.-C. Zhang, "Optical rectification in an area with a diameter comparable to or smaller than the center wavelength of terahertz radiation," Opt. Lett. 27, 1067-1069 (2002).
[CrossRef]

2001

O. Mitrofanov, M. Lee, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, J. D. Wynn, and J. F. Federici, "Terahertz pulse propagation through small apertures," Appl. Phys. Lett. 79, 907-909 (2001).
[CrossRef]

2000

1999

1998

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, "THz near-field imaging," Opt. Commun. 150, 22-26 (1998).
[CrossRef]

1996

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, "T-ray imaging," IEEE J. Sel. Top. Quantum Electron. 2, 679-692 (1996).
[CrossRef]

1995

1977

J. R. Morris and Y. R. Shen, "Theory of far-infrared generation by optical mixing," Phys. Rev. A 15, 1143-1156 (1977).
[CrossRef]

1976

J. H. Bechtel and W. L. Smith, "Two-photon absorption in semiconductors with picosecond laser pulses," Phys. Rev. B 13, 3515-3522 (1976).
[CrossRef]

1944

H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944).
[CrossRef]

Auston, D. H.

D. H. Auston, "Ultrafast optoelectronics," in Ultrashort Laser Pulses: Generation and Applications, 2nd ed., W.Kaiser, ed. (Springer-Verlag, 1993), pp. 183-235 and references therein.

Barkan, A.

K. L. Wang, A. Barkan, and D. M. Mittleman, "Propagation effects in apertureless near-field optical antennas," Appl. Phys. Lett. 84, 305-307 (2004).
[CrossRef]

Bechtel, J. H.

J. H. Bechtel and W. L. Smith, "Two-photon absorption in semiconductors with picosecond laser pulses," Phys. Rev. B 13, 3515-3522 (1976).
[CrossRef]

Bethe, H. A.

H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944).
[CrossRef]

Brener, I.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, "THz near-field imaging," Opt. Commun. 150, 22-26 (1998).
[CrossRef]

Chen, H. T.

H. T. Chen, R. Kersting, and G. C. Cho, "Terahertz imaging with nanometer resolution," Appl. Phys. Lett. 83, 3009-3011 (2003).
[CrossRef]

Chen, Q.

Cho, G. C.

H. T. Chen, R. Kersting, and G. C. Cho, "Terahertz imaging with nanometer resolution," Appl. Phys. Lett. 83, 3009-3011 (2003).
[CrossRef]

Côté, D.

Dakovski, G. L.

B. Kubera, G. L. Dakovski, and J. Shan, "Numerical study of apertureless terahertz near-field microscopy based on nonlinear optics" (available from the authors at the address on the title page).

Federici, J. F.

O. Mitrofanov, M. Lee, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, J. D. Wynn, and J. F. Federici, "Terahertz pulse propagation through small apertures," Appl. Phys. Lett. 79, 907-909 (2001).
[CrossRef]

Grischkowsky, D. R.

D. R. Grischkowsky, "Nonlinear generation of sub-psec pulses of THz electromagnetic radiation by optoelectronics--applications to time-domain spectroscopy," in Frontiers in Nonlinear Optics, H.Walther, N.Koroteev, and M.O.Scully, eds. (Institute of Physics, 1993), pp. 196-227.

Heinz, T. F.

J. Shan, A. Nahata, and T. F. Heinz, "Terahertz time-domain spectroscopy based on nonlinear optics," J. Nonlinear Opt. Phys. Mater. 11, 31-48 (2002).
[CrossRef]

Hsu, J. W.

O. Mitrofanov, M. Lee, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, J. D. Wynn, and J. F. Federici, "Terahertz pulse propagation through small apertures," Appl. Phys. Lett. 79, 907-909 (2001).
[CrossRef]

Hu, B. B.

Hunsche, S.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, "THz near-field imaging," Opt. Commun. 150, 22-26 (1998).
[CrossRef]

Jacobsen, R. H.

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, "T-ray imaging," IEEE J. Sel. Top. Quantum Electron. 2, 679-692 (1996).
[CrossRef]

Jiang, Z.

Kersting, R.

H. T. Chen, R. Kersting, and G. C. Cho, "Terahertz imaging with nanometer resolution," Appl. Phys. Lett. 83, 3009-3011 (2003).
[CrossRef]

Koch, M.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, "THz near-field imaging," Opt. Commun. 150, 22-26 (1998).
[CrossRef]

Kubera, B.

B. Kubera, G. L. Dakovski, and J. Shan, "Numerical study of apertureless terahertz near-field microscopy based on nonlinear optics" (available from the authors at the address on the title page).

Laman, N.

D. Côté, N. Laman, and H. M. van Driel, "Rectification and shift currents in GaAs," Appl. Phys. Lett. 80, 905-907 (2002).
[CrossRef]

Lee, M.

O. Mitrofanov, M. Lee, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, J. D. Wynn, and J. F. Federici, "Terahertz pulse propagation through small apertures," Appl. Phys. Lett. 79, 907-909 (2001).
[CrossRef]

Mitrofanov, O.

