Abstract

We present a detailed investigation of the propagation properties of beams of ultrashort terahertz (THz) pulses emitted from large-aperture (LA) antennas. The large area of the emitter is demonstrated to have substantial influence on the temporal pulse profile in both the near field and the far field. We perform a numerical analysis based on scalar and vectorial broadband diffraction theory and are able to distinguish between near-field and far-field contributions to the total THz signal. We find that the THz beam from a LA antenna propagates like a Gaussian beam and that the temporal profile of the THz pulse, measured in the near field, contains information about the temporal and spatial field distribution on the emitter surface, which is intrinsically connected to the carrier dynamics of the antenna substrate. As a result of pulse reshaping, focusing of the THz beam leads to a reduced relative pulse momentum, with implications in THz field-ionization experiments.

© 2000 Optical Society of America

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References

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  1. P. Uhd Jepsen, S. R. Keiding, “Radiation patterns from lens-coupled terahertz antennas,” Opt. Lett. 20, 807–809 (1995).
    [CrossRef]
  2. P. Uhd Jepsen, R. H. Jacobsen, S. R. Keiding, “Generation and detection of terahertz pulses from biased semiconductor antennas,” J. Opt. Soc. Am. B 13, 2424–2436 (1996).
    [CrossRef]
  3. J. Bromage, S. Radic, G. P. Agrewal, C. R. Stroud, P. M. Fauchet, R. Sobolewski, “Spatiotemporal shaping of terahertz pulses,” Opt. Lett. 22, 627–629 (1997).
    [CrossRef] [PubMed]
  4. J. Bromage, S. Radic, G. P. Agrawal, C. R. Stroud, P. M. Fauchet, R. Sobolewski, “Spatiotemporal shaping of half-cycle terahertz pulses by diffraction through conductive apertures of finite thickness,” J. Opt. Soc. Am. B 15, 1953–1959 (1998).
    [CrossRef]
  5. D. You, P. H. Bucksbaum, “Propagation of half-cycle far infrared pulses,” J. Opt. Soc. Am. B 14, 1651–1655 (1997).
    [CrossRef]
  6. S. Feng, H. G. Winful, R. W. Hellwarth, “Gouy shift and temporal reshaping of focused single-cycle electromagnetic pulses,” Opt. Lett. 23, 385–387 (1998).
    [CrossRef]
  7. C. Winnewisser, F. Lewen, H. Helm, “Transmission characteristics of dichroic filters measured by THz time-domain spectroscopy,” Appl. Phys. A: Solids Surf. 66, 593–598 (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. C. Raman, C. W. S. Conover, C. I. Sukenik, P. H. Bucksbaum, “Ionization of Rydberg wave packets by subpicosecond, half-cycle electromagnetic pulses,” Phys. Rev. Lett. 76, 2436–2439 (1996).
    [CrossRef] [PubMed]
  10. R. R. Jones, “Creating and probing electronic wavepackets using half-cycle pulses,” Phys. Rev. Lett. 76, 3927–3930 (1996).
    [CrossRef] [PubMed]
  11. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  12. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).
  13. J. T. Darrow, X.-C. Zhang, D. H. Auston, J. D. Morse, “Saturation properties of large-aperture photoconducting antennas,” IEEE J. Quantum Electron. 28, 1607–1614 (1992).
    [CrossRef]
  14. M. C. Nuss, D. H. Auston, F. Capasso, “Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide,” Phys. Rev. Lett. 58, 2355–2358 (1987).
    [CrossRef] [PubMed]
  15. J. A. Kash, J. C. Tsang, J. M. Hvam, “Subpicosecond time-resolved Raman spectroscopy of LO phonons in GaAs,” Phys. Rev. Lett. 54, 2151–2154 (1985).
    [CrossRef] [PubMed]
  16. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).
  17. Homepage of the Terahertz Group, Department of Molecular and Optical Physics, University of Freiburg, Freiburg, Germany: http://frhewww.physik.uni-freiburg.de/∼puhd/homepage .
  18. Q. Wu, X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
    [CrossRef]
  19. P. Uhd Jepsen, M. Schall, V. Schyja, S. R. Keiding, H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
    [CrossRef]
  20. C. Winnewisser, P. Uhd Jepsen, M. Schall, V. Schyja, H. Helm, “Electro-optic detection of THz radiation in LiTaO3,LiNbO3, and ZnTe,” Appl. Phys. Lett. 70, 3069–3071 (1997).
    [CrossRef]

