Abstract

We investigate experimentally and numerically the properties of single-cycle terahertz pulses propagating through a focus. The experimental data clearly show changes in pulse shape resulting from the Gouy phase shift and apparent superluminal pulse propagation. The pulses are also considerably distorted by diffraction effects. A solution of the time-domain diffraction integral is necessary to explain the details of the data and leads to an excellent agreement between experiment and theory.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. C. Nuss, J. Orenstein, “Terahertz time-domain spectroscopy,” in Millimeter-Wave Spectroscopy of Solids (Springer, Berlin, 1998), pp. 7–50.
  2. M. Lenzner, M. Schnürer, C. Spielmann, F. Krausz, “Extreme nonlinear optics with few cycle laser pulses,” IEICE Trans. Electron. E81-C, 112–122 (1998).
  3. R. B. Vrijen, G. M. Lankhuijzen, L. D. Noordam, “Delayed electron emission in the ionization of Rydberg atoms with half cycle THz pulses,” Phys. Rev. Lett. 79, 617–620 (1997).
    [CrossRef]
  4. A. de Bohan, P. Antoine, D. B. Milosevic, B. Piraux, “Phase dependent harmonic emission with ultrashort laser pulses,” Phys. Rev. Lett. 81, 1837–1840 (1998).
    [CrossRef]
  5. S. M. Feng, H. G. Winful, R. W. Hellwarth, “Gouy shift and temporal reshaping of focused single-cycle electromagnetic pulses,” Opt. Lett. 23, 385–387 (1998); errata, Opt. Lett.23, 1141 (1998).
    [CrossRef]
  6. D. You, P. H. Bucksbaum, “Propagation of half-cycle far infrared pulses,” J. Opt. Soc. Am. B 14, 1651–1655 (1997).
    [CrossRef]
  7. A. E. Kaplan, “Diffraction-induced transformation of near-cycle and subcycle pulses,” J. Opt. Soc. Am. B 15, 951–956 (1998).
    [CrossRef]
  8. E. Budiarto, N.-W. Pu, S. Jeong, J. Bokor, “Near-field propagation of terahertz pulses from a large-aperture antenna,” Opt. Lett. 23, 213–215 (1998).
    [CrossRef]
  9. A. E. Siegmann, Lasers (University Science Books, Mill Valley, Calif., 1986).
  10. R. Jacobsen, “Optoelectronic terahertz switching,” Ph.D. thesis (Aarhus Universitet, Aarhus, Denmark, 1997).
  11. P. Uhd Jespen, R. Jacobsen, S. Keiding, “Generation and detection of terahertz pulses from biased semiconductor antennas,” J. Opt. Soc. Am. B 13, 2424–2436 (1996).
    [CrossRef]
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw Hill, New York, 1996).
  13. The ripples after the main pulse at z=0 in the time-domain data and the dips in the spectra at z=0 may arise from interference with scattered light. This possibility is included in the simulations by addition of a small contribution of background light treated as a plane wave. Without this additional contribution, the simulated data show no ripples or dips.

1998 (5)

1997 (2)

D. You, P. H. Bucksbaum, “Propagation of half-cycle far infrared pulses,” J. Opt. Soc. Am. B 14, 1651–1655 (1997).
[CrossRef]

R. B. Vrijen, G. M. Lankhuijzen, L. D. Noordam, “Delayed electron emission in the ionization of Rydberg atoms with half cycle THz pulses,” Phys. Rev. Lett. 79, 617–620 (1997).
[CrossRef]

1996 (1)

Antoine, P.

A. de Bohan, P. Antoine, D. B. Milosevic, B. Piraux, “Phase dependent harmonic emission with ultrashort laser pulses,” Phys. Rev. Lett. 81, 1837–1840 (1998).
[CrossRef]

Bokor, J.

Bucksbaum, P. H.

Budiarto, E.

de Bohan, A.

A. de Bohan, P. Antoine, D. B. Milosevic, B. Piraux, “Phase dependent harmonic emission with ultrashort laser pulses,” Phys. Rev. Lett. 81, 1837–1840 (1998).
[CrossRef]

Feng, S. M.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw Hill, New York, 1996).

Hellwarth, R. W.

Jacobsen, R.

Jeong, S.

Kaplan, A. E.

Keiding, S.

Krausz, F.

M. Lenzner, M. Schnürer, C. Spielmann, F. Krausz, “Extreme nonlinear optics with few cycle laser pulses,” IEICE Trans. Electron. E81-C, 112–122 (1998).

Lankhuijzen, G. M.

R. B. Vrijen, G. M. Lankhuijzen, L. D. Noordam, “Delayed electron emission in the ionization of Rydberg atoms with half cycle THz pulses,” Phys. Rev. Lett. 79, 617–620 (1997).
[CrossRef]

Lenzner, M.