O. Mitrofanov, M. Lee, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, J. D. Wynn, and J. F. Federici, "Terahertz pulse propagation through small apertures," Appl. Phys. Lett. 79, 907-909 (2001).
[CrossRef]

Mittleman, D. M.

K. L. Wang, D. M. Mittleman, N. C. J. Van der Valk, and P. C. M. Planken, "Antenna effects in terahertz apertureless near-field optical microscopy," Appl. Phys. Lett. 85, 2715-2717 (2004).
[CrossRef]

K. L. Wang, A. Barkan, and D. M. Mittleman, "Propagation effects in apertureless near-field optical antennas," Appl. Phys. Lett. 84, 305-307 (2004).
[CrossRef]

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, "T-ray imaging," IEEE J. Sel. Top. Quantum Electron. 2, 679-692 (1996).
[CrossRef]

Morris, J. R.

J. R. Morris and Y. R. Shen, "Theory of far-infrared generation by optical mixing," Phys. Rev. A 15, 1143-1156 (1977).
[CrossRef]

Nahata, A.

J. Shan, A. Nahata, and T. F. Heinz, "Terahertz time-domain spectroscopy based on nonlinear optics," J. Nonlinear Opt. Phys. Mater. 11, 31-48 (2002).
[CrossRef]

Nuss, M. C.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, "THz near-field imaging," Opt. Commun. 150, 22-26 (1998).
[CrossRef]

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, "T-ray imaging," IEEE J. Sel. Top. Quantum Electron. 2, 679-692 (1996).
[CrossRef]

B. B. Hu and M. C. Nuss, "Imaging with terahertz waves," Opt. Lett. 20, 1716-1718 (1995).
[CrossRef] [PubMed]

Pfeiffer, L. N.

O. Mitrofanov, M. Lee, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, J. D. Wynn, and J. F. Federici, "Terahertz pulse propagation through small apertures," Appl. Phys. Lett. 79, 907-909 (2001).
[CrossRef]

Planken, P. C.

K. L. Wang, D. M. Mittleman, N. C. J. Van der Valk, and P. C. M. Planken, "Antenna effects in terahertz apertureless near-field optical microscopy," Appl. Phys. Lett. 85, 2715-2717 (2004).
[CrossRef]

N. C. J. van der Valk and P. C. M. Planken, "Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip," Appl. Phys. Lett. 81, 1558-1560 (2002).
[CrossRef]

Shan, J.

J. Shan, A. Nahata, and T. F. Heinz, "Terahertz time-domain spectroscopy based on nonlinear optics," J. Nonlinear Opt. Phys. Mater. 11, 31-48 (2002).
[CrossRef]

B. Kubera, G. L. Dakovski, and J. Shan, "Numerical study of apertureless terahertz near-field microscopy based on nonlinear optics" (available from the authors at the address on the title page).

Shen, Y. R.

J. R. Morris and Y. R. Shen, "Theory of far-infrared generation by optical mixing," Phys. Rev. A 15, 1143-1156 (1977).
[CrossRef]

Sipe, J. E.

Smith, W. L.

J. H. Bechtel and W. L. Smith, "Two-photon absorption in semiconductors with picosecond laser pulses," Phys. Rev. B 13, 3515-3522 (1976).
[CrossRef]

Van der Valk, N. C.

K. L. Wang, D. M. Mittleman, N. C. J. Van der Valk, and P. C. M. Planken, "Antenna effects in terahertz apertureless near-field optical microscopy," Appl. Phys. Lett. 85, 2715-2717 (2004).
[CrossRef]

N. C. J. van der Valk and P. C. M. Planken, "Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip," Appl. Phys. Lett. 81, 1558-1560 (2002).
[CrossRef]

van Driel, H. M.

Wang, K. L.

K. L. Wang, A. Barkan, and D. M. Mittleman, "Propagation effects in apertureless near-field optical antennas," Appl. Phys. Lett. 84, 305-307 (2004).
[CrossRef]

K. L. Wang, D. M. Mittleman, N. C. J. Van der Valk, and P. C. M. Planken, "Antenna effects in terahertz apertureless near-field optical microscopy," Appl. Phys. Lett. 85, 2715-2717 (2004).
[CrossRef]

West, K. W.

O. Mitrofanov, M. Lee, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, J. D. Wynn, and J. F. Federici, "Terahertz pulse propagation through small apertures," Appl. Phys. Lett. 79, 907-909 (2001).
[CrossRef]

Wynn, J. D.

O. Mitrofanov, M. Lee, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, J. D. Wynn, and J. F. Federici, "Terahertz pulse propagation through small apertures," Appl. Phys. Lett. 79, 907-909 (2001).
[CrossRef]

Xu, G. X.

Xu, J. Z.