1998 (4)

1997 (3)

1996 (4)

P. Uhd Jepsen, M. Schall, V. Schyja, S. R. Keiding, H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

P. Uhd Jepsen, R. H. Jacobsen, S. R. Keiding, “Generation and detection of terahertz pulses from biased semiconductor antennas,” J. Opt. Soc. Am. B 13, 2424–2436 (1996).
[CrossRef]

C. Raman, C. W. S. Conover, C. I. Sukenik, P. H. Bucksbaum, “Ionization of Rydberg wave packets by subpicosecond, half-cycle electromagnetic pulses,” Phys. Rev. Lett. 76, 2436–2439 (1996).
[CrossRef] [PubMed]

R. R. Jones, “Creating and probing electronic wavepackets using half-cycle pulses,” Phys. Rev. Lett. 76, 3927–3930 (1996).
[CrossRef] [PubMed]

1995 (2)

P. Uhd Jepsen, S. R. Keiding, “Radiation patterns from lens-coupled terahertz antennas,” Opt. Lett. 20, 807–809 (1995).
[CrossRef]

Q. Wu, X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

1992 (1)

J. T. Darrow, X.-C. Zhang, D. H. Auston, J. D. Morse, “Saturation properties of large-aperture photoconducting antennas,” IEEE J. Quantum Electron. 28, 1607–1614 (1992).
[CrossRef]

1987 (1)

M. C. Nuss, D. H. Auston, F. Capasso, “Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide,” Phys. Rev. Lett. 58, 2355–2358 (1987).
[CrossRef] [PubMed]

1985 (1)

J. A. Kash, J. C. Tsang, J. M. Hvam, “Subpicosecond time-resolved Raman spectroscopy of LO phonons in GaAs,” Phys. Rev. Lett. 54, 2151–2154 (1985).
[CrossRef] [PubMed]

Agrawal, G. P.

Agrewal, G. P.

Auston, D. H.

J. T. Darrow, X.-C. Zhang, D. H. Auston, J. D. Morse, “Saturation properties of large-aperture photoconducting antennas,” IEEE J. Quantum Electron. 28, 1607–1614 (1992).
[CrossRef]

M. C. Nuss, D. H. Auston, F. Capasso, “Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide,” Phys. Rev. Lett. 58, 2355–2358 (1987).
[CrossRef] [PubMed]

Bokor, J.

Bromage, J.

Bucksbaum, P. H.

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

C. Raman, C. W. S. Conover, C. I. Sukenik, P. H. Bucksbaum, “Ionization of Rydberg wave packets by subpicosecond, half-cycle electromagnetic pulses,” Phys. Rev. Lett. 76, 2436–2439 (1996).
[CrossRef] [PubMed]

Budiarto, E.

Capasso, F.

M. C. Nuss, D. H. Auston, F. Capasso, “Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide,” Phys. Rev. Lett. 58, 2355–2358 (1987).
[CrossRef] [PubMed]

Conover, C. W. S.

C. Raman, C. W. S. Conover, C. I. Sukenik, P. H. Bucksbaum, “Ionization of Rydberg wave packets by subpicosecond, half-cycle electromagnetic pulses,” Phys. Rev. Lett. 76, 2436–2439 (1996).
[CrossRef] [PubMed]

Darrow, J. T.