M. Lenzner, M. Schnürer, C. Spielmann, F. Krausz, “Extreme nonlinear optics with few cycle laser pulses,” IEICE Trans. Electron. E81-C, 112–122 (1998).

Milosevic, D. B.

A. de Bohan, P. Antoine, D. B. Milosevic, B. Piraux, “Phase dependent harmonic emission with ultrashort laser pulses,” Phys. Rev. Lett. 81, 1837–1840 (1998).
[CrossRef]

Noordam, L. D.

R. B. Vrijen, G. M. Lankhuijzen, L. D. Noordam, “Delayed electron emission in the ionization of Rydberg atoms with half cycle THz pulses,” Phys. Rev. Lett. 79, 617–620 (1997).
[CrossRef]

Nuss, M. C.

M. C. Nuss, J. Orenstein, “Terahertz time-domain spectroscopy,” in Millimeter-Wave Spectroscopy of Solids (Springer, Berlin, 1998), pp. 7–50.

Orenstein, J.

M. C. Nuss, J. Orenstein, “Terahertz time-domain spectroscopy,” in Millimeter-Wave Spectroscopy of Solids (Springer, Berlin, 1998), pp. 7–50.

Piraux, B.

A. de Bohan, P. Antoine, D. B. Milosevic, B. Piraux, “Phase dependent harmonic emission with ultrashort laser pulses,” Phys. Rev. Lett. 81, 1837–1840 (1998).
[CrossRef]

Pu, N.-W.

Schnürer, M.

M. Lenzner, M. Schnürer, C. Spielmann, F. Krausz, “Extreme nonlinear optics with few cycle laser pulses,” IEICE Trans. Electron. E81-C, 112–122 (1998).

Siegmann, A. E.

A. E. Siegmann, Lasers (University Science Books, Mill Valley, Calif., 1986).

Spielmann, C.

M. Lenzner, M. Schnürer, C. Spielmann, F. Krausz, “Extreme nonlinear optics with few cycle laser pulses,” IEICE Trans. Electron. E81-C, 112–122 (1998).

Uhd Jespen, P.

Vrijen, R. B.

R. B. Vrijen, G. M. Lankhuijzen, L. D. Noordam, “Delayed electron emission in the ionization of Rydberg atoms with half cycle THz pulses,” Phys. Rev. Lett. 79, 617–620 (1997).
[CrossRef]

Winful, H. G.

You, D.

IEICE Trans. Electron. (1)

M. Lenzner, M. Schnürer, C. Spielmann, F. Krausz, “Extreme nonlinear optics with few cycle laser pulses,” IEICE Trans. Electron. E81-C, 112–122 (1998).

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

Opt. Lett. (2)

Phys. Rev. Lett. (2)

R. B. Vrijen, G. M. Lankhuijzen, L. D. Noordam, “Delayed electron emission in the ionization of Rydberg atoms with half cycle THz pulses,” Phys. Rev. Lett. 79, 617–620 (1997).
[CrossRef]

A. de Bohan, P. Antoine, D. B. Milosevic, B. Piraux, “Phase dependent harmonic emission with ultrashort laser pulses,” Phys. Rev. Lett. 81, 1837–1840 (1998).
[CrossRef]

Other (5)

A. E. Siegmann, Lasers (University Science Books, Mill Valley, Calif., 1986).

R. Jacobsen, “Optoelectronic terahertz switching,” Ph.D. thesis (Aarhus Universitet, Aarhus, Denmark, 1997).

J. W. Goodman, Introduction to Fourier Optics (McGraw Hill, New York, 1996).

The ripples after the main pulse at z=0 in the time-domain data and the dips in the spectra at z=0 may arise from interference with scattered light. This possibility is included in the simulations by addition of a small contribution of background light treated as a plane wave. Without this additional contribution, the simulated data show no ripples or dips.

M. C. Nuss, J. Orenstein, “Terahertz time-domain spectroscopy,” in Millimeter-Wave Spectroscopy of Solids (Springer, Berlin, 1998), pp. 7–50.

Cited By

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

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Measured THz waveforms and (b) simulations for several positions along the optical axis z, where negative and positive values indicate positions before and behind the focal plane, respectively. Individual traces are offset for clarity.

Fig. 2
Fig. 2

Normalized amplitude spectra of the THz pulses at different z: (a) experimental data, (b) simulations.

Fig. 3
Fig. 3

Normalized signal amplitude variation along z at different frequencies: (a) experimental data, (b) simulations.

Fig. 4
Fig. 4

Calculated THz pulses from the inverse Fourier transform of Eq. (1) for different detector positions z.

Equations (3)

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

E(f, z)=fn exp(ikz)1+iq2zf exp-2πfc q1,
q1=nc2πfp,n=ln 2b-ln b-1,
u(P0, t)=Σ cos(n, r10)2πcr10 ddt uP1, t-r10cds,

Metrics