T. Yuan, J. Z. Xu, and X.-C. Zhang, "Development of terahertz wave microscopes," Infrared Phys. Technol. 45, 417-425 (2004), and references therein.
[CrossRef]

J. Z. Xu and X.-C. Zhang, "Optical rectification in an area with a diameter comparable to or smaller than the center wavelength of terahertz radiation," Opt. Lett. 27, 1067-1069 (2002).
[CrossRef]

Yuan, T.

T. Yuan, J. Z. Xu, and X.-C. Zhang, "Development of terahertz wave microscopes," Infrared Phys. Technol. 45, 417-425 (2004), and references therein.
[CrossRef]

Zhang, X.-C.

Appl. Phys. Lett.

O. Mitrofanov, M. Lee, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, J. D. Wynn, and J. F. Federici, "Terahertz pulse propagation through small apertures," Appl. Phys. Lett. 79, 907-909 (2001).
[CrossRef]

H. T. Chen, R. Kersting, and G. C. Cho, "Terahertz imaging with nanometer resolution," Appl. Phys. Lett. 83, 3009-3011 (2003).
[CrossRef]

N. C. J. van der Valk and P. C. M. Planken, "Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip," Appl. Phys. Lett. 81, 1558-1560 (2002).
[CrossRef]

K. L. Wang, A. Barkan, and D. M. Mittleman, "Propagation effects in apertureless near-field optical antennas," Appl. Phys. Lett. 84, 305-307 (2004).
[CrossRef]

K. L. Wang, D. M. Mittleman, N. C. J. Van der Valk, and P. C. M. Planken, "Antenna effects in terahertz apertureless near-field optical microscopy," Appl. Phys. Lett. 85, 2715-2717 (2004).
[CrossRef]

D. Côté, N. Laman, and H. M. van Driel, "Rectification and shift currents in GaAs," Appl. Phys. Lett. 80, 905-907 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, "T-ray imaging," IEEE J. Sel. Top. Quantum Electron. 2, 679-692 (1996).
[CrossRef]

Infrared Phys. Technol.

T. Yuan, J. Z. Xu, and X.-C. Zhang, "Development of terahertz wave microscopes," Infrared Phys. Technol. 45, 417-425 (2004), and references therein.
[CrossRef]

J. Nonlinear Opt. Phys. Mater.

J. Shan, A. Nahata, and T. F. Heinz, "Terahertz time-domain spectroscopy based on nonlinear optics," J. Nonlinear Opt. Phys. Mater. 11, 31-48 (2002).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, "THz near-field imaging," Opt. Commun. 150, 22-26 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944).
[CrossRef]

Phys. Rev. A

J. R. Morris and Y. R. Shen, "Theory of far-infrared generation by optical mixing," Phys. Rev. A 15, 1143-1156 (1977).
[CrossRef]

Phys. Rev. B

J. H. Bechtel and W. L. Smith, "Two-photon absorption in semiconductors with picosecond laser pulses," Phys. Rev. B 13, 3515-3522 (1976).
[CrossRef]

Other

B. Kubera, G. L. Dakovski, and J. Shan, "Numerical study of apertureless terahertz near-field microscopy based on nonlinear optics" (available from the authors at the address on the title page).

D. R. Grischkowsky, "Nonlinear generation of sub-psec pulses of THz electromagnetic radiation by optoelectronics--applications to time-domain spectroscopy," in Frontiers in Nonlinear Optics, H.Walther, N.Koroteev, and M.O.Scully, eds. (Institute of Physics, 1993), pp. 196-227.

D. H. Auston, "Ultrafast optoelectronics," in Ultrashort Laser Pulses: Generation and Applications, 2nd ed., W.Kaiser, ed. (Springer-Verlag, 1993), pp. 183-235 and references therein.

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Figures (4)

Fig. 1
Fig. 1

Sketch of the THz emitter employed in the measurement (not to scale): optical pump beam (800 nm) is focused onto a 20 μ m ZnTe emitter ([110] orientation) on a 500 μ m ZnTe substrate ([100] orientation). Translation of the lens allows variation of the effective size of the emitter.

Fig. 2
Fig. 2

Normalized spectral density E ( ω ) 2 versus the FWHM of the optical excitation a. Three representative frequencies are shown in symbols. Solid curve is a fit with expression (2). Inset: size dependence of the total THz power (normalized) in the regime of two-photon absorption, using 100% (filled diamonds) and 50% (open diamonds) of the available excitation power.

Fig. 3
Fig. 3

Characteristic size of the emitter a c as defined in the text for the transition of spectral density behavior (from a 0 to a 2 dependence) versus the THz wavelength λ THz . Symbols, experiment; line, simulation.

Fig. 4
Fig. 4

(a): Simulated spectral density E ( ω ) 2 at 0.9, 1.4, and 1.9 THz (solid curves) versus the FWHM of the optical excitation a for a 30° collection angle. (b) Simulated spectral density E ( ω ) 2 at 1.4 THz for collection angles of 30°, 15°, and 7.5°. Dashed lines illustrate the a 2 dependence.

Equations (2)

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

E THz 2 a 2 l P NL 2 a 0 .
E THz 2 a 2 l P opt a 2 + β P opt L 2 ,

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