J. T. Darrow, X.-C. Zhang, D. H. Auston, J. D. Morse, “Saturation properties of large-aperture photoconducting antennas,” IEEE J. Quantum Electron. 28, 1607–1614 (1992).
[CrossRef]

Fauchet, P. M.

Feng, S.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Hellwarth, R. W.

Helm, H.

C. Winnewisser, F. Lewen, H. Helm, “Transmission characteristics of dichroic filters measured by THz time-domain spectroscopy,” Appl. Phys. A: Solids Surf. 66, 593–598 (1998).
[CrossRef]

C. Winnewisser, P. Uhd Jepsen, M. Schall, V. Schyja, H. Helm, “Electro-optic detection of THz radiation in LiTaO3,LiNbO3, and ZnTe,” Appl. Phys. Lett. 70, 3069–3071 (1997).
[CrossRef]

P. Uhd Jepsen, M. Schall, V. Schyja, S. R. Keiding, H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Hvam, J. M.

J. A. Kash, J. C. Tsang, J. M. Hvam, “Subpicosecond time-resolved Raman spectroscopy of LO phonons in GaAs,” Phys. Rev. Lett. 54, 2151–2154 (1985).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).

Jacobsen, R. H.

Jeong, S.

Jones, R. R.

R. R. Jones, “Creating and probing electronic wavepackets using half-cycle pulses,” Phys. Rev. Lett. 76, 3927–3930 (1996).
[CrossRef] [PubMed]

Kash, J. A.

J. A. Kash, J. C. Tsang, J. M. Hvam, “Subpicosecond time-resolved Raman spectroscopy of LO phonons in GaAs,” Phys. Rev. Lett. 54, 2151–2154 (1985).
[CrossRef] [PubMed]

Keiding, S. R.

Lewen, F.

C. Winnewisser, F. Lewen, H. Helm, “Transmission characteristics of dichroic filters measured by THz time-domain spectroscopy,” Appl. Phys. A: Solids Surf. 66, 593–598 (1998).
[CrossRef]

Morse, J. D.

J. T. Darrow, X.-C. Zhang, D. H. Auston, J. D. Morse, “Saturation properties of large-aperture photoconducting antennas,” IEEE J. Quantum Electron. 28, 1607–1614 (1992).
[CrossRef]

Nuss, M. C.

M. C. Nuss, D. H. Auston, F. Capasso, “Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide,” Phys. Rev. Lett. 58, 2355–2358 (1987).
[CrossRef] [PubMed]

Pu, N.-W.

Radic, S.

Raman, C.

C. Raman, C. W. S. Conover, C. I. Sukenik, P. H. Bucksbaum, “Ionization of Rydberg wave packets by subpicosecond, half-cycle electromagnetic pulses,” Phys. Rev. Lett. 76, 2436–2439 (1996).
[CrossRef] [PubMed]

Schall, M.

C. Winnewisser, P. Uhd Jepsen, M. Schall, V. Schyja, H. Helm, “Electro-optic detection of THz radiation in LiTaO3,LiNbO3, and ZnTe,” Appl. Phys. Lett. 70, 3069–3071 (1997).
[CrossRef]

P. Uhd Jepsen, M. Schall, V. Schyja, S. R. Keiding, H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Schyja, V.

C. Winnewisser, P. Uhd Jepsen, M. Schall, V. Schyja, H. Helm, “Electro-optic detection of THz radiation in LiTaO3,LiNbO3, and ZnTe,” Appl. Phys. Lett. 70, 3069–3071 (1997).
[CrossRef]

P. Uhd Jepsen, M. Schall, V. Schyja, S. R. Keiding, H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Sobolewski, R.

Stroud, C. R.

Sukenik, C. I.

C. Raman, C. W. S. Conover, C. I. Sukenik, P. H. Bucksbaum, “Ionization of Rydberg wave packets by subpicosecond, half-cycle electromagnetic pulses,” Phys. Rev. Lett. 76, 2436–2439 (1996).
[CrossRef] [PubMed]

Tsang, J. C.

J. A. Kash, J. C. Tsang, J. M. Hvam, “Subpicosecond time-resolved Raman spectroscopy of LO phonons in GaAs,” Phys. Rev. Lett. 54, 2151–2154 (1985).
[CrossRef] [PubMed]

Uhd Jepsen, P.

C. Winnewisser, P. Uhd Jepsen, M. Schall, V. Schyja, H. Helm, “Electro-optic detection of THz radiation in LiTaO3,LiNbO3, and ZnTe,” Appl. Phys. Lett. 70, 3069–3071 (1997).
[CrossRef]

P. Uhd Jepsen, M. Schall, V. Schyja, S. R. Keiding, H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

P. Uhd Jepsen, R. H. Jacobsen, S. R. Keiding, “Generation and detection of terahertz pulses from biased semiconductor antennas,” J. Opt. Soc. Am. B 13, 2424–2436 (1996).
[CrossRef]

P. Uhd Jepsen, S. R. Keiding, “Radiation patterns from lens-coupled terahertz antennas,” Opt. Lett. 20, 807–809 (1995).
[CrossRef]

Winful, H. G.

Winnewisser, C.

C. Winnewisser, F. Lewen, H. Helm, “Transmission characteristics of dichroic filters measured by THz time-domain spectroscopy,” Appl. Phys. A: Solids Surf. 66, 593–598 (1998).
[CrossRef]

C. Winnewisser, P. Uhd Jepsen, M. Schall, V. Schyja, H. Helm, “Electro-optic detection of THz radiation in LiTaO3,LiNbO3, and ZnTe,” Appl. Phys. Lett. 70, 3069–3071 (1997).
[CrossRef]

Wu, Q.

Q. Wu, X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

You, D.

Zhang, X.-C.

Q. Wu, X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

J. T. Darrow, X.-C. Zhang, D. H. Auston, J. D. Morse, “Saturation properties of large-aperture photoconducting antennas,” IEEE J. Quantum Electron. 28, 1607–1614 (1992).
[CrossRef]

Appl. Phys. A: Solids Surf. (1)

C. Winnewisser, F. Lewen, H. Helm, “Transmission characteristics of dichroic filters measured by THz time-domain spectroscopy,” Appl. Phys. A: Solids Surf. 66, 593–598 (1998).
[CrossRef]

Appl. Phys. Lett. (2)

Q. Wu, X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

C. Winnewisser, P. Uhd Jepsen, M. Schall, V. Schyja, H. Helm, “Electro-optic detection of THz radiation in LiTaO3,LiNbO3, and ZnTe,” Appl. Phys. Lett. 70, 3069–3071 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. T. Darrow, X.-C. Zhang, D. H. Auston, J. D. Morse, “Saturation properties of large-aperture photoconducting antennas,” IEEE J. Quantum Electron. 28, 1607–1614 (1992).
[CrossRef]

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

Opt. Lett. (4)

Phys. Rev. E (1)

P. Uhd Jepsen, M. Schall, V. Schyja, S. R. Keiding, H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Phys. Rev. Lett. (4)

M. C. Nuss, D. H. Auston, F. Capasso, “Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide,” Phys. Rev. Lett. 58, 2355–2358 (1987).
[CrossRef] [PubMed]

J. A. Kash, J. C. Tsang, J. M. Hvam, “Subpicosecond time-resolved Raman spectroscopy of LO phonons in GaAs,” Phys. Rev. Lett. 54, 2151–2154 (1985).
[CrossRef] [PubMed]

C. Raman, C. W. S. Conover, C. I. Sukenik, P. H. Bucksbaum, “Ionization of Rydberg wave packets by subpicosecond, half-cycle electromagnetic pulses,” Phys. Rev. Lett. 76, 2436–2439 (1996).
[CrossRef] [PubMed]

R. R. Jones, “Creating and probing electronic wavepackets using half-cycle pulses,” Phys. Rev. Lett. 76, 3927–3930 (1996).
[CrossRef] [PubMed]

Other (4)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

Homepage of the Terahertz Group, Department of Molecular and Optical Physics, University of Freiburg, Freiburg, Germany: http://frhewww.physik.uni-freiburg.de/∼puhd/homepage .

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Figures (13)

Fig. 1
Fig. 1

THz pulses generated by optical rectification (solid curve) and transient photocurrent (dashed curve).

Fig. 2
Fig. 2

Model electric field on emitter surface for different parameter choices: effect of varying (a) the static mobility, (b) the carrier relaxation rate, and (c) the carrier recombination time.

Fig. 3
Fig. 3

Spot sizes of an unfocused 1 Hz beam and a focused THz beam with an initial spot size w0=3.4 mm and the field strength enhancement due to focusing.

Fig. 4
Fig. 4

(a) Unfocused and (b) focused propagation of a Gaussian beam. The 1/e diameter of the beam is plotted for frequencies from 0.1 to 1.9 THz.

Fig. 5
Fig. 5

(a and b) Density plots of the spatiotemporal distribution of the x and z components of the THz field 333 ps after excitation; (c and d) the x and z components of the THz field 33 ps after excitation.

Fig. 6
Fig. 6

(a) Experimental setup for near-field measurements; (b) setup for far-field measurements. GM, guiding mirror (plane or off-axis paraboloidal); NBS, nonpolarizing beam splitter; PBS, polarizing beam splitter; PD, photodiode; EO, electro-optic crystal; +HV, high-voltage supply.

Fig. 7
Fig. 7

Temporal traces of the THz pulse at various positions of the detector perpendicular to the propagation axis of the THz beam are shown for (a) the unfocused beam and (b) the focused beam.

Fig. 8
Fig. 8

Fourier transform of the traces of Fig. 7. Data for (a) the unfocused beam and (b) the focused beam.

Fig. 9
Fig. 9

Experimental and theoretically predicted radiation patterns of (a) the unfocused beam and (b) the focused beam.

Fig. 10
Fig. 10

Comparison between an experimental beam and a Gaussian beam profile.

Fig. 11
Fig. 11

Off-axis THz pulse shapes measured at z=16 mm from the emitter.

Fig. 12
Fig. 12

Numerical determination of off-axis THz pulse shape at z=16 mm. One experimental data set is shown to illustrate the agreement with experiment.

Fig. 13
Fig. 13

On-axis THz pulse shape as a function of distance to the emitter.

Equations (15)

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

U(x, ν)=νicAU(x)exp(i2πνr/c)rcos(n, r)dx,
u(x, t)=Acos(n, r)2πcrddtu(x, t-r/c)dx.
E(x, ν)=12π×A[n×E(x)]exp(i2πνr)rdx.
E(x, t)=-E(x, ν)exp(-i2πνt)dν.
E(x, t)=-12π×A[n×E(x, ν)]×exp(i2πνr/c)rdxexp(-i2πνt)dν
=×-12πn×AE(x, ν)×exp(i2πνr/c)rdxexp(-i2πνt)dν
=×A12πrn×-E(x, ν)×exp[-i2πν(t-r/c)]dνdx.
E(x, t)=×A12πr[n×E(x, t-r/c)]dx.
ETHz(t)=-Ebσs(t)η0σs(t)η0+1+.
σs(t)=e(1-R)hν-tμ(t-t)Iopt(t)×exp[-(t-t)/τcar]dt,
μ(t)-μdc-(μdc-μi)exp(-Γt),
Eb(x)=Ec+(Ee-Ec)(x/l)n,
wunfocused(ν)=cLνπw0[1+(νπw02/cL)2]1/2.
wfocused(ν)=fc/νπw0.
Efocused/Eunfocused=2[1+(νπw02/2cf)2]1/2.